diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample2.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample2.m" index ccdd18f7e1b937830892362ce4a9ceb70bd3e030..b751311840338a564058f79aaa777841534106a6 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample2.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample2.m" @@ -1,3 +1,51 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d28d6aa66649955368e3b7c92223bcff0a32f3bb95f36f1d9f413cc5cee38488 -size 1466 +function [f,f0] = ThrSample2 (x,y,y2_1, y2_N,x0) +syms t; +f = 0.0; +f0 = 0.0; + +if(length(x) == length(y)) + n = length(x); +else + disp('xºÍyµÄάÊý²»ÏàµÈ£¡'); + return; +end %άÊý¼ì²é + +for i=1:n + if(x(i)<=x0)&& (x(i+1)>=x0) + index = i; + break; + end +end %ÕÒµ½x0ËùÔÚÇø¼ä + +for i=1:n + if(x(i)<=x0)&& (x(i+1)>=x0) + index = i; + break; + end +end %ÕÒµ½x0ËùÔÚÇø¼ä + +A = diag(2*ones(1,n)); %Çó½âmµÄϵÊý¾ØÕó +A(1,2) = 1; +A(n,n-1) = 1; +u = zeros(n-2,1); +lamda = zeros(n-1,1); +c = zeros(n,1); +for i=2:n-1 + u(i-1) = (x(i)-x(i-1))/(x(i+1)-x(i-1)); + lamda(i) = (x(i+1)-x(i))/(x(i+1)-x(i-1)); + c(i) = 3*lamda(i)*(y(i)-y(i-1))/(x(i)-x(i-1))+ ... + 3*u(i-1)*(y(i+1)-y(i))/(x(i+1)-x(i)); + A(i, i+1) = u(i-1); + A(i, i-1) = lamda(i); %ÐγÉϵÊý¾ØÕó¼°ÏòÁ¿c +end +c(1) = 3*(y(2)-y(1))/(x(2)-x(1))-(x(2)-x(1))*y2_1/2; +c(n) = 3*(y(n)-y(n-1))/(x(n)-x(n-1))-(x(n)-x(n-1))*y2_N/2; + +m = followup(A,c); %ÓÃ×·¸Ï·¨Çó½â·½³Ì×é +h = x(index+1) - x(index); %x0ËùÔÚÇø¼ä³¤¶È +f = y(index)*(2*(t-x(index))+h)*(t-x(index+1))^2/h/h/h + ... + y(index+1)*(2*(x(index+1)-t)+h)*(t-x(index))^2/h/h/h + ... + m(index)*(t-x(index))*(x(index+1)-t)^2/h/h - ... + m(index+1)*(x(index+1)-t)*(t-x(index))^2/h/h; + %x0ËùÔÚÇø¼äµÄ²åÖµº¯Êý +f0 = subs(f,'t',x0); %x0´¦µÄ²åÖµ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample3.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample3.m" index 63715bf86af66d7c961517a676f2a138844322bb..edae7cf33013b733d3e8a905f3dd5d4fbba750d9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample3.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2544\347\253\240 \346\217\222\345\200\274/ThrSample3.m" @@ -1,3 +1,57 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:6f8000d9d2a9f9aa94a9e4db120bf5b1e599329e2d8db2b631f0888acdaf7b92 -size 1573 +function [f,f0] = ThrSample3 (x,y,x0) +syms t; +f = 0.0; +f0 = 0.0; + +if(length(x) == length(y)) + n = length(x); +else + disp('xºÍyµÄάÊý²»ÏàµÈ£¡'); + return; +end %άÊý¼ì²é + +for i=1:n + if(x(i)<=x0)&& (x(i+1)>=x0) + index = i; + break; + end +end %ÕÒµ½x0ËùÔÚÇø¼ä + +for i=1:n + if(x(i)<=x0)&& (x(i+1)>=x0) + index = i; + break; + end +end %ÕÒµ½x0ËùÔÚÇø¼ä + +A = diag(2*ones(1,n-1)); %Çó½âmµÄϵÊý¾ØÕó +h0 = x(2)-x(1); +h1 = x(3)¨Cx(2); +he = x(n)-x(n-1); +A(1,2) = h0/(h0+h1); +A(1,n-1) = 1 - A(1,2); +A(n-1,1) = he/(h0+he); +A(n-1,n-2) = 1 - A(n-1,1); + +c = zeros(n-1,1); +c(1) = 3* A(1,n-1)*(y(2)-y(1))/h0 + 3* A(1,2)*(y(3)-y(2))/h1; +for i=2:n-2 + u = (x(i)-x(i-1))/(x(i+1)-x(i-1)); + lamda = (x(i+1)-x(i))/(x(i+1)-x(i-1)); + c(i) = 3*lamda*(y(i)-y(i-1))/(x(i)-x(i-1))+ ... + 3*u*(y(i+1)-y(i))/(x(i+1)-x(i)); + A(i, i+1) = u; + A(i, i-1) = lamda; %ÐγÉϵÊý¾ØÕó¼°ÏòÁ¿c +end +c(n-1) = 3*( he*(y(2)-y(1))/h0+h0*( y(n)-y(n-1))/he)/(h0+he); + +m = zeros(n,1); +[m(2:n),Q,R] = qrxq(A,c); %ÓÃqr·Ö½â·¨·¨Çó½â·½³Ì×é +m(1) = m(n); +h = x(index+1) - x(index); %x0ËùÔÚÇø¼ä³¤¶È +f = y(index)*(2*(t-x(index))+h)*(t-x(index+1))^2/h/h/h + ... + y(index+1)*(2*(x(index+1)-t)+h)*(t-x(index))^2/h/h/h + ... + m(index)*(t-x(index))*(x(index+1)-t)^2/h/h - ... + m(index+1)*(x(index+1)-t)*(t-x(index))^2/h/h; + %x0ËùÔÚÇø¼äµÄ²åÖµº¯Êý +f0 = subs(f,'t',x0); %x0´¦µÄ²åÖµ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Chebyshev.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Chebyshev.m" index f483c3467979a341dedbe4fce988cf8f48228157..0e0a641e0183398c55721793e1559c582d54c036 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Chebyshev.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Chebyshev.m" @@ -1,3 +1,25 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:744983abe28e924f1fc5e40ec8e77e7d05c4bb349e164ad76bcccfe19edad289 -size 575 +function f = Chebyshev(y,k,x0) +syms t; +T(1:k+1) = t; +T(1) = 1; +T(2) = t; +c(1:k+1) = 0.0; + +c(1)=int(subs(y,findsym(sym(y)),sym('t'))*T(1)/sqrt(1-t^2),t,-1,1)/pi; +c(2)=2*int(subs(y,findsym(sym(y)),sym('t'))*T(2)/sqrt(1-t^2),t,-1,1)/pi; +f = c(1)+c(2)*t; + +for i=3:k+1 + T(i) = 2*t*T(i-1)-T(i-2); + c(i) = 2*int(subs(y,findsym(sym(y)),sym('t'))*T(i)/sqrt(1-t^2),t,-1,1)/2; + f = f + c(i)*T(i); + f = vpa(f,6); + + if(i==k+1) + if(nargin == 3) + f = subs(f,'t',x0); + else + f = vpa(f,6); + end + end +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/DFF.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/DFF.m" index f3078639beffc71a2c8f96f3eed37655cd503e21..6c4e00d6fabc690e3ccef1b865a0182dee3ab263 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/DFF.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/DFF.m" @@ -1,3 +1,8 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2c5220c80afc3ecd451ea7cfc689a35e4bf95833b1fc91a016d452882cd78c80 -size 136 +function c = DFF(f,N) +c(1:N)=0; +for(m=1:N) + for(n=1:N) + c(m)=c(m)+f(n)*exp(-i*m*n*2*pi/N); + end + c(m)=c(m)/N; +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/FZZ.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/FZZ.m" index bd1a7ebb87ce7a6ccbd21112aff2b62ddb8ba805..639aa7d2658068dcc1a78c856b1f8151ea0aa5b0 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/FZZ.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/FZZ.m" @@ -1,3 +1,11 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:04e895cb4d427ec23fb76d6cf6d3ab98c61f59404c7e250153a42c7fbad0a7a9 -size 303 +function [A0,A,B]=FZZ(func,T, n) +syms t; +func = subs(sym(func), findsym(sym(func)),sym('t')); +A0=int(sym(func),t,-T/2,T/2)/T; +for(k=1:n) + A(k)=int(func*cos(2*pi*k*t/T), t,-T/2,T/2)*2/T; + A(k)=vpa(A(k),4); + B(k)=int(func*sin(2*pi*k*t/T), t,-T/2,T/2)*2/T; + B(k)=vpa(B(k),4); +end + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/LZXEC.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/LZXEC.m" index b4b244fff73d1af844b8b7bf62e2744c48cb58f4..5433b9b9898a1226a861d2982eb350f2b779c5e7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/LZXEC.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/LZXEC.m" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:4657e781854a873e1a3886176200f91b20bda752c6943b49a997ed1ab259e6e9 -size 408 +function [a,b]=LZXEC(x,y) +if(length(x) == length(y)) + n = length(x); +else + disp('xºÍyµÄάÊý²»ÏàµÈ£¡'); + return; +end %άÊý¼ì²é + +A = zeros(2,2); +A(2,2) = n; +B = zeros(2,1); +for i=1:n + A(1,1) = A(1,1) + x(i)*x(i); + A(1,2) = A(1,2) + x(i); + B(1,1) = B(1,1) + x(i)*y(i); + B(2,1) = B(2,1) + y(i); +end +A(2,1) = A(1,2); + +s = A\B; +a = s(1); +b = s(2); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Legendre.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Legendre.m" index 39ba294dccb856d822742bfa7c8cdd5d3733bc27..ee9ea48305585ed02f6c5c57a3ead8ddc795054d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Legendre.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Legendre.m" @@ -1,3 +1,24 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b58a9bba317f4b32e59a4fd8d78589e2d8116610d1694b7a9ab971b35c116b48 -size 526 +function f = Legendre(y,k,x0) +syms t; +P(1:k+1) = t; +P(1) = 1; +P(2) = t; +c(1:k+1) = 0.0; + +c(1)=int(subs(y,findsym(sym(y)),sym('t'))*P(1),t,-1,1)/2; +c(2)=int(subs(y,findsym(sym(y)),sym('t'))*P(2),t,-1,1)/2; +f = c(1)+c(2)*t; + +for i=3:k+1 + P(i) = ((2*i-3)*P(i-1)*t-(i-2)*P(i-2))/(i-1); + c(i) = int(subs(y,findsym(sym(y)),t)*P(i),t,-1,1)/2; + f = f + c(i)*P(i); + + if(i==k+1) + if(nargin == 3) + f = subs(f,'t',x0); + else + f = vpa(f,6); + end + end +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Pade.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Pade.m" index c5952bb8d338127d7f3cfeba2400055f4e9756c0..790b793b2c39fc7b3bcdb03214dd4ad1ae091e20 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Pade.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/Pade.m" @@ -1,3 +1,48 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8731a5f6d804a4da9b34825c7e3307cb0e4c9e31a8a889d77236377143178584 -size 780 +function f = Pade(y,n,x0) +syms t; + +A = zeros(n,n); +q = zeros(n,1); +p = zeros(n+1,1); +b = zeros(n,1); +yy = 0; +a(1:2*n) = 0.0; + +for(i=1:2*n) + yy = diff(sym(y),findsym(sym(y)),n); + a(i) = subs(sym(yy), findsym(sym(yy)), 0.0)/factorial(i); +end; + +for(i=1:n) + for(j=1:n) + A(i,j)=a(i+j-1); + end; + b(i,1) = -a(n+i); +end; + +q = A\b; +p(1) = subs(sym(y),findsym(sym(y)),0.0); +for(i=1:n) + p(i+1) = a(n)+q(i)*subs(sym(y),findsym(sym(y)),0.0); + for(j=2:i-1) + p(i+1)=p(i+1)+q(j)*a(i-j); + end +end + +f_1 = 0; +f_2 = 1; +for(i=1:n+1) + f_1 = f_1 + p(i)*(t^(i-1)); +end + +for(i=1:n) + f_2 = f_2 + q(i)*(t^i); +end + +if(nargin == 3) + f = f_1/f_2; + f = subs(f,'t',x0); +else + f = f_1/f_2; + f = vpa(f,6); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartBJ.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartBJ.m" index 172d41dcfed8f579dae9ab3685d6f2ba2dc17eb3..ad35158d447fb553c903659841ec3553fa258c44 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartBJ.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartBJ.m" @@ -1,3 +1,64 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:84e0d55abb83831270b6bb2e75328e320f844cba1cb5b7f7739415f8cf22846b -size 1728 +function [node,err] = SmartBJ(func,a,b,maxtol) +format long; +node(1) = a; +node(2) = b; +num = 2; +if(b-a)<10 + n = 5; +else + n = 10; +end +err = 0; +bSign = 1; +while (bSign) + bSign = 0; + knode = node; + tnum = num; + insert_num = 0; + for i=1:(tnum-1) + [mx,mv] = FindMX(func,knode(i),knode(i+1),n); + %ÕÒµ½Çø¼ä[knode(i),knode(i+1)]ÉϵÄÎó²î×î´óµÄµã + if mv > maxtol + %Èç¹ûÎó²î³¬¹ý¸ø¶¨¾«¶È£¬Ôڴ˵㽫Çø¼ä[knode(i),knode(i+1)]·ÖΪÁ½¶Î + d(1:(i+insert_num)) = node(1:(i+insert_num)); + d(i+insert_num+1) = mx; + num = num+1; + d((i+insert_num+2):num) = node((i+insert_num+1):(num-1)); + node = d; + bSign = 1; + insert_num = insert_num + 1; + else + if(mv>err) + err = mv; %¼Ç¼ËùÓзֶÎÏßÐÔ²åÖµÇø¼äÉϵÄ×î´óÎó²î + end + end + end +end +format short; + +function [max_x,max_v] = FindMX(func,a,b,n) +format long; +eps = 1.e-3; +max_v = 0; +max_x = a; +fa = subs(sym(func), findsym(sym(func)),a); %×ó¶Ëµãº¯ÊýÖµ +fb = subs(sym(func), findsym(sym(func)),b); %ÓҶ˵㺯ÊýÖµ +step = n/5; +tol = 1; +tmp = 0; +while tol>eps + t = a; + for j=0:(n/step) %´ËÑ­»·ÕÒ³öÈ¡×î´óÖµµÄx + t = a + j*step*(b-a)/n; + pt = fa + (t-a)*(fb-fa)/(b-a); %ÏßÐÔ²åÖµµÃ³öµÄº¯ÊýÖµ + ft = subs(sym(func), findsym(sym(func)),t); + if abs(ft-pt)>max_v %abs(f(x)-p(x)) + max_v = abs(ft-pt); %¼Ç¼×î´óÎó²î + max_x = t; %¼Ç¼´Ëµã×ø±ê + end + end + tol = abs(max_x-tmp); + tmp = max_x; + step = step/2; +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartYTBJ.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartYTBJ.m" index c3987a18a19542d2cd289b51c5b711f889528263..c33655a47221f0ccd7ff4bb8771053944644b58c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartYTBJ.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/SmartYTBJ.m" @@ -1,3 +1,70 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f0e1c41450dff43029a5af2d65b8a716dbcd580e61ce4c8f6c6a056a9e0e3878 -size 1991 +function [node,err] = SmartYTBJ(func,a,b,y_s,y_e,maxtol) +format long; +node(1) = a; +node(2) = b; +num = 2; +if(b-a)<10 + n = 5; +else + n = 10; +end +err = 0; +bSign = 1; +while (bSign) + bSign = 0; + for l=1:num + y(l) = subs(subs(sym(func), findsym(sym(func)),node(l))); + end + knode = node; + tnum = num; + insert_num = 0; + for i=1:(tnum-1) + pfx = ThrSample1(knode,y,y_s,y_e,((knode(i)+knode(i+1))/2)); + %ÉÏʽ¸ø³öÿ¸ö·Ö¶ÎÇø¼äÉϵÄÑùÌõ²åÖµº¯Êý + [mx,mv] = FindMX(func,pfx,knode(i),knode(i+1),n); + %ÕÒµ½Çø¼ä[knode(i),knode(i+1)]ÉϵÄÎó²î×î´óµÄµã + if mv > maxtol + %Èç¹ûÎó²î³¬¹ý¸ø¶¨¾«¶È£¬Ôڴ˵㽫Çø¼ä[knode(i),knode(i+1)]·ÖΪÁ½¶Î£¬¼´½«´Ëµã¼Ó + %Èë½áµãÊý×éÖÐ + d(1:(i+insert_num)) = node(1:(i+insert_num)); + d(i+insert_num+1) = mx; + num = num+1; + d((i+insert_num+2):num) = node((i+insert_num+1):(num-1)); + node = d; + bSign = 1; + insert_num = insert_num + 1; + else + if(mv>err) + err = mv; %¼Ç¼ËùÓÐÑùÌõ²åÖµÇø¼äÉϵÄ×î´óÎó²î + end + end + end +end +format short; + +function [max_x,max_v] = FindMX(func,pfx,a,b,n) +format long; +eps = 1.e-3; +max_v = 0; +max_x = a; +fa = subs(sym(func), findsym(sym(func)),a); %×ó¶Ëµãº¯ÊýÖµ +fb = subs(sym(func), findsym(sym(func)),b); %ÓҶ˵㺯ÊýÖµ +step = n/5; +tol = 1; +tmp = 0; +while tol>eps + t = a; + for j=0:(n/step) %´ËÑ­»·ÕÒ³öÈ¡×î´óÖµµÄx + t = a + j*step*(b-a)/n; + pt = subs(sym(pfx), findsym(sym(pfx)),t); %ÑùÌõ²åÖµµÃ³öµÄº¯ÊýÖµ + ft = subs(sym(func), findsym(sym(func)),t); + if abs(ft-pt)>max_v %abs(f(x)-p(x)) + max_v = abs(ft-pt); %¼Ç¼×î´óÎó²î + max_x = t; %¼Ç¼´Ëµã×ø±ê + end + end + tol = abs(max_x-tmp); + tmp = max_x; + step = step/2; +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJPF.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJPF.m" index 64dd469117e13942ab87805bcc76d7e93facf153..15eb0150b2c0c92e67878bc9fd25d3e8cb961b42 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJPF.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJPF.m" @@ -1,3 +1,17 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5af4f34a836591f79125ed43a871bb1e3ba9d0fcde562ad9d78128fd8f8a7b60 -size 492 +function coff=ZJPF(func,n,a,b) +C = zeros(n+1,n+1); +var = findsym(sym(func)); +func = func/var; +for i=1:n+1 + C(1,i)=(power(b,i)-power(a,i))/i; %Ëã·¨ÖеÄC¾ØÕóµÄµÚÒ»ÐÐ + func = func*var; + d(i,1)=int(sym(func),var,a,b); %Ëã·¨ÖеÄDÏòÁ¿µÄµÚÒ»ÐÐ +end + +for i=2:n+1 + C(i,1:n)=C(i-1,2:n+1); + f1 = power(b,n+i); + f2 = power(a,n+i); + C(i,n+1)=(f1-f2)/(n+i); %ÐγÉC¾ØÕó +end +coff = C\d; %Çó½â±Æ½ü¶àÏîʽµÄϵÊý diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJZXEC.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJZXEC.m" index 05f05dcc68b0fc4b4240ef1dbf250d7c2b3665f4..ef534cb48fa327ccc439647d62b08fda872f060f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJZXEC.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/ZJZXEC.m" @@ -1,3 +1,61 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b60ab187a4949ac9b4a8d8d5631feb3372f02d5d247da7542e684452570cc1fb -size 1350 +function a=ZJZXEC(x,y,m) +if(length(x) == length(y)) + n = length(x); +else + disp('xºÍyµÄάÊý²»ÏàµÈ£¡'); + return; +end %άÊý¼ì²é + +syms v; +d = zeros(1,m+1); +q = zeros(1,m+1); +alpha = zeros(1,m+1); +for k=0:m + px(k+1)=power(v,k); +end %xµÄÃݶàÏîʽ +B2 = [1]; +d(1) = n; +for l=1:n + q(1) = q(1) + y(l); + alpha(1) = alpha(1) + x(l); +end +q(1) = q(1)/d(1); +alpha(1) = alpha(1)/d(1); +a(1) = q(1); +B1 = [-alpha(1) 1]; +for l=1:n + d(2) = d(2) + (x(l)-alpha(1))^2; + q(2) = q(2) + y(l)*(x(l)-alpha(1)); + alpha(2) = alpha(2) + x(l)*(x(l)-alpha(1))^2; +end +q(2) = q(2)/d(2); +alpha(2) = alpha(2)/d(2); +a(1) = a(1)+q(2)*(-alpha(1)); +a(2) = q(2); +beta = d(2)/d(1); + +for i=3:(m+1) + B = zeros(1,i); + B(i) = B1(i-1); + B(i-1) = -alpha(i-1)*B1(i-1)+B1(i-2); + for j=2:i-2 + B(j) = -alpha(i-1)*B1(j)+B1(j-1)-beta*B2(j); + end + B(1) = -alpha(i-1)*B1(1)-beta*B2(1); + BF = B*transpose(px(1:i)); + for l=1:n + Qx = subs(BF,'v',x(l)); + d(i) = d(i) + (Qx)^2; + q(i) = q(i) + y(l)*Qx; + alpha(i) = alpha(i) + x(l)*(Qx)^2; + end + alpha(i) = alpha(i)/d(i); + q(i) = q(i)/d(i); + beta = d(i)/d(i-1); + for k=1:i-1 + a(k) = a(k)+q(i)*B(k); + end + a(i) = q(i)*B(i); + B2 = B1; + B1 = B; +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/lmz.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/lmz.m" index 69f5bc806270a24afb15237a959375eee5c2fa0e..73886b2147c26ca4bca02b53a8c55aa851665021 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/lmz.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/lmz.m" @@ -1,3 +1,101 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bdb73dff13de67c0feb69924fd464245701b07e9f9d6164b30710a21a7d0df9d -size 2997 +function [coff,err]= lmz(func,m,a,b,eps) +if(nargin == 4) + eps=1.0e-6; +end +syms v; +maxv = 0.0; +max_x = a; %¼Ç¼abs(f(x)-p(x))È¡×î´óÖµµÄx +for k=0:m + px(k+1)=power(v,k); +end %p£¨x£©¶àÏîʽ +for i=1:m+2 + x(i)=0.5*(a+b+(b-a)*cos(3.14159265*(m+2-i)/(m+1))); + fx(i)=subs(sym(func), findsym(sym(func)),x(i)); +end %³õʼµÄxºÍf(x) +A = zeros(m+2,m+2); +for i=1:m+2 + for j=1:m+1 + A(i,j)=power(x(i),j-1); + end + A(i,m+2)=(-1)^i; +end +c =A\transpose(fx); %p(x)µÄ³õʼϵÊý +u = c(m+2); %Ëã·¨ÖеÄu +tol = 1; %¾«¶È + +while(tol>eps) + t = a; + while(tmaxv + maxv = abs(ft-pt); + max_x = t; + end + end + if max_x>b + max_x = b; + end + %ÒÔÏ¿ɲο¼Ëã·¨µÄÈý¸öÈ·¶¨Ðµ㼯µÄÇé¿ö + if (a<=max_x)&&(max_x<=x(2)) %µÚÒ»ÖÖÇé¿ö + f0 = subs(sym(func), findsym(sym(func)),x(2)); + px1 = subs(px,'v',x(2)); + pt = px1*c(1:m+1); + d1 = f0 - pt; + fm = subs(sym(func), findsym(sym(func)),max_x); + pm1 = subs(px,'v',max_x); + pm = pm1*c(1:m+1); + d2 = fm - pm; + if d1*d2>0 + x(2) = max_x; + end + else + if (x(m+1)<=max_x)&&(max_x<=b) %µÚ¶þÖÖÇé¿ö + f0 = subs(sym(func), findsym(sym(func)),x(m+1)); + px1 = subs(px,'v',x(m+1)); + pt = px1*c(1:m+1); + d1 = f0 - pt; + fm = subs(sym(func), findsym(sym(func)),max_x); + pm1 = subs(px,'v',max_x); + pm = pm1*c(1:m+1); + d2 = fm - pm; + if d1*d2>0 + x(m+1) = max_x; + end + else %µÚÈýÖÖÇé¿ö + for i=2:m + if(x(i)<=max_x)&& (x(i+1)>=max_x) + index_x = i; + break; + end + end %ÕÒµ½max_xËùÔÚÇø¼ä + f0 = subs(sym(func), findsym(sym(func)),x(index_x)); + px1 = subs(px,'v',x(index_x)); + pt = px1*c(1:m+1); + d1 = f0 - pt; + fm = subs(sym(func), findsym(sym(func)),max_x); + pm1 = subs(px,'v',max_x); + pm = pm1*c(1:m+1); + d2 = fm - pm; + if d1*d2>0 + x(index_x) = max_x; + end + end + end + for i=1:m+2 %ÖØмÆËãf£¨x£© + fx(i)=subs(sym(func), findsym(sym(func)),x(i)); + end + for i=1:m+2 + for j=1:m+1 + A(i,j)=power(x(i),j-1); + end + A(i,m+2)=(-1)^i; + end + c =A\transpose(fx); %ÖØмÆËãp£¨x£©µÄϵÊý + tol = abs(c(m+2)-u); + u = c(m+2); +end +coff = c(1:m+1); +err = u; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/multifit.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/multifit.m" index cd64491ba9921af9f1284bf5df6edd87e757d55b..8b7c49d09d9696a12f3bf79b3526d802f07d7e7e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/multifit.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2545\347\253\240 \345\207\275\346\225\260\351\200\274\350\277\221/multifit.m" @@ -1,3 +1,28 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:7c7114ce01ec338f77a0b7d1ee4a8f677ef30dc61ff39057ccf08d51f7f03f16 -size 472 +function A=multifit(X,Y,m) +%A--Êä³öµÄÄâºÏ¶àÏîʽµÄϵÊý +N=length(X); +M=length(Y); +if(N ~= M) + disp('Êý¾Ýµã×ø±ê²»Æ¥Å䣡'); + return; +end + +c(1:(2*m+1))=0; +b(1:(m+1))=0; + +for j=1:(2*m+1) %Çó³öcºÍb + for k=1:N + c(j)=c(j)+X(k)^(j-1); + if(j<(m+2)) + b(j)=b(j)+Y(k)*X(k)^(j-1); + end + end +end + +C(1,:)=c(1:(m+1)); +for s=2:(m+1) + C(s,:)=c(s:(m+s)); +end + +A=b'\C; %Ö±½ÓÇó½â·¨Çó³öÄâºÏϵÊý + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/Chapoly.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/Chapoly.m" index f7fc1f2c148216425fd7cc045cdf0f91f38cbf9f..f6dec6b1c52e05a2c686dc2ac9dbf8d66dc09c0b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/Chapoly.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/Chapoly.m" @@ -1,3 +1,9 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f3b9e59fed41cd64c7a677b337855ce01ff77aaa42c36e2a02e3a35196fb381c -size 142 +function l = Chapoly(A) +syms t; + +N = size(A); +n = N(1,1); + +y = det(A-t*eye(n,n)); +l = solve(y); +l = vpa(l, 5); %½á¹ûÈ¡Îåλ¾«¶È \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/dimethod.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/dimethod.m" index d0f4d589553f43bdc2b3b5ad90b1cf8bfd9ea047..8fee7c4541b94f6e551c807a251a54e80b3ee087 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/dimethod.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2546\347\253\240 \347\237\251\351\230\265\347\211\271\345\276\201\345\200\274\350\256\241\347\256\227/dimethod.m" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c2949abcfb9abdf153c35963be343cfec45916ef00feb559ecda6b3c7dde2260 -size 574 +function [l,v]=dimethod(A,x0,u,eps) +if nargin==3 + eps = 1.0e-6; +end + +N = size(A); +n = N(1,1); %nΪAµÄ½× +v = x0; +M = 5000; %µü´ú²½ÊýÏÞÖÆ +m = 0; +l = 0; +for(k=1:M) + y = (A-u*eye(n,n))\v; + m = max(y); %mΪ°´Ä£×î´óµÄ·ÖÁ¿ + v = y/m; + + if(abs(m - l)1) + m=(y*v')/(v*v'); + end + v = y/m; + + if(abs(m - l)eps + n=n+1; + h=(b-a)/n; + I1=I2; + I2=0; + for i=0:n-1 + x=a+h*i; + x1=x+h; + I2=I2+(h/2)*(subs(sym(f),findsym(sym(f)),x)+subs(sym(f),findsym(sym(f)),x1)); + end +end + +I=I2; +step=n; + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDBuer.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDBuer.m" index 431d4ee940a6dd78b3cf842c0be6b65d817ff4fc..a9e6bcefda2b87db7efa27935ba59bdad0cd9d2a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDBuer.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDBuer.m" @@ -1,3 +1,30 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b2bbb635a0f36f61afcf3740b6e12289fd76543a8a252854259ccddeb4c6e7b8 -size 673 +function [I,step] = DDBuer(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end; +n=1; +h=b-a; +I1=0; +I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h/2; +tol=1; +while tol>eps + n=n+1; + h=h/4; + I1=I2; + I2=0; + for i=0:(4^(n-1)-1) + x=a+h*4*i; + x1=x+h; + x2=x1+h; + x3=x2+h; + x4=x3+h; + I2=I2+(2*h/45)*(7*subs(sym(f),findsym(sym(f)),x)+... + 32*subs(sym(f),findsym(sym(f)),x1)+... + 12*subs(sym(f),findsym(sym(f)),x2)+... + 32*subs(sym(f),findsym(sym(f)),x3)+... + 7*subs(sym(f),findsym(sym(f)),x4)); + end + tol=abs(I2-I1); +end +I=I2; +step=n; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDSimpson.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDSimpson.m" index 5a7c5fb01790e2a5f6cb22171f4f25cd118be075..e1b0ddf14c24db81c4cfbc0af60df876aebdef96 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDSimpson.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDSimpson.m" @@ -1,3 +1,27 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f7e19d1dad409599a4a3dbca8a4211e17c316a2696c97d0f790baa6ac74f0e70 -size 537 +function [I,step] = DDSimpson(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end; +n=1; +h=b-a; +I1=0; +I2=(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))/h/2; +tol=1; +while tol>eps + n=n+1; + h=h/2; + I1=I2; + I2=0; + for i=0:(2^(n-1)-1) + x=a+h*2*i; + x1=x+h; + x2=x1+h; + I2=I2+(h/3)*(subs(sym(f),findsym(sym(f)),x)+... + 4*subs(sym(f),findsym(sym(f)),x1)+... + subs(sym(f),findsym(sym(f)),x2)); + end + tol=abs(I2-I1); +end +I=I2; +step=n; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDTraprl.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDTraprl.m" index bb7c6429db9243c57e1765521c6890997dd10570..97a1de8a99f429cc43a75aa1cf7f2874eccc8246 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDTraprl.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DDTraprl.m" @@ -1,3 +1,24 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:87c6dbceaa0dfeaeb56e3a924cd2936aaa90abcbb6807b0786937ef5987fd506 -size 497 +function [I,step] = DDTraprl(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end; +n=0; +h=(b-a); +I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h/2; +tol=1; +while tol>eps + n=n+1; + h=h/2; %Çø¼äÖð´Î·Ö°ë + I1=I2; + I2=0; + for i=0:(2^n-1) + x=a+h*i; + x1=x+h; + I2=I2+(h/2)*(subs(sym(f),findsym(sym(f)),x)+... + subs(sym(f),findsym(sym(f)),x1)); %ÌÝÐι«Ê½ + end + tol=abs(I2-I1); +end + +I=I2; +step=n; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblSimpson.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblSimpson.m" index a9da5fd83051fa51f7fa8b2457e0ed4511efda3e..62eb1df7e36188d3e49541aa1537ae915af1fd07 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblSimpson.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblSimpson.m" @@ -1,3 +1,37 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2c4f093879a0c64ff489c3a7ec36a74db4822627b42a9c027a88cc69bc173d1e -size 1483 +function q=DblSimpson(f,a,A,b,B,m,n) +if(m==1 && n==1) %ÐÁÆÕÉ­¹«Ê½ + q=((B-b)*(A-a)/9)*(subs(sym(f),findsym(sym(f)),{a,b})+... + subs(sym(f),findsym(sym(f)),{a,B})+... + subs(sym(f),findsym(sym(f)),{A,b})+... + subs(sym(f),findsym(sym(f)),{A,B})+... + 4*subs(sym(f),findsym(sym(f)),{(A-a)/2,b})+... + 4*subs(sym(f),findsym(sym(f)),{(A-a)/2,B})+... + 4*subs(sym(f),findsym(sym(f)),{a,(B-b)/2})+... + 4*subs(sym(f),findsym(sym(f)),{A,(B-b)/2})+... + 16*subs(sym(f),findsym(sym(f)),{(A-a)/2,(B-b)/2})); + +else %¸´ºÏÐÁÆÕÉ­¹«Ê½ + q=0; + for i=0:n-1 + for j=0:m-1 + x=a+2*i*(A-a)/2/n; + y=b+2*j*(B-b)/2/m; + x1=a+(2*i+1)*(A-a)/2/n; + y1=b+(2*j+1)*(B-b)/2/m; + x2=a+2*(i+1)*(A-a)/2/n; + y2=b+2*(j+1)*(B-b)/2/m; + + q=q+subs(sym(f),findsym(sym(f)),{x,y})+... + subs(sym(f),findsym(sym(f)),{x,y2})+... + subs(sym(f),findsym(sym(f)),{x2,y})+... + subs(sym(f),findsym(sym(f)),{x2,y2})+... + 4*subs(sym(f),findsym(sym(f)),{x,y1})+... + 4*subs(sym(f),findsym(sym(f)),{x2,y1})+... + 4*subs(sym(f),findsym(sym(f)),{x1,y})+... + 4*subs(sym(f),findsym(sym(f)),{x1,y2})+... + 16*subs(sym(f),findsym(sym(f)),{x1,y1}); + end + end +end + +q=((B-b)*(A-a)/36/m/n)*q; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblTraprl.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblTraprl.m" index 4a7278736086d55fb0c994c5f4dbb71b215784d9..bdb5eb7bf348a45954b858178858c7dac83fdf7d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblTraprl.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/DblTraprl.m" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:db9423d111cbcc8ee3d627881b8c5b93cd6a98238834ab5ad10c46ed25cb8540 -size 733 +function q=DblTraprl(f,a,A,b,B,m,n) +if(m==1 && n==1) %ÌÝÐι«Ê½ + q=((B-b)*(A-a)/4)*(subs(sym(f),findsym(sym(f)),{a,b})+... + subs(sym(f),findsym(sym(f)),{a,B})+... + subs(sym(f),findsym(sym(f)),{A,b})+... + subs(sym(f),findsym(sym(f)),{A,B})); + +else %¸´ºÏÌÝÐι«Ê½ + C=4*ones(n+1,m+1); + C(1,:)=2; + C(:,1)=2; + C(n+1,:)=2; + C(:,m+1)=2; + C(1,1)=1; + C(1,m+1)=1; + C(n+1,1)=1; + C(n+1,m+1)=1; %C¾ØÕó +end + +F=zeros(n+1,m+1); +q=0; +for i=0:n + for j=0:m + x=a+i*(A-a)/n; + y=b+j*(B-b)/m; + F(i+1,j+1)=subs(sym(f),findsym(sym(f)),{x,y}); + q=q+F(i+1,j+1)*C(i+1,j+1); + end +end + +q=((B-b)*(A-a)/4/m/n)*q; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntDBGauss.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntDBGauss.m" index 6cd7be099712c3d35e47c1aca0e1f3b9dc916458..134d2fd928e9778d56a85134b26c2bf6d3249a51 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntDBGauss.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntDBGauss.m" @@ -1,3 +1,23 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2329c20c12dba2a33311abc291afdad4224fbb5ddc3d6959506c83178e98deb8 -size 797 +function q = IntDBGauss(func,a,b,c,d,m,n) +format long; +ta = (b-a)/2; +tb = (a+b)/2; +tc = (d-c)/2; +td = (c+d)/2; +f = zeros(n,m); +node_x = [0 0 0 0 0;-0.5773503 0.5773503 0 0 0;-0.7745967 0 0.7745967 0 0; + -0.8611363 -0.3398810 0.3398810 0.8611363 0; + -0.9061793 -0.5384693 0 0.5384693 0.9061793]; %¸ß˹»ý·Öµã×ø±ê¾ØÕó +node_A = [2 0 0 0 0;1 1 0 0 0;0.5555556 0.8888889 0.5555556 0 0; + 0.3478548 0.6521453 0.6521453 0.3478548 0; + 0.2369269 0.4786287 0.5688889 0.4786287 0.2369269]; + %¸ß˹»ý·ÖϵÊý¾ØÕó +for i=1:m + for j=1:n + f(j,i) = subs(sym(func),findsym(sym(func)),[ta*node_x(m,i)+tb tc*node_x(n,i)+td]); + end +end +Am = transpose(node_A(m,1:m)); +An = node_A(n,1:n); +q =ta*tc* An*f*Am; +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGauss.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGauss.m" index de031275b256371787fd182d175fee127525437a..ad0dd75da313c9b02df7077f8ac6d077fe2a2181 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGauss.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGauss.m" @@ -1,3 +1,41 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:0f8d62b90e3601b672fa2924d19beb8254bf18a6a43321ca38e6dccb7f542860 -size 1386 +function I = IntGauss(f,a,b,n,AK,XK) +if(n<5 && nargin == 4) + AK = 0; + XK = 0; +else + XK1=((b-a)/2)*XK+((a+b)/2); + I=((b-a)/2)*sum(AK.*subs(sym(f),findsym(f),XK1)); +end + +ta = (b-a)/2; +tb = (a+b)/2; +switch n + case 0, + I=2*ta*subs(sym(f),findsym(sym(f)),tb); + + case 1, + I=ta*(subs(sym(f),findsym(sym(f)),ta*0.5773503+tb)+... + subs(sym(f),findsym(sym(f)),-ta*0.5773503+tb)); + + case 2, + I=ta*(0.55555556*subs(sym(f),findsym(sym(f)),ta*0.7745967+tb)+... + 0.55555556*subs(sym(f),findsym(sym(f)),-ta*0.7745967+tb)+... + 0.88888889*subs(sym(f),findsym(sym(f)),tb)); + + case 3, + I=ta*(0.3478548*subs(sym(f),findsym(sym(f)),ta*0.8611363+tb)+... + 0.3478548*subs(sym(f),findsym(sym(f)),-ta*0.8611363+tb)+... + 0.6521452*subs(sym(f),findsym(sym(f)),ta*0.3398810+tb)... + +0.6521452*subs(sym(f),findsym(sym(f)),-ta*0.3398810+tb)); + + + case 4, + I=ta*(0.2369269*subs(sym(f),findsym(sym(f)),ta*0.9061793+tb)+... + 0.2369269*subs(sym(f),findsym(sym(f)),-ta*0.9061793+tb)+... + 0.4786287*subs(sym(f),findsym(sym(f)),ta*0.5384693+tb)... + +0.4786287*subs(sym(f),findsym(sym(f)),-ta*0.5384693+tb)+... + 0.5688889*subs(sym(f),findsym(sym(f)),tb)); +end + + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussHermite.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussHermite.m" index be1ece833b62ba7f3d894634d7d3d61d6e963ff8..f366add9e1a6c36398c9ea7f1b0f0a822934c795 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussHermite.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussHermite.m" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d54acb989c2d14ee0e014b08c55f2a1f823255e7e46d3e7fd8a4a31e1aaf654c -size 1079 +function I = IntGaussHermite(f,n,AK,XK) +if(n<6 && nargin == 2) + AK = 0; + XK = 0; +else + I=sum(AK.*subs(sym(f),findsym(sym(f)),XK)); +end + +switch n + case 2, + I=0.886227*(subs(sym(f),findsym(sym(f)),-0.707107)+... + subs(sym(f),findsym(sym(f)),0.707107)); + + case 3, + I=1.181636*subs(sym(f),findsym(sym(f)),0)+... + 0.295409*(subs(sym(f),findsym(sym(f)),1.224745)+... + subs(sym(f),findsym(sym(f)),-1.224745)); + + case 4, + I=0.544444*(subs(sym(f),findsym(sym(f)),0.524648)+... + subs(sym(f),findsym(sym(f)),-0.524648))+... + 0.100000*(subs(sym(f),findsym(sym(f)),1.650680)+... + subs(sym(f),findsym(sym(f)),-1.650680)); + + case 5, + I=0.945309*subs(sym(f),findsym(sym(f)),0)+... + 0.393619*(subs(sym(f),findsym(sym(f)),0.958572)+... + subs(sym(f),findsym(sym(f)),-0.958572))+... + 0.199532*(subs(sym(f),findsym(sym(f)),2.020183)+... + subs(sym(f),findsym(sym(f)),-2.020183)); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLada.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLada.m" index 5f2399907619bc8c2fbbacb3dc3b0d5f3f36ed0b..070c59cb74148c3d9c5b15178c9af400dcc70fa6 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLada.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLada.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:61332ada613e1c995585aa048e7c0f8eb4a59cbe3ea129d3ec57238a3297aef9 -size 1338 +function I = IntGaussLada(f,a,b,n,AK,XK) +if(n<6 && nargin == 4) + AK = 0; + XK = 0; +else + XK1=((b-a)/2)*XK+((a+b)/2); + I=((b-a)/2)*((2/n/n)*subs(sym(f),findsym(sym(f)),a)+... + sum(AK.*subs(sym(f),findsym(sym(f)),XK1))); +end + +ta = (b-a)/2; +tb = (a+b)/2; +switch n + case 2, + I=ta*0.5*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+... + 1.5*ta*subs(sym(f),findsym(sym(f)),ta*(1/3)+tb); + + case 3, + I=ta*((2/9)*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+... + 0.752806*subs(sym(f),findsym(sym(f)),ta*(-0.289898)+tb)+... + 1.024972*subs(sym(f),findsym(sym(f)),ta*0.689898+tb)); + + case 4, + I=ta*(0.125*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+... + 0.657689*subs(sym(f),findsym(sym(f)),-ta*0.575319+tb)+... + 0.776387*subs(sym(f),findsym(sym(f)),ta*0.181066+tb)+... + 0.440925*subs(sym(f),findsym(sym(f)),ta*0.822824+tb)); + + case 5, + I=ta*(0.08*subs(sym(f),findsym(sym(f)),ta*(-1)+tb)+... + 0.446207*subs(sym(f),findsym(sym(f)),-ta*0.720480+tb)+... + 0.623653*subs(sym(f),findsym(sym(f)),-ta*0.167181+tb)+... + 0.562712*subs(sym(f),findsym(sym(f)),ta*0.446314+tb)+... + 0.287427*subs(sym(f),findsym(sym(f)),ta*0.885792+tb)); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLager.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLager.m" index 3a9cf39db98df3615834687e16b8de2390640649..05915cb49cfe60883bcf23f9b012094a952cedf3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLager.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLager.m" @@ -1,3 +1,31 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:0e2ffc28cb4e47e6a14e04525ab33bf2e21b3f69bb49fe013263dc7fc86c47e2 -size 1141 +function I = IntGaussLager(f,n,AK,XK) +if(n<6 && nargin == 2) + AK = 0; + XK = 0; +else + I=sum(AK.*subs(sym(f),findsym(sym(f)),XK)); +end + +switch n + case 2, + I=0.853553*subs(sym(f),findsym(sym(f)),-0.585786)+... + 0.146447*subs(sym(f),findsym(sym(f)),3.414214); + + case 3, + I=0.711093*subs(sym(f),findsym(sym(f)),0.415575)+... + 0.278518*subs(sym(f),findsym(sym(f)),2.294280)+... + 0.0103893*subs(sym(f),findsym(sym(f)),6.289945); + + case 4, + I=0.603154*subs(sym(f),findsym(sym(f)),0.322548)+... + 0.357419*subs(sym(f),findsym(sym(f)),1.745761)+... + 0.0388879*subs(sym(f),findsym(sym(f)),4.536620)+... + 0.000539295*subs(sym(f),findsym(sym(f)),9.395071); + + case 5, + I=0.521756*subs(sym(f),findsym(sym(f)),0.263560)+... + 0.398667*subs(sym(f),findsym(sym(f)),1.413403)+... + 0.0759424*subs(sym(f),findsym(sym(f)),3.596426)+... + 0.00361176*subs(sym(f),findsym(sym(f)),7.085810)+... + 0.0000233700*subs(sym(f),findsym(sym(f)),12.640801); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLobato.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLobato.m" index 511a1888d191424dfeac918cc2a25aa97392ec9e..8fcdfeb31bd38091595dab5bf579babab16d7d6b 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLobato.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntGaussLobato.m" @@ -1,3 +1,38 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:123c955d0949a96767b7960a7d0fc728412c886cc011eefd643425e912b50309 -size 1483 +function I = IntGaussLobato(f,a,b,n,AK,XK) +if(n<7 && nargin == 4) + AK = 0; + XK = 0; +else + XK1=((b-a)/2)*XK+((a+b)/2); + I=((b-a)/2)*((2/n/(n-1))*(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))+sum(AK.*subs(sym(f),findsym(sym(f)),XK1))); +end + +ta = (b-a)/2; +tb = (a+b)/2; +switch n + case 3, + I=ta*((1/3)*(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))+1.333333*subs(sym(f),findsym(sym(f)),tb)); + + case 4, + I=ta*((1/6)*(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))+0.833333*... + (subs(sym(f),findsym(sym(f)),ta*0.447214+tb)+... + subs(sym(f),findsym(sym(f)),-ta*0.447214+tb))); + + case 5, + I=ta*((1/10)*(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))+0.544444*... + (subs(sym(f),findsym(sym(f)),ta*0.654654+tb)+... + subs(sym(f),findsym(sym(f)),-ta*0.654654+tb))+... + 0.711111*subs(sym(f),findsym(sym(f)),tb)); + + case 6, + I=ta*((1/15)*(subs(sym(f),findsym(sym(f)),a)+... + subs(sym(f),findsym(sym(f)),b))+0.554858*... + (subs(sym(f),findsym(sym(f)),ta*0.285232+tb)+... + subs(sym(f),findsym(sym(f)),-ta*0.285232+tb))+... + 0.378475*(subs(sym(f),findsym(sym(f)),ta*0.765055+tb)+... + subs(sym(f),findsym(sym(f)),-ta*0.765055+tb))); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntPWC.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntPWC.m" index b4db20ef5d546b6e93584f3cc28f8ca42df3d05d..bbd82ae175c9383adc1224bd9d376a68d20428fd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntPWC.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntPWC.m" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a2faa03632a4b6f259422b1f061f055d1289e1c3c5e9ba6344deb5417bbcd623 -size 680 +function q = IntPWC(X,Y,n) +format long; +h = zeros(n-1,1); +lamda = zeros(n,1); +L = zeros(n-2,1); +R = zeros(n-2,1); +Dlta = zeros(n-2,1); +h(1) = X(2)-X(1); +for j=1:n-2 %¼ÆËãÿ¸ö×ÓÇø¼äµÄ»ý·Ö²ÎÊý + h(j+1) = X(j+2)-X(j+1); + lamda(j) = h(j)/h(j+1); + Dlta(j) = h(j+1)/h(j); + L(j) = (Dlta(j)*Dlta(j))*Y(j)/(1+Dlta(j))-Dlta(j)*Y(j+1)+... + +Dlta(j)*Y(j+2)/(1+Dlta(j)); + R(j) = (lamda(j)*lamda(j))*Y(j+2)/(1+lamda(j))-lamda(j)*Y(j+1)+... + +lamda(j)*Y(j)/(1+lamda(j)); +end +q = h(1)*(3*Y(1)+3*Y(2)-R(1))/6+h(n-1)*(3*Y(n-1)+3*Y(n)-L(n-2))/6; +for k=2:n-2 + q = q + h(k)*(3*Y(k)+3*Y(k+1)-0.5*R(k)-0.5*L(k-1))/6; +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF1.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF1.m" index 638cc66b8f0bfeb3e0415598d22c4b9e577697d4..f338a148027f82f275148ec01dfc724309289c39 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF1.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF1.m" @@ -1,3 +1,12 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:546ecc80282dd1ae498c8f0c7585d7fdcc2c185f2bf5b5fcb4839c3fb6823245 -size 253 +function q = IntQBXF1(func,n) +format long; +pi = 3.1415926535; +q = 0; +A = zeros(n,1); +x = zeros(n,1); +for i=1:n + A(i) = pi/n; + x(i) = cos(pi*(2*i-1)/2/n); + y(i) = subs(sym(func), findsym(sym(func)), x(i)); + q = q + A(i)*y(i); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF2.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF2.m" index 224befd2665d12004f8d7130f1c74b987f145f2b..bf86695747d347d9a1c71b56ba91033d91d3c46e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF2.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntQBXF2.m" @@ -1,3 +1,12 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8f17044d192f2e943226a35ecf08eb9d79620737ab6119a125576c1f3f5917ef -size 289 +function q = IntQBXF2(func,n) +format long; +pi = 3.1415926535; +q = 0; +A = zeros(n,1); +x = zeros(n,1); +for i=1:n + A(i) = sin((i*pi)/(n+1))*sin((i*pi)/(n+1))*pi/(n+1); + x(i) = cos(pi*i/(n+1)); + y(i) = subs(sym(func), findsym(sym(func)), x(i)); + q = q + A(i)*y(i); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSample.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSample.m" index e19584ef3dd1c622626f017b1e5ce4f5f8b034c2..5b0a5c55995f2818847c328d1785838e9fa4a08a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSample.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSample.m" @@ -1,3 +1,37 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9e8a9662f0194217accfc678939674bde5209a016ce753b4f23e581f5a9a89d3 -size 992 +function q = IntSample(func,a,b,n) +format long; +node_num = n + 3; %¼ÓÉÏÑÓÍصÄ2¸ö½Úµã¹²n+3¸ö½Úµã +h = (b-a)/n; +for i=1:node_num + y(i) = subs(sym(func), findsym(sym(func)), a+i*h-2*h); +end + +y_1 = (-3*y(1)+4*y(2)-y(3))/(2*h); +y_N = (3*y(node_num)-4*y(node_num-1)+3*y(node_num-2))/(2*h); +c = SubBSample(h,node_num-1,y,y_1,y_N); %ÓÃÑùÌõ±Æ½ü·¨Çó³öÑùÌõϵÊý +q = h*(c(1)+c(node_num+2))/24+h*(c(2)+c(node_num+1))/2+23*h*(c(3)+c(node_num))/24;; +for j=4:node_num-1 + q = q+h*c(j); +end +format short; + +function c = SubBSample(h,n,y,y_1,y_N) +f0 = 0.0; +c = zeros(n+3,1); +b = zeros(n+1,1); + + +A = diag(4*ones(n+1,1)); +I = eye(n+1,n+1); +AL = [I(2:n+1,:);zeros(1,n+1)]; +AU = [zeros(1,n+1);I(1:n,:)]; +A = A+AL+AU; %ÐγÉϵÊý¾ØÕó +for i=2:n + b(i,1) = 6*y(i); +end +b(1) = 6*y(1)+2*h*y_1; +b(n+1) = 6*y(n+1)-2*h*y_N; +d = followup(A,b); %ÓÃ×·¸Ï·¨Çó³öϵÊý +c(2:n+2) = d; +c(1) = c(2) - 2*h*y_1; %c(-1) +c(n+3) = c(3)+2*h*y_N; %c(n+1) diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSimpson.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSimpson.m" index 23e5cfcaca1daaf9478f4357e75e69631d753bdb..6daf36562526a59d66be067f68b535a48629af7e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSimpson.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/IntSimpson.m" @@ -1,3 +1,46 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:839267cede9c77280dafb9bc3be63656861ada34460acb9d1238680179d3b79d -size 1262 +function [I,step] = IntSimpson(f,a,b,type,eps) +%type = 1 ÐÁÆÕÉ­¹«Ê½ +%type = 2 ÐÁÆÕÉ­3/8¹«Ê½ +%type = 3 ¸´ºÏÐÁÆÕÉ­¹«Ê½ + +if(type==3 && nargin==4) + eps=1.0e-4; %ȱʡ¾«¶ÈΪ0.0001 +end + +I=0; +switch type + case 1, + I=((b-a)/6)*(subs(sym(f),findsym(sym(f)),a)+... + 4*subs(sym(f),findsym(sym(f)),(a+b)/2)+... + subs(sym(f),findsym(sym(f)),b)); + step=1; + + case 2, + I=((b-a)/8)*(subs(sym(f),findsym(sym(f)),a)+... + 3*subs(sym(f),findsym(sym(f)),(2*a+b)/3)+ ... + 3*subs(sym(f),findsym(sym(f)),(a+2*b)/3)+subs(sym(f),findsym(sym(f)),b)); + step=1; + + case 3, + n=2; + h=(b-a)/2; + I1=0; + I2=(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b))/h; + while abs(I2-I1)>eps + n=n+1; + h=(b-a)/n; + I1=I2; + I2=0; + for i=0:n-1 + x=a+h*i; + x1=x+h; + I2=I2+(h/6)*(subs(sym(f),findsym(sym(f)),x)+... + 4*subs(sym(f),findsym(sym(f)),(x+x1)/2)+... + subs(sym(f),findsym(sym(f)),x1)); + end + end + I=I2; + step=n; +end + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/NewtonCotes.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/NewtonCotes.m" index ae732a91b033420123b4cb2fdeab3f4030cc8792..455bb010cf578655f866beeb85f99b171c7a735d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/NewtonCotes.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/NewtonCotes.m" @@ -1,3 +1,28 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d6ef2bee6712f692c0a0202d465ca2327f17ab912d3d865cf90aa868c95606f7 -size 1193 +function I = NewtonCotes(f,a,b,type) +%type = 1 ¿Æ´Ä¹«Ê½ +%type = 2 Å£¶Ù£­¿Æ´ÄÁùµã¹«Ê½ +%type = 3 Å£¶Ù£­¿Æ´ÄÆߵ㹫ʽ + +I=0; +switch type + case 1, + I=((b-a)/90)*(7*subs(sym(f),findsym(sym(f)),a)+... + 32*subs(sym(f),findsym(sym(f)),(3*a+b)/4)+... + 12*subs(sym(f),findsym(sym(f)),(a+b)/2)+... + 32*subs(sym(f),findsym(sym(f)),(a+3*b)/4)+7*subs(sym(f),findsym(sym(f)),b)); + + case 2, + I=((b-a)/288)*(19*subs(sym(f),findsym(sym(f)),a)+... + 75*subs(sym(f),findsym(sym(f)),(4*a+b)/5)+... + 50*subs(sym(f),findsym(sym(f)),(3*a+2*b)/5)+... + 50*subs(sym(f),findsym(sym(f)),(2*a+3*b)/5)+... + 75*subs(sym(f),findsym(sym(f)),(a+4*b)/5)+19*subs(sym(f),findsym(sym(f)),b)); + + case 3, + I=((b-a)/840)*(41*subs(sym(f),findsym(sym(f)),a)+... + 216*subs(sym(f),findsym(sym(f)),(5*a+b)/6)+... + 27*subs(sym(f),findsym(sym(f)),(2*a+b)/3)+... + 272*subs(sym(f),findsym(sym(f)),(a+b)/2)+... + 27*subs(sym(f),findsym(sym(f)),(a+2*b)/3)+... + 216*subs(sym(f),findsym(sym(f)),(a+5*b)/6)+41*subs(sym(f),findsym(sym(f)),b)); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/Roberg.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/Roberg.m" index c37dbf7b5e83881f86a82ead88967fd60b5f56ab..9c5183767036026afa9fb2bb02f65c2c56b46189 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/Roberg.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/Roberg.m" @@ -1,3 +1,28 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f54c6c27d78a677b4779ea8b929b48fc722b3bad532a52403f9482b541a1ee0a -size 524 +function [I,step]=Roberg(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end; +M=1; +tol=10; +k=0; +T=zeros(1,1); +h=b-a; +T(1,1)=(h/2)*(subs(sym(f),findsym(sym(f)),a)+subs(sym(f),findsym(sym(f)),b)); + +while tol>eps + k=k+1; + h=h/2; + Q=0; + for i=1:M + x=a+h*(2*i-1); + Q=Q+subs(sym(f),findsym(sym(f)),x); + end + T(k+1,1)=T(k,1)/2+h*Q; + M=2*M; + for j=1:k + T(k+1,j+1)=T(k+1,j)+(T(k+1,j)-T(k,j))/(4^j-1); + end + tol=abs(T(k+1,j+1)-T(k,j)); +end +I=T(k+1,k+1); +step=k; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/SmartSimpson.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/SmartSimpson.m" index f75dce8d3724e328e95841d3bf9e9a91efccb9a7..666b81a32619cbc267ffe770165351e83deffe24 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/SmartSimpson.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/SmartSimpson.m" @@ -1,3 +1,19 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b1ff3cc4f3bebede6e45dd2ca1877e6e10c424b9a0166d8b5fb6d5003669c012 -size 393 +function I=SmartSimpson(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end; +e=5*eps; +I=SubSmartSimpson(f,a,b,e); + +function q=SubSmartSimpson(f,a,b,eps) +QA=IntSimpson(f,a,b,1,eps); +QLeft=IntSimpson(f,a,(a+b)/2,1,eps); +QRight=IntSimpson(f,(a+b)/2,b,1,eps); + +if(abs(QLeft+QRight-QA)<=eps) + q=QA; +else + q=SubSmartSimpson(f,a,(a+b)/2,eps)+SubSmartSimpson(f,(a+b)/2,b,eps); +end + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/followup.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/followup.m" index 5a8b97805cfc3dac8c9adfe6707d180f9baf57e7..955cb44527eb39df808c1cde6c744c64d41aea68 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/followup.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2548\347\253\240 \346\225\260\345\200\274\347\247\257\345\210\206/followup.m" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5eb568e1ef362f0a20864aa292645b4b4be6bfde31eca3fe78937c61b33fe2f6 -size 765 +function x=followup(A,b) +%²ÉÓÃ×·¸Ï·¨ÇóÏßÐÔ·½³Ì×éAx=bµÄ½â +%ÏßÐÔ·½³Ì×éµÄϵÊý¾ØÕó£ºA +%ÏßÐÔ·½³Ì×éÖеij£ÊýÏòÁ¿£ºb +%ÏßÐÔ·½³Ì×éµÄ½â£ºx + +n = rank(A); +for(i=1:n) + if(A(i,i)==0) + disp('Error: ¶Ô½ÇÓÐÔªËØΪ0£¡'); + return; + end +end; +d = ones(n,1); +a = ones(n-1,1); +c = ones(n-1); +for(i=1:n-1) + a(i,1)=A(i+1,i); + c(i,1)=A(i,i+1); + d(i,1)=A(i,i); +end +d(n,1) = A(n,n); +%Çó½âLy=bµÄ½ây£¬½â±£´æÔÚbÖУ¬ +for(i=2:n) + d(i,1)=d(i,1) - (a(i-1,1)/d(i-1,1))*c(i-1,1); + b(i,1)=b(i,1) - (a(i-1,1)/d(i-1,1))*b(i-1,1); +end +%Çó½âUx=yµÄ½âx£¬ +x(n,1) = b(n,1)/d(n,1); +for(i=(n-1):-1:1) + x(i,1) = (b(i,1)-c(i,1)*x(i+1,1))/d(i,1); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/AtkenStablePoint.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/AtkenStablePoint.m" index 7f1924305a311e9bd6682d52deb4caf6ee392ace..a0bf8b9b866f64577ca7ffd4dc45dc05ae38e195 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/AtkenStablePoint.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/AtkenStablePoint.m" @@ -1,3 +1,24 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:aa772065eb6926397cfd6b8c0f24324374d34ed195aac9c3da748cf78432c79f -size 387 +function [root,n]=AtkenStablePoint(f,x0,eps) +if(nargin==2) + eps=1.0e-4; +end + +tol=1; +root=x0; +x(1:2)=0; +n=0; +m=0; +a2=x0; +while(tol>eps) + n=n+1; + a1=a2; + r1=root; + root=subs(sym(f),findsym(sym(f)),r1)+r1; + x(n)=root; + if(n>2) + m=m+1; + a2=x(m)-(x(m+1)-x(m))^2/(x(m+2)-2*x(m+1)+x(m)); + tol=abs(a2-a1); + end +end +root=a2; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMAX.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMAX.m" index 4193fe481026a42514582eb81be75ae69dd06205..695f176d6c489e57188cd3861f80205959fb68af 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMAX.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMAX.m" @@ -1,3 +1,18 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ce3eb88b0b64157b161abb9dec70bb895adacccdc33c399293ba54be11aaf095 -size 299 +function xm = BenvliMAX(a,eps) +format long; +if(nargin==1) + eps=1.0e-4; +end +n = length(a); +y = zeros(n+1,1); +y(n) =1; +tol = 1; +xm = inf; +while tol>eps + xm1 = xm; + y(n+1) =dot(-a,y(1:n)); + y(1:n) = y(2:n+1); + xm = y(n)/y(n-1); + tol = abs(xm-xm1); +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMIN.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMIN.m" index 4677114d45f25b32606bd72a660a8b2a32f60c52..fd7faf8613406b7c1ea46df4854a21a78418ed89 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMIN.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/BenvliMIN.m" @@ -1,3 +1,23 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a0f864705ccd825ed581dad6a2646e4d934e3853a57643cddc873305668ea6d6 -size 389 +function xm = BenvliMIN(a,eps) +format long; +if(nargin==1) + eps=1.0e-4; +end +n = length(a); +y = zeros(n+1,1); +y(n) =1; +am(1:n) = a(n:-1:1); +c = am(n); +am(2:n) = am(1:n-1); +am(1) = 1; +am(1:n) = -am(1:n)/c; +tol = 1; +xm = inf; +while tol>eps + xm1 = xm; + y(n+1) =dot(am,y(1:n)); + y(1:n) = y(2:n+1); + xm =y(n-1)/y(n); + tol = abs(xm-xm1); +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/DblSecant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/DblSecant.m" index f7125d0dff4f386acd0d85f289fa0808f3b9ee42..0265a501bded143c23b413d42413e6255a71aa52 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/DblSecant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/DblSecant.m" @@ -1,3 +1,39 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a35b8deb0fc8146d20fe978e703d7936ab7908fda824b3dad241d7cc5f82c906 -size 767 +function root=DblSecant(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + root=b; + r2=a; %µü´ú³õʼֵ + while(tol>eps) + n = n+1; + r1 = r2; + r2 = root; + f1=subs(sym(f),findsym(sym(f)),r1); + f2=subs(sym(f),findsym(sym(f)),r2); + if(f1==0) + root=r1; + else + if(f2==0) + root = r2; + else + root=r2-(r2-r1)*f2/(f2-f1); + end + end + tol=abs(root-r2); + end +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/HalfInterval.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/HalfInterval.m" index 61e2ac1c33ce7afa63fb9e7e67324e431ee9c9ee..af9270013c337d358cc46f64116cc831f359639c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/HalfInterval.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/HalfInterval.m" @@ -1,3 +1,42 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:cfba27c9f5784a8b791478f38692037cdd1173631c846e2eabb7c9c88fee9bbb -size 744 +function root=HalfInterval(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + root=FindRoots(f,a,b,eps); +end + + +function r=FindRoots(f,a,b,eps) +f_1=subs(sym(f),findsym(sym(f)),a); +f_2=subs(sym(f),findsym(sym(f)),b); +mf=subs(sym(f),findsym(sym(f)),(a+b)/2); +if(f_1*mf>0) + t=(a+b)/2; + r=FindRoots(f,t,b,eps); +else + if(f_1*mf==0) + r=(a+b)/2; + else + if(abs(b-a)<=eps) + r=(b+3*a)/4; + else + s=(a+b)/2; + r=FindRoots(f,a,s,eps); + end + end +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/ModifSecant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/ModifSecant.m" index 389bd76d2a419f8e85db379d83df7ba6b44dae07..e4faef083b82717e8e58fa498e36ee1801a7a5bc 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/ModifSecant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/ModifSecant.m" @@ -1,3 +1,40 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d0a648c89c2b1643eaf1dbd061d5eaf47f7f6f723cf5829f4681aa0e0749f593 -size 886 +function root=ModifSecant(f,a,b,eps) +format long; +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol = 1; + r1 = a; %µü´ú³õʼֵ + r2 = b; + fv = subs(sym(f),findsym(sym(f)),a); + while(tol>eps) + f2=subs(sym(f),findsym(sym(f)),r2); + root=r2-(r2-r1)*f2/(f2-fv); + fr=subs(sym(f),findsym(sym(f)),root); + if(f2*fr<0) + tol=abs(root-r2); + r1 = r2; + r2 = root; + fv = subs(sym(f),findsym(sym(f)),r1); + else + tol=abs(root-r2); + r2 = root; + fv = 0.5*subs(sym(f),findsym(sym(f)),r1); + end + end +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Montecarlo.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Montecarlo.m" index c24a7f39ff89b0dd4402d4903fef7e98d35aaff3..88b4aec979f3b2ef48980b69fc5c0395c2b4bced 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Montecarlo.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Montecarlo.m" @@ -1,3 +1,19 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a499992016f27e39d8f160a39a8bdfa44bcbc08d9c7d24c0c5b17676e7c08190 -size 414 +function root = Montecarlo(f,B,x0,eps) +format long; +if(nargin==3) + eps=1.0e-4; +end +Fx = subs(sym(f),findsym(sym(f)),x0); + +while abs(Fx)>eps + Fx = subs(sym(f),findsym(sym(f)),x0); + Fx1 = abs(Fx) + 10; + while (abs(Fx1) >= abs(Fx)) + r = 2*B*rand()-B; + x1 = x0 + r; + Fx1 = subs(sym(f),findsym(sym(f)),x1); + end + x0 = x1; +end +root = x1; +format short; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/MultiRoot.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/MultiRoot.m" index 3c19e194dabb7922d22a2506a9823f463d514d19..219d6ef4067d6dde3738ce0b2a8e259af97de18d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/MultiRoot.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/MultiRoot.m" @@ -1,3 +1,39 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bbb4804fa80df0d1838a2881e9b9b1c0f94d1d6bf54de9a0491f67caab510e80 -size 845 +function root=MultiRoot(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fun=diff(sym(f)); + ddf=diff(sym(fun)); + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + dfa=subs(sym(fun),findsym(sym(fun)),a); + dfb=subs(sym(fun),findsym(sym(fun)),b); + if(dfa>dfb) + root=a; + else + root=b; + end + while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + dfx=subs(sym(fun),findsym(sym(fun)),r1); + ddfx=subs(sym(ddf),findsym(sym(ddf)),r1); + root=r1-fx*dfx/(dfx*dfx-fx*ddfx); + tol=abs(root-r1); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonDown.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonDown.m" index 3a2161782186ff7946069262ec6dc6098206517f..fd6deddaad66d1c0c5469fe769a17e913eafdd5e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonDown.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonDown.m" @@ -1,3 +1,44 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8a4a0f0c358683de44096962310f204fda594e625e1275ffb672dba083647ca9 -size 956 +function root=NewtonDown(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fun=diff(sym(f)); + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + dfa=subs(sym(fun),findsym(sym(fun)),a); + dfb=subs(sym(fun),findsym(sym(fun)),b); + if(dfa>dfb) + root=a; + else + root=b; + end + while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + dfx=subs(sym(fun),findsym(sym(fun)),r1); + toldf=1; + alpha=2; + while toldf>0 + alpha=alpha/2; + root=r1-alpha*fx/dfx; + fv=subs(sym(f),findsym(sym(f)),root); + toldf=abs(fv)-abs(fx); + end + tol=abs(root-r1); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonRoot.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonRoot.m" index 0bf9db7ebb8152da16aebf013e4d0f88c0660529..d6bf97b57e0b17f15859f310701974196cb79b8f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonRoot.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/NewtonRoot.m" @@ -1,3 +1,33 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8bddf1e3c2448e952cd644aa2ab4035821ee98ad75ae08f04f4ebf1d37576e09 -size 810 +function root=NewtonRoot(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +tol=1; +fun=diff(sym(f)); %Çóµ¼Êý +fa=subs(sym(f),findsym(sym(f)),a); +fb=subs(sym(f),findsym(sym(f)),b); +dfa=subs(sym(fun),findsym(sym(fun)),a); +dfb=subs(sym(fun),findsym(sym(fun)),b); +if(dfa>dfb) %³õʼֵȡÁ½¶Ëµãµ¼Êý½Ï´óÕß + root=a-fa/dfa; +else + root=b-fb/dfb; +end +while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + dfx=subs(sym(fun),findsym(sym(fun)),r1); %Çó¸ÃµãµÄµ¼ÊýÖµ + root=r1-fx/dfx; %µü´úµÄºËÐĹ«Ê½ + tol=abs(root-r1); +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PYZ.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PYZ.m" index b3b062c3358be87e2f0cb3619ac2e4e319fc5957..3fbf034d53104c4e5e78b33de3ca77b175c7a8c4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PYZ.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PYZ.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:857117db7e731335144aa926776a22be71521f8255b0cdbcd7d82b6d7f710bcd -size 629 +function [p,q]=PYZ(a,M,p0,q0) +format long; +n = length(a); +b = zeros(n,1); +c = zeros(n-1,1); +p = p0; +q = q0; + +for k=1:M + b(1) = 0; + b(2) = 1; + for i=3:n + b(i) = a(i-2) - p*b(i-1)-q*b(i-2); + end + r1 = a(n-1) - p*b(n)-q*b(n-1); + r2 = a(n) - q*b(n); + + c(1) = 0; + c(2) = 1; + for i=3:n-1 + c(i) = b(i) - p*c(i-1)-q*c(i-2); + end + R11 = b(n) - p*c(n-1)-q*c(n-2); + R12 = -q*c(n-1); + + R21 = b(n-1) - p*c(n-2)-q*c(n-3); + R22 = b(n)-q*c(n-2); + + A = [R11 R21;R22 R12]; + B = [r1;r2]; + u = A\B; + p = p+u(1); + q = q+u(2); +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PallSecant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PallSecant.m" index b31614c9a7b192216fd8723b7204f41444298995..7add7b89eb2263491ffa06e76481ea7447a92da3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PallSecant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/PallSecant.m" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fe938d389965398556370f26a6e2a1eb537d25cad61dbf74fff12c9892062929 -size 627 +function root=PallSecant(f,a,b,eps) +format long; +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + root=a; %µü´ú³õʼֵ + c = (b-a)/(f2-f1); + while(tol>eps) + r1 = root; + fx=subs(sym(f),findsym(sym(f)),r1); + if(f1==0) + root=r1; + else + root=r1-c*fx; + end + tol=abs(root-r1); + end +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Parabola.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Parabola.m" index 4cec79e60b06310b69c93141befb342d08a4f954..4dbe1026a698d54715150c41531dc7eb390e1f30 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Parabola.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Parabola.m" @@ -1,3 +1,46 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:072d1cdd2c353040494b03943ae6dbe41487a2073bfcc4cc4b7f48a4bd2c188f -size 1053 +function root=Parabola(f,a,b,x,eps) +if(nargin==4) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + fx=subs(sym(f),findsym(sym(f)),x); + d1=(fb-fa)/(b-a); + d2=(fx-fb)/(x-b); + d3=(d2-d1)/(x-a); + B=d2+d3*(x-b); + root=x-2*fx/(B+sign(B)*sqrt(B^2-4*fx*d3)); + t=zeros(3); + t(1)=a; + t(2)=b; + t(3)=x; + while(tol>eps) + t(1)=t(2); + t(2)=t(3); + t(3)=root; + f1=subs(sym(f),findsym(sym(f)),t(1)); + f2=subs(sym(f),findsym(sym(f)),t(2)); + f3=subs(sym(f),findsym(sym(f)),t(3)); + d1=(f2-f1)/(t(2)-t(1)); + d2=(f3-f2)/(t(3)-t(2)); + d3=(d2-d1)/(t(3)-t(1)); + B=d2+d3*(t(3)-t(2)); + root=t(3)-2*f3/(B+sign(B)*sqrt(B^2-4*f3*d3)); + tol=abs(root-t(3)); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS.m" index 079c7e7fced65b8da257387a2f3177ae32b52375..91bbf9ad279565d38d50e8fd0a0604e623489d12 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS.m" @@ -1,3 +1,70 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5631ca510e7a161787e663758a7a27007da0ca871c65c99e42615d94a860a40c -size 1720 +function root=QBS(f,a,b,x,eps) +format long; +if(nargin==4) + eps=1.0e-6; +end + +fa=subs(sym(f),findsym(sym(f)),a); +fb=subs(sym(f),findsym(sym(f)),b); +fx=subs(sym(f),findsym(sym(f)),x); +if(fa==0) + root=a; + return; +end +if(fb==0) + root=b; + return; +end + +if(fx == 0) + root = x; + return; +else + tol=1; + t=zeros(3); + t(1)=a; + t(2)=x; + t(3)=b; + while(tol>eps) + f1=subs(sym(f),findsym(sym(f)),t(1)); %¼ÆËãÈýµãµÄº¯ÊýÖµ + f2=subs(sym(f),findsym(sym(f)),t(2)); + f3=subs(sym(f),findsym(sym(f)),t(3)); + d1=f2-f1; + d2=f3-f2; + d3=f3-f1; + if (d1 == 0 || d2 == 0 || d3 == 0) + disp('³ý0´íÎó£¬ÇëÖØÐÂÑ¡ÔñÈý¸ö³õʼµã£¡'); + root = NaN; + return; + end + root=t(1)*f2*f3/d1/d3+t(2)*f1*f3/d1/d2+t(3)*f2*f1/d2/d3; + tol=abs(root-t(3)); + ft = subs(sym(f),findsym(sym(f)),root); + if( f2*ft < 0) + if root > t(2) + t(1)=t(2); + t(2)=root; + else + t(3) = t(2); + t(2) = root; + end + else + if f2 < 0 + if root > t(2) + t(1)=t(2); + t(2)=root; + else + t(1) = root; + end + else + if root > t(2) + t(3) = root; + else + t(3) = t(2); + t(2) = root; + end + end + end + end +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS2.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS2.m" index a18ffa79bc97a881aedf23ae5679fa7ab242d196..1b81543f133e8c653b2676bc62c10778f1d33d4f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS2.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/QBS2.m" @@ -1,3 +1,40 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bf991c530db752e7f64e24fa59c418e647a7b5e31d6062a2f43d46e1d7f37d80 -size 917 +function root=QBS2(f,a,b,x,eps) +format long; +if(nargin==4) + eps=1.0e-6; +end + +fa=subs(sym(f),findsym(sym(f)),a); +fb=subs(sym(f),findsym(sym(f)),b); +if(fa==0) + root=a; +end +if(fb==0) + root=b; +end + +if(fa*fb>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + t=zeros(3); + t(1)=a; + t(2)=b; + t(3)=x; + while(tol>eps) + f1=subs(sym(f),findsym(sym(f)),t(1)); %¼ÆËãÈýµãµÄº¯ÊýÖµ + f2=subs(sym(f),findsym(sym(f)),t(2)); + tx = (t(3)+t(2))/2; + f3=subs(sym(f),findsym(sym(f)),tx); + d1=f2-f1; + d2=f3-f2; + d3=f3-f1; + root=t(1)*f2*f3/d1/d3+t(2)*f1*f3/d1/d2+tx*f2*f1/d2/d3; + tol=abs(root-tx); + t(1)=t(2); %±£´æÈý¸öµã + t(2)=t(3); + t(3)=root; + end +end +format short; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Secant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Secant.m" index c6f1177eeec3ddf61236731d568e7b459d08a1c8..5a324e9dc6c9bce53713eccb4f9a7278a5a4ea88 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Secant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Secant.m" @@ -1,3 +1,38 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fb9ecc7e8e2e91748587be4c99dd0fbf15444b3417e0c490c7d86408f05649b6 -size 748 +function root=Secant(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + root=a-(b-a)*fa/(fb-fa); + while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + s=fx*fa; + if(s==0) + root=r1; + else + if(s>0) + root=b-(r1-b)*fb/(fx-fb); + else + root=a-(r1-a)*fa/(fx-fa); + end + end + tol=abs(root-r1); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SimpleNewton.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SimpleNewton.m" index b73bc8b457f4ed175a650e19223b76b8b832f048..fc3eb58e3c1ead50c36d03656c2193a82953169d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SimpleNewton.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SimpleNewton.m" @@ -1,3 +1,39 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:33bf5cccf11fef77ab35c768b64ad663684b0de30fea0796470834d7c1176c29 -size 766 +function root=SimpleNewton(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fun=diff(sym(f)); + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + dfa=subs(sym(fun),findsym(sym(fun)),a); + dfb=subs(sym(fun),findsym(sym(fun)),b); + + if(dfa>dfb) + df0=1/dfa; + root=a-df0*fa; + else + df0=1/dfb; + root=b-df0*fb; + end + while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + root=r1-df0*fx; + tol=abs(root-r1); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SinleSecant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SinleSecant.m" index badb7518ee84b863eba4008a4e7bbc7641e2009f..2a3381c3e178d60b80449ffeea42cb34bd8f7d02 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SinleSecant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/SinleSecant.m" @@ -1,3 +1,35 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:929dbec384e2bc7187d9ada85ef95b6f4cdbc94b6d982e7436f5b1b232eafd00 -size 711 +function root=SinleSecant(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + root=b; %µü´ú³õʼֵ + while(tol>eps) + n = n+1; + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + s=fx*fa; + if(s==0) + root=r1; + else + root=r1-(r1-a)*fx/(fx-fa); %ÓõÝÍƹ«Ê½1 + end + tol=abs(root-r1); + end +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StablePoint.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StablePoint.m" index 3b484d9df47a883eeada63d6cea96e32b9657b16..390047001fcc9b6bc4fb96550c2d687d2371fabf 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StablePoint.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StablePoint.m" @@ -1,3 +1,15 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:64844ac30fc54ae0cb0c5a29638d5d6084f657a4897ba26d963f7cc8d9394645 -size 222 +function [root,n]=StablePoint(f,x0,eps) +if(nargin==2) + eps=1.0e-4; +end + +tol=1; +root=x0; +n=0; +while(tol>eps) + n=n+1; + r1=root; + root=subs(sym(f),findsym(sym(f)),r1)+r1; + tol=abs(root-r1); +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenSecant.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenSecant.m" index 94d9a640b079902d3b4c09b05e93c642edf0af12..b84734ac15f6c0cdd108f12a4b08d494abdfa358 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenSecant.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenSecant.m" @@ -1,3 +1,32 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a46c6c2b0df50f86133da5b08d6e38586437d66172989a0a63fe448f79bf7622 -size 664 +function root=StevenSecant(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + faa=subs(sym(f),findsym(sym(f)),fa+a); + root=a-fa*fa/(faa-fa); + while(tol>eps) + r1=root; + fx=subs(sym(f),findsym(sym(f)),r1); + v=fx+r1; + fxx=subs(sym(f),findsym(sym(f)),v); + root=r1-fx*fx/(fxx-fx); + tol=abs(root-r1); + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenStablePoint.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenStablePoint.m" index 9aa85a1e57661788c7da0598c35a1c02a5cf4996..069fd6904bfa7088676ad28021f8db02082cc369 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenStablePoint.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/StevenStablePoint.m" @@ -1,3 +1,16 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:50eef68d5236c043072f0f26ff3286059b29f32dcac1bc3501667324a1a09034 -size 296 +function [root,n]=StevenStablePoint(f,x0,eps) +if(nargin==2) + eps=1.0e-4; +end + +tol=1; +root=x0; +n=0; +while(tol>eps) + n=n+1; + r1=root; + y=subs(sym(f),findsym(sym(f)),r1)+r1; + z=subs(sym(f),findsym(sym(f)),y)+y; + root=r1-(y-r1)^2/(z-2*y+r1); + tol=abs(root-r1); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/TwoStep.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/TwoStep.m" index c2bc87f42978650788a5e4633e60d451b39fe27a..6efa6281db77e2292120a789d88a850a38e46488 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/TwoStep.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/TwoStep.m" @@ -1,3 +1,49 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2237b737adb7db11d64036c273e73f4c39f7e2cff50c1306ced667ecdefc0bf3 -size 1183 +function root=TwoStep(f,a,b,type,eps) +if(nargin==4) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + tol=1; + fun=diff(sym(f)); + fa=subs(sym(f),findsym(sym(f)),a); + fb=subs(sym(f),findsym(sym(f)),b); + dfa=subs(sym(fun),findsym(sym(fun)),a); + dfb=subs(sym(fun),findsym(sym(fun)),b); + if(dfa>dfb) + root=a; + else + root=b; + end + while(tol>eps) + if(type==1) + r1=root; + fx1=subs(sym(f),findsym(sym(f)),r1); + dfx=subs(sym(fun),findsym(sym(fun)),r1); + r2=r1-fx1/dfx; + fx2=subs(sym(f),findsym(sym(f)),r2); + root=r2-fx2/dfx; + tol=abs(root-r1); + else + r1=root; + fx1=subs(sym(f),findsym(sym(f)),r1); + dfx=subs(sym(fun),findsym(sym(fun)),r1); + r2=r1-fx1/dfx; + fx2=subs(sym(f),findsym(sym(f)),r2); + root=r2-fx2*(r2-r1)/(2*fx2-fx1); + tol=abs(root-r1); + end + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union1.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union1.m" index c42bcece45b0be4d4138cb1d8d596054b6a5639f..e97477a6201a10e6802c896b46df085b148f8f8f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union1.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union1.m" @@ -1,3 +1,33 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:da1a990e12eea70e48b4b7023279e15e16d3ffd87339054bb8c8948aa6c56d65 -size 689 +function root = Union1(f,a,b,eps) +format long; +if(nargin==3) + eps=1.0e-6; +end + +fa=subs(sym(f),findsym(sym(f)),a); +fb=subs(sym(f),findsym(sym(f)),b); +if(fa==0) + root=a; +end +if(fb==0) + root=b; +end + +tol=1; +df=diff(sym(f)); %Çóµ¼Êý +dfa=subs(sym(df),findsym(sym(df)),a); +x1 = a - fa/dfa; +x1_s = b - fb*(b-a)/(fb-fa); + +while tol>eps + fn=subs(sym(f),findsym(sym(f)),x1); + dfn=subs(sym(df),findsym(sym(df)),x1); + fn_s=subs(sym(f),findsym(sym(f)),x1_s); + x2 = x1 - fn/dfn; + x2_s = x1_s - (x1 - x1_s)*fn_s/(fn - fn_s); + tol = abs(x2_s - x1_s); + x1 = x2; + x1_s = x2_s; +end +root = x2_s; +format short; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union2.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union2.m" index ff07f8910d307c5f2b291c855211e22315ebe77d..472ed654cd0d92ffc1dee0f665de06c9919551fa 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union2.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/Union2.m" @@ -1,3 +1,33 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fb7e0fb762686f1a8b1c80c23552992d9978df3bb784aa9d3980b862a36f0ef0 -size 699 +function root = Union2(f,a,b,eps) +format long; +if(nargin==3) + eps=1.0e-4; +end + +fa=subs(sym(f),findsym(sym(f)),a); +fb=subs(sym(f),findsym(sym(f)),b); +if(fa==0) + root=a; +end +if(fb==0) + root=b; +end + +tol=1; +df=diff(sym(f)); %Çóµ¼Êý +dfb=subs(sym(df),findsym(sym(df)),b); +x1 = a - (b-a)*fa/(fb-fa); +x1_s = b - fb/dfb; + +while tol>eps + fn = subs(sym(f),findsym(sym(f)),x1); + dfn_s = subs(sym(df),findsym(sym(df)),x1_s); + fn_s = subs(sym(f),findsym(sym(f)),x1_s); + x2 = x1 - (x1_s - x1)*fn/(fn_s - fn); + x2_s = x1_s - fn_s/dfn_s ; + tol = abs(x2_s - x1_s); + x1 = x2; + x1_s = x2_s; +end +root = x2_s; +format short; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/YSNewton.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/YSNewton.m" index d0c6d92969b040642e7a78936bb734e4c45945c8..8bbf968e62a8b18b3c9ec886f8df27b8586758ea 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/YSNewton.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/YSNewton.m" @@ -1,3 +1,25 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:97eb3da8b5b60aa23667757fda67b32c637e801a3e0d608b21366b9e348ea291 -size 459 +function x=YSNewton(a) +format long; +n = length(a); +max_X = BenvliMAX(a); +b = zeros(n,1); +x = zeros(n,1); +syms t real; +f = power(t,n); +m = 0:n-1; +s = power(t,m); +f = f + dot(s, a(n:-1:1)); + +for k=1:n + x(k) = NewtonRoot(f,-max_X,max_X); + b = 0; + b(1) = 1; + for i=2:n-k+1 + b(i) = a(i-1) + x(k)*b(i-1); + end + m = 0:n-k; + s = power(t,m); + f = dot(s, b(n-k+1:-1:1)); + a = b(2:length(b)); +end +format short; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/hj.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/hj.m" index 089f721b401581fe482a3314c66886739d84e1ec..51ba86820441c73ebc747777d524202804a3e4fb 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/hj.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/MATLAB\350\257\255\350\250\200\345\270\270\347\224\250\347\256\227\346\263\225\347\250\213\345\272\217\351\233\206/\347\254\2549\347\253\240 \346\226\271\347\250\213\346\261\202\346\240\271/hj.m" @@ -1,3 +1,45 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:908f92144c29e0a11dc51e8cccccc19d1d60d57ee4136fb7ecd5cb2a26014ec9 -size 979 +function root=hj(f,a,b,eps) +if(nargin==3) + eps=1.0e-4; +end + +f1=subs(sym(f),findsym(sym(f)),a); +f2=subs(sym(f),findsym(sym(f)),b); +if(f1==0) + root=a; +end +if(f2==0) + root=b; +end + +if(f1*f2>0) + disp('Á½¶Ëµãº¯ÊýÖµ³Ë»ý´óÓÚ0!'); + return; +else + t1=a+(b-a)*0.382; + t2=a+(b-a)*0.618; + f_1=subs(sym(f),findsym(sym(f)),t1); + f_2=subs(sym(f),findsym(sym(f)),t2); + tol=abs(t1-t2); + while(tol>eps) %¾«¶È¿ØÖÆ + if(f_1*f_2<0) + a=t1; + b=t2; + else + fa=subs(sym(f),findsym(sym(f)),a); + if(f_1*fa>0) + a=t2; + else + b=t1; + end + end + t1=a+(b-a)*0.382; + t2=a+(b-a)*0.618; + f_1=subs(sym(f),findsym(sym(f)),t1); + f_2=subs(sym(f),findsym(sym(f)),t2); + tol=abs(t2-t1); + end + root=(t1+t2)/2; %Êä³ö¸ù +end + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\345\277\205\347\234\213\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201.docx" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\345\277\205\347\234\213\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201.docx" index 6b661447f39a315c6375029d23c0edf5dc0e5189..4d39ee364302bad77b738ff4f5e58e0c50f9c11c 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\345\277\205\347\234\213\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201.docx" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\345\277\205\347\234\213\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201\357\274\201.docx" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96A.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96A.M" index f6a5c0ccafed2de99375abf849e75b223701861c..db2909e2d15daf507f31049420539bfdfd8fdd86 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96A.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96A.M" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:7df12d337a27d498d95497de8238f2800d29eed2aec02241a4bdf54c62f1e621 -size 1636 +%96ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüAÌâ:²¶Óã +%²Î¿¼£º¡¶ÊýѧµÄʵ¼ùÓëÈÏʶ¡·1997£¬1£¬50-57 +%x1,x2,x3,x4--¸÷ÁäÓãµÄÊýÁ¿ +%k--4ÁäÓ㲶ÀÌϵÊý +%y3,y4--¸÷ÁäÓãµÄ²¶ÀÌÊýÁ¿ +%y--ÓãµÄ²¶»ñÖØÁ¿ +%n--²úÂÑÊýÁ¿ + +%L.J.HU +clear; +%΢·Ö·½³ÌÇó½â +x1=dsolve('Dx1=-0.8*x1','x1(0)=a','t'); +x11=subs(x1,'t',1); +x2=dsolve('Dx2=-0.8*x2','x2(0)=b','t'); +x21=subs(x2,'t',1); +x21=subs(x21,'b',x11); +x3a=dsolve('Dx3a=-0.8*x3a-0.42*k*x3a','x3a(0)=c','t'); +x3a=subs(x3a,'c',x21); +x3a2=subs(x3a,'t',2/3); +x3b=dsolve('Dx3b=-0.8*x3b','x3b(2/3)=x3b0','t'); +x3b=subs(x3b,'x3b0',x3a2); +x3b=simple(x3b); +x31=subs(x3b,'t',1); +x4a=dsolve('Dx4a=-0.8*x4a-k*x4a','x4a(0)=d','t'); +x4a2=subs(x4a,'t',2/3); +x4b=dsolve('Dx4b=-0.8*x4b','x4b(2/3)=x4b0','t'); +x4b=subs(x4b,'x4b0',x4a2); +x4b=simple(x4b); +x41=subs(x4b,'t',1); +%²¶»ñÁ¿²úÂÑÁ¿ +syms k;dy3=0.42*k*x3a;dy4=k*x4a; +y3=int(dy3,'t',0,2/3); +y4=int(dy4,'t',0,2/3); +y=17.86*y3+22.99*y4; +n=1.109e5*3*int(0.5*x3b+x4b,'t',2/3,1); +x10=122*n/(122+n); +%ÓÅ»¯ +y=subs(y,{'a','d',k},{'x(1)','x(2)','x(3)'}); +x10=subs(x10,{'a','d',k},{'x(1)','x(2)','x(3)'}); +x31=subs(x31,{'a',k},{'x(1)','x(3)'}); +x41=subs(x41,{'a','d',k},{'x(1)','x(2)','x(3)'}); +funf = ['f =',char(-y),';']; +fung = ['g =[x(1)-',char(x10),';x(2)-',char(x31+x41),'];']; +funn = [funf fung]; +options(13)=2; +[x,options]=constr(funn,[122,3.29,1],options); +y=-options(8); +x11=vpa(subs(x11,'a',x(1)),4); +x21=vpa(subs(x21,'a',x(1)),4); +%Êä³ö +disp(['¿É³ÖÐø²¶»ñ3,4ÁäÓ㲶ÀÌϵÊý:',num2str([x(3)*0.42,x(3)])]); +disp(['ÿÄ겶»ñÖØÁ¿(10^9):',num2str(y)]); +disp(['Äê³õ¸÷ÁäÓã·Ö²¼(10^9):',num2str(x(1)),' ',char(x11),... + ' ',char(x21),' ',num2str(x(2))]); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96B.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96B.M" index 3698a4a0371aa45e861d1aff492e597fa57085f8..a882a3b6fcacbc63f9ac088fb297c778b542fd93 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96B.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM96B.M" @@ -1,3 +1,22 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:03160d754d382b044845311410fc6671116a240e956cbfac79bf340551c14ed4 -size 495 +%96ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüBÌâ:Ï´Ò»ú +%Ö÷³ÌÐò +%²Î¿¼£º¡¶ÊýѧµÄʵ¼ùÓëÈÏʶ¡·1997£¬1£¬67-70 +%Ïà¹ØMÎļþ£ºjm96bfun + +%L.J.HU +clear;vmin0=inf; +for t=2:5 + vini=30*ones(1,t); + vlb=20*ones(1,t);%×îСˮÁ¿ + vub=40*ones(1,t);%×î´óË®Á¿ + opt([2:3,14])=[1e-8,1e-8,500]; + [vmin,options]=constr('washfun',vini,opt,vlb,vub); + vmin %ÿÂÖË®Á¿ + if sum(vmin)options(8) + minfee=options(8); + grad=VARI;mark=x0; + end; + end; + end; + end; + end; +end; +disp(['±ê¶¨Öµ:',num2str(mark)]); +disp(['ÈݲîµÈ¼¶:',num2str(grad)]); +disp(['·ÑÓÃ:',num2str(minfee)]); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Afun.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Afun.m" index 9045c0e132b53aa428e7e3f2e3c8b92fec3b4f92..ee44b3843beee8a506354019cdd78f89c77885d8 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Afun.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Afun.m" @@ -1,3 +1,11 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:74941615371de4c13461a87b71ccc24a8fafa75ca8d799dd69ca3da7c917f4fe -size 314 +function y=jm97afun(x) +% 97ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüAÌ⺯Êý¹Øϵ +% Ó÷¨£º y=jm97afun(x) +% x--7¸öÁã¼þ²ÎÊý +% y--·ÖÀëÆ÷²ÎÊý +% Ïà¹ØMÎļþ£ºjm97a, jm97aoptim + +% L.J.HU +y=174.42*(x(1)/x(5))*(x(3)/(x(2)-x(1)))^... +0.85*((1-2.62*(1-0.36*(x(4)/x(2))^(-0.56))^... +1.5*(x(4)/x(2))^1.16)/(x(6)*x(7)))^0.5; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Aoptim.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Aoptim.m" index ad2965af27be5cac34f4fc3c89a716aa4636d0ee..40fa6cf6d414251be352f43b578d92f20d5ad195 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Aoptim.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97Aoptim.m" @@ -1,3 +1,25 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f932744f87cdbd52365621bd725c9a47dc495c830aa5a390cef3849ef6e41830 -size 631 +function [f,g]=JM97Aoptim(x) +% 97ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüAÌâÄ¿±êº¯Êý +% Ó÷¨£º [f,g]=jm97aoptim(x) +% x--7¸öÁã¼þ²ÎÊý +% f--Ä¿±êº¯Êý +% g--ÐéÄâ²ÎÊý£¬ÓÅ»¯¹¤¾ßÏäʵÓà +% È«³Ì±äÁ¿£ºCOST(³É±¾¾ØÕ󣩣¬VARI(ÈݲîµÈ¼¶£© +% Ïà¹ØMÎļþ£ºjm97a, jm97afun + +global COST VARI; +y=jm97afun(x); +sig=0;h=0.0001; +for i=1:7 + xh=x;xh(i)=x(i)+h; + dy=(jm97afun(xh)-jm97afun(x))/h; + sig=sig+dy^2*(VARI(i)/300*x(i))^2; +end +sig=sig^0.5; +f=9000-8000*(normcdf(1.8,y,sig)-normcdf(1.2,y,sig))... + -1000*(normcdf(1.6,y,sig)-normcdf(1.4,y,sig)); +gra=[10 5 1]; +for i=1:7 + f=f+sum((VARI(i)==gra).*COST(i,:)); +end +g=-1; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97B.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97B.M" index 5a68658865bab7726978db122aee02caa9c4bdc3..141597bc12d2dedad0ccb5f48063a66302a38a30 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97B.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM97B.M" @@ -1,3 +1,211 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:6f2bf2f6d49d5f627f8de909ce13c69e76f2918190ca4a5098858c6848f4c288 -size 4353 +function [mincost,bestorder]=jm97b(r,e) +%97ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüBÌ⣨ö¾Ù·¨£© +%¡¶ÊýѧµÄʵ¼ùÓëÈÏʶ¡·1998£¬1 +%·ÑÓú¯Êý¼ÆËã²ÉÓõü´úËã·¨ +%Ó÷¨£º[mincost,bestorder]=jm97bcount(r,e) +% mincost--×îС·ÑÓà +% bestorder--×îÓÅ´ÎÐò +% r--ˮƽÇиî·ÑÓÃ±È +% e--´¹Ö±»»µ¶·ÑÓà +%½á¹û˵Ã÷£º1-×ó£¬2-ÓÒ£¬3-Ç°£¬4-ºó£¬5-ÉÏ£¬6-Ï +%Ïà¹ØMÎļþ£ºjm97brule + +% L.J.HU +mincost=inf;minorder=[]; +p=perms(1:6); +for i=1:length(p) + order=p(i,:); + cost=jm97bcostf(order,r,e); + if cost0,Ôò°´ÕÕEXP(-D/T)µÄ¸ÅÂʽøÐе÷Õû +²½8:T*0.9-->T,½µÎ +*/ + +#include +#include +#define TFACTR 0.9 +#define MAX 10000.0 +#define MBIG 1000000000 +#define MSEED 161803398 +#define MZ 0 +#define FAC (1.0/MBIG) +float weight[54][54]; +int iorder[54]; +void anneal (int ncity) + +{ int irbit(unsigned long *iseed); + +int metrop(float de,float t); +float ran(long *idum); +float reverse_len(int ncity,int n[]); +void reverse(int ncity,int n[]); +float transe_len(int ncity,int n[]); +void transe(int ncity,int n[]); +int ans,nover,nlimit,i1,i2; +int i,j,nsucc,nn,idec; +unsigned long k; +static int n[7]; +long idum; +unsigned long iseed; +float path,de,t,T; +nlimit=100*ncity;/*max succ try numbers */ +path =0.0; + +for(i=1;i=n[1]) ++n[2]; + nn=1+((n[1]-n[2]+ncity-1)%ncity); + } while (nn<3); + idec=irbit(&iseed); + + if(idec==0){ + n[3]=n[2]+(int) (abs(nn-2)*ran(&idum))+1; + n[3]=1+((n[3]-1)%ncity); + de=transe_len(ncity,n); + ans=metrop(de,T); + if (ans){ ++nsucc; + path+=de; + transe(ncity,n); + } + } + else { + de=reverse_len(ncity,n); + ans=metrop(de,T); + if (ans) {++nsucc; + path+=de; + reverse(ncity,n); + } + } + if(nsucc>=nlimit) break; + } + + printf("\n %s %10.6f %s %10.6f j=%d","T=",T,"path len=",path,j); + printf("successful moves: %6d\n",nsucc); + + for(i=1;i<=53;i++) printf("\%5d",iorder[i]); + + + + + T*=TFACTR; + if(nsucc==0) return; + } + + + } + +float reverse_len(int ncity,int n[]) + { + float de; + int xx[5],yy[5]; + int j,ii; + n[3]=1+((n[1]+ncity-2)%ncity); + n[4]=1+(n[2]%ncity); + for(j=1;j<=4;j++) { + xx[j]=iorder[n[j]]; + } + de=-weight[xx[1]][xx[3]]; + de-=weight[xx[2]][xx[4]]; + de+=weight[xx[1]][xx[4]]; + de+=weight[xx[2]][xx[3]]; + + return de; + } + + void reverse (int ncity,int n[]) + { int nn,j,k,l,itmp; + nn=(1+((n[2]-n[1]+ncity)%ncity))/2; + for(j=1;j<=nn;j++){ k=1+((n[1]+j-2)%ncity); + l=1+((n[2]-j+ncity)%ncity); + itmp=iorder[k]; + iorder[k]=iorder[l]; + iorder[l]=itmp; + } + } + + float transe_len(int ncity,int n[]) + { + float /*xx[7],yy[7],*/ de; + int j,ii,xx[7]; + n[4]=1+(n[3]%ncity); + n[5]=1+((n[1]+ncity-2)%ncity); + n[6]=1+(n[2]%ncity); + for(j=1;j<=6;j++){ + /*ii=iorder[n[j]]; + xx[j]=x[ii]; + yy[j]=y[ii];*/ + xx[j]=iorder[n[j]]; + } + de=-weight[xx[2]][xx[6]]; + de-=weight[xx[1]][xx[5]]; + de-=weight[xx[3]][xx[4]]; + de+=weight[xx[1]][xx[3]]; + de+=weight[xx[2]][xx[4]]; + de+=weight[xx[5]][xx[6]]; + return de; + } + void transe(int ncity,int n[]) + { + int m1,m2,m3,nn,j,jj,jorder[100]; + m1=1+((n[2]-n[1]+ncity) %ncity); /* n[1] to n[2] city numbers*/ + m2=1+((n[5]-n[4]+ncity) %ncity); /*n[4] to n[5] */ + + m3=1+((n[3]-n[6]+ncity) %ncity); /*n[3].. n[6] .....*/ + nn=1; + for(j=1;j<=m1;j++) + {jj=1+((j+n[1]-2)%ncity); + jorder[nn++]=iorder[jj]; + } + if(m2>0) for(j=1;j<=m2;j++) + { jj=1+((j+n[4]-2)%ncity); + jorder[nn++]=iorder[jj]; + } + if(m3>0) for(j=1;j<=m3;j++){ jj=1+((j+n[6]-2)%ncity); + jorder[nn++]=iorder[jj]; + } + for(j=1;j<=ncity;j++) + iorder[j]=jorder[j]; + } + int metrop(float de,float t) + { + float ran(long *idum); + static long gljdum=1; + return de<0.0 ||ran(&gljdum)>17 + ^(*iseed&16)>>4 + ^(*iseed &2)>>1 + ^(*iseed &1); + *iseed=(*iseed<<1)|newbit; + return newbit; +} +main() +{ + + int ncity=53; + int i,j,k,l; + for(i=0;i<=53;i++) iorder[i]=i; + for(i=1;i<=53;i++) + for(j=1;j<=53;j++) + weight[i][j]=0; + +weight[53][1]=6; +weight[53][50]=10.1; +weight[1][38]=11.2; +weight[3][39]=8.2; + weight[5][39]=11.3; + weight[6][48]=9.5; + weight[8][40]=8; +weight[11][40]=14.2; +weight[12][42]=7.8; +weight[13][44]=16.4; +weight[15][44]=8.8; +weight[17][46]=9.8; +weight[19][20]=9.3; +weight[20][25]=6.5; +weight[21][46]=4.1; +weight[23][49]=7.9; +weight[25][49]=8.8; +weight[27][28]=7.9; +weight[29][51]=7.2; +weight[31][32]=8.1; +weight[33][35]=20.3; +weight[34][37]=17.6; +weight[44][45]=15.8; +weight[53][2]=9.2; +weight[53][52]=12.9; +weight[2][3]=4.8; +weight[4][8]=20.4; +weight[5][48]=11.4; +weight[7][39]=15.1; +weight[9][40]=7.8; +weight[11][42]=6.8; +weight[12][43]=10.2; +weight[13][45]=9.8; +weight[16][17]=6.8; +weight[18][44]=8.2; +weight[19][45]=8.1; +weight[20][47]=5.5; +weight[22][23]=10; +weight[24][27]=18.8; +weight[26][27]=7.8; +weight[28][50]=12.1; +weight[29][52]=7.9; +weight[31][33]=7.3; +weight[33][36]=7.4; +weight[36][37]=12.2; +weight[48][49]=14.2; +weight[53][38]=11.5; +weight[1][36]=10.3; +weight[2][5]=8.3; +weight[4][39]=12.7; +weight[6][7]=7.3; +weight[7][40]=7.2; +weight[9][41]=5.6; +weight[11][45]=13.2; +weight[13][14]=8.6; +weight[14][15]=15; +weight[16][44]=11.8; +weight[18][45]=8.2; +weight[19][47]=7.2; +weight[21][23]=9.1; +weight[22][46]=10.1; +weight[24][49]=13.2; +weight[26][49]=10.5; +weight[28][51]=8.3; +weight[30][32]=10.3; +weight[31][52]=9.2; +weight[34][35]=8.2; +weight[36][52]=8.8; +weight[53][48]=19.8; +weight[1][37]=5.9; +weight[3][38]=7.9; +weight[5][6]=9.7; +weight[6][47]=11.8; +weight[7][47]=14.5; +weight[10][41]=10.8; +weight[12][41]=12.2; +weight[13][42]=8.6; +weight[14][43]=9.9; +weight[17][22]=6.7; +weight[18][46]=9.2; +weight[20][21]=7.9; +weight[21][25]=7.8; +weight[23][24]=8.9; +weight[25][48]=12; +weight[26][50]=10.5; +weight[29][50]=15.2; +weight[30][51]=7.7; +weight[32][35]=14.9; +weight[34][36]=11.5; +weight[37][38]=11; +for(i=1;i<=53;i++) +for(j=1;j<=53;j++) +if(weight[i][j]!=0)weight[j][i]=weight[i][j]; +for(i=1;i<=53;i++) +for(j=1;j<=53;j++) +if(weight[i][j]==0) weight[i][j]=MAX; + for(k=1;k<=53;k++) + for(i=1;i<=53;i++) + for(j=1;j<=53;j++) + +if(!(i==j)&&!(i==k)&&!(k==j)) + if( weight[i][k]+weight[k][j]0,Ôò°´ÕÕEXP(-D/T)µÄ¸ÅÂʽøÐе÷Õû +%²½8:T*0.9-->T,½µÎ + +%±¾³ÌÐòÓÃCÓïÑÔ±àдjm98b.c diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM99A.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM99A.M" index 34c14d45c5b8b1da57e8e3c132da7a2390efe36e..3f8a1bd5581ba8e50452cd6a4441e9c501841621 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM99A.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/JM99A.M" @@ -1,3 +1,12 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:6808f39d7e0d67bbea793febc4329da8b140cc69599aba4acc0dcd7c5c9e35d9 -size 272 +function [x,opt]=jm99a(n,m) +%99ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüaÌ⣺×Ô¶¯»¯³µ´²ÎÊ +%²Î¼û¡¶ÊýѧµÄʵ¼ùÓëÈÏʶ¡·2000.1.p36-40 +opt=inf; +for n=10:5:30 + for m=300:10:400 + [x0,op]=fmins('jm99afun',[n m]); + if op(8)100*eps).*(x=u/M/100).*max(x,u/M); +y=y.*p; +f=lemda*xx(len)-(1-lemda)*sum(r.*x-y); +g(1)=sum(x+y)-1; +g(2:(len-1))=q(1:(len-2)).*x(1:(len-2))-xx(len);g=g(:); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/jm99a1simu.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/jm99a1simu.m" index 9debe0411cd49a3758ce4b6253f14b03797f8fb8..1d9064898751efcaa62070c2447f0e4cd5e18a60 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/jm99a1simu.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/jm99a1simu.m" @@ -1,3 +1,21 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a784f087037a1eb8f6cea9db934c72e38030850725ab43f6bcfe3e0fe4ea3bf3 -size 412 +%99ÄêÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüaÌ⣺×Ô¶¯»¯³µ´²¹ÜÀíÄ£ÐÍÒ» +%²Î¼û¡¶ÊýѧµÄʵ¼ùÓëÈÏʶ¡·2000.1.p36-40 +%Ëæ»úÄ£Äâ +clear; +data=normrnd(600*0.95,196.6292*0.95,1,10000); +out=find((data>1200)|(data<=0)); +data(out)=[]; +leng=length(data); +minfee=inf; +for n=1:20 + for m=310:10:390 + f=jm99asmfun(data,n,m); + if fnum_prod)+1000*(x==num_prod).*(num_prod==m); +loss=bad_prod*200+exam_times*10+knife_fee; +f=mean(loss)/mean(num_prod); + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/\346\226\260\345\273\272 \346\226\207\346\234\254\346\226\207\346\241\243.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/\346\226\260\345\273\272 \346\226\207\346\234\254\346\226\207\346\241\243.txt" index 65466627f14489f5d0692d77f1317859ad82c35b..77d9312cb505f4c7c638af72a54a0ef678e79413 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/\346\226\260\345\273\272 \346\226\207\346\234\254\346\226\207\346\241\243.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\344\270\255\345\233\275\345\244\247\345\255\246\347\224\237\346\225\260\345\255\246\345\273\272\346\250\241\347\253\236\350\265\233\351\242\230\350\247\243/\346\226\260\345\273\272 \346\226\207\346\234\254\346\226\207\346\241\243.txt" @@ -1,3 +1,19 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c3660ff86857f7afd66459e6b0156fdd30469f77c1c7b8b08f3b82e21303d8cb -size 592 +%Öйú´óѧÉúÊýѧ½¨Ä£¾ºÈüÌâ½â +% jm96a - ²¶Óã²ßÂÔ +% jm96b - ½ÚˮϴÒ»ú +% jm96bfun - ½ÚˮϴÒ»úÓÅ»¯º¯Êý +% jm97a - Áã¼þ²ÎÊýÉè¼Æ +% jm97afun - Áã¼þ²ÎÊýº¯Êý +% jm97aoptim - Áã¼þ²ÎÊýÉè¼ÆÓÅ»¯º¯Êý +% jm97b - ½Ø¶ÏÇиî +% jm97bcount - ½Ø¶ÏÇиîö¾Ù·¨ +% jm97brule - ½Ø¶ÏÇиîÓÅ»¯×¼Ôò +% jm98a1 - ·çÏÕͶ×ÊÄ£ÐÍÇó½â +% jm98a2 - ·çÏÕͶ×ÊÄ£ÐÍÌÖÂÛ +% jm98a3 - ÊÕÒæÓë·çÏÕ·ÇÏßÐÔÄ£ÐÍÇó½â +% jm98a3fun - ÊÕÒæÓë·çÏÕ·ÇÏßÐÔÄ£ÐÍÓÅ»¯º¯Êý +% jm98b - ÔÖÇéѲÊÓ·Ïߣ¨C³ÌÐò£© +% jm99a1 - ×Ô¶¯»¯³µ´²Ä£ÐÍÒ» +% jm99a1fun - ×Ô¶¯»¯³µ´²Ä£ÐÍÄ¿±êº¯Êý +% jm99a1simu - ×Ô¶¯»¯³µ´²Ä£ÐÍËæ»úÄ£Äâ +% jm99asmfun - ×Ô¶¯»¯³µ´²Ä£ÐÍ·ÑÓú¯Êý \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/DRAW.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/DRAW.M" index 8adb66bd2528b26c8551ddd5f8d18193dc4d299f..ce252589598284dbec3098cdbaccf785c7adf018 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/DRAW.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/DRAW.M" @@ -1,3 +1,178 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f26ea281bc3ed65d316c2789f7f4cf5404870d2d5f8089568a7d99667a71ee86 -size 5528 +function fig = draw() +% ÊÖ»­¹â»¬ÇúÏßͼÐνçÃæ +% ÏÈÓÃRangeÈ·¶¨´óÖ·¶Î§£»È»ºóÓÃginputÓÃÊó±êµ¥»÷´óÖÂÊý¾Ýµã£»×îºóÓÃDraw it»­Í¼¡£ +% ±¾³ÌÐò²ÉÓÃÑùÌõÄâºÏ + +% By L. J. Hu, 2000 +% This is the machine-generated representation of a Handle Graphics object +% and its children. Note that handle values may change when these objects +% are re-created. This may cause problems with any callbacks written to +% depend on the value of the handle at the time the object was saved. +% +% To reopen this object, just type the name of the M-file at the MATLAB +% prompt. The M-file and its associated MAT-file must be on your path. + +load draw + +h0 = figure('Color',[0.8 0.8 0.8], ... + 'Colormap',mat0, ... + 'Name','Smooth Draw', ... + 'NumberTitle','off', ... + 'PointerShapeCData',mat1, ... + 'Position',[40 45 560 375], ... + 'Resize','off', ... + 'Tag','drawfig', ... + 'UserData',mat2); +h1 = axes('Parent',h0, ... + 'Units','pixels', ... + 'Box','on', ... + 'CameraUpVector',[0 1 0], ... + 'CameraUpVectorMode','manual', ... + 'Color',[1 1 1], ... + 'ColorOrder',mat3, ... + 'HandleVisibility','callback', ... + 'Position',[52 135 347 218], ... + 'Tag','Axes1', ... + 'XColor',[0 0 0], ... + 'XGrid','on', ... + 'XLimMode','manual', ... + 'YColor',[0 0 0], ... + 'YGrid','on', ... + 'YLimMode','manual', ... + 'ZColor',[0 0 0], ... + 'ZGrid','on'); +h2 = text('Parent',h1, ... + 'Color',[0 0 0], ... + 'HandleVisibility','off', ... + 'HorizontalAlignment','center', ... + 'Position',[0.4971098265895954 -0.1105990783410138 9.160254037844386], ... + 'Tag','Axes1Text4', ... + 'VerticalAlignment','cap'); +set(get(h2,'Parent'),'XLabel',h2); +h2 = text('Parent',h1, ... + 'Color',[0 0 0], ... + 'HandleVisibility','off', ... + 'HorizontalAlignment','center', ... + 'Position',[-0.08959537572254335 0.4930875576036867 9.160254037844386], ... + 'Rotation',90, ... + 'Tag','Axes1Text3', ... + 'VerticalAlignment','baseline'); +set(get(h2,'Parent'),'YLabel',h2); +h2 = text('Parent',h1, ... + 'Color',[0 0 0], ... + 'HandleVisibility','off', ... + 'HorizontalAlignment','right', ... + 'Position',[-0.1502890173410405 1.101382488479263 9.160254037844386], ... + 'Tag','Axes1Text2', ... + 'Visible','off'); +set(get(h2,'Parent'),'ZLabel',h2); +h2 = text('Parent',h1, ... + 'Color',[0 0 0], ... + 'HandleVisibility','off', ... + 'HorizontalAlignment','center', ... + 'Position',[0.4971098265895954 1.032258064516129 9.160254037844386], ... + 'Tag','Axes1Text1', ... + 'VerticalAlignment','bottom'); +set(get(h2,'Parent'),'Title',h2); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ... + 'ListboxTop',0, ... + 'Position',[325.5 3 85.5 263.25], ... + 'Style','frame', ... + 'Tag','Frame1'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','clear;[x,y]=ginput;', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[333 222 72 25.5], ... + 'String','Ginput', ... + 'Tag','Pushbutton1'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','pp=csaps(x,y,0.9999);fnplt(pp,''b'',2);', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[333.75 192 72 24.75], ... + 'String','Draw It', ... + 'Tag','Pushbutton2'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','gline', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[333.75 163.5 72 24.75], ... + 'String','Line', ... + 'Tag','Pushbutton3'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback',mat4, ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[334.5 102 72 25.5], ... + 'String','Range', ... + 'Tag','Pushbutton4'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','cla;axis([0 1 0 1]);hold off', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[334.5 13.5 71.25 26.25], ... + 'String','Erase', ... + 'Tag','Pushbutton5'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','grid', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[334.5 133.5 72 25.5], ... + 'String','Grid', ... + 'Tag','Pushbutton6'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'ListboxTop',0, ... + 'Position',[21.75 9 273 63.75], ... + 'Style','frame', ... + 'Tag','Frame2'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'BackgroundColor',[1 1 1], ... + 'Callback','eval(get(gcbo,''string''))', ... + 'ListboxTop',0, ... + 'Position',[32.25 9.75 261 46.5], ... + 'Style','edit', ... + 'Tag','EditText1'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback',mat5, ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[334.5 73.5 71.25 23.25], ... + 'String','Labels', ... + 'Tag','Pushbutton7'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ... + 'ListboxTop',0, ... + 'Position',[27 57.75 81 12], ... + 'String','Command Window', ... + 'Style','text', ... + 'Tag','StaticText1'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'BackgroundColor',[0.752941176470588 0.752941176470588 0.752941176470588], ... + 'ListboxTop',0, ... + 'Position',[332.25 248.25 75.75 15], ... + 'String','Control Panel', ... + 'Style','text', ... + 'Tag','StaticText2'); +h1 = uicontrol('Parent',h0, ... + 'Units','points', ... + 'Callback','hold', ... + 'FontSize',14, ... + 'ListboxTop',0, ... + 'Position',[334.5 43.5 70.5 24.75], ... + 'String','Hold', ... + 'Tag','Pushbutton8'); +if nargout > 0, fig = h0; end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/MESH.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/MESH.M" index da8eb525219cb749471b08a314e245ba18f76ac0..400039b5acf6af6e3b591d1c375cce9741c9f594 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/MESH.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/MESH.M" @@ -1,3 +1,99 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:df6ca8fde901a0f2d5920b1d76b201be124eba28398cbb89e6f7b65a037c41fb -size 3626 +function h = mesh(x,y,z,c) +%¿Õ¼äÇúÃæͼ +% mesh(x,y,z)ÆäÖÐx,y,zΪͬ½×¾ØÕó£¬Ã¿Ò»×é¶ÔÓ¦ÔªËØ´ú±íÒ»¸öÍø¸ñµã¡£ +% +%ÀýÈç ÇúÃæ z=x.*exp(-x^2-y^2),-2 ÓÒÈý½ÇÐÎ +% h Áù½ÇÐÎ +% p Îå½ÇÐÎ +%ÀýÈç +% x=0:0.2:2*pi;y=sin(x); +% plot(x,y,'r*') +% +%PLOT Linear plot. +% PLOT(X,Y) plots vector Y versus vector X. If X or Y is a matrix, +% then the vector is plotted versus the rows or columns of the matrix, +% whichever line up. +% +% PLOT(Y) plots the columns of Y versus their index. +% If Y is complex, PLOT(Y) is equivalent to PLOT(real(Y),imag(Y)). +% In all other uses of PLOT, the imaginary part is ignored. +% +% Various line types, plot symbols and colors may be obtained with +% PLOT(X,Y,S) where S is a character string made from one element +% from any or all the following 3 colunms: +% +% y yellow . point - solid +% m magenta o circle : dotted +% c cyan x x-mark -. dashdot +% r red + plus -- dashed +% g green * star +% b blue s square +% w white d diamond +% k black v triangle (down) +% ^ triangle (up) +% < triangle (left) +% > triangle (right) +% p pentagram +% h hexagram +% +% For example, PLOT(X,Y,'c+:') plots a cyan dotted line with a plus +% at each data point; PLOT(X,Y,'bd') plots blue diamond at each data +% point but does not draw any line. +% +% PLOT(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...) combines the plots defined by +% the (X,Y,S) triples, where the X's and Y's are vectors or matrices +% and the S's are strings. +% +% For example, PLOT(X,Y,'y-',X,Y,'go') plots the data twice, with a +% solid yellow line interpolating green circles at the data points. +% +% The PLOT command, if no color is specified, makes automatic use of +% the colors specified by the axes ColorOrder property. The default +% ColorOrder is listed in the table above for color systems where the +% default is yellow for one line, and for multiple lines, to cycle +% through the first six colors in the table. For monochrome systems, +% PLOT cycles over the axes LineStyleOrder property. +% +% PLOT returns a column vector of handles to LINE objects, one +% handle per line. +% +% The X,Y pairs, or X,Y,S triples, can be followed by +% parameter/value pairs to specify additional properties +% of the lines. +% +% See also SEMILOGX, SEMILOGY, LOGLOG, GRID, CLF, CLC, TITLE, +% XLABEL, YLABEL, AXIS, AXES, HOLD, COLORDEF, and SUBPLOT. + +% If the NextPlot axes property is "replace" (HOLD is off), PLOT resets +% all axes properties, except Position, to their default values, +% deletes all axes children (line, patch, text, surface, and +% image objects), and sets the View property to [0 90]. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.7 $ $Date: 1997/11/21 23:33:07 $ +% Built-in function. + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/PLOT3.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/PLOT3.M" index 2bce8c9a310b39e12c0a7cce8582254e2b71f90a..d63514bd116eed8474c457b1a731fe3ca7100415 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/PLOT3.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\233\276\345\275\242/PLOT3.M" @@ -1,3 +1,50 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b3ca4b4713386f0e0241a233ecfbb9b68a36c392d1a9a52ecce213e55b23185a -size 1937 +%¿Õ¼äÇúÏßͼ +% PLOT3(x,y,z,s)ÆäÖÐx,y,zΪÏòÁ¿£¬Ã¿Ò»×é·ÖÁ¿´ú±íÒ»¸öÊý¾Ýµã¡£ +% sΪ±íʾÑÕÉ«¡¢Á¬Ïߺͱê¼ÇÑ¡ÔñµÄ×Ö·û´® +%ÀýÈç ÇúÏßx=exp(-0.2*z)*cos(0.5*pi*z),y=exp(-0.2*z)*sin(0.5*pi*z), 0= size(X,DIM), DIFF takes +% successive differences along the next non-singleton dimension. +% DIFF(X,N,DIM) is the Nth difference function along dimension DIM. +% If N >= size(X,DIM), DIFF returns an empty array. +% +% Examples: +% h = .001; x = 0:h:pi; +% diff(sin(x.^2))/h is an approximation to 2*cos(x.^2).*x +% diff((1:10).^2) is 3:2:19 +% +% If X = [3 7 5 +% 0 9 2] +% then diff(X,1,1) is [-3 2 -3], diff(X,1,2) is [4 -2 +% 9 -7], +% diff(X,2,2) is the 2nd order difference along the dimension 2, and +% diff(X,3,2) is the empty matrix. +% +% See also GRADIENT, SUM, PROD. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.20 $ $Date: 1997/11/21 23:23:41 $ +% Built-in function. diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/DSOLVE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/DSOLVE.M" index 9dd1299f9777063da6ad4d627be8a36e5f5b6700..93604c1dad755f97357138bc0b46809e732d8bc0 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/DSOLVE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/DSOLVE.M" @@ -1,3 +1,290 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:60120bd1976bb5addb16a00a9f8a0f9857527965b56f5760c595127c272a9e80 -size 9680 +function varargout = dsolve(varargin) +%s=dsolve('·½³Ì1','·½³Ì2',...,'³õʼÌõ¼þ1','³õʼÌõ¼þ2',...,'×Ô±äÁ¿'). +% ¾ùÓÃ×Ö·û´®·½Ê½±íʾ,×Ô±äÁ¿È±Ê¡ÖµÎªt. +% µ¼ÊýÓÃD±íʾ,2½×µ¼ÊýÓÃD2±íʾ,ÒÔ´ËÀàÍÆ. +% s·µ»Ø½âÎö½â.·½³Ì×éÇéÐÎ,sΪһ¸ö·ûºÅ½á¹¹. +% +%DSOLVE Symbolic solution of ordinary differential equations. +% DSOLVE('eqn1','eqn2', ...) accepts symbolic equations representing +% ordinary differential equations and initial conditions. Several +% equations or initial conditions may be grouped together, separated +% by commas, in a single input argument. +% +% By default, the independent variable is 't'. The independent variable +% may be changed from 't' to some other symbolic variable by including +% that variable as the last input argument. +% +% The letter 'D' denotes differentiation with respect to the independent +% variable, i.e. usually d/dt. A "D" followed by a digit denotes +% repeated differentiation; e.g., D2 is d^2/dt^2. Any characters +% immediately following these differentiation operators are taken to be +% the dependent variables; e.g., D3y denotes the third derivative +% of y(t). Note that the names of symbolic variables should not contain +% the letter "D". +% +% Initial conditions are specified by equations like 'y(a)=b' or +% 'Dy(a) = b' where y is one of the dependent variables and a and b are +% constants. If the number of initial conditions given is less than the +% number of dependent variables, the resulting solutions will obtain +% arbitrary constants, C1, C2, etc. +% +% Three different types of output are possible. For one equation and one +% output, the resulting solution is returned, with multiple solutions to +% a nonlinear equation in a symbolic vector. For several equations and +% an equal number of outputs, the results are sorted in lexicographic +% order and assigned to the outputs. For several equations and a single +% output, a structure containing the solutions is returned. +% +% If no closed-form solution is found, a warning is given. +% +% Examples: +% +% dsolve('Dx = -a*x') returns +% +% ans = exp(-a*t)*C1 +% +% x = dsolve('Dx = -a*x','x(0) = 1','s') returns +% +% x = exp(-a*s) +% +% y = dsolve('(Dy)^2 + y^2 = 1','y(0) = 0') returns +% +% y = +% [ sin(t)] +% [ -sin(t)] +% +% S = dsolve('Df = f + g','Dg = -f + g','f(0) = 1','g(0) = 2') +% returns a structure S with fields +% +% S.f = exp(t)*cos(t)+2*exp(t)*sin(t) +% S.g = -exp(t)*sin(t)+2*exp(t)*cos(t) +% +% dsolve('Df = f + sin(t)', 'f(pi/2) = 0') +% dsolve('D2y = -a^2*y', 'y(0) = 1, Dy(pi/a) = 0') +% S = dsolve('Dx = y', 'Dy = -x', 'x(0)=0', 'y(0)=1') +% S = dsolve('Du=v, Dv=w, Dw=-u','u(0)=0, v(0)=0, w(0)=1') +% w = dsolve('D3w = -w','w(0)=1, Dw(0)=0, D2w(0)=0') +% +% See also SOLVE, SUBS. + +% Copyright (c) 1993-98 by The MathWorks, Inc. +% $Revision: 1.26 $ $Date: 1997/11/29 01:06:23 $pj costa + +narg = nargin; + +% The default independent variable is t. +x = 't'; +% Pick up the independent variable, if specified. +if all(varargin{narg} ~= '='), + x = varargin{narg}; narg = narg-1; +end; + +% Concatenate equation(s) and initial condition(s) inputs into SYS. +sys = varargin{1}; +for k = 2: narg + sys = [sys ', ' varargin{k}];; +end + +% Break SYS into pieces. Each such piece, Dstr, begins with the first +% character following a "D" and ends with the character preceding the +% next consecutive "D". Loop over each Dstr and do the following: +% o add to the list of dependent variables +% o replace derivative notation. E.g., "D3y" --> "(D@@3)y" +% +% A dependent variable is defined as a variable that is preceded by "Dk", +% where k is an integer. +% +% new_sys looks like: eqn(s), initial condition(s) (i.e., no brackets) +% var_set looks like: { x(t), y2(t), ... } (i.e., with brackets) + +var_set = '{'; % string representing Maple set of dependent variables + +% Add dummy "D" so that last Dstr acts like all Dstr's +d = [find(sys == 'D') length(sys)+1]; + +new_sys = sys(1:d-1); % SYS rewritten with (D@@k)y notation + +for kd = 1:length(d)-1 + Dstr = sys(d(kd)+1:d(kd+1)-1); + iletter = find(isletter(Dstr)); % index to letters in Dstr + + % Replace Dky with (D@@k)y + if iletter(1)==1 % First derivative case (Dy) + new_sys = [new_sys '(D' Dstr(1:iletter(1)-1) ')' Dstr(iletter(1):end)]; + else + new_sys = [new_sys '(D@@' Dstr(1:iletter(1)-1) ')' Dstr(iletter(1):end)]; + end + + % Store the dependent variable. Find this variable by looking at the + % characters following the derivative order and pulling off the first + % consecutive chunk of alphanumeric characters. + Dstr1 = Dstr(iletter(1):end); + ialphanum = find(~isletter(Dstr1) & (Dstr1 < '0' | Dstr1 > '9')); + var_set = [var_set Dstr1(1:ialphanum(1)-1) ',']; +end + +% Get rid of duplicate entries in var_set +var_set(end) = '}'; +var_set = maple([var_set ' intersect ' var_set]); + +% Generate var_str, the Maple string representing the set of dependent +% variables. +% Replace all dependent variables with their functional equivalents, +% i.e., replace y -> (y)(x). + +% Break the system string into its equation and initial condition parts. +% This is done by looking for the first occurrence of "y(", where y is a +% dependent variable. +indx_ic = length(new_sys); % points to starting character of ic string +ic_str = []; % initialize the initial condition string +eq_str = new_sys; % initialize the equation string +var_str = '{'; % Maple set of dependent variables +vars = [',' var_set(2:end-1) ',']; % preceding comma delimits variable +vars(find(vars==' '))=[]; % deblank +kommas = find(vars==','); + +for k = 1: length(kommas)-1 + v = vars(kommas(k)+1:kommas(k+1)-1); % v is a dependent variable + + % Add to set of dependent variables. + var_str = [var_str v '(' x '),']; + + % Look for first occurrence of "v(". If it's before the first occurrence + % of the previous dependent variable, change value of indx_ic and + % shorten the equation string. + indx = findstr(eq_str, [v '(']); % index to current dependent var. + if isempty(indx), indx = indx_ic; end + indx_ic = min(indx_ic,indx(1)); + eq_str = new_sys(1:min(indx_ic)); +end + +% Finish var_str +var_str(end) = '}'; + +% Stuff after the last comma belongs in the initial condition string +if indx_ic < length(new_sys) + last_comma = max(find(eq_str==',')); + ic_str = new_sys(last_comma:end); + eq_str = eq_str(1: last_comma-1); +end + +% In the equation string, replace all occurrences of "y" with "(y)(x)". +for j = 1:length(kommas)-1 + v = vars(kommas(j)+1:kommas(j+1)-1); + m = length(v); + e = length(eq_str); + for k = fliplr(findstr(v,eq_str)) + if k+m > e | ~isvarname(eq_str(k:k+m)) + eq_str = [eq_str(1:k-1) '(' v ')(' x ')' eq_str(k+m:end)]; + end + end +end + +% In the ic string, replace all occurrences of "y" with "(y)". +for j = 1:length(kommas)-1 + v = vars(kommas(j)+1:kommas(j+1)-1); + m = length(v); + e = length(ic_str); + for k = fliplr(findstr(v,ic_str)) + if k+m > e | ~isvarname(ic_str(k:k+m)) + ic_str = [ic_str(1:k-1) '(' v ')' ic_str(k+m:end)]; + end + end +end + +% Convert system to rational form and solve +[R,stat] = maple('dsolve', ... + ['convert({',eq_str,ic_str,'},fraction)'], var_str, 'explicit'); +if stat + error(R) +end + +% If no solution, give up. + +if isempty(R) | ~isempty(findstr(R,'DESol')) + warning('Explicit solution could not be found.'); + varargout = cell(1,nargout); + varargout{1} = sym([]); + return +end + +% Eliminate underscores in constants. + +R(findstr(R,'_C')) = []; + +% Parse the result. + +if R(1) ~= '{', R = ['{' R '}']; end +vars(1) = '['; vars(end) = ']'; +vars = maple('sort',vars); +vars(1) = '{'; vars(end) = '}'; +nvars = sum(commas(vars))+1; + +if nvars == 1 & nargout <= 1 + + % One variable and at most one output. + % Return a single scalar or vector sym. + + S = sym([]); + c = find(commas(R) | R == '}'); + for p = find(R == '=') + q = min(c(c>p)); + t = trim(R(p+1:q-1)); + S = [S; sym(t)]; + end + varargout{1} = S; + +else + + % Several variables. + % Create a skeleton structure. + + c = [1 find(commas(vars)) length(vars)]; + S = []; + for j = 1:nvars + v = trim(vars(c(j)+1:c(j+1)-1)); + S = setfield(S,v,[]); + end + + % Complete the structure. + + c = [1 find(commas(R) | R == '{' | R == '}') length(R)]; + for p = find(R == '=') + q = max(c(cp)); + t = trim(R(p+1:q-1)); + S = setfield(S,v,[getfield(S,v); sym(t)]); + end + + if nargout <= 1 + + % At most one output, return the structure. + varargout{1} = S; + + elseif nargout == nvars + + % Same number of outputs as variables. + % Match results in lexicographic order to outputs. + v = fieldnames(S); + for j = 1:nvars + varargout{j} = getfield(S,v{j}); + end + + else + error([int2str(nvars) ' variables does not match ' ... + int2str(nargout) ' outputs.']) + end +end + +function s = trim(s); +%TRIM TRIM(s) deletes any leading or trailing blanks. +while s(1) == ' ', s(1) = []; end +while s(end) == ' ', s(end) = []; end + + +function c = commas(s) +%COMMAS COMMAS(s) is true for commas not inside parentheses. +p = cumsum((s == '(') - (s == ')')); +c = (s == ',') & (p == 0); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/INT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/INT.M" index c61c7b5b132e8b6f80b329bbc6d4e237d9b95e70..876b568413c76211b769d69d543b3ef905564a09 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/INT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/INT.M" @@ -1,3 +1,78 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:752ecfe3baeb84941fe566a8e90d9052fa593a239bf31acd0e4e50fd0caabea6 -size 2579 +function r = int(f,x,a,b) +%·ûºÅ»ý·Ö·¨ +% int(s)·ûºÅ±í´ïʽsµÄ²»¶¨»ý·Ö. +% int(s,v)·ûºÅ±í´ïʽs¹ØÓÚ±äÁ¿vµÄ²»¶¨»ý·Ö. +% int(s,a,b)·ûºÅ±í´ïʽsµÄ¶¨»ý·Ö, a,b·Ö±ðΪÉÏ©pÏÂÏÞ. +% int(s,v,a,b)·ûºÅ±í´ïʽs¹ØÓÚ±äÁ¿v´Ó aµ½bµÄ¶¨»ý·Ö. +% µ±intÇó²»³ö·ûºÅ½â,»á×Ô¶¯×ªÇóÊýÖµ½â. +%Àý£¨ Çó²»³ö·ûºÅ½â,»á×Ô¶¯×ªÇóÊýÖµ½â£© +% syms x;t=int(exp(-x^sin(x)),0,1),vpa(t,5) +% ½á¹ûΪ +% Warning: Explicit integral could not be found. +% > In D:\MATLAB5\toolbox\symbolic\@sym\int.m at line 58 +% t = +% int(exp(-x^sin(x)),x = 0 .. 1)%±íʾÎÞ½âÎö½â +% ans = +% .45491 %ÊýÖµ½â +%¸ü¶àµÄÀý×Ó¼ûÏÂÁÐÓ¢ÎIJ¿·Ö +% +%INT Integrate. +% INT(S) is the indefinite integral of S with respect to its symbolic +% variable as defined by FINDSYM. S is a SYM (matrix or scalar). +% If S is a constant, the integral is with respect to 'x'. +% INT(S,v) is the indefinite integral of S with respect to v. v is a +% scalar SYM. +% INT(S,a,b) is the definite integral of S with respect to its +% symbolic variable from a to b. a and b are each double or +% symbolic scalars. +% INT(S,v,a,b) is the definite integral of S with respect to v +% from a to b. +% +% Examples: +% syms x x1 alpha u t; +% A = [cos(x*t),sin(x*t);-sin(x*t),cos(x*t)]; +% int(1/(1+x^2)) returns atan(x) +% int(sin(alpha*u),alpha) returns -cos(alpha*u)/u +% int(besselj(1,x),x) returns -besselj(0,x) +% int(x1*log(1+x1),0,1) returns 1/4 +% int(4*x*t,x,2,sin(t)) returns 2*sin(t)^2*t-8*t +% int([exp(t),exp(alpha*t)]) returns [exp(t), 1/alpha*exp(alpha*t)] +% int(A,t) returns [sin(x*t)/x, -cos(x*t)/x] +% [cos(x*t)/x, sin(x*t)/x] + +% Copyright (c) 1993-98 by The MathWorks, Inc. +% $Revision: 1.15 $ $Date: 1997/11/29 01:05:44 $pj costa + +f = sym(f); + +if nargin <= 2 + % Indefinite integral + if nargin < 2 + x = findsym(f,1); + if isempty(x), x = 'x'; end + else + x = char(sym(x)); + end + r = maple('map','int',f,x); +else + % Definite integral + if nargin < 4 + b = a; + a = x; + x = findsym(f,1); + if isempty(x), x = 'x'; end + end + x = sym(x); + b = sym(b); + a = sym(a); + r = maple('map','int',f,[x.s '=' a.s '..' b.s]); +end + +if ~isempty(findstr('int(',char(r))) + for k = 1:prod(size(r)); + rc = char(r(k)); + if length(rc) >= 4 & isequal(rc(1:4),'int(') + warning('Explicit integral could not be found.') + end + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/ODE45.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/ODE45.M" index bcaef47fa0439ee79b2445c6760d2716c7ba2796..8135794108ddf70d83bee0d5e32e015995e7ff89 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/ODE45.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/ODE45.M" @@ -1,3 +1,567 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8f7d0e056c15c81d6ea9d6ae90c2f26a3ca065598c2594f753eab8d77f1b5f1a -size 19036 +function [tout,yout,varargout] = ode45(odefile,tspan,y0,options,varargin) +%[tout,yout] = ode45('ypfun', tspan, y0, options) +%ÕâÀï×Ö·û´®ypfunÊÇÓÃÒÔ±íʾf(t, y)µÄMÎļþÃû, +%tspan=[t0, tfinal]±íʾ×Ô±äÁ¿³õÖµt0ºÍÖÕÖµtf +% y0±íʾ³õÖµÏòÁ¿y0£¬¿ÉÑ¡²ÎÊýoptionsΪÓÃodesetÉèÖþ«¶ÈµÈ²ÎÊý¡£ +% Êä³öÁÐÏòÁ¿tout±íʾ½Úµã (t0 , t1 , ¡­ , tn)' +% Êä³ö¾ØÕóyout ±íʾÊýÖµ½â£¬Ã¿Ò»ÁжÔÓ¦yµÄÒ»¸ö·ÖÁ¿ +% ÈôÎÞÊä³ö²ÎÊý£¬Ôò×÷³öͼÐΡ£ +%Àý ½â΢·Ö·½³Ì +% y' = y-2t/y, y(0)=1, 0 0 + outfun = odeget(options,'OutputFcn'); +else + outfun = odeget(options,'OutputFcn','odeplot'); +end +if isempty(outfun) + haveoutfun = false; +else + haveoutfun = true; + outputs = odeget(options,'OutputSel',1:neq); +end +refine = odeget(options,'Refine',4); % Necessary for smooth plots. +printstats = strcmp(odeget(options,'Stats','off'),'on'); + +if strcmp(odeget(options,'Mass','off'),'on') | ... + strcmp(odeget(options,'MassConstant','off'),'on') + error(['Solver does not handle mass matrices, M*y'' or M(t)*y''. '... + 'See ODE15S, ODE23S, ODE23T, or ODE23TB.']); +end + +% Set the output flag. +if ntspan > 2 + outflag = 1; % output only at tspan points +elseif refine <= 1 + outflag = 2; % computed points, no refinement +else + outflag = 3; % computed points, with refinement + S = (1:refine-1)' / refine; +end + +% Allocate memory if we're generating output. +if nargout > 0 + if ntspan > 2 % output only at tspan points + tout = zeros(ntspan,1); + yout = zeros(ntspan,neq); + else % alloc in chunks + chunk = max(ceil(128 / neq),refine); + tout = zeros(chunk,1); + yout = zeros(chunk,neq); + end + nout = 1; + tout(nout) = t; + yout(nout,:) = y.'; +end + +% Initialize method parameters. +pow = 1/5; +A = [1/5; 3/10; 4/5; 8/9; 1; 1]; +B = [ + 1/5 3/40 44/45 19372/6561 9017/3168 35/384 + 0 9/40 -56/15 -25360/2187 -355/33 0 + 0 0 32/9 64448/6561 46732/5247 500/1113 + 0 0 0 -212/729 49/176 125/192 + 0 0 0 0 -5103/18656 -2187/6784 + 0 0 0 0 0 11/84 + 0 0 0 0 0 0 + ]; +E = [71/57600; 0; -71/16695; 71/1920; -17253/339200; 22/525; -1/40]; +f = zeros(neq,7); + +% The input arguments of odefile determine the args to use to evaluate f. +if nargin(odefile) == 2 + args = {}; % odefile accepts only (t,y) +else + args = [{''} varargin]; % use (t,y,'',p1,p2,...) +end + +f0 = feval(odefile,t,y,args{:}); +nfevals = nfevals + 1; % stats +[m,n] = size(f0); +if n > 1 + error([upper(odefile) ' must return a column vector.']) +elseif m ~= neq + msg = sprintf('an initial condition vector of length %d.',m); + error(['Solving ' upper(odefile) ' requires ' msg]); +end + +hmin = 16*eps*abs(t); +if isempty(htry) + % Compute an initial step size h using y'(t). + absh = min(hmax, abs(tspan(next) - t)); + if normcontrol + rh = (norm(f0) / max(normy,threshold)) / (0.8 * rtol^pow); + else + rh = norm(f0 ./ max(abs(y),threshold),inf) / (0.8 * rtol^pow); + end + if absh * rh > 1 + absh = 1 / rh; + end + absh = max(absh, hmin); +else + absh = min(hmax, max(hmin, htry)); +end +f(:,1) = f0; + +% Initialize the output function. +if haveoutfun + feval(outfun,[t tfinal],y(outputs),'init'); +end + +% THE MAIN LOOP + +done = false; +while ~done + + % By default, hmin is a small number such that t+hmin is only slightly + % different than t. It might be 0 if t is 0. + hmin = 16*eps*abs(t); + absh = min(hmax, max(hmin, absh)); % couldn't limit absh until new hmin + h = tdir * absh; + + % Stretch the step if within 10% of tfinal-t. + if 1.1*absh >= abs(tfinal - t) + h = tfinal - t; + absh = abs(h); + done = true; + end + + % LOOP FOR ADVANCING ONE STEP. + nofailed = true; % no failed attempts + while true + hA = h * A; + hB = h * B; + f(:,2) = feval(odefile, t + hA(1), y + f*hB(:,1), args{:}); + f(:,3) = feval(odefile, t + hA(2), y + f*hB(:,2), args{:}); + f(:,4) = feval(odefile, t + hA(3), y + f*hB(:,3), args{:}); + f(:,5) = feval(odefile, t + hA(4), y + f*hB(:,4), args{:}); + f(:,6) = feval(odefile, t + hA(5), y + f*hB(:,5), args{:}); + tnew = t + hA(6); + ynew = y + f*hB(:,6); + f(:,7) = feval(odefile, tnew, ynew, args{:}); + nfevals = nfevals + 6; % stats + + % Estimate the error. + if normcontrol + normynew = norm(ynew); + err = absh * (norm(f * E) / max(max(normy,normynew),threshold)); + else + err = absh * norm((f * E) ./ max(max(abs(y),abs(ynew)),threshold),inf); + end + + % Accept the solution only if the weighted error is no more than the + % tolerance rtol. Estimate an h that will yield an error of rtol on + % the next step or the next try at taking this step, as the case may be, + % and use 0.8 of this value to avoid failures. + if err > rtol % Failed step + nfailed = nfailed + 1; % stats + if absh <= hmin + msg = sprintf(['Failure at t=%e. Unable to meet integration ' ... + 'tolerances without reducing the step size below ' ... + 'the smallest value allowed (%e) at time t.\n'],t,hmin); + warning(msg); + if haveoutfun + feval(outfun,[],[],'done'); + end + if printstats % print cost statistics + fprintf('%g successful steps\n', nsteps); + fprintf('%g failed attempts\n', nfailed); + fprintf('%g function evaluations\n', nfevals); + fprintf('%g partial derivatives\n', npds); + fprintf('%g LU decompositions\n', ndecomps); + fprintf('%g solutions of linear systems\n', nsolves); + end + if nargout > 0 + tout = tout(1:nout); + yout = yout(1:nout,:); + if haveeventfun + varargout{1} = teout; + varargout{2} = yeout; + varargout{3} = ieout; + varargout{4} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + else + varargout{1} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + end + end + return; + end + + if nofailed + nofailed = false; + absh = max(hmin, absh * max(0.1, 0.8*(rtol/err)^pow)); + else + absh = max(hmin, 0.5 * absh); + end + h = tdir * absh; + done = false; + + else % Successful step + break; + + end + end + nsteps = nsteps + 1; % stats + + if haveeventfun + [te,ye,ie,valt,stop] = ... + odezero('ntrp45',odefile,valt,t,y,tnew,ynew,t0,varargin,h,f); + nte = length(te); + if nte > 0 + if nargout > 2 + teout = [teout; te]; + yeout = [yeout; ye.']; + ieout = [ieout; ie]; + end + if stop % stop on a terminal event + tnew = te(nte); + ynew = ye(:,nte); + done = true; + end + end + end + + if nargout > 0 + oldnout = nout; + if outflag == 3 % computed points, with refinement + nout = nout + refine; + if nout > length(tout) + tout = [tout; zeros(chunk,1)]; % requires chunk >= refine + yout = [yout; zeros(chunk,neq)]; + end + i = oldnout+1:nout-1; + tout(i) = t + (tnew-t)*S; + yout(i,:) = ntrp45(tout(i),t,y,[],[],h,f).'; + tout(nout) = tnew; + yout(nout,:) = ynew.'; + elseif outflag == 2 % computed points, no refinement + nout = nout + 1; + if nout > length(tout) + tout = [tout; zeros(chunk,1)]; + yout = [yout; zeros(chunk,neq)]; + end + tout(nout) = tnew; + yout(nout,:) = ynew.'; + elseif outflag == 1 % output only at tspan points + while next <= ntspan + if tdir * (tnew - tspan(next)) < 0 + if haveeventfun & done + nout = nout + 1; + tout(nout) = tnew; + yout(nout,:) = ynew.'; + end + break; + elseif tnew == tspan(next) + nout = nout + 1; + tout(nout) = tnew; + yout(nout,:) = ynew.'; + next = next + 1; + break; + end + nout = nout + 1; % tout and yout are already allocated + tout(nout) = tspan(next); + yout(nout,:) = ntrp45(tspan(next),t,y,[],[],h,f).'; + next = next + 1; + end + end + + if haveoutfun + i = oldnout+1:nout; + if ~isempty(i) & (feval(outfun,tout(i),yout(i,outputs).') == 1) + tout = tout(1:nout); + yout = yout(1:nout,:); + if haveeventfun + varargout{1} = teout; + varargout{2} = yeout; + varargout{3} = ieout; + varargout{4} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + else + varargout{1} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + end + return; + end + end + + elseif haveoutfun + if outflag == 3 % computed points, with refinement + tinterp = t + (tnew-t)*S; + yinterp = ntrp45(tinterp,t,y,[],[],h,f); + if feval(outfun,[tinterp; tnew],[yinterp(outputs,:), ynew(outputs)]) == 1 + return; + end + elseif outflag == 2 + if feval(outfun,tnew,ynew(outputs)) == 1 + return; + end + elseif outflag == 1 % output only at tspan points + ninterp = 0; + while next <= ntspan + if tdir * (tnew - tspan(next)) < 0 + if haveeventfun & done + ninterp = ninterp + 1; + tinterp(ninterp,1) = tnew; + yinterp(:,ninterp) = ynew; + end + break; + elseif tnew == tspan(next) + ninterp = ninterp + 1; + tinterp(ninterp,1) = tnew; + yinterp(:,ninterp) = ynew; + next = next + 1; + break; + end + ninterp = ninterp + 1; + tinterp(ninterp,1) = tspan(next); + yinterp(:,ninterp) = ntrp45(tspan(next),t,y,[],[],h,f); + next = next + 1; + end + if ninterp > 0 + if feval(outfun,tinterp(1:ninterp),yinterp(outputs,1:ninterp)) == 1 + return; + end + end + end + end + + % If there were no failures compute a new h. + if nofailed + % Note that absh may shrink by 0.8, and that err may be 0. + temp = 1.25*(err/rtol)^pow; + if temp > 0.2 + absh = absh / temp; + else + absh = 5.0*absh; + end + end + + % Advance the integration one step. + t = tnew; + y = ynew; + if normcontrol + normy = normynew; + end + f(:,1) = f(:,7); % Already evaluated odefile(tnew,ynew) + +end + +if haveoutfun + feval(outfun,[],[],'done'); +end + +if printstats % print cost statistics + fprintf('%g successful steps\n', nsteps); + fprintf('%g failed attempts\n', nfailed); + fprintf('%g function evaluations\n', nfevals); + fprintf('%g partial derivatives\n', npds); + fprintf('%g LU decompositions\n', ndecomps); + fprintf('%g solutions of linear systems\n', nsolves); +end + +if nargout > 0 + tout = tout(1:nout); + yout = yout(1:nout,:); + if haveeventfun + varargout{1} = teout; + varargout{2} = yeout; + varargout{3} = ieout; + varargout{4} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + else + varargout{1} = [nsteps; nfailed; nfevals; npds; ndecomps; nsolves]; + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/POLYINT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/POLYINT.M" index c06ff4ff40a7b98d7c6958d630a0def190eab9cf..283c6c650866f57bc85f1452c7224adaece717a3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/POLYINT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/POLYINT.M" @@ -1,3 +1,14 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1ba0e0ff32b5f5242e84024738236f9a554ce0b50eaa14a45d41d3b0f0675419 -size 300 + function q = polyint(p,a,b) + %POLYINT ¶àÏîʽ»ý·Ö¿ìËÙËã·¨ + %polyint(p)·µ»Ø¶àÏîʽpµÄ²»¶¨»ý·Ö,³£ÊýÏîÓÃ0; + %polyint(p,a,b) ·µ»Ø¶àÏîʽpÔÚ[a,b]µÄ¶¨»ý·Ö. + + %by L.J. Hu 1999 + + p=p(:)'; + n=length(p); + q=p./[n:-1:1]; + q=[q,0]; + if nargin>2, + q=polyval(q,b)-polyval(q,a); + end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD2DG.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD2DG.M" index 168cfb8342dc4ff4698f0576f68bb0b714bc3384..89b7fef61419029cfe83964983e72064bf248396 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD2DG.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD2DG.M" @@ -1,3 +1,140 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e451d1f76fd5ac72919d1b54767c6cc62cb50360748e947a096e37220a352d0f -size 4843 +function [int, tol1,k] = quad2dg(fun,xlow,xhigh,ylow,yhigh,tol,p1,p2,p3,p4,p5,p6,p7,p8,p9) +%¾ØÐÎÇøÓòGAUSS»ý·Ö·¨ +%Ó÷¨: int = quad2dg('Fun',xlow,xhigh,ylow,yhigh) +% +% int -- »ý·ÖÖµ +% Fun -- ¶þÔª±»»ýº¯ÊýFun(x,y) +% xlow -- x ÏÂÏÞ +% xhigh -- x ÉÏÏÞ +% ylow -- y ÏÂÏÞ +% yhigh -- y ÉÏÏÞ +% +%usage: [int tol] = quad2dg('Fun',xlow,xhigh,ylow,yhigh) +%or +% [int tol] = quad2dg('Fun',xlow,xhigh,ylow,yhigh,reltol,p1,p2,...) +% +%This function is similar to QUAD or QUAD8 for 2-dimensional integration, +%but it uses a Gaussian quadrature integration scheme. +% int -- value of the integral +% tol -- absolute tolerance abs( int-intold) +% Fun -- Fun(x,y) (function to be integrated) +% xlow -- lower x limit of integration +% xhigh -- upper x limit of integration +% ylow -- lower y limit of integration +% yhigh -- upper y limit of integration +% reltol -- relative tolerance parameter (optional) +%Note that if there are discontinuities the region of integration +%should be broken up into separate pieces. And if there are singularities, +%a more appropriate integration quadrature should be used +%(such as the Gauss-Chebyshev for a specific type of singularity). +% +%modified by Per A. Brodtkorb 17.11.98 : +% -accept multiple integrations limits +% -optimized by saving the weights as global constants and only +% computing the integrals which did not converge +% -enabled the integration of directly given functions enclosed in +% parenthesis +% +%Example: integration from 0 to 2 and from 2 to 4 for both x and y is done by: +% +% quad2dg('(x.^2.*y)',[0 2],[2 4],[0 2],[2 4]) +% + +global bpx2 bpy2 wfxy2; + + +if isempty(bpx2)| isempty(bpy2)| isempty(wfxy2) + [bpx2,bpy2,wfxy2] = grule2d(2,2); +end + + +if exist('tol')~=1, + tol=1e-3; +elseif isempty(tol), + tol=1e-3; +end +[errorcode ,xlow,xhigh,ylow,yhigh]=distchck(4,xlow,xhigh,ylow,yhigh); +if errorcode > 0 + error('Requires non-scalar arguments to match in size.'); +end +%size(xlow),size(xhigh), size(ylow),size(yhigh) +%if prod(size(xlow))==1, +% xlow=xlow(ones(size(xhigh)));; +%elseif prod(size(xhigh))==1, +% xhigh=xhigh(ones(size(xlow)));; +%elseif any( size(xhigh)~=size(xlow) ) +% error('The input must have equal size!') +%end + + +[N M]=size(xlow); +%setup mapping parameters & make sure they all are column vectors +xlow=xlow(:); xhigh=xhigh(:);ylow=ylow(:);yhigh=yhigh(:); +nk=N*M; + + +%Map to x +qx=(xhigh-xlow)/2; +px=(xhigh+xlow)/2; +x=permute(qx(:,ones(1,2), ones(1,2) ),[ 2 3 1]).*bpx2(:,:,ones(1,nk)) ... + +permute(px(:,ones(1,2), ones(1,2) ),[2 3 1]); +%Map to y +qy=(yhigh-ylow)/2; +py=(yhigh+ylow)/2; +y=permute(qy(:,ones(1,2), ones(1,2) ),[ 2 3 1]).*bpy2(:,:,ones(1,nk)) ... + +permute(py(:,ones(1,2), ones(1,2) ),[2 3 1]); + + +if any(fun=='(') & any(fun=='y')& any(fun=='x'), + exec_string=['fv=', fun, ';']; %the call function is already setup +else%set up the call function + exec_string=['fv=', fun, ' (x,y']; + num_parameters=nargin-6; + for i=1:num_parameters, + exec_string=[exec_string,',p',int2str(i)]; + end + exec_string=[exec_string,');']; +end +eval(exec_string); +int_old = squeeze(sum(sum(wfxy2(:,:,ones(1,nk)).*fv))).*qx.*qy; +int=zeros(size(int_old));tol1=int; +k=1:nk; + + +% Break out of the iteration loop for three reasons: +% 1) the last update is very small (compared to int) +% 2) the last update is very small (compared to tol) +% 3) There are more than 8 iterations. This should NEVER happen. + + +converge='n'; +for i=1:8, + gnum=int2str(2^(i+1)); + eval(['global bpx',gnum,' wfxy',gnum,' bpy',gnum,';']); + if isempty(eval(['bpx',gnum]))| isempty(eval(['bpy',gnum])) , + eval(['[bpx',gnum,',bpy',gnum,',wfxy',gnum,']=grule2d(',gnum,',', gnum,');']); + end + eval(['x=permute(qx(k,ones(1,',gnum,'), ones(1,',gnum,') ),[ 2 3 1]).*bpx',gnum,'(:,:,ones(1,nk)) +permute(px(k,ones(1,',gnum,'), ones(1,',gnum,') ),[2 3 1]);']); + + + eval(['y=permute(qy(k,ones(1,',gnum,'), ones(1,',gnum,') ),[ 2 3 1]).*bpy',gnum,'(:,:,ones(1,nk)) +permute(py(k,ones(1,',gnum,'), ones(1,',gnum,') ),[2 3 1]);']); + eval(exec_string); + eval(['int(k) = squeeze(sum(sum((wfxy',gnum,'(:,:,ones(1,nk)).*fv)))).*qx(k).*qy(k);']); + tol1(k)=abs(int_old(k)-int(k)); % absolute tolerance + k=find(tol1 > abs(tol*int)|tol1 > abs(tol));%indices to integrals which did not converge + + if any(k), % compute integrals again + nk=length(k);%# of integrals we have to compute again + else + converge='y'; + break; + end + + int_old(k)=int(k); +end +int=reshape(int,[N M]); % reshape int to the same size as input arguments +if converge=='n', + disp('Integral did not converge--singularity likely') +end + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD8.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD8.M" index b9a8cdc47ec2c8008116d0249875105cb93657d0..b5d10695f5147bde797b54d56f18a0bdd35d93d6 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD8.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUAD8.M" @@ -1,3 +1,148 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5776ae8718b8e9216c46ffd243823282702ba9d63c7db350f5d43d14213e5aab -size 5084 +function [Q,cnt] = quad8(funfcn,a,b,tol,trace,varargin) +%ÊýÖµ»ý·Ö +%z=quad8('Fun',A,B,Tol,trace,p1,p2,L) +% ÆäÖÐ:"Fun"-±íʾ±»»ýº¯ÊýµÄMº¯ÊýÃû. +% A,B-ÉÏ©pÏÂÏÞ. +% Tol-¾«¶È,ȱʡֵΪ1e-3. +% trace-·ÇÁãʱÏÔʾ¼ÆËã¹ý³Ì,ȱʡֵΪ0. +% p1,p2,L-²Î±äÁ¿,Ò»°ãȱʡ. +%ÀýÈçÇó exp(-x^2)ÔÚ[-1£¬1]»ý·Ö +% ÏÈдMº¯Êýquadeg3fun.m +% function y=quadeg3fun(x) +% y=exp(-x.^2); +% Óà +% z=quad8('quadeg3fun',-1,1) +% +%QUAD8 Numerically evaluate integral, higher order method. +% Q = QUAD8('F',A,B) approximates the integral of F(X) from A to B to +% within a relative error of 1e-3 using an adaptive recursive Newton +% Cotes 8 panel rule. 'F' is a string containing the name of the +% function. The function must return a vector of output values if +% given a vector of input values. Q = Inf is returned if an excessive +% recursion level is reached, indicating a possibly singular integral. +% +% Q = QUAD8('F',A,B,TOL) integrates to a relative error of TOL. Use +% a two element tolerance, TOL = [rel_tol abs_tol], to specify a +% combination of relative and absolute error. +% +% Q = QUAD8('F',A,B,TOL,TRACE) integrates to a relative error of TOL and +% for non-zero TRACE traces the function evaluations with a point plot +% of the integrand. +% +% Q = QUAD8('F',A,B,TOL,TRACE,P1,P2,...) allows coefficients P1, P2, ... +% to be passed directly to function F: G = F(X,P1,P2,...). +% To use default values for TOL or TRACE, you may pass in the empty +% matrix ([]). +% +% See also QUAD, DBLQUAD. + +% Cleve Moler, 5-08-88. +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.16 $ $Date: 1997/11/21 23:31:14 $ + +% [Q,cnt] = quad8(F,a,b,tol) also returns a function evaluation count. + +if nargin < 4, tol = [1.e-3 0]; trace = 0; end +if nargin < 5, trace = 0; end +if isempty(tol), tol = [1.e-3 0]; end +if length(tol)==1, tol = [tol 0]; end +if isempty(trace), trace = 0; end +% QUAD8 usually does better than the default 1e-3. +h = b - a; + +% Top level initialization, Newton-Cotes weights +w = [3956 23552 -3712 41984 -18160 41984 -3712 23552 3956]/14175; +x = a + (0:8)*(b-a)/8; +y = feval(funfcn,x,varargin{:}); + +yllow = min([min(real(y)) min(imag(y))]); +ylhi = max([max(real(y)) max(imag(y))]); +lims = [min(x) max(x) yllow ylhi]; +ind = find(~isfinite(lims)); +if ~isempty(ind) + [mind,nind] = size(ind); + lims(ind) = 1.e30*(-ones(mind,nind) .^ rem(ind,2)); +end +if trace + axis(lims); +% doesn't take care of complex case + plot([a b],[real(y(1)) real(y(9))],'.'), hold on + if ~isreal(y) + plot([a b],[imag(y(1)) imag(y(9))],'+') + end + drawnow +end +lev = 1; + +% Adaptive, recursive Newton-Cotes 8 panel quadrature +if ~isreal(y) + Q0 = 1e30; +else + Q0 = inf; +end +recur_lev_excess = 0; +[Q,cnt,recur_lev_excess] = quad8stp(funfcn,a,b,tol,lev,w,x,y,Q0,trace,recur_lev_excess,varargin{:}); +cnt = cnt + 9; +if trace + hold off + axis('auto'); +end +if (recur_lev_excess > 1) + warning(sprintf('Recursion level limit reached %d times.', ... + recur_lev_excess )) +end + +%------------------------------------------------------------------ +function [Q,cnt,recur_lev_excess] = quad8stp(FunFcn,a,b,tol,lev,w,x0,f0,Q0,trace,recur_lev_excess,varargin) +%QUAD8STP Recursive function used by QUAD8. +% [Q,cnt] = quad8stp(F,a,b,tol,lev,w,f,Q0) tries to approximate +% the integral of f(x) from a to b to within a relative error of tol. +% F is a string containing the name of f. The remaining arguments are +% generated by quad8 or by the recursion. lev is the recursion level. +% w is the weights in the 8 panel Newton Cotes formula. +% x0 is a vector of 9 equally spaced abscissa is the interval. +% f0 is a vector of the 9 function values at x. +% Q0 is an approximate value of the integral. +% See also QUAD8 and QUAD. + +% Cleve Moler, 5-08-88. + +LEVMAX = 10; + +% Evaluate function at midpoints of left and right half intervals. +x = zeros(1,17); +f = zeros(1,17); +x(1:2:17) = x0; +f(1:2:17) = f0; +x(2:2:16) = (x0(1:8) + x0(2:9))/2; +f(2:2:16) = feval(FunFcn,x(2:2:16),varargin{:}); +if trace + plot(x(2:2:16),f(2:2:16),'.'); + if ~isreal(f) + plot(x(2:2:16),imag(f(2:2:16)),'+'); + end + drawnow +end +cnt = 8; + +% Integrate over half intervals. +h = (b-a)/16; +Q1 = h*w*f(1:9).'; +Q2 = h*w*f(9:17).'; +Q = Q1 + Q2; + +% Recursively refine approximations. +if (abs(Q - Q0) > tol(1)*abs(Q)+tol(2)) & (lev <= LEVMAX) + c = (a+b)/2; + [Q1,cnt1,recur_lev_excess] = quad8stp(FunFcn,a,c,tol/2,lev+1,w,x(1:9),f(1:9),Q1,trace,recur_lev_excess,varargin{:}); + [Q2,cnt2,recur_lev_excess] = quad8stp(FunFcn,c,b,tol/2,lev+1,w,x(9:17),f(9:17),Q2,trace,recur_lev_excess,varargin{:}); + Q = Q1 + Q2; + cnt = cnt + cnt1 + cnt2; +elseif (lev > LEVMAX) + if ~recur_lev_excess + warning('Recursion level limit reached in quad8. Singularity likely.') + recur_lev_excess = 1; + else + recur_lev_excess = recur_lev_excess + 1; + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUADG.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUADG.M" index 0e1057df4b27c30f504395480acc9fe1729b0594..6e567aac147521193fc37dd07909174c4b8963a2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUADG.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/QUADG.M" @@ -1,3 +1,156 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:cf765ff5101649d2ae6be8edebe5028c6c938f1d0bcad6109d8fd89adc7aa80d -size 4707 +function [int, tol1,ix]= quadg(fun,xlow,xhigh,tol,trace,p1,p2,p3,p4,p5,p6,p7,p8,p9) +%GAUSS»ý·Ö·¨ +%Ó÷¨: int = quadg('Fun',xlow,xhigh) +% +% int -- »ý·ÖÖµ +% Fun -- ±»»ýº¯ÊýFun(x) £¨º¯ÊýÃû»ò×Ö·û´®£© +% xlow -- x ÏÂÏÞ +% xhigh -- x ÉÏÏÞ +% +%usage: int = quadg('Fun',xlow,xhigh) +%or +% [int,tol] = quadg('Fun',xlow,xhigh,reltol) +%or +% [int, tol] = quadg('Fun',xlow,xhigh,reltol,trace,p1,p2,....) +% +% reltol=relative tolerance default=1e-3 +% tol = absolute tolerance abs(int-intold) +% +%This function works just like QUAD or QUAD8 but uses a Gaussian quadrature +%integration scheme. Use this routine instead of QUAD or QUAD8: +% +% if higher accuracy is desired (this works best if the function, +% 'Fun', can be approximated by a power series) +% +% if many similar integrations are going to be done +% (I think less function evaluations will typically be done, +% but the integration points and the weights must be calculated. +% These are saved between integrations so when QUADG is called +% again, the points and weights are all ready known.) +% +% if the function evaluations are time consuming. +% +%Note that if there are discontinuities the integral should be broken up into separate +%pieces. And if there are singularities, a more appropriate integration quadrature +%should be used (such as the Gauss-Chebyshev). +% +% modified by Per A. Brodtkorb 17.11.98 : +% -accept multiple integrationlimits +% -optimized by only computing the integrals which did not converge. +% -enabled the integration of directly given functions enclosed in +% parenthesis. Example: integration from 0 to 2 and from 2 to 4 for x is done by: +% +% quadg('(x.^2)',[0 2],[2 4]) +% +global b2 +global w2 + + +if exist('tol')~=1, + tol=1e-3; +elseif isempty(tol), + tol=1e-3; +end +if exist('trace')~=1, + trace=0; +elseif isempty(trace), + trace=0; +else, + trace=1; +end + + +if prod(size(xlow))==1,% make sure the integration limits have correct size + xlow=xlow(ones(size(xhigh)));; +elseif prod(size(xhigh))==1, + xhigh=xhigh(ones(size(xlow)));; +elseif any( size(xhigh)~=size(xlow) ) + error('The input must have equal size!') +end + + +if any(fun=='(') & any(fun=='x'), + exec_string=['y=',fun ';']; %the call function is already setup +else + %setup string to call the function + exec_string=['y=',fun,'(x']; + num_parameters=nargin-5; + for i=1:num_parameters, + %if exist('p1') ~=1, + xvar=['p' int2str(i)]; % variable # i + if eval(['~ischar(' ,xvar,') &all(size(xlow)==size(' xvar,')) & length(',xvar,'(:)) ~=1' ]) , + eval([xvar, '=' ,xvar ,'(:);']); %make sure it is a column + exec_string=[exec_string,',' xvar '(k,ones(1,gn) )']; %enable integration with multiple arguments + else + exec_string=[exec_string,',' xvar]; + end + end + exec_string=[exec_string,');']; +end +[N M]=size(xlow); +%setup mapping parameters +xlow=xlow(:); +jacob=(xhigh(:)-xlow(:))/2; +nk=N*M;%length of jacob +k=1:nk; +%generate the first two sets of integration points and weights +if isempty(b2), + [b2 w2]=grule(2); +end +gn=2; +x=(b2(ones(nk,1),:)+1).*jacob(k,ones(1,gn))+xlow(k,ones(1,gn)); +eval(exec_string); +%size(x),size(y),size(w2) +int_old=sum(w2(ones(nk,1),:).*y,2).*jacob; +int=int_old;tol1=int; +if trace==1, + x_trace=x(:); + y_trace=y(:); +end + + +% Break out of the iteration loop for three reasons: +% 1) the last update is very small (compared to int and compared to tol) +% 2) There are more than 10 iterations. This should NEVER happen. + + +converge='n'; +for i=1:10, + gn=2^(i+1); + gntxt=int2str(gn);% # of weights + eval(['global b',gntxt,' w',gntxt,';']); + if isempty(eval(['b',gntxt])) , % calculate the weights if necessary + eval(['[b',gntxt,',w',gntxt,']=grule(',gntxt,');']); + end + eval(['x=(b',gntxt,'(ones(nk,1),:)+1).*jacob(k,ones(1, gn ))+xlow(k,ones(1,gn ));']); + eval(exec_string); + eval(['int(k)=sum(w',gntxt,'(ones(nk,1),:).*y,2).*jacob(k);']); + + + if trace==1, + x_trace=[x_trace;x(:)]; + y_trace=[y_trace;y(:)]; + end + tol1(k)=abs(int_old(k)-int(k)); %absolute tolerance + k=find(tol1 > abs(tol*int)| tol1 > abs(tol));%indices to integrals which did not converge + + if any(k),% compute integrals again + nk=length(k);%# of integrals we have to compute again + else + converge='y'; + break; + end + int_old=int; +end +int=reshape(int,N,M); % make sure int is the same size as the integration limits +tol1=reshape(tol1,N,M); + + +if converge=='n', + disp('Integral did not converge--singularity likely') +end + + +if trace==1, + plot(x_trace,y_trace,'+') +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/RK4.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/RK4.M" index 5b86f9250dc372deff92d29e15b0a9452a6ffd98..824f1cc07f2877277fe9251e1a349d91cc6e2a4a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/RK4.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\345\276\256\347\247\257\345\210\206\345\222\214\345\276\256\345\210\206\346\226\271\347\250\213/RK4.M" @@ -1,3 +1,52 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5603a8452acabc777ad3aa4d82f7cafc57ee80242c1fad992f7b4b6249fd2fb4 -size 1724 +function [tout, yout] = rk4(ypfun, tspan, y0, h) +%¶¨²½³¤ËĽ×Runge-Kutta·¨Çó³£Î¢·Ö·½³ÌÊýÖµ½â +%[tout,yout] = rk4('ypfun', tspan, y0,h) +% ÕâÀï×Ö·û´®ypfunÊÇÓÃÒÔ±íʾf(t, y)µÄMÎļþÃû, +% tspan=[t0, tfinal]±íʾ×Ô±äÁ¿³õÖµt0ºÍÖÕÖµtf +% y0±íʾ³õÖµÏòÁ¿y0£¬hÊDz½³¤¡£ +% Êä³öÁÐÏòÁ¿tout±íʾ½Úµã (t0 , t1 , ¡­ , tn)' +% Êä³ö¾ØÕóyout ±íʾÊýÖµ½â£¬Ã¿Ò»ÁжÔÓ¦yµÄÒ»¸ö·ÖÁ¿ +%Àý ½â΢·Ö·½³Ì +% y' = y-2t/y, y(0)=1, 0=0 +% x+2*y+2*z<=72 +% 10<=y<=20 +% x-y=10 +% ÏÈ»¯Îª +% min -x(1)*x(2)*x(3) +% x(1)-x(2)-10=0 +% x(1)-x(2)-2*x(3)<=0 +% x(1)+2*x(2)+2*x(3)-72<=0 +% 10<=x(2)<=20 +% дMº¯Êýoptfun2.m +% function [f,g]=optfun2(x) +% f=-x(1)*x(2)*x(3) +% g(1)=x(1)-x(2)-10; +% g(2)=x(1)-x(2)-2*x(3); +% g(3)=x(1)+2*x(2)+2*x(3)-72 +% Çó½â +% x0=[10,10,10]; +% options(13)=1; +% [x,options]=constr('fun',x0,options,[-inf,10,-inf]',[inf,20,inf]); +% x,-options(8) +% +%CONSTR Finds the constrained minimum of a function of several variables. +% CONSTR has been replaced with FMINCON. CONSTR currently works but +% will be removed in the future. Use FMINCON instead. +% +% X=CONSTR('FUN',X0) starts at X0 and finds a constrained minimum to +% the function which is described in FUN (usually an M-file: FUN.M). +% The function 'FUN' should return two arguments: a scalar value of the +% function to be minimized, F, and a matrix of constraints, G: +% [F,G]=FUN(X). F is minimized such that G <= zeros(size(G)). +% +% X=CONSTR('FUN',X,OPTIONS) allows a vector of optional parameters to +% be defined. For more information type HELP FOPTIONS. +% +% X=CONSTR('FUN',X,OPTIONS,VLB,VUB) defines a set of lower and upper +% bounds on the design variables, X, so that the solution is always in +% the range VLB <= X <= VUB. +% +% X=CONSTR('FUN',X,OPTIONS,VLB,VUB,'GRADFUN') allows a function +% 'GRADFUN' to be entered which returns the partial derivatives of the +% function and the constraints at X: [gf,GC] = GRADFUN(X). +% Use OPTIONS(9)=1 to check analytic gradients in GRADFUN against +% numeric gradients during the first iteration. +% +% X=CONSTR('FUN',X,OPTIONS,VLB,VUB,'GRADFUN',P1,P2,...) passes the +% problem-dependent parameters P1,P2,... directly to the functions FUN +% and GRADFUN: FUN(X,P1,P2,...) and GRADFUN(X,P1,P2,...). Pass +% empty matrices for OPTIONS, VLB, VUB, and 'GRADFUN' to use the +% default values. +% +% [X,OPTIONS]=CONSTR('FUN',X0,...) returns the parameters used in the +% optimization method. For example, OPTIONS(10) contains the number +% of function evaluations used. +% +% [X,OPTIONS,LAMBDA]=CONSTR('FUN',X0,...) returns the Lagrange multipliers +% at the solution X in the vector LAMBDA. +% +% [X,OPTIONS,LAMBDA,HESS]=CONSTR('FUN',X0,...) returns the quasi-Newton +% approximation to the Hessian matrix at the solution X. +% +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.45 $ $Date: 1998/08/31 22:29:17 $ + +% +% X=CONSTR('FUN',X,OPTIONS,VLB,VUB,GRADFUN,P1,P2,..) allows +% extra parameters, P1, P2, ... to be passed directly to FUN: +% [F,G]=FUN(X,P1,P2,...). Empty arguments ([]) are ignored. + + +if nargin < 2, error('constr requires two input arguments'); end +if nargin < 3, OPTIONS=[]; end +if nargin < 4, VLB=[]; end +if nargin < 5, VUB=[]; end +if nargin < 6, GRADFUN=[]; end + +caller='constr'; +lenVarIn = length(varargin); + +% Convert to inline function as needed. +gradflag = 0; +[funfcn,msg] = prefcnchk(FUN,caller,lenVarIn,gradflag); +if ~isempty(msg) + error(msg); +end + +if ~isempty(GRADFUN) + gradflag = 1; + [gradfcn,msg] = prefcnchk(GRADFUN,caller,lenVarIn,gradflag); + if ~isempty(msg) + error(msg); + end +else + gradfcn = []; +end + +[x,OPTIONS,lambda,HESS]=nlconstold(funfcn,x,OPTIONS,VLB,VUB,gradfcn,varargin{:}); + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMIN.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMIN.M" index 164196b64f46c25c050cd3ca5078fb46e2eea40c..9ea16c0347b1203eb2f346440bd5667aa97848fd 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMIN.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMIN.M" @@ -1,3 +1,166 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d384a65bc7f2638b3202c92ddab5eee0a317afa8d3085e32c989232581c0702f -size 5234 +function [xf,options] = fmin(funfcn,ax,bx,options,varargin) +%x=fmin('fun',a,b) ÇóÒ»Ôªº¯Êýy=f(x)ÔÚ[a,b]Äڵľֲ¿¼«Ð¡Öµµã¡£ +% ÕâÀïfun ¿ÉÖ±½ÓÓÃ×Ö·û´®±íʾ£¬Ò²¿ÉÒÔÊÇmº¯ÊýÃû¡£ +%x=fmin('fun',a,b,options)ÊäÈëoptionsÊÇÓÅ»¯ÖÐËã·¨²ÎÊýÏòÁ¿ÉèÖÃ, +% ÓÃhelp foptions¿É¿´µ½¸÷·ÖÁ¿µÄº¬Òå¡£ +%x=fmin('fun',a,b,options,p1,p2,¡­) p1,p2,..ÊDZíʾfunµÄMº¯ÊýÖеIJÎÊý¡£ +%[x,options]=fmin('fun',a,b,¡­)Êä³öoptionsÏÔʾËã·¨²ÎÊý¡£ +%ÀýÌâ Çóf(x)=x^3-x-1ÔÚ[-1,1]Äڵļ«´óÖµµã¡£ +% ÏÈдMº¯Êýoptfun.m +% function f=optfun(x) +% f=-(x.^3-x-1); +% Çó½â +% clear; +% [x,options]=fmin('optfun',-1,1); +% x,-options(8) + +%FMIN Minimize function of one variable. +% X = FMIN('F',x1,x2) attempts to return a value of x which is a local +% minimizer of F(x) in the interval x1 < x < x2. 'F' is a string +% containing the name of the objective function to be minimized. +% +% X = FMIN('F',x1,x2,OPTIONS) uses a vector of control parameters. +% If OPTIONS(1) is positive, intermediate steps in the solution are +% displayed; the default is OPTIONS(1) = 0. OPTIONS(2) is the termination +% tolerance for x; the default is 1.e-4. OPTIONS(14) is the maximum +% number of function evaluations; the default is OPTIONS(14) = 500. +% The other components of OPTIONS are not used as input control +% parameters by FMIN. For more information, see FOPTIONS. +% +% X = FMIN('F',x1,x2,OPTIONS,P1,P2,...) provides for additional +% arguments which are passed to the objective function, F(X,P1,P2,...) +% +% [X,OPTIONS] = FMIN(...) returns a count of the number of steps +% taken in OPTIONS(10). +% +% Examples +% fmin('cos',3,4) computes pi to a few decimal places. +% fmin('cos',3,4,[1,1.e-12]) displays the steps taken +% to compute pi to about 12 decimal places. +% +% See also FMINS. + +% Reference: "Computer Methods for Mathematical Computations", +% Forsythe, Malcolm, and Moler, Prentice-Hall, 1976. + +% Original coding by Duane Hanselman, University of Maine. +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.14 $ $Date: 1997/11/21 23:30:43 $ + +% initialization +if nargin<4, options = []; end +options = foptions(options); +print = options(1); +tol = options(2); +if (~options(14)) + options(14) = 500; + end +if nargin < 3 + error('fmin requires three input arguments.') +end + +header = ' Func evals x f(x) Procedure'; +step=' initial'; + +% Convert to inline function as needed. +funfcn = fcnchk(funfcn,length(varargin)); + +num = 1; +seps = sqrt(eps); +c = 0.5*(3.0 - sqrt(5.0)); +a = ax; b = bx; +v = a + c*(b-a); +w = v; xf = v; +d = 0.0; e = 0.0; +x= xf; fx = feval(funfcn,x,varargin{:}); +fmin_data = [ 1 xf fx ]; +if print > 0 + disp(header) + disp([sprintf('%5.0f %12.6g %12.6g ',fmin_data), step]) +end +fv = fx; fw = fx; +xm = 0.5*(a+b); +tol1 = seps*abs(xf) + tol/3.0; tol2 = 2.0*tol1; + +% Main loop + +options(10) = 0; +while ( abs(xf-xm) > (tol2 - 0.5*(b-a)) ) + + num = num+1; + gs = 1; + + % Is a parabolic fit possible + if abs(e) > tol1 + % Yes, so fit parabola + gs = 0; + r = (xf-w)*(fx-fv); + q = (xf-v)*(fx-fw); + p = (xf-v)*q-(xf-w)*r; + q = 2.0*(q-r); + if q > 0.0, p = -p; end + q = abs(q); + r = e; e = d; + + % Is the parabola acceptable + if ( (abs(p)q*(a-xf)) & (p= xm, e = a-xf; else, e = b-xf; end + d = c*e; + step = ' golden'; + end + + % The function must not be evaluated too close to xf + si = sign(d) + (d == 0); + x = xf + si * max( abs(d), tol1 ); + fu = feval(funfcn,x,varargin{:}); + fmin_data = [num x fu]; + if print > 0 + disp([sprintf('%5.0f %12.6g %12.6g ',fmin_data), step]) + end + + % Update a, b, v, w, x, xm, tol1, tol2 + if fu <= fx + if x >= xf, a = xf; else, b = xf; end + v = w; fv = fw; + w = xf; fw = fx; + xf = x; fx = fu; + else % fu > fx + if x < xf, a = x; else,b = x; end + if ( (fu <= fw) | (w == xf) ) + v = w; fv = fw; + w = x; fw = fu; + elseif ( (fu <= fv) | (v == xf) | (v == w) ) + v = x; fv = fu; + end + end + xm = 0.5*(a+b); + tol1 = seps*abs(xf) + tol/3.0; tol2 = 2.0*tol1; + if num > options(14) + if options(1) >= 0 + disp('Warning: Maximum number of function evaluations has been'); + disp(' exceeded - increase options(14).') + options(10)=num; + return + end + end +end +options(8) = feval(funfcn,x,varargin{:}); +options(10)=num; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINCON.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINCON.M" index 783dee0767c3ab1d2336c60bbabafbc23ae599e5..53c1c3861f2606da3982155c7702b1aaaa38a5e7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINCON.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINCON.M" @@ -1,3 +1,723 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:89c5206d774118d0f32a8d586ed3df210ef44b3b4f34272ae53a54230498cccd -size 25676 +function [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = fmincon(FUN,X,A,B,Aeq,Beq,LB,UB,NONLCON,options,varargin) +%Çó½âÏÂÁÐÐÎʽ·ÇÏßÐԹ滮ÎÊÌ⣺ +% min f(x) s.t. Ax<= b, Aeqx=beq, +% c(x)<=0, ceq(x) = 0, lb<=x<=ub +%µ÷ÓøñʽΪ£º +% x=fmincon(fun, ³õÖµ,A,b,Aeq,beq,lb,ub,nonlcon) +% ´Ëʱµ±Ô¼ÊøÌõ¼þÖÐȱAºÍb¡¢AeqºÍbeq»òlbºÍubʱ£¬ +% Ïà¹ØÏî¿ÉÓÃ[ ]´úÌæÒÔ±íʾʡÂÔ¡£ +% funд³ÉÈçϵÄM-º¯ÊýÐÎʽ (fun.m) £º +% function f = fun (x) +% f = f(x); +% ·ÇÏßÐÔÔ¼ÊøÌõ¼þд³ÉÈçϵÄM-º¯ÊýÐÎʽ (nonlcon.m) £º +% function [c,ceq]=nonlcon(x) +% c = c(x);ceq=ceq(x); +% ×¢Ò⣺·½³Ì±äÁ¿±ØÐëÆ´³ÉÒ»¸öÏòÁ¿±äÁ¿£¬¼´ÓÃx(1),x(2),... +% +%ÀýÌâ +% max x*y*z +% -x+x*y+2*z>=0 +% x+2*y+2*z<=72 +% 10<=y<=20 +% x-y=10 +% ÏÈ»¯Îª +% min -x(1)*x(2)*x(3) +% x(1)+2*x(2)+2*x(3)<=72 +% x(1)-x(2)=10 +% x(1)-x(1)*x(2)-2*x(3)<=0 +% 10<=x(2)<=20 +% дMº¯Êý fconfun.m +% function f=fconfun(x) +% f=-x(1)*x(2)*x(3) +% ÔÙдMº¯Êý fconfun2.m +% function [g,geq]=fconfun2(x) +% g=x(1)-x(1)*x(2)-2*x(3); +% geq=0; +% Çó½â +% x0=[10,10,10]; +% A=[1 2 2];b=72; +% Aeq=[1 -1 0];beq=10; +% [x,f]=fmincon('fconfun',x0,A,b,Aeq,beq,[-inf,10,-inf]',[inf,20,inf],'fconfun2') +% +%FMINCON Finds the constrained minimum of a function of several variables. +% FMINCON solves problems of the form: +% min F(X) subject to: A*X <= B, Aeq*X = Beq (linear constraints) +% X C(X) <= 0, Ceq(X) = 0 (nonlinear constraints) +% LB <= X <= UB +% +% X=FMINCON(FUN,X0,A,B) starts at X0 and finds a minimum X to the function +% described in FUN, subject to the linear inequalities A*X <= B. X0 may be a +% scalar, vector or matrix. The function FUN (usually an M-file or inline object) +% should return a scalar function value F evaluated at X when called with +% feval: F=feval(FUN,X). +% +% X=FMINCON(FUN,X0,A,B,Aeq,Beq) minimizes FUN subject to the linear equalities +% Aeq*X = Beq as well as A*X <= B. (Set A=[] and B=[] if no inequalities exist.) +% +% X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB) defines a set of lower and upper +% bounds on the design variables, X, so that the solution is in +% the range LB <= X <= UB. Use empty matrices for LB and UB +% if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below; +% set UB(i) = Inf if X(i) is unbounded above. +% +% X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON) subjects the minimization to the +% constraints defined in NONLCON. The function NONLCON should return the vectors +% C and Ceq, representing the nonlinear inequalities and equalities respectively, +% when called with feval: [C, Ceq] = feval(NONLCON,X). FMINCON minimizes +% FUN such that C(X)<=0 and Ceq(X)=0. (Set LB=[] and/or UB=[] if no bounds exist.) +% +% X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS) minimizes with the +% default optimization parameters replaced by values in the structure OPTIONS, +% an argument created with the OPTIMSET function. See OPTIMSET for details. Used +% options are Display, TolX, TolFun, TolCon, DerivativeCheck, Diagnostics, GradObj, +% GradConstr, Hessian, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, +% LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX, HessPattern. +% Use the GradObj option to specify that FUN may be called with two output +% arguments where the second, G, is the partial derivatives of the +% function df/dX, at the point X: [F,G] = feval(FUN,X). Use the GradConstr +% option to specify that NONLCON may be called with four output arguments: +% [C,Ceq,GC,GCeq] = feval(NONLCON,X) where GC is the partial derivatives of the +% constraint vector of inequalities C an GCeq is the partial derivatives of the +% constraint vector of equalities Ceq. Use OPTIONS = [] as a place holder if +% no options are set. +% +% X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS,P1,P2,...) passes the +% problem-dependent parameters P1,P2,... directly to the functions FUN +% and NONLCON: feval(FUN,X,P1,P2,...) and feval(NONLCON,X,P1,P2,...). Pass +% empty matrices for A, B, Aeq, Beq, OPTIONS, LB, UB, and NONLCON to use the +% default values. +% +% [X,FVAL]=FMINCON(FUN,X0,...) returns the value of the objective +% function FUN at the solution X. +% +% [X,FVAL,EXITFLAG]=FMINCON(FUN,X0,...) returns a string EXITFLAG that +% describes the exit condition of FMINCON. +% If EXITFLAG is: +% > 0 then FMINCON converged to a solution X. +% 0 then the maximum number of function evaluations was reached. +% < 0 then FMINCON did not converge to a solution. +% +% [X,FVAL,EXITFLAG,OUTPUT]=FMINCON(FUN,X0,...) returns a structure +% OUTPUT with the number of iterations taken in OUTPUT.iterations, the number +% of function evaluations in OUTPUT.funcCount, the algorithm used in +% OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, +% and the first-order optimality (if used) in OUTPUT.firstorderopt. +% +% [X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=FMINCON(FUN,X0,...) returns the Lagrange multipliers +% at the solution X: LAMBDA.lower for LB, LAMBDA.upper for UB, LAMBDA.ineqlin is +% for the linear inequalities, LAMBDA.eqlin is for the linear equalities, +% LAMBDA.ineqnonlin is for the nonlinear inequalities, and LAMBDA.eqnonlin +% is for the nonlinear equalities. +% +% [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD]=FMINCON(FUN,X0,...) returns the value of +% the gradient of FUN at the solution X. +% +% [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN]=FMINCON(FUN,X0,...) returns the +% value of the HESSIAN of FUN at the solution X. +% +% See also OPTIMSET, FMINUNC, FMINBND, FMINSEARCH. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.19 $ $Date: 1998/10/22 20:11:07 $ + +defaultopt = optimset('display','final','LargeScale','on', ... + 'TolX',1e-6,'TolFun',1e-6,'TolCon',1e-6,'DerivativeCheck','off',... + 'Diagnostics','off',... + 'GradObj','off','GradConstr','off','Hessian','off','MaxFunEvals','100*numberOfVariables',... + 'DiffMaxChange',1e-1,'DiffMinChange',1e-8,... + 'PrecondBandWidth',0,'TypicalX','ones(numberOfVariables,1)','MaxPCGIter','max(1,floor(numberOfVariables/2))', ... + 'TolPCG',0.1,'MaxIter',400,'HessPattern',[]); +% If just 'defaults' passed in, return the default options in X +if nargin==1 & nargout <= 1 & isequal(FUN,'defaults') + X = defaultopt; + return +end + +large = 'large-scale'; +medium = 'medium-scale'; + +if nargin < 4, error('FMINCON requires at least four input arguments'); end +if nargin < 10, options=[]; + if nargin < 9, NONLCON=[]; + if nargin < 8, UB = []; + if nargin < 7, LB = []; + if nargin < 6, Beq=[]; + if nargin < 5, Aeq =[]; + end, end, end, end, end, end +if isempty(NONLCON) & isempty(A) & isempty(Aeq) & isempty(UB) & isempty(LB) + error('FMINCON is for constrained problems. Use FMINUNC for unconstrained problems.') +end + +if nargout > 4 + computeLambda = 1; +else + computeLambda = 0; +end + +caller='constr'; +lenVarIn = length(varargin); +XOUT=X(:); +numberOfVariables=length(XOUT); + +options = optimset(defaultopt,options); +switch optimget(options,'display') +case {'off','none'} + verbosity = 0; +case 'iter' + verbosity = 2; +case 'final' + verbosity = 1; +otherwise + verbosity = 1; +end + +% Set to column vectors +B = B(:); +Beq = Beq(:); + +[XOUT,l,u,msg] = checkbounds(XOUT,LB,UB,numberOfVariables); +if ~isempty(msg) + EXITFLAG = -1; + [FVAL,OUTPUT,LAMBDA,GRAD,HESSIAN] = deal([]); + X(:)=XOUT; + if verbosity > 0 + disp(msg) + end + return +end +lFinite = l(~isinf(l)); +uFinite = u(~isinf(u)); + + +meritFunctionType = 0; + +diagnostics = isequal(optimget(options,'diagnostics','off'),'on'); +gradflag = strcmp(optimget(options,'GradObj'),'on'); +hessflag = strcmp(optimget(options,'Hessian'),'on'); +if isempty(NONLCON) + constflag = 0; +else + constflag = 1; +end +gradconstflag = strcmp(optimget(options,'GradConstr'),'on'); +line_search = strcmp(optimget(options,'largescale','off'),'off'); % 0 means trust-region, 1 means line-search + +% Convert to inline function as needed +if ~isempty(FUN) % will detect empty string, empty matrix, empty cell array + [funfcn, msg] = fprefcnchk(FUN,'fmincon',length(varargin),gradflag,hessflag); +else + errmsg = sprintf('%s\n%s', ... + 'FUN must be a function name, valid string expression, or inline object;', ... + ' or, FUN may be a cell array that contains these type of objects.'); + error(errmsg) +end + +if constflag % NONLCON is non-empty + [confcn, msg] = fprefcnchk(NONLCON,'fmincon',length(varargin),gradconstflag,[],1); +else + confcn{1} = ''; +end + +[rowAeq,colAeq]=size(Aeq); +% if only l and u then call sfminbx +if ~line_search & isempty(NONLCON) & isempty(A) & isempty(Aeq) & gradflag + OUTPUT.algorithm = large; + % if only Aeq beq and Aeq has as many columns as rows, then call sfminle +elseif ~line_search & isempty(NONLCON) & isempty(A) & isempty(lFinite) & isempty(uFinite) & gradflag ... + & colAeq >= rowAeq + OUTPUT.algorithm = large; +elseif ~line_search + warning(['Trust region method does not currently solve this type of problem,',... + sprintf('\n'), 'switching to line search.']) + if isequal(funfcn{1},'fungradhess') + funfcn{1}='fungrad'; + warning('Hessian provided by user will be ignored in line search algorithm') + + elseif isequal(funfcn{1},'fun_then_grad_then_hess') + funfcn{1}='fun_then_grad'; + warning('Hessian provided by user will be ignored in line search algorithm') + end + hessflag = 0; + OUTPUT.algorithm = medium; +elseif line_search + OUTPUT.algorithm = medium; + if issparse(Aeq) | issparse(A) + warning('can not do sparse with line_search, converting to full') + end + + % else call nlconst +else + error('Unrecognized combination of OPTIONS flags and calling sequence.') +end + + +lenvlb=length(l); +lenvub=length(u); + +if isequal(OUTPUT.algorithm,medium) + CHG = 1e-7*abs(XOUT)+1e-7*ones(numberOfVariables,1); + i=1:lenvlb; + lindex = XOUT(i)u(i); + if any(uindex) + XOUT(uindex)=u(uindex); + CHG(uindex)=-CHG(uindex); + end + X(:) = XOUT; +else + arg = (u >= 1e10); arg2 = (l <= -1e10); + u(arg) = inf*ones(length(arg(arg>0)),1); + l(arg2) = -inf*ones(length(arg2(arg2>0)),1); + if min(min(u-XOUT),min(XOUT-l)) < 0, + XOUT = startx(u,l); + X(:) = XOUT; + end +end + +% Evaluate function +GRAD=zeros(numberOfVariables,1); +HESS = []; + +switch funfcn{1} +case 'fun' + try + f = feval(funfcn{3},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +case 'fungrad' + try + [f,GRAD(:)] = feval(funfcn{3},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +case 'fungradhess' + try + [f,GRAD(:),HESS] = feval(funfcn{3},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +case 'fun_then_grad' + try + f = feval(funfcn{3},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end + try + GRAD(:) = feval(funfcn{4},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective gradient function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +case 'fun_then_grad_then_hess' + try + f = feval(funfcn{3},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end + try + GRAD(:) = feval(funfcn{4},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective gradient function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end + try + HESS = feval(funfcn{5},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied objective Hessian function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +otherwise + error('Undefined calltype in FMINCON'); +end + +% Evaluate constraints +switch confcn{1} +case 'fun' + try + [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:}); + c = ctmp(:); ceq = ceqtmp(:); + cGRAD = zeros(numberOfVariables,length(c)); + ceqGRAD = zeros(numberOfVariables,length(ceq)); + catch + if findstr(xlate('Too many output arguments'),lasterr) + if isa(confcn{3},'inline') + errmsg = sprintf('%s%s%s\n%s\n%s\n%s', ... + 'The inline function ',formula(confcn{3}),' representing the constraints',... + ' must return two outputs: the nonlinear inequality constraints and', ... + ' the nonlinear equality constraints. At this time, inline objects may',... + ' only return one output argument: use an M-file function instead.'); + else + errmsg = sprintf('%s%s%s\n%s%s', ... + 'The constraint function ',confcn{3},' must return two outputs:',... + ' the nonlinear inequality constraints and', ... + ' the nonlinear equality constraints.'); + end + error(errmsg) + else + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied nonlinear constraint function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end + end + +case 'fungrad' + try + [ctmp,ceqtmp,cGRAD,ceqGRAD] = feval(confcn{3},X,varargin{:}); + c = ctmp(:); ceq = ceqtmp(:); + catch + errmsg = sprintf('%s\n%s\n\n%s',... + 'FMINCON cannot continue because user supplied nonlinear constraint function', ... + ' failed with the following error:', lasterr); + error(errmsg); + end +case 'fun_then_grad' + try + [ctmp,ceqtmp] = feval(confcn{3},X,varargin{:}); + c = ctmp(:); ceq = ceqtmp(:); + [cGRAD,ceqGRAD] = feval(confcn{4},X,varargin{:}); + catch + errmsg = sprintf('%s\n%s%s\n\n%s',... + 'FMINCON cannot continue because user supplied nonlinear constraint function', ... + 'or nonlinear constraint gradient function',... + ' failed with the following error:', lasterr); + error(errmsg); + end +case '' + c=[]; ceq =[]; + cGRAD = zeros(numberOfVariables,length(c)); + ceqGRAD = zeros(numberOfVariables,length(ceq)); +otherwise + error('Undefined calltype in FMINCON'); +end + +non_eq = length(ceq); +non_ineq = length(c); +[lin_eq,Aeqcol] = size(Aeq); +[lin_ineq,Acol] = size(A); +[cgrow, cgcol]= size(cGRAD); +[ceqgrow, ceqgcol]= size(ceqGRAD); + +eq = non_eq + lin_eq; +ineq = non_ineq + lin_ineq; + +if ~isempty(Aeq) & Aeqcol ~= numberOfVariables + error('Aeq has the wrong number of columns.') +end +if ~isempty(A) & Acol ~= numberOfVariables + error('A has the wrong number of columns.') +end +if cgrow~=numberOfVariables & cgcol~=non_ineq + error('Gradient of the nonlinear inequality constraints is the wrong size.') +end +if ceqgrow~=numberOfVariables & ceqgcol~=non_eq + error('Gradient of the nonlinear equality constraints is the wrong size.') +end + +if diagnostics > 0 + % Do diagnostics on information so far + msg = diagnose('fmincon',OUTPUT,gradflag,hessflag,constflag,gradconstflag,... + line_search,options,XOUT,non_eq,... + non_ineq,lin_eq,lin_ineq,l,u,funfcn,confcn,f,GRAD,HESS,c,ceq,cGRAD,ceqGRAD); +end + + +% call algorithm +if isequal(OUTPUT.algorithm,medium) + [X,FVAL,lambda,EXITFLAG,OUTPUT,GRAD,HESSIAN]=... + nlconst(funfcn,X,l,u,full(A),B,full(Aeq),Beq,confcn,options, ... + verbosity,gradflag,gradconstflag,hessflag,meritFunctionType,... + CHG,f,GRAD,HESS,c,ceq,cGRAD,ceqGRAD,varargin{:}); + LAMBDA=lambda; + + +else + if (isequal(funfcn{1}, 'fun_then_grad_then_hess') | isequal(funfcn{1}, 'fungradhess')) + Hstr=[]; + elseif (isequal(funfcn{1}, 'fun_then_grad') | isequal(funfcn{1}, 'fungrad')) + n = length(XOUT); + Hstr = optimget(options,'HessPattern',[]); + if isempty(Hstr) + % Put this code separate as it might generate OUT OF MEMORY error + Hstr = sparse(ones(n)); + end + if ischar(Hstr) + Hstr = eval(Hstr); + end + end + + if isempty(Aeq) + [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] = ... + sfminbx(funfcn,X,l,u,verbosity,options,computeLambda,f,GRAD,HESS,Hstr,varargin{:}); + else + [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN] = ... + sfminle(funfcn,X,sparse(Aeq),Beq,verbosity,options,computeLambda,f,GRAD,HESS,Hstr,varargin{:}); + end +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +function [allfcns,msg] = fprefcnchk(funstr,caller,lenVarIn,gradflag,hessflag,constrflag) +%PREFCNCHK Pre- and post-process function expression for FUNCHK. +% [ALLFCNS,MSG] = PREFUNCHK(FUNSTR,CALLER,lenVarIn,GRADFLAG) takes +% the (nonempty) expression FUNSTR from CALLER with LenVarIn extra arguments, +% parses it according to what CALLER is, then returns a string or inline +% object in ALLFCNS. If an error occurs, this message is put in MSG. +% +% ALLFCNS is a cell array: +% ALLFCNS{1} contains a flag +% that says if the objective and gradients are together in one function +% (calltype=='fungrad') or in two functions (calltype='fun_then_grad') +% or there is no gradient (calltype=='fun'), etc. +% ALLFCNS{2} contains the string CALLER. +% ALLFCNS{3} contains the objective (or constraint) function +% ALLFCNS{4} contains the gradient function +% ALLFCNS{5} contains the hessian function (not used for constraint function). +% +% NOTE: we assume FUNSTR is nonempty. +% Initialize +if nargin < 6 + constrflag = 0; +end +if constrflag + graderrmsg = 'Constraint gradient function expected (OPTIONS.GradConstr==''on'') but not found.'; + warnstr = ... + sprintf('%s\n%s\n%s\n','Constraint gradient function provided but OPTIONS.GradConstr==''off'';', ... + ' ignoring constraint gradient function and using finite-differencing.', ... + ' Rerun with OPTIONS.GradConstr==''on'' to use constraint gradient function.'); +else + graderrmsg = 'Gradient function expected OPTIONS.GradObj==''on'' but not found.'; + warnstr = ... + sprintf('%s\n%s\n%s\n','Gradient function provided but OPTIONS.GradObj==''off'';', ... + ' ignoring gradient function and using finite-differencing.', ... + ' Rerun with OPTIONS.GradObj==''on'' to use gradient function.'); + +end +msg=''; +allfcns = {}; +funfcn = []; +gradfcn = []; +hessfcn = []; +if gradflag & hessflag + calltype = 'fungradhess'; +elseif gradflag + calltype = 'fungrad'; +else + calltype = 'fun'; +end + +% {fun} +if isa(funstr, 'cell') & length(funstr)==1 + % take the cellarray apart: we know it is nonempty + if gradflag + error(graderrmsg) + end + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + + % {fun,[]} +elseif isa(funstr, 'cell') & length(funstr)==2 & isempty(funstr{2}) + if gradflag + error(graderrmsg) + end + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + + % {fun, grad} +elseif isa(funstr, 'cell') & length(funstr)==2 % and ~isempty(funstr{2}) + + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + error(msg); + end + [gradfcn, msg] = fcnchk(funstr{2},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + calltype = 'fun_then_grad'; + if ~gradflag + warning(warnstr); + calltype = 'fun'; + end + + + % {fun, [], []} +elseif isa(funstr, 'cell') & length(funstr)==3 ... + & ~isempty(funstr{1}) & isempty(funstr{2}) & isempty(funstr{3}) + if gradflag + error(graderrmsg) + end + if hessflag + error('Hessian function expected but not found.') + end + + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + + % {fun, grad, hess} +elseif isa(funstr, 'cell') & length(funstr)==3 ... + & ~isempty(funstr{2}) & ~isempty(funstr{3}) + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + [gradfcn, msg] = fcnchk(funstr{2},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + [hessfcn, msg] = fcnchk(funstr{3},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + calltype = 'fun_then_grad_then_hess'; + if ~hessflag & ~gradflag + hwarnstr = sprintf('%s\n%s\n%s\n','Hessian and gradient functions provided ', ... + ' but OPTIONS.Hessian==''off'' and OPTIONS.GradObj==''off''; ignoring Hessian and gradient functions.', ... + ' Rerun with OPTIONS.Hessian==''on'' and OPTIONS.GradObj==''on'' to use derivative functions.'); + warning(hwarnstr) + calltype = 'fun'; + elseif hessflag & ~gradflag + warnstr = ... + sprintf('%s\n%s\n%s\n','Hessian and gradient functions provided ', ... + ' but OPTIONS.GradObj==''off''; ignoring Hessian and gradient functions.', ... + ' Rerun with OPTIONS.Hessian==''on'' and OPTIONS.GradObj==''on'' to use derivative functions.'); + warning(warnstr) + calltype = 'fun'; + elseif ~hessflag & gradflag + hwarnstr = ... + sprintf('%s\n%s\n%s\n','Hessian function provided but OPTIONS.Hessian==''off'';', ... + ' ignoring Hessian function,', ... + ' Rerun with OPTIONS.Hessian==''on'' to use Hessian function.'); + warning(hwarnstr); + calltype = 'fun_then_grad'; + end + + % {fun, grad, []} +elseif isa(funstr, 'cell') & length(funstr)==3 ... + & ~isempty(funstr{2}) & isempty(funstr{3}) + if hessflag + error('Hessian function expected but not found.') + end + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + [gradfcn, msg] = fcnchk(funstr{2},lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + calltype = 'fun_then_grad'; + if ~gradflag + warning(warnstr); + calltype = 'fun'; + end + + % {fun, [], hess} +elseif isa(funstr, 'cell') & length(funstr)==3 ... + & isempty(funstr{2}) & ~isempty(funstr{3}) + error('Hessian function given without gradient function.') + +elseif ~isa(funstr, 'cell') %Not a cell; is a string expression, function name string or inline object + [funfcn, msg] = fcnchk(funstr,lenVarIn); + if ~isempty(msg) + if constrflag + msg = ['NONLCON must be a function name.']; + end + + error(msg); + end + if gradflag % gradient and function in one function/M-file + gradfcn = funfcn; % Do this so graderr will print the correct name + end + if hessflag & ~gradflag + hwarnstr = ... + sprintf('%s\n%s\n%s\n','OPTIONS.Hessian==''on'' ', ... + ' but OPTIONS.GradObj==''off''; ignoring Hessian and gradient functions.', ... + ' Rerun with OPTIONS.Hessian==''on'' and OPTIONS.GradObj==''on'' to use derivative functions.'); + warning(hwarnstr) + end + +else + errmsg = sprintf('%s\n%s', ... + 'FUN must be a function name or inline object;', ... + ' or, FUN may be a cell array that contains these type of objects.'); + error(errmsg) +end + +allfcns{1} = calltype; +allfcns{2} = caller; +allfcns{3} = funfcn; +allfcns{4} = gradfcn; +allfcns{5} = hessfcn; + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINS.M" index e2d22441e419ea4d2c57a952ff279c5668cb65f8..d07759ec1d60122f6a2dc006b60cc9519140f2fc 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINS.M" @@ -1,3 +1,226 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:750d711cadbd77fa38429a7bd507ba49b21b78b4c7547a380ca2f56eabfb6dd5 -size 7127 +function [x, options] = fmins(funfcn,x,options,grad,varargin) +%¶àÔªº¯Êý¼«ÖµËü²ÉÓõ¥´¿ÐÔËÑË÷·¨£¬ÊÊÓÃÓڷǹ⻬º¯ÊýÓÅ»¯¡£ +%x=fmins('fun',x0)Å£¶Ù·¨Çó¶àÔªº¯Êýy=f(x)ÔÚx0³ö·¢µÄ¾Ö²¿¼«Ð¡Öµµã£ +% ÕâÀï x,x0¾ùΪÏòÁ¿¡£ +%x=fmins('fun',x0,options)ÊäÈëoptionsÊÇÓÅ»¯ÖÐËã·¨²ÎÊýÏòÁ¿ÉèÖÃ, +% ÓÃhelp foptions¿É¿´µ½¸÷·ÖÁ¿µÄº¬Òå¡£ +%x=fmins('fun',x0,options,'grad') grad¸ø¶¨f(x)µÄÌݶȺ¯Êý±í´ïʽ¼Ó¿ì¼ÆËãËٶȡ£ +%x=fmins('fun',x0,options,'grad',p1,p2¡­)p1,p2,..ÊDZíʾfunµÄMº¯ÊýÖеIJÎÊý¡£ +% ×¢Ò⣺·½³Ì±äÁ¿±ØÐëÆ´³ÉÒ»¸öÏòÁ¿±äÁ¿£¬¼´ÓÃx(1),x(2),... +% +%ÀýÌâ Çóf(x)=100(y-x^2)^2+(1-x)^2ÔÚ[-1.2,1]¸½½üµÄ¼«Ð¡Öµ¡£ +% ÏÈдMº¯Êýoptfun1.m +% function f=optfun1(x) +% f=100*(x(2)-x(1).^2).^2+(1-x(1)).^2 +% Çó½â +% clear; +% x=[-1.2,1]; +% [x,options]=fmins('optfun1',x,options); +% x,options(8) +% +%FMINS Minimize function of several variables. +% X = FMINS('F',X0) attempts to return a vector X which is a local +% minimizer of F(x) near the starting vector X0. 'F' is a string +% containing the name of the objective function to be minimized, +% a string expression representing the objective function, or an +% inline function object. F(x) should be a scalar valued function +% of a vector variable. +% +% X = FMINS('F',X0,OPTIONS) uses a vector of control parameters. If +% OPTIONS(1) is positive, intermediate steps in the solution are +% displayed; the default is OPTIONS(1) = 0. OPTIONS(2) is the +% termination tolerance for x; the default is 1.e-4. OPTIONS(3) is +% the termination tolerance for F(x); the default is 1.e-4. +% OPTIONS(14) is the maximum number of function evaluations; the +% default is OPTIONS(14) = 200*length(x). The other components of +% OPTIONS are not used by FMINS. For more information, see FOPTIONS. +% +% X = FMINS('F',X0,OPTIONS,[],P1,P2,...) provides for additional +% arguments which are passed to the objective function, F(X,P1,P2,...) +% Pass an empty matrix for OPTIONS to use the default values. +% +% [X,OPTIONS] = FMINS(...) returns the number of function evaluations +% in OPTIONS(10). +% +% FMINS uses the Nelder-Mead simplex (direct search) method. +% +% See also FMIN, FOPTIONS. + +% Reference: Jeffrey C. Lagarias, James A. Reeds, Margaret H. Wright, +% Paul E. Wright, "Convergence Properties of the Nelder-Mead Simplex +% Algorithm in Low Dimensions", May 1, 1997. To appear in the SIAM +% Journal of Optimization. +% +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.14 $ $Date: 1997/11/21 23:30:44 $ + +if nargin<3, options = []; end +options = foptions(options); +prnt = options(1); +tolx = options(2); +tolf = options(3); +% The input argument grad is there for compatability with FMINU in +% the Optimization Toolbox, but is not used by this function. + +% Convert to inline function as needed. +funfcn = fcnchk(funfcn,length(varargin)); + +n = prod(size(x)); +if (~options(14)) + options(14) = 200*n; +end + +% Initialize parameters +rho = 1; chi = 2; psi = 0.5; sigma = 0.5; +onesn = ones(1,n); +two2np1 = 2:n+1; +one2n = 1:n; + +% Set up a simplex near the initial guess. +xin = x(:); % Force xin to be a column vector +v = zeros(n,n+1); fv = zeros(1,n+1); +v = xin; % Place input guess in the simplex! (credit L.Pfeffer at Stanford) +x(:) = xin; % Change x to the form expected by funfcn +fv = feval(funfcn,x,varargin{:}); + +% Following improvement suggested by L.Pfeffer at Stanford +usual_delta = 0.05; % 5 percent deltas for non-zero terms +zero_term_delta = 0.00025; % Even smaller delta for zero elements of x +for j = 1:n + y = xin; + if y(j) ~= 0 + y(j) = (1 + usual_delta)*y(j); + else + y(j) = zero_term_delta; + end + v(:,j+1) = y; + x(:) = y; f = feval(funfcn,x,varargin{:}); + fv(1,j+1) = f; +end + +% sort so v(1,:) has the lowest function value +[fv,j] = sort(fv); +v = v(:,j); + +func_evals = n+1; +if prnt > 0 + clc + formatsave = get(0,{'format','formatspacing'}); + format compact + format short e + disp(' ') + disp('initial') + v + fv + func_evals +end + +% Main algorithm +% Iterate until the diameter of the simplex is less than tolx +% AND the function values differ from the least by less than tolf, +% or the max function evaluations are exceeded. +while func_evals < options(14) + if max(max(abs(v(:,two2np1)-v(:,onesn)))) <= tolx &... + max(abs(fv(1)-fv(two2np1))) <= tolf + break + end + how = ''; + + % Compute the reflection point + + % xbar = average of the n (NOT n+1) best points + xbar = sum(v(:,one2n), 2)/n; + xr = (1 + rho)*xbar - rho*v(:,end); + x(:) = xr; fxr = feval(funfcn,x,varargin{:}); + func_evals = func_evals+1; + + if fxr < fv(:,1) + % Calculate the expansion point + xe = (1 + rho*chi)*xbar - rho*chi*v(:,end); + x(:) = xe; fxe = feval(funfcn,x,varargin{:}); + func_evals = func_evals+1; + if fxe < fxr + v(:,end) = xe; + fv(:,end) = fxe; + how = 'expand'; + else + v(:,end) = xr; + fv(:,end) = fxr; + how = 'reflect'; + end + else % fv(:,1) <= fxr + if fxr < fv(:,n) + v(:,end) = xr; + fv(:,end) = fxr; + how = 'reflect'; + else % fxr >= fv(:,n) + % Perform contraction + if fxr < fv(:,end) + % Perform an outside contraction + xc = (1 + psi*rho)*xbar - psi*rho*v(:,end); + x(:) = xc; fxc = feval(funfcn,x,varargin{:}); + func_evals = func_evals+1; + + if fxc <= fxr + v(:,end) = xc; + fv(:,end) = fxc; + how = 'contract outside'; + else + % perform a shrink + how = 'shrink'; + end + else + % Perform an inside contraction + xcc = (1-psi)*xbar + psi*v(:,end); + x(:) = xcc; fxcc = feval(funfcn,x,varargin{:}); + func_evals = func_evals+1; + + if fxcc < fv(:,end) + v(:,end) = xcc; + fv(:,end) = fxcc; + how = 'contract inside'; + else + % perform a shrink + how = 'shrink'; + end + end + if strcmp(how,'shrink') + for j=two2np1 + v(:,j)=v(:,1)+sigma*(v(:,j) - v(:,1)); + x(:) = v(:,j); fxcc = feval(funfcn,x,varargin{:}); + end + func_evals = func_evals + n; + end + end + end + [fv,j] = sort(fv); + v = v(:,j); + if prnt > 0 + disp(' ') + disp(how) + v + fv + func_evals + end +end % while + + +x(:) = v(:,1); +if prnt > 0, + % reset format + set(0,{'format','formatspacing'},formatsave); +end +options(10)=func_evals; +options(8)=min(fv); +if func_evals >= options(14) + if options(1) >= 0 + disp(' ') + disp(['Maximum number of function evaluations (', ... + int2str(options(14)),') has been exceeded']); + disp( ' (increase OPTIONS(14)).') + end +end + + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINU.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINU.M" index e5e04f69eeedb0e6665255a8b8159ab46a2ccbb7..88ae5eb31f0e4cfe9dbd454d335e65323f1246f5 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINU.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/FMINU.M" @@ -1,3 +1,300 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:da0a355c3e96d0f1ec635455821e9b02935f585b4e5d91b605589a8a3a0b6240 -size 10500 +function [x,OPTIONS] = fminu(FUN,x,OPTIONS,GRADFUN,varargin) +%¶àÔªº¯Êý¼«ÖµÄâÅ£¶Ù·¨£¬ÊÊÓÃÓڹ⻬º¯ÊýÓÅ»¯? +%x=fminu('fun',x0)Å£¶Ù·¨Çó¶àÔªº¯Êýy=f(x)ÔÚx0³ö·¢µÄ¾Ö²¿¼«Ð¡Öµµã? +% ÕâÀï x,x0¾ùΪÏòÁ¿¡£ +%x=fminu('fun',x0,options)ÊäÈëoptionsÊÇÓÅ»¯ÖÐËã·¨²ÎÊýÏòÁ¿ÉèÖÃ, +% ÓÃhelp foptions¿É¿´µ½¸÷·ÖÁ¿µÄº¬Òå¡£ +%x=fminu('fun',x0,options,'grad') grad¸ø¶¨f(x)µÄÌݶȺ¯Êý±í´ïʽ£¿É¼Ó¿ì¼ÆËãËٶȡ? +%x=fminu('fun',x0,options,'grad',p1,p2¡­)p1,p2,..ÊDZíʾfunµÄMº¯ÊýÖеIJÎÊý¡£ +%ÀýÌâ Çóf(x)=100(x2-x1^2)^2+(1-x1)^2ÔÚ[-1.2,1]¸½½üµÄ¼«Ð¡Öµ¡£ +% ÏÈдMº¯Êýoptfun1.m +% function f=optfun1(x) +% f=100*(x(2)-x(1).^2).^2+(1-x(1)).^2; +% Çó½â +% clear; +% x=[-1.2,1]; +% [x,options]=fminu('optfun1',x,options); +% x,options(8) +% +%FMINU Finds the minimum of a function of several variables. +% X=FMINU('FUN',X0) starts at the matrix X0 and finds a minimum to the +% function which is described in FUN (usually an M-file: FUN.M). +% The function 'FUN' should return a scalar function value: F=FUN(X). +% +% X=FMINU('FUN',X0,OPTIONS) allows a vector of optional parameters to +% be defined. OPTIONS(1) controls how much display output is given; set +% to 1 for a tabular display of results, (default is no display: 0). +% OPTIONS(2) is a measure of the precision required for the values of +% X at the solution. OPTIONS(3) is a measure of the precision +% required of the objective function at the solution. +% For more information type HELP FOPTIONS. +% +% X=FMINU('FUN',X0,OPTIONS,'GRADFUN') enables a function'GRADFUN' +% to be entered which returns the partial derivatives of the function, +% df/dX, at the point X: gf = GRADFUN(X). +% +% X=FMINU('FUN',X0,OPTIONS,'GRADFUN',P1,P2,...) passes the problem- +% dependent parameters P1,P2,... directly to the functions FUN +% and GRADFUN: FUN(X,P1,P2,...) and GRADFUN(X,P1,P2,...). Pass +% empty matrices for OPTIONS, and 'GRADFUN' to use the default +% values. +% +% [X,OPTIONS]=FMINU('FUN',X0,...) returns the parameters used in the +% optimization method. For example, options(10) contains the number +% of function evaluations used. +% +% The default algorithm is the BFGS Quasi-Newton method with a +% mixed quadratic and cubic line search procedure. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.27 $ $Date: 1997/11/29 01:23:11 $ +% Andy Grace 7-9-90. + + +% ------------Initialization---------------- +XOUT=x(:); +nvars=length(XOUT); + +if nargin < 2, error('fminu requires two input arguments');end +if nargin < 3, OPTIONS=[]; end +if nargin < 4, GRADFUN=[]; end + +% Convert to inline function as needed. +if ~isempty(FUN) + [funfcn, msg] = fcnchk(FUN,length(varargin)); + if ~isempty(msg) + error(msg); + end +else + error('FUN must be a function name or valid expression.') +end + +if ~isempty(GRADFUN) + [gradfcn, msg] = fcnchk(GRADFUN,length(varargin)); + if ~isempty(msg) + error(msg); + end +else + gradfcn = []; +end + +f = feval(funfcn,x,varargin{:}); +n = length(XOUT); +GRAD=zeros(nvars,1); +OLDX=XOUT; +MATX=zeros(3,1); +MATL=[f;0;0]; +OLDF=f; +FIRSTF=f; +[OLDX,OLDF,HESS,OPTIONS]=optint(XOUT,f,OPTIONS); +CHG = 1e-7*abs(XOUT)+1e-7*ones(nvars,1); +SD = zeros(nvars,1); +diff = zeros(nvars,1); +PCNT = 0; +how = ''; + + +OPTIONS(10)=2; % Function evaluation count (add 1 for last evaluation) +status =-1; + +while status ~= 1 +% Work Out Gradients + if isempty(gradfcn) | OPTIONS(9) + OLDF=f; +% Finite difference perturbation levels +% First check perturbation level is not less than search direction. + f = find(10*abs(CHG)>abs(SD)); + CHG(f) = -0.1*SD(f); +% Ensure within user-defined limits + CHG = sign(CHG+eps).*min(max(abs(CHG),OPTIONS(16)),OPTIONS(17)); + for gcnt=1:nvars + XOUT(gcnt,1)=XOUT(gcnt)+CHG(gcnt); + x(:) = XOUT; + f = feval(funfcn,x,varargin{:}); + GRAD(gcnt)=(f-OLDF)/(CHG(gcnt)); + if f < OLDF + OLDF=f; + else + XOUT(gcnt)=XOUT(gcnt)-CHG(gcnt); + end + end +% Try to set difference to 1e-8 for next iteration +% Add eps for machines that can't handle divide by zero. + CHG = 1e-8./(GRAD + eps); + f = OLDF; + OPTIONS(10)=OPTIONS(10)+nvars; +% Gradient check + if OPTIONS(9) == 1 + GRADFD = GRAD; + x(:)=XOUT; + GRAD(:) = feval(gradfcn,x,varargin{:}); + if isa(gradfcn,'inline') + graderr(GRADFD, GRAD, formula(gradfcn)); + else + graderr(GRADFD, GRAD, gradfcn); + end + OPTIONS(9) = 0; + end + + else + OPTIONS(11)=OPTIONS(11)+1; + x(:)=XOUT; + GRAD(:) = feval(gradfcn,x,varargin{:}); + end +%---------------Initialization of Search Direction------------------ +if status == -1 + SD=-GRAD; + FIRSTF=f; + OLDG=GRAD; + GDOLD=GRAD'*SD; +% For initial step-size guess assume the minimum is at zero. + OPTIONS(18) = max(0.001, min([1,2*abs(f/GDOLD)])); + if OPTIONS(1)>0 + disp([sprintf('%5.0f %12.6g %12.6g ',OPTIONS(10),f,OPTIONS(18)),sprintf('%12.3g ',GDOLD)]); + end + XOUT=XOUT+OPTIONS(18)*SD; + status=4; + if OPTIONS(7)==0; PCNT=1; end + +else +%-------------Direction Update------------------ + gdnew=GRAD'*SD; + if OPTIONS(1)>0, + num=[sprintf('%5.0f %12.6g %12.6g ',OPTIONS(10),f,OPTIONS(18)),sprintf('%12.3g ',gdnew)]; + end + if (gdnew>0 & f>FIRSTF)|~finite(f) +% Case 1: New function is bigger than last and gradient w.r.t. SD -ve +% ...interpolate. + how='inter'; + [stepsize]=cubici1(f,FIRSTF,gdnew,GDOLD,OPTIONS(18)); + if stepsize<0|isnan(stepsize), stepsize=OPTIONS(18)/2; how='C1f '; end + if OPTIONS(18)<0.1&OPTIONS(6)==0 + if stepsize*norm(SD)1e-20 +% Case 2: New function less than old fun. and OK for updating HESS +% .... update and calculate new direction. + how=''; + if gdnew<0 + how='incstep'; + if newstep0 + if OPTIONS(18)>0.9 + how='int_st'; + OPTIONS(18)=min([1,abs(newstep)]); + end + end %if gdnew + [HESS,SD]=updhess(XOUT,OLDX,GRAD,OLDG,HESS,OPTIONS); + gdnew=GRAD'*SD; + OLDX=XOUT; + status=4; +% Save Variables for next update + FIRSTF=f; + OLDG=GRAD; + GDOLD=gdnew; +% If mixed interpolation set PCNT + if OPTIONS(7)==0, PCNT=1; MATX=zeros(3,1); MATL(1)=f; end + elseif gdnew>0 %sk<=0 +% Case 3: No good for updating HESSIAN .. interpolate or halve step length. + how='inter_st'; + if OPTIONS(18)>0.01 + OPTIONS(18)=0.9*newstep; + XOUT=OLDX; + end + if OPTIONS(18)>1, OPTIONS(18)=1; end + else +% Increase step, replace starting point + OPTIONS(18)=max([min([newstep-OPTIONS(18),3]),0.5*OPTIONS(18)]); + how='incst2'; + OLDX=XOUT; + FIRSTF=f; + OLDG=GRAD; + GDOLD=GRAD'*SD; + OLDX=XOUT; + end % if sk> +% Case 4: New function bigger than old but gradient in on +% ...reduce step length. + else %gdnew<0 & F>FIRSTF + if gdnew<0&f>FIRSTF + how='red_step'; + if norm(GRAD-OLDG)<1e-10; HESS=eye(nvars); end + if abs(OPTIONS(18))0 + end % if (gdnew>0 & F>FIRSTF)|~finite(F) + XOUT=XOUT+OPTIONS(18)*SD; + if isinf(OPTIONS(1)) + disp([num,how]) + elseif OPTIONS(1)>0 + disp(num) + end +end %----------End of Direction Update------------------- + +% Check Termination + if max(abs(SD))<2*OPTIONS(2) & (-GRAD'*SD) < 2*OPTIONS(3) + if OPTIONS(1) > 0 + disp('Optimization Terminated Successfully') + disp(' Search direction less than 2*options(2)') + disp(' Gradient in the search direction less than 2*options(3)') + disp([' NUMBER OF FUNCTION EVALUATIONS=', int2str(OPTIONS(10))]); + end + status=1; + elseif OPTIONS(10)>OPTIONS(14) + if OPTIONS(1) >= 0 + disp('Maximum number of function evaluations exceeded;') + disp(' increase options(14).') + end + status=1; + else + +% Line search using mixed polynomial interpolation and extrapolation. + if PCNT~=0 + while PCNT > 0 & OPTIONS(10) <= OPTIONS(14) + x(:) = XOUT; + f = feval(funfcn,x,varargin{:}); + OPTIONS(10)=OPTIONS(10)+1; + [PCNT,MATL,MATX,steplen,f, how]=searchq(PCNT,f,OLDX,MATL,MATX,SD,GDOLD,OPTIONS(18), how); + OPTIONS(18)=steplen; + XOUT=OLDX+steplen*SD; + end + if OPTIONS(10)>OPTIONS(14) + if OPTIONS(1) >= 0 + disp('Maximum number of function evaluations exceeded;') + disp(' increase options(14).') + end + status=1; + end + else + x(:)=XOUT; + f = feval(funfcn,x,varargin{:}); + OPTIONS(10)=OPTIONS(10)+1; + end + end +end + +x(:)=XOUT; +f = feval(funfcn,x,varargin{:}); +if f > FIRSTF + OPTIONS(8) = FIRSTF; + x(:)=OLDX; +else + OPTIONS(8) = f; +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LINPROG.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LINPROG.M" index 4f06dbc7bfc78e04e3815eeb42affe59db64fda6..bc83284658deadf3ed6507eb1a5328a6949dbfcc 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LINPROG.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LINPROG.M" @@ -1,3 +1,223 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1fd6513fa1fd64bf41ee74b1cc55ae47f1e0134d48d04487593879f674f03c9b -size 8141 +function [x,fval,exitflag,output,lambda]=linprog(f,A,B,Aeq,Beq,lb,ub,x0,options) +%x=linprog(f, A, b)Çó½âÏßÐԹ滮 +% min z = f'x, Ax ¡Ü b£» +%x=linprog(f, A, b, Aeq, beq)Çó½âÏßÐԹ滮£º +% min z = f'x, Ax ¡Ü b, Aeqx = beq£» +%x=linprog(f, A, b, Aeq, beq, lb, ub)Ö¸¶¨lb ¡Ü x ¡Ü ub£» +%x=linprog(f, A, b, Aeq, beq, lb, ub, x0)Ö¸¶¨µü´ú³õÖµx0£¬ +%Èç¹ûûÓв»µÈʽԼÊø£¬¿ÉÓÃ[ ]Ìæ´úAºÍb±íʾȱʡ£¬Èç¹ûûÓеÈʽԼÊø£¬¿ÉÓÃ[ ]Ìæ´úAeqºÍbeq±íʾȱʡ +%Èç¹ûij¸öxiÏÂÎÞ½ç»òÉÏÎ޽磬É趨lb(i) = -inf»òub(i) = inf£» +%ÓÃ[x, Fval]´úÌæÉÏÊö¸÷ÃüÁîÐÐÖÐ×ó±ßµÄx£¬Ôò¿ÉµÃµ½×îÓŽ⴦µÄº¯ÊýÖµFval¡£ +% +%Àý max z=10x1+5x2 +% s.t. 5x1+2x2<=8 +% 3x1+4x2=9 +% x1+x2>=1 +% x1,x2>=0 +% Ê×ÏÈ»¯Îª£ºmin - z = -10x1 -5x2 +% s.t. 5x1+2x1<=8 +% -x1-x2<=-1 +% 3x1+4x2=9 +% x1,x2>=0 +% ½â·¨ +% clear; +% C=[-10,-5]'; +% A=[5 2;-1 -1];Aeq=[3 4]; +% b=[8,-1]';beq=9; +% [x,fval]=linprog(C,A,b,Aeq,beq,zeros(2,1)); +% xmax=x,zmax=-fval +% +%LINPROG Linear programming. +% X=LINPROG(f,A,b) solves the linear programming problem: +% +% min f'*x subject to: A*x <= b +% x +% +% X=LINPROG(f,A,b,Aeq,beq) solves the problem above while additionally +% satisfying the equality constraints Aeq*x = beq. +% +% X=LINPROG(f,A,b,Aeq,beq,LB,UB) defines a set of lower and upper +% bounds on the design variables, X, so that the solution is in +% the range LB <= X <= UB. Use empty matrices for LB and UB +% if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below; +% set UB(i) = Inf if X(i) is unbounded above. +% +% X=LINPROG(f,A,b,Aeq,beq,LB,UB,X0) sets the starting point to X0. This +% option is only available with the active-set algorithm. The default +% interior point algorithm will ignore any non-empty starting point. +% +% X=LINPROG(f,A,b,Aeq,Beq,LB,UB,X0,OPTIONS) minimizes with the default +% optimization parameters replaced by values in the structure OPTIONS, an +% argument created with the OPTIMSET function. See OPTIMSET for details. +% Use options are Display, Diagnostics, TolFun, LargeScale, MaxIter. +% Currently, only 'final' and 'off' are valid values for the parameter +% Display when LargeScale is 'off' ('iter' is valid when LargeScale is 'on'). +% +% [X,FVAL]=LINPROG(f,A,b) returns the value of the objective function at X: +% FVAL = f'*X. +% +% [X,FVAL,EXITFLAG] = LINPROG(f,A,b) returns EXITFLAG that +% describes the exit condition of LINPROG. +% If EXITFLAG is: +% > 0 then LINPROG converged with a solution X. +% 0 then LINPROG reached the maximum number of iterations without converging. +% < 0 then the problem was infeasible or LINPROG failed. +% +% [X,FVAL,EXITFLAG,OUTPUT] = LINPROG(f,A,b) returns a structure +% OUTPUT with the number of iterations taken in OUTPUT.iterations, the type +% of algorithm used in OUTPUT.algorithm, the number of conjugate gradient +% iterations (if used) in OUTPUT.cgiterations. +% +% [X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=LINPROG(f,A,b) returns the set of +% Lagrangian multipliers LAMBDA, at the solution: LAMBDA.ineqlin for the +% linear inequalities A, LAMBDA.eqlin for the linear equalities Aeq, +% LAMBDA.lower for LB, and LAMBDA.upper for UB. +% +% NOTE: the LargeScale (the default) version of LINPROG uses a primal-dual +% method. Both the primal problem and the dual problem must be feasible +% for convergence. Infeasibility messages of either the primal or dual, +% or both, are given as appropriate. The primal problem in standard +% form is +% min f'*x such that A*x = b, x >= 0. +% The dual problem is +% max b'*y such that A'*y + s = f, s >= 0. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.17 $ $Date: 1998/10/22 20:11:09 $ +% If just 'defaults' passed in, return the default options in X + +defaultopt = optimset('display','final',... + 'TolFun',1e-8,'Diagnostics','off',... + 'LargeScale','on','maxiter',85); + +if nargin==1 & nargout <= 1 & isequal(f,'defaults') + x = defaultopt; + return +end + +% Handle missing arguments +if nargin < 9, options = []; + if nargin < 8, x0 = []; + if nargin < 7, ub = []; + if nargin < 6, lb = []; + if nargin < 5, Beq = []; + if nargin < 4, Aeq = []; + end, end, end, end, end, end +if nargout > 4 + computeLambda = 1; +else + computeLambda = 0; +end + +% Options setup +options = optimset(defaultopt,options); +largescale = isequal(optimget(options,'largescale'),'on'); +diagnostics = isequal(optimget(options,'diagnostics','off'),'on'); +switch optimget(options,'display') +case {'off','none'} + verbosity = 0; +case 'iter' + verbosity = 2; +case 'final' + verbosity = 1; +otherwise + verbosity = 1; +end + +% Set the constraints up: defaults and check size +[nineqcstr,nvars]=size(A); +[neqcstr, nvarseq]=size(Aeq); +nvars = max([length(f),nvars,nvarseq]); % In case A is empty +ncstr = nineqcstr + neqcstr; + +if isempty(A), A=zeros(0,nvars); end +if isempty(B), B=zeros(0,1); end +if isempty(Aeq), Aeq=zeros(0,nvars); end +if isempty(Beq), Beq=zeros(0,1); end + +% Set to column vectors +f = f(:); +B = B(:); +Beq = Beq(:); + +[x0,lb,ub,msg] = checkbounds(x0,lb,ub,nvars); +if ~isempty(msg) + exitflag = -1; + output = []; x=x0; fval = []; lambda = []; + if verbosity > 0 + disp(msg) + end + return +end + +caller = 'linprog'; +ncstr = nineqcstr + neqcstr; + +if largescale + OUTPUT.algorithm = 'large-scale: interior point'; +else + OUTPUT.algorithm = 'medium-scale: active-set'; +end + +if diagnostics + % Do diagnostics on information so far + gradflag = []; hessflag = []; line_search=[]; + constflag = 0; gradconstflag = 0; non_eq=0;non_ineq=0; + lin_eq=size(Aeq,1); lin_ineq=size(A,1); XOUT=ones(nvars,1); + funfcn{1} = [];ff=[]; GRAD=[];HESS=[]; + confcn{1}=[];c=[];ceq=[];cGRAD=[];ceqGRAD=[]; + msg = diagnose('linprog',OUTPUT,gradflag,hessflag,constflag,gradconstflag,... + line_search,options,XOUT,non_eq,... + non_ineq,lin_eq,lin_ineq,lb,ub,funfcn,confcn,ff,GRAD,HESS,c,ceq,cGRAD,ceqGRAD); +end + +if (largescale) + if ~isempty(x0) & verbosity > 0 + warning('Interior Point method is ignoring starting point') + end + [x,fval,lambda,exitflag,output] = lipsol(f,A,B,Aeq,Beq,lb,ub,options,computeLambda); + output.algorithm = 'lipsol'; +else + if ~largescale & (issparse(A) | issparse(Aeq) )% asked for medium-scale but sparse + if verbosity > 0 + disp('The medium-scale (active-set) algorithm does not currently handle sparse matrices.') + disp('Converting to full matrices to solve.') + end + end + if isempty(x0), x0=zeros(nvars,1); end + [x,lambdaqp,exitflag,output]= ... + qpsub([],full(f),full([Aeq;A]),full([Beq;B]),lb,ub,x0,neqcstr,verbosity,caller,ncstr,nvars,options); + output.algorithm = 'medium-scale: activeset'; +end + +if isequal(output.algorithm , 'medium-scale: activeset') + fval = f'*x; + llb = length(lb); + lub = length(ub); + lambda.lower = zeros(llb,1); + lambda.upper = zeros(lub,1); + arglb = ~isinf(lb); lenarglb = nnz(arglb); + argub = ~isinf(ub); lenargub = nnz(argub); + lambda.eqlin = lambdaqp(1:neqcstr,1); + lambda.ineqlin = lambdaqp(neqcstr+1:neqcstr+nineqcstr,1); + lambda.lower(arglb) = lambdaqp(neqcstr+nineqcstr+1:neqcstr+nineqcstr+lenarglb); + lambda.upper(argub) = lambdaqp(neqcstr+nineqcstr+lenarglb+1:neqcstr+nineqcstr+lenarglb+lenargub); + + output.firstorderopt=[]; + output.cgiterations =[]; + + if verbosity > 0 + if ( exitflag ==1 ) + disp('Optimization terminated successfully.'); + end + if ( exitflag == 2) + % do some sort of check here to see how unreliable + disp('Optimization completed.'); + end + if (exitflag ==0) + disp('Maximum number of iterations exceeded;') + disp(' increase options.MaxIter') + end + + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LP.M" index e1df8f628e80edda602e01f4b22402e9441f2617..3c2c3dd75ba94fb3dd1f33b23c1d4cea6d7c139c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/LP.M" @@ -1,3 +1,86 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:c6b7bdc82511fa86bcba8f31c173dabb8f0ba645e7822f3b7c09aaa840e3d55c -size 2733 +function [x,lambda,how]=lp(f,A,B,vlb,vub,x,neqcstr,verbosity) +%ÏßÐԹ滮lp +%Çó½âÏßÐԹ滮ÎÊÌ⣺ +% min c'x +% s.t. Ax<=b +%ÕâÀïAΪm*n¾ØÕó,CΪm*1ÏòÁ¿,bΪm*1ÏòÁ¿,nΪ±äÁ¿¸öÊý +%Ó÷¨ +% x=lp(C,A,b)ÇóµÃÉÏÊöÏßÐԹ滮µÄ½â¡£ +% x=lp(C,A,b,vlb,vub) Ö¸¶¨ÉÏϽçvlb<=x<=vub +% x=lp(C,A,b,vlb,vub,x0)¸ø¶¨µü´ú³õÖµ +% x=lp(C,A,b,vlb,vub,x0,k)Ç°k¸öÔ¼ÊøΪµÈʽ +%Àý max z=10x1+5x2 +% s.t. 5x1+2x2<=8 +% 3x1+4x2=9 +% x1+x2>=1 +% x1,x2>=0 +% Ê×ÏÈ»¯Îª£ºmin - z = -10x1 -5x2 +% s.t. 3x1+4x2=9 +% 5x1+2x1<=8 +% -x1-x2<=-1 +% x1,x2>=0 +% ½â·¨ +% clear; +% C=[-10,-5]'; +% A=[3 4;5 2;-1 -1]; +% b=[9,8,-1]'; +% x=lp(C,A,b,zeros(2,1),[],[],1) +%LP Linear programming. +% LP has been replaced with LINPROG. LP currently works but +% will be removed in the future. Use LINPROG instead. +% +% X=LP(f,A,b) solves the linear programming problem: +% +% min f'x subject to: Ax <= b +% x +% +% X=LP(f,A,b,VLB,VUB) defines a set of lower and upper +% bounds on the design variables, X, so that the solution is always in +% the range VLB <= X <= VUB. +% +% X=LP(f,A,b,VLB,VUB,X0) sets the initial starting point to X0. +% +% X=LP(f,A,b,VLB,VUB,X0,N) indicates that the first N constraints defined +% by A and b are equality constraints. +% +% X=LP(f,A,b,VLB,VUB,X0,N,DISPLAY) controls the level of warning +% messages displayed. Warning messages can be turned off with +% DISPLAY = -1. +% +% [x,LAMBDA]=LP(f,A,b) returns the set of Lagrangian multipliers, +% LAMBDA, at the solution. +% +% [X,LAMBDA,HOW] = LP(f,A,b) also returns a string how that indicates +% error conditions at the final iteration. +% +% LP produces warning messages when the solution is either unbounded +% or infeasible. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.13 $ $Date: 1998/08/31 22:29:20 $ +% Andy Grace 7-9-90. Mary Ann Branch 9-30-96. + +if nargin<8, verbosity = 0; + if nargin<7, neqcstr = 0; + if nargin<6, x = []; + if nargin<5, vub = []; + if nargin<4, vlb = []; + end, end, end, end, end +[ncstr,nvars]=size(A); +nvars = max([length(f),nvars]); % In case A is empty + +if isempty(verbosity), verbosity = 0; end +if isempty(neqcstr), neqcstr = 0; end +if isempty(x), x=zeros(nvars,1); end + +if isempty(A), A=zeros(0,nvars); end +if isempty(B), B=zeros(0,1); end + +% Set to column vectors +f = f(:); +B = B(:); +x = x(:); + +caller = 'lp'; +[x,lambda,how]=qpsubold([],f,A,B,vlb,vub,x,neqcstr,verbosity,caller,ncstr,nvars); + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/\346\225\260\345\255\246\350\247\204\345\210\222.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/\346\225\260\345\255\246\350\247\204\345\210\222.txt" index 06d268df6c8f263c9bae3ee029ab704b8d067c40..58ded4a972d5dca4a4b340e9112601453d2877f1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/\346\225\260\345\255\246\350\247\204\345\210\222.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\345\255\246\350\247\204\345\210\222/\346\225\260\345\255\246\350\247\204\345\210\222.txt" @@ -1,3 +1,8 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f5d61a2e2b00f56af17cc266f03a312912b0add77e89e8a7ab5f62aa57329e93 -size 221 +% Êýѧ¹æ»® +% lp - ÏßÐԹ滮 +% linprog - ÏßÐԹ滮(ÔÚMATLAB5.3ʹÓÃ) +% fmin - Ò»Ôªº¯Êý¼«Öµ +% fminu - ¶àÔªº¯Êý¼«ÖµÄâÅ£¶Ù·¨ +% fmins - ¶àÔªº¯Êý¼«Öµµ¥´¿ÐÎËÑË÷·¨ +% constr - ·ÇÏßÐԹ滮 +% fmincon - ·ÇÏßÐԹ滮(ÔÚMATLAB5.3ʹÓÃ) \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/CURVEFIT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/CURVEFIT.M" index beab2cc08fd47b9d2c16db8fb9476e536cd0ebf1..6944dd11dec1acc1c2e90c0eb04c38c3dcd1bca1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/CURVEFIT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/CURVEFIT.M" @@ -1,3 +1,148 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:6495015c7a9ca3d6c202ea1d3a836d9bb620c6c9133511d4845ad143fa5602dd -size 5663 +function [x,OPTIONS,CostFunction,JACOB] = curvefit(FUN,x0,XDATA,YDATA,OPTIONS,GRADFUN,varargin) +%ÇúÏßÄâºÏ +% C=CURVEFIT('ÄâºÏÄ£ÐÍ',²ÎÊýC³õÖµ,XÊý¾Ý,YÊý¾Ý) +%Çó²ÎÊýCʹµÃ sum {(FUN(C,XÊý¾Ý)-YÊý¾Ý).^2}×îС»¯ +%Àý +% x | 0.1 0.2 0.15 0.0 -0.2 0.3 +% --|------------------------------ +% y | 0.95 0.84 0.86 1.06 1.50 0.72 +%ÄâºÏ y=a*exp(b*x).ÏÈдM-º¯Êýfitfun2.m +% function f=fitfun2(c,x) +% f=c(1)*exp(c(2)*x); +% ½â·¨ +% x=[0.1,0.2,0.15,0,-0.2,0.3]; +% y=[0.95,0.84,0.86,1.06,1.50,0.72]; +% c=curvefit('fitfun2',[1,1]',x,y); +% a=c(1),b=c(2) +% f='a*exp(b*xi)'; +% xi=-0.2:0.01:0.3; +% yi=eval(f); +% plot(x,y,'o',xi,yi,'k') +% title('CURVEFIT'); + +%CURVEFIT Solves non-linear least squares problems. +% CURVEFIT solves problems of the form: +% min sum {(FUN(X,XDATA)-YDATA).^2} where FUN, XDATA and YDATA are +% X matrices. +% +% X=CURVEFIT('FUN',X0,XDATA,YDATA) starts at X0 and finds +% coefficients X to best fit the nonlinear function FUN(X,XDATA) +% to the data YDATA (in the least-squares sense). FUN is an M-file +% that computes a function of X and XDATA and returns a matrix of +% the objective function values: F=FUN(X,XDATA). +% NOTE: YDATA must be the same size as the matrix F returned by FUN. +% +% X=CURVEFIT('FUN',X0,XDATA,YDATA,OPTIONS) allows a vector of optional +% parameters to be defined. OPTIONS(2) is a measure of the precision +% required for the values of X at the solution. OPTIONS(3) is a measure +% of the precision required of the objective function at the solution. +% See HELP FOPTIONS. +% +% X=CURVEFIT('FUN',X0,XDATA,YDATA,OPTIONS,'GRADFUN') enables a +% function 'GRADFUN' to be entered which returns the partial derivatives +% of the functions, dF/dX, (stored in columns) at the point X: +% gf = GRADFUN(X,XDATA). +% +% X=CURVEFIT('FUN',X,XDATA,YDATA,OPTIONS,'GRADFUN',P1,P2,..) passes the +% problem-dependent parameters P1,P2,... directly to the functions FUN +% and GRADFUN: FUN(X,XDATA,P1,P2,...) and GRADFUN(X,XDATA,P1,P2,...). +% Pass empty matrices for OPTIONS and 'GRADFUN' to use the default values. +% +% [X,OPTIONS,F,J]=CURVEFIT('FUN',X0,XDATA,YDATA,...) returns, F, +% the value of FUN(X,XDATA)-YDATA at the solution X, and J the Jacobian +% of the function FUN at the solution. +% +% FUN must be an M-file and not an inline object or expression. Use LEASTSQ +% instead on inline objects or expressions. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.6 $ $Date: 1997/11/29 01:23:03 $ +% Mary Ann Branch 8-22-96. + +% The default algorithm is the Levenberg-Marquardt method with a +% mixed quadratic and cubic line search procedure. A Gauss-Newton +% method is selected by setting OPTIONS(5)=1. +% + +% ------------Initialization---------------- + +if nargin < 4, error('curvefit requires four input arguments');end +if nargin < 5, OPTIONS=[]; end +if nargin < 6, GRADFUN=[]; end + +% Need extra argname for XDATA +curvefitarg = 1; +lenVarIn = length(varargin); + +% Convert to inline function as needed. +if isempty(FUN) + error('FUN must be a function name.'); +elseif isa(FUN,'inline') + error('FUN must be a function name, not an inline object. Use LEASTSQ instead.'); +elseif isstr(FUN) + % Make sure FUN isn't an expression via fcnchk + fun0 = fcnchk(FUN); + if isa(fun0,'inline') + error('FUN must be a function name, not a string expression. Use LEASTSQ instead.'); + else + % Momentarily turn FUN into an inline to get at the argnames and formula + fun1 = inline(FUN,lenVarIn+1); + fun1args = argnames(fun1); + % Compute the inline function that is the difference with YDATA + arglist = sprintf('%s(', formula(fun1)); + for k = 1:(nargin(fun1)-1); + arglist = sprintf('%s%s,', arglist, deblank(fun1args{k,:})); + end + arglist = sprintf('%s%s)',arglist, deblank(fun1args{nargin(fun1),:})); + funfcn = inline([arglist, ... + '-P',int2str(lenVarIn+2)],lenVarIn+2); + end +else + error('FUN is an unrecognized data type.') +end + +if ~isempty(GRADFUN) + if isa(GRADFUN,'inline') + error('GRADFUN must be a function name and not an inline object.'); + elseif isstr(GRADFUN) + % Make sure FUN isn't an expression via fcnchk + fun0 = fcnchk(GRADFUN); + if isa(fun0,'inline') + error('GRADFUN must be a function name, not a string expression.'); + else + % Momentarily turn GRADFUN into an inline to get at the argnames and formula + fun1 = inline(GRADFUN,lenVarIn+1); + fun1args = argnames(fun1); + % Compute the inline function that is the difference with YDATA + arglist = sprintf('%s(', formula(fun1)); + for k = 1:(nargin(fun1)-1); + arglist = sprintf('%s%s,', arglist, deblank(fun1args{k,:})); + end + arglist = sprintf('%s%s)',arglist, deblank(fun1args{nargin(fun1),:})); + gradfcn = inline(arglist,lenVarIn+2); + end + else + error('GRADFUN is an unrecognized data type.') + end +else + gradfcn = []; +end + + +% Check the size of f and YDATA +try + f = feval(FUN,x0,XDATA,varargin{:}); +catch + error(['Error in evaluating user supplied function: ',FUN]) +end + +if ~isequal(size(f), size(YDATA)) + error('Function value and YDATA sizes are incommensurate.') +end + +% The order YDATA, XDATA is relevant: match P2 to YDATA +[x,OPTIONS,CostFunction,JACOB] = ... + nlsqold(funfcn,x0,OPTIONS,gradfcn,XDATA,varargin{:},YDATA); + +%--end of curvefit-- + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/GRIDDATA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/GRIDDATA.M" index 9650c9b7fbf413d3518f587712f0dc60360e3073..13676f9da13eaa18c7367f7a5fd9dbb032dca71e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/GRIDDATA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/GRIDDATA.M" @@ -1,3 +1,435 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:197e2a2476595149d2a3ed7db357460d6c850931d7fe1ed761e89aacd582c6fa -size 15769 +function [xi,yi,zi] = griddata(x,y,z,xi,yi,method) +%²»¹æÔòÊý¾ÝµÄÇúÃæ²åÖµ +%ZI=griddata(x,y,z,XI,YI) +% ÕâÀïx,y,z¾ùΪÏòÁ¿(²»±Øµ¥µ÷)±íʾÊý¾Ý. +% XI,YIΪÍø¸ñÊý¾Ý¾ØÕó.griddata²ÉÓÃÈý½ÇÐÎÏßÐÔ²åÖµ. +%ZI=griddata(x,y,z,XI,YI,'cubic') ²ÉÓÃÈý½ÇÐÎÈý´Î²åÖµ +%ÀýÌâ Èç¹ûÊý¾Ý²Ðȱ²»È«(x,y,z) +% | 0 1 2 3 4 +%-----|------------------------ +% 2 | * * 80 82 84 +% 3 | 79 * 61 65 * +% 4 | 84 84 * * 86 +% ʹÓà +% x=[2,3,4,0,2,3,0,1,4]; +% y=[2,2,2,3,3,3,4,4,4]; +% z=[80,82,84,79,61,65,84,84,86]; +% subplot(2,1,1);stem3(x,y,z);title('RAW DATA'); +% xi=0:0.1:4;yi=2:0.2:4; +% [XI,YI]=meshgrid(xi,yi); +% ZI=griddata(x,y,z,XI,YI,'cubic'); +% subplot(2,1,2);mesh(XI,YI,ZI);title('GRIDDATA'); +% +%GRIDDATA Data gridding and surface fitting. +% ZI = GRIDDATA(X,Y,Z,XI,YI) fits a surface of the form Z = F(X,Y) +% to the data in the (usually) nonuniformly-spaced vectors (X,Y,Z) +% GRIDDATA interpolates this surface at the points specified by +% (XI,YI) to produce ZI. The surface always goes through the data +% points. XI and YI are usually a uniform grid (as produced by +% MESHGRID) and is where GRIDDATA gets its name. +% +% XI can be a row vector, in which case it specifies a matrix with +% constant columns. Similarly, YI can be a column vector and it +% specifies a matrix with constant rows. +% +% [XI,YI,ZI] = GRIDDATA(X,Y,Z,XI,YI) also returns the XI and YI +% formed this way (the results of [XI,YI] = MESHGRID(XI,YI)). +% +% [...] = GRIDDATA(...,'method') where 'method' is one of +% 'linear' - Triangle-based linear interpolation (default). +% 'cubic' - Triangle-based cubic interpolation. +% 'nearest' - Nearest neighbor interpolation. +% 'v4' - MATLAB 4 griddata method. +% defines the type of surface fit to the data. The 'cubic' and 'v4' +% methods produce smooth surfaces while 'linear' and 'nearest' have +% discontinuities in the first and zero-th derivative respectively. All +% the methods except 'v4' are based on a Delaunay triangulation of the +% data. +% +% See also INTERP2, DELAUNAY, MESHGRID. + +% Clay M. Thompson 8-21-95 +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.22 $ $Date: 1997/11/21 23:40:37 $ + +error(nargchk(5,6,nargin)) + +[msg,x,y,z,xi,yi] = xyzchk(x,y,z,xi,yi); +if ~isempty(msg), error(msg); end + +if nargin<6, method = 'linear'; end +if ~isstr(method), + error('METHOD must be one of ''linear'',''cubic'',''nearest'', or ''v4''.'); +end + + +% Sort x and y so duplicate points can be averaged before passing to delaunay + +% Need x,y and z to be column vectors +sz = prod(size(x)); +x = reshape(x,sz,1); +y = reshape(y,sz,1); +z = reshape(z,sz,1); +sxyz = sortrows([x y z],[2 1]); +x = sxyz(:,1); +y = sxyz(:,2); +z = sxyz(:,3); +ind = [0; y(2:end) == y(1:end-1) & x(2:end) == x(1:end-1); 0]; +if sum(ind) > 0 + warning('Duplicate x-y data points detected: using average of the z values'); + fs = find(ind(1:end-1) == 0 & ind(2:end) == 1); + fe = find(ind(1:end-1) == 1 & ind(2:end) == 0); + for i = 1 : length(fs) + % averaging z values + z(fe(i)) = mean(z(fs(i):fe(i))); + end + x = x(~ind(2:end)); + y = y(~ind(2:end)); + z = z(~ind(2:end)); +end + +switch lower(method), + case 'linear' + zi = linear(x,y,z,xi,yi); + case 'cubic' + zi = cubic(x,y,z,xi,yi); + case 'nearest' + zi = nearest(x,y,z,xi,yi); + case {'invdist','v4'} + zi = gdatav4(x,y,z,xi,yi); + otherwise + error('Unknown method.'); +end + +if nargout<=1, xi = zi; end + + +%------------------------------------------------------------ +function zi = linear(x,y,z,xi,yi) +%LINEAR Triangle-based linear interpolation + +% Reference: David F. Watson, "Contouring: A guide +% to the analysis and display of spacial data", Pergamon, 1994. + +siz = size(xi); +xi = xi(:); yi = yi(:); % Treat these as columns +x = x(:); y = y(:); % Treat these as columns + +% Triangularize the data +tri = delaunay(x,y,'sorted'); +if isempty(tri), + warning('Data cannot be triangulated.'); + zi = repmat(NaN,size(xi)); + return +end + +% Find the nearest triangle (t) +t = tsearch(x,y,tri,xi,yi); + +% Only keep the relevant triangles. +out = find(isnan(t)); +if ~isempty(out), t(out) = ones(size(out)); end +tri = tri(t,:); + +% Compute Barycentric coordinates (w). P. 78 in Watson. +del = (x(tri(:,2))-x(tri(:,1))) .* (y(tri(:,3))-y(tri(:,1))) - ... + (x(tri(:,3))-x(tri(:,1))) .* (y(tri(:,2))-y(tri(:,1))); +w(:,3) = ((x(tri(:,1))-xi).*(y(tri(:,2))-yi) - ... + (x(tri(:,2))-xi).*(y(tri(:,1))-yi)) ./ del; +w(:,2) = ((x(tri(:,3))-xi).*(y(tri(:,1))-yi) - ... + (x(tri(:,1))-xi).*(y(tri(:,3))-yi)) ./ del; +w(:,1) = ((x(tri(:,2))-xi).*(y(tri(:,3))-yi) - ... + (x(tri(:,3))-xi).*(y(tri(:,2))-yi)) ./ del; +w(out,:) = zeros(length(out),3); + +z = z(:).'; % Treat z as a row so that code below involving + % z(tri) works even when tri is 1-by-3. +zi = sum(z(tri) .* w,2); + +zi = reshape(zi,siz); + +if ~isempty(out), zi(out) = NaN; end +%------------------------------------------------------------ + +%------------------------------------------------------------ +function zi = cubic(x,y,z,xi,yi) +%TRIANGLE Triangle-based cubic interpolation + +% Reference: T. Y. Yang, "Finite Element Structural Analysis", +% Prentice Hall, 1986. pp. 446-449. +% +% Reference: David F. Watson, "Contouring: A guide +% to the analysis and display of spacial data", Pergamon, 1994. + +siz = size(xi); +xi = xi(:); yi = yi(:); % Treat these as columns +x = x(:); y = y(:); z = z(:); % Treat these as columns + +% Triangularize the data +tri = delaunay(x,y,'sorted'); +if isempty(tri), + warning('Data cannot be triangulated.'); + zi = repmat(NaN,size(xi)); + return +end + +% +% Estimate the gradient as the average the triangle slopes connected +% to each vertex +% +t1 = [x(tri(:,1)) y(tri(:,1)) z(tri(:,1))]; +t2 = [x(tri(:,2)) y(tri(:,2)) z(tri(:,2))]; +t3 = [x(tri(:,3)) y(tri(:,3)) z(tri(:,3))]; +Area = ((x(tri(:,2))-x(tri(:,1))) .* (y(tri(:,3))-y(tri(:,1))) - ... + (x(tri(:,3))-x(tri(:,1))) .* (y(tri(:,2))-y(tri(:,1))))/2; +nv = cross((t3-t1).',(t2-t1).').'; + +% Normalize normals +nv = nv ./ repmat(nv(:,3),1,3); + +% Sparse matrix is non-zero if the triangle specified the row +% index is connected to the point specified by the column index. +% Gradient estimate is area weighted average of triangles +% around a datum. +m = size(tri,1); +n = length(x); +i = repmat((1:m)',1,3); +T = sparse(i,tri,repmat(-nv(1:m,1).*Area,1,3),m,n); +A = sparse(i,tri,repmat(Area,1,3),m,n); +s = full(sum(A)); +gx = (full(sum(T))./(s + (s==0)))'; +T = sparse(i,tri,repmat(-nv(1:m,2).*Area,1,3),m,n); +gy = (full(sum(T))./(s + (s==0)))'; + +% Compute triangle areas and side lengths +i1 = [1 2 3]; i2 = [2 3 1]; i3 = [3 1 2]; +xx = x(tri); +yy = y(tri); +zz = z(tri); +gx = gx(tri); +gy = gy(tri); +len = sqrt((xx(:,i3)-xx(:,i2)).^2 + (yy(:,i3)-yy(:,i2)).^2); + +% Compute average normal slope +gn = ((gx(:,i2)+gx(:,i3)).*(yy(:,i2)-yy(:,i3)) - ... + (gy(:,i2)+gy(:,i3)).*(xx(:,i2)-xx(:,i3)))/2./len; + +% Compute triangle normal edge gradient at the center of each side (Wn) +Area = repmat(Area,1,3); +Wna = 1/4*(-2*yy(:,i2).*yy(:,i3)+yy(:,i2).^2+yy(:,i3).^2+xx(:,i2).^2 - ... + 2*xx(:,i2).*xx(:,i3)+xx(:,i3).^2).*zz; +Wna(:) = Wna-1/16.*(yy(:,i2).^2-2*yy(:,i2).*yy(:,i3)+yy(:,i3).^2+xx(:,i2).^2- ... + 2.*xx(:,i2).*xx(:,i3)+xx(:,i3).^2).*(-xx(:,i2)+2.*xx(:,i1)-xx(:,i3)).*gx; +Wna(:) = Wna-1/16.*(yy(:,i2).^2-2.*yy(:,i2).*yy(:,i3)+yy(:,i3).^2+xx(:,i2).^2- ... + 2.*xx(:,i2).*xx(:,i3)+xx(:,i3).^2).*(-yy(:,i2)+2.*yy(:,i1)-yy(:,i3)).*gy; +Wna(:) = Wna./Area./len(:,i1); + +Wnb = 1/4*(yy(:,i1).^2+yy(:,i1).*yy(:,i3)-3.*yy(:,i2).*yy(:,i1)+ ... + 3.*yy(:,i2).*yy(:,i3)-2.*yy(:,i3).^2+xx(:,i1).^2+xx(:,i1).*xx(:,i3)- ... + 3.*xx(:,i2).*xx(:,i1)+3.*xx(:,i2).*xx(:,i3)-2.*xx(:,i3).^2).*zz; +Wnb(:) = Wnb-1/16*(6*yy(:,i1).*xx(:,i2).*yy(:,i3)-3*yy(:,i1).^2.*xx(:,i2)- ... + 2*yy(:,i1).*xx(:,i1).*yy(:,i3)+2*yy(:,i1).^2.*xx(:,i1)- ... + 4*yy(:,i1).*xx(:,i3).*yy(:,i3)+yy(:,i1).^2.*xx(:,i3)- ... + 2*yy(:,i2).*xx(:,i3).*yy(:,i3)+2*yy(:,i2).*xx(:,i3).*yy(:,i1)+ ... + 2*yy(:,i2).*xx(:,i1).*yy(:,i3)-2*yy(:,i2).*xx(:,i1).*yy(:,i1)+ ... + 3*yy(:,i3).^2.*xx(:,i3)-3*yy(:,i3).^2.*xx(:,i2)-xx(:,i1).^2.*xx(:,i3)+ ... + 2*xx(:,i1).^3+10*xx(:,i2).*xx(:,i1).*xx(:,i3)-5*xx(:,i2).*xx(:,i1).^2- ... + 4*xx(:,i1).*xx(:,i3).^2-5*xx(:,i3).^2.*xx(:,i2)+3*xx(:,i3).^3).*gx; +Wnb(:) = Wnb-1/16*(-yy(:,i1).^2.*yy(:,i3)+2*yy(:,i1).^3+ ... + 10*yy(:,i2).*yy(:,i1).*yy(:,i3)-5*yy(:,i2).*yy(:,i1).^2- ... + 4*yy(:,i1).*yy(:,i3).^2-5*yy(:,i3).^2.*yy(:,i2)+3*yy(:,i3).^3+ ... + 6*yy(:,i2).*xx(:,i1).*xx(:,i3)-3*yy(:,i2).*xx(:,i1).^2- ... + 2*yy(:,i1).*xx(:,i1).*xx(:,i3)+2*yy(:,i1).*xx(:,i1).^2- ... + 4*yy(:,i3).*xx(:,i1).*xx(:,i3)+yy(:,i3).*xx(:,i1).^2- ... + 2*yy(:,i3).*xx(:,i2).*xx(:,i3)+2*yy(:,i3).*xx(:,i2).*xx(:,i1)+ ... + 2*yy(:,i1).*xx(:,i2).*xx(:,i3)-2*yy(:,i1).*xx(:,i2).*xx(:,i1)+ ... + 3*xx(:,i3).^2.*yy(:,i3)-3*yy(:,i2).*xx(:,i3).^2).*gy; +Wnb(:) = Wnb./Area./len(:,i2); + +Wnc = 1/4*(yy(:,i2).*yy(:,i1)+yy(:,i1).^2-2*yy(:,i2).^2+3*yy(:,i2).*yy(:,i3)- ... + 3.*yy(:,i1).*yy(:,i3)+xx(:,i2).*xx(:,i1)+xx(:,i1).^2-2.*xx(:,i2).^2+ ... + 3.*xx(:,i2).*xx(:,i3)-3.*xx(:,i1).*xx(:,i3)).*zz; +Wnc(:) = Wnc-1/16*(yy(:,i1).^2.*xx(:,i2)-4*yy(:,i1).*xx(:,i2).*yy(:,i2)+ ... + 2*yy(:,i1).^2.*xx(:,i1)-2*yy(:,i2).*xx(:,i1).*yy(:,i1)- ... + 3*yy(:,i1).^2.*xx(:,i3)+6*yy(:,i2).*xx(:,i3).*yy(:,i1)- ... + 3*yy(:,i2).^2.*xx(:,i3)+3*yy(:,i2).^2.*xx(:,i2)+ ... + 2*yy(:,i1).*xx(:,i2).*yy(:,i3)-2*yy(:,i2).*xx(:,i2).*yy(:,i3)- ... + 2*yy(:,i1).*xx(:,i1).*yy(:,i3)+2*yy(:,i2).*xx(:,i1).*yy(:,i3)+ ... + 2*xx(:,i1).^3-xx(:,i2).*xx(:,i1).^2-4*xx(:,i2).^2.*xx(:,i1)- ... + 5*xx(:,i1).^2.*xx(:,i3)+10*xx(:,i2).*xx(:,i1).*xx(:,i3)+ ... + 3*xx(:,i2).^3-5*xx(:,i2).^2.*xx(:,i3)).*gx; +Wnc(:) = Wnc-1/16*(2*yy(:,i1).^3-yy(:,i2).*yy(:,i1).^2- ... + 4*yy(:,i2).^2.*yy(:,i1)-5*yy(:,i1).^2.*yy(:,i3)+ ... + 10*yy(:,i2).*yy(:,i1).*yy(:,i3)+3*yy(:,i2).^3- ... + 5*yy(:,i2).^2.*yy(:,i3)+yy(:,i2).*xx(:,i1).^2- ... + 4*yy(:,i2).*xx(:,i1).*xx(:,i2)+2*yy(:,i1).*xx(:,i1).^2- ... + 2*yy(:,i1).*xx(:,i2).*xx(:,i1)-3*yy(:,i3).*xx(:,i1).^2+ ... + 6*yy(:,i3).*xx(:,i2).*xx(:,i1)-3*yy(:,i3).*xx(:,i2).^2+ ... + 3*yy(:,i2).*xx(:,i2).^2+2*yy(:,i2).*xx(:,i1).*xx(:,i3)- ... + 2*yy(:,i2).*xx(:,i2).*xx(:,i3)-2*yy(:,i1).*xx(:,i1).*xx(:,i3)+ ... + 2*yy(:,i1).*xx(:,i2).*xx(:,i3)).*gy; +Wnc(:) = Wnc./Area./len(:,i3); + +Wn = Wna(:,[1 2 3]) + Wnb(:,[3 1 2]) + Wnc(:,[2 3 1]); + +% Find the nearest triangle (t) +t = tsearch(x,y,tri,xi,yi); + +% Only keep the relevant triangles. +out = find(isnan(t)); +if ~isempty(out), t(out) = ones(size(out)); end +tri = tri(t,:); +Area = Area(t,:); +len = len(t,:); +xx = xx(t,:); +yy = yy(t,:); +zz = zz(t,:); +gx = gx(t,:); +gy = gy(t,:); +gn = gn(t,:); +Wn = Wn(t,:); + +% Compute Barycentric coordinates (w). P. 78 in Watson. +w = 1/2.*((xx(:,i2)-repmat(xi,1,3)).*(yy(:,i3)-repmat(yi,1,3)) - ... + (xx(:,i3)-repmat(xi,1,3)).*(yy(:,i2)-repmat(yi,1,3)))./Area; +w(out,:) = ones(length(out),3); + +N1 = w(:,i1) + w(:,i1).^2.*w(:,i2) + w(:,i1).^2.*w(:,i3) - ... + w(:,i1).*w(:,i2).^2 - w(:,i1).*w(:,i3).^2; +N2 = (xx(:,i2)-xx(:,i1)).*(w(:,i1).^2.*w(:,i2)+1/2.*w(:,i1).*w(:,i2).*w(:,i3))+ ... + (xx(:,i3)-xx(:,i1)).*(w(:,i1).^2.*w(:,i3)+1/2.*w(:,i1).*w(:,i2).*w(:,i3)); +N3 = (yy(:,i2)-yy(:,i1)).*(w(:,i1).^2.*w(:,i2)+1/2.*w(:,i1).*w(:,i2).*w(:,i3))+ ... + (yy(:,i3)-yy(:,i1)).*(w(:,i1).^2.*w(:,i3)+1/2.*w(:,i1).*w(:,i2).*w(:,i3)); +N1(out) = zeros(size(out)); +N2(out) = zeros(size(out)); +N3(out) = zeros(size(out)); + +M = 8*Area./len.*w(:,i1).*w(:,i2).^2.*w(:,i3).^2 ./ ... + (w(:,i1)+w(:,i2)+(w(:,i1)+w(:,i2)==0)) ./ ... + (w(:,i1)+w(:,i3)+(w(:,i1)+w(:,i3)==0)); +M(out,:) = zeros(length(out),3); + +zi = sum((N1.*zz + N2.*gx + N3.*gy + M.*(gn - Wn)).').'; + +zi = reshape(zi,siz); + +if ~isempty(out), zi(out) = NaN; end +%------------------------------------------------------------ + +%------------------------------------------------------------ +function zi = nearest(x,y,z,xi,yi) +%NEAREST Triangle-based nearest neightbor interpolation + +% Reference: David F. Watson, "Contouring: A guide +% to the analysis and display of spacial data", Pergamon, 1994. + +siz = size(xi); +xi = xi(:); yi = yi(:); % Treat these a columns +x = x(:); y = y(:); z = z(:); % Treat these as columns + +% Triangularize the data +tri = delaunay(x,y,'sorted'); +if isempty(tri), + warning('Data cannot be triangulated.'); + zi = repmat(NaN,size(xi)); + return +end + +% Find the nearest vertex +k = dsearch(x,y,tri,xi,yi); + +zi = k; +d = find(isfinite(k)); +zi(d) = z(k(d)); +zi = reshape(zi,siz); +%---------------------------------------------------------- + + +%---------------------------------------------------------- +function [xi,yi,zi] = gdatav4(x,y,z,xi,yi) +%GDATAV4 MATLAB 4 GRIDDATA interpolation + +% Reference: David T. Sandwell, Biharmonic spline +% interpolation of GEOS-3 and SEASAT altimeter +% data, Geophysical Research Letters, 2, 139-142, +% 1987. Describes interpolation using value or +% gradient of value in any dimension. + +xy = x(:) + y(:)*sqrt(-1); + +% Determine distances between points +d = xy(:,ones(1,length(xy))); +d = abs(d - d.'); +n = size(d,1); +% Replace zeros along diagonal with ones (so these don't show up in the +% find below or in the Green's function calculation). +d(1:n+1:prod(size(d))) = ones(1,n); + +non = find(d == 0); +if ~isempty(non), + % If we've made it to here, then some points aren't distinct. Remove + % the non-distinct points by averaging. + [r,c] = find(d == 0); + k = find(r < c); + r = r(k); c = c(k); % Extract unique (row,col) pairs + v = (z(r) + z(c))/2; % Average non-distinct pairs + + rep = find(diff(c)==0); + if ~isempty(rep), % More than two points need to be averaged. + runs = find(diff(diff(c)==0)==1)+1; + for i=1:length(runs), + k = find(c==c(runs(i))); % All the points in a run + v(runs(i)) = mean(z([r(k);c(runs(i))])); % Average (again) + end + end + z(r) = v; + if ~isempty(rep), + z(r(runs)) = v(runs); % Make sure average is in the dataset + end + + % Now remove the extra points. + x(c) = []; + y(c) = []; + z(c) = []; + xy(c,:) = []; + xy(:,c) = []; + d(c,:) = []; + d(:,c) = []; + + % Determine the non distinct points + ndp = sort([r;c]); + ndp(find(ndp(1:length(ndp)-1)==ndp(2:length(ndp)))) = []; + + warning(sprintf(['Averaged %d non-distinct points.\n' ... + ' Indices are: %s.'],length(ndp),num2str(ndp'))) +end + +% Determine weights for interpolation +g = (d.^2) .* (log(d)-1); % Green's function. +% Fixup value of Green's function along diagonal +g(1:size(d,1)+1:prod(size(d))) = zeros(size(d,1),1); +weights = g \ z(:); + +[m,n] = size(xi); +zi = zeros(size(xi)); +jay = sqrt(-1); +xy = xy.'; + +% Evaluate at requested points (xi,yi). Loop to save memory. +for i=1:m + for j=1:n + d = abs(xi(i,j)+jay*yi(i,j) - xy); + mask = find(d == 0); + if length(mask)>0, d(mask) = ones(length(mask),1); end + g = (d.^2) .* (log(d)-1); % Green's function. + % Value of Green's function at zero + if length(mask)>0, g(mask) = zeros(length(mask),1); end + zi(i,j) = g * weights; + end +end + +if nargout<=1, + xi = zi; +end +%---------------------------------------------------------- + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP.M" index e95e3fb558f4513f1c7a127bd81d3c33db7ff644..5382da39c0fe98a701768b3af5333ea995f4dba3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP.M" @@ -1,3 +1,12 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2133aec16fa1b31b7b239691bf9c02f01c46bb6d333bc4812c1b5aebce53a5c8 -size 220 +function yi=interp(x,y,xi,method) +% һά·Çµ¥µ÷Êý¾Ý²åÖµ +% Ó÷¨²Î¿¼interp1£¬Î¨Ò»Çø±ðÊÇinterp²»ÒªÇó½ÚµãÊǵ¥µ÷µÄ + +% L.J.HU 4-15-1999 + +x=x(:);y=y(:); +z=[x,y]; +z=sortrows(z); +yi=interp1(z(:,1),z(:,2),xi,method); + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP1.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP1.M" index ed1cddbfd3263496f058b2e1bcefe12bcab4c3f4..fa00d68c09001f627c2cf6a0fc805ad44219ad90 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP1.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP1.M" @@ -1,3 +1,416 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:0c2a23417b98f31bbc6e035b358569010c58018c508b4aef0198702604834ce9 -size 13206 +function yi = interp1(varargin) +% yi=interp1(x,y,xi)¸ù¾ÝÊý¾Ý(x,y)¸ø³öÔÚxiµÄÏßÐÔ²åÖµ½á¹ûyi. +% yi=interp1(x,y,xi,'spline')ʹÓÃÈý´ÎÑùÌõ²åÖµ. +% yi=interp1(x,y,xi,'cubic')ʹÓÃÈý´Î²åÖµ. +% ÀýÈç +% clear;close;fplot('sin',[0,2*pi]);hold on; +% x=0:2*pi;y=sin(x); +% h1=plot(x,y,'ko'); +% xi=[1:5]+0.5; +% yi=interp1(x,y,xi,'linear'); +% h2=plot(xi,yi,'kx'); +% yi=interp1(x,y,xi,'spline'); +% h3=plot(xi,yi,'k*'); +% legend([h1;h2;h3],'data','linear','spline'); +% hold off; +% +%INTERP1 1-D interpolation (table lookup). +% YI = INTERP1(X,Y,XI) interpolates to find YI, the values of +% the underlying function Y at the points in the vector XI. +% The vector X specifies the points at which the data Y is +% given. If Y is a matrix, then the interpolation is performed +% for each column of Y and YI will be length(XI)-by-size(Y,2). +% Out of range values are returned as NaN. +% +% YI = INTERP1(Y,XI) assumes X = 1:N, where N is the length(Y) +% for vector Y or SIZE(Y,1) for matrix Y. +% +% Interpolation is the same operation as "table lookup". Described in +% "table lookup" terms, the "table" is [X,Y] and INTERP1 "looks-up" +% the elements of XI in X, and, based upon their location, returns +% values YI interpolated within the elements of Y. +% +% YI = INTERP1(X,Y,XI,'method') specifies alternate methods. +% The default is linear interpolation. Available methods are: +% +% 'nearest' - nearest neighbor interpolation +% 'linear' - linear interpolation +% 'spline' - cubic spline interpolation +% 'cubic' - cubic interpolation +% +% All the interpolation methods require that X be monotonic. X can be +% non-uniformly spaced. For faster interpolation when X is equally +% spaced and monotonic, use the methods '*linear', '*cubic', '*nearest'. +% For faster linear interpolation when X is non-uniformly spaced +% see INTERP1Q. +% +% For example, generate a coarse sine curve and interpolate over a +% finer abscissa: +% x = 0:10; y = sin(x); xi = 0:.25:10; +% yi = interp1(x,y,xi); plot(x,y,'o',xi,yi) +% +% See also INTERP1Q, INTERPFT, SPLINE, INTERP2, INTERP3, INTERPN. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.25 $ $Date: 1997/11/21 23:40:40 $ + +error(nargchk(2,4,nargin)); + +bypass = 0; +uniform = 1; +if isstr(varargin{end}), + narg = nargin-1; + method = [varargin{end} ' ']; % Protect against short string. + if method(1)=='*', % Direct call bypass. + if method(2)=='l', % linear interpolation. + yi = linear(varargin{1:end-1}); + return + + elseif method(2)=='c', % cubic interpolation + yi = cubic(varargin{1:end-1}); + return + + elseif method(2)=='n', % Nearest neighbor interpolation + yi = nearest(varargin{1:end-1}); + return + + elseif method(2)=='s', % Spline interpolation + method = 'spline'; bypass = 1; + + else + error([deblank(method),' is an invalid method.']); + + end + elseif method(1)=='s', % Spline interpolation + method = 'spline'; bypass = 1; + end + +else + narg = nargin; + method = 'linear'; +end + +if narg==2, % interp1(y,xi) + y = varargin{1}; + if min(size(y))==1, x = 1:length(y); else x = 1:size(y,1); end + [msg,x,y,xi] = xychk(x,varargin{1:2}); + +elseif narg==3, % interp1(x,y,xi) + [msg,x,y,xi] = xychk(varargin{1:3}); + +end + +if ~isempty(msg), error(msg); end + +if isempty(xi), yi = []; return, end +if min(size(xi))~=1, error('XI must be a vector.'); end + +x = x(:); % Make sure x is a column vector. +if min(size(y))==1, y = y(:); end % Make sure y is a column vector. +siz = size(xi); xi = xi(:); % Make sure xi is a column vector. + +% +% Check for non-equally spaced data. If so, map x and +% xi to matrix (row,col) coordinate system. +% +if length(x)>2 & ~bypass, + dx = diff(x); + if max(abs(diff(dx))) > eps*max(x), + if any(dx < 0), % Flip orientation of data so x is increasing. + if size(x,1)==1, + x = fliplr(x); y = fliplr(y); + dx = -fliplr(dx); + else + x(:) = flipud(x); y(:) = flipud(y); + dx(:) = -flipud(dx); + end + end + + if any(dx<=0), + error('X must be monotonic.'); + return + end + + % Only nearest needs this mapping code now + if method(1)=='n', + + % Determine the nearest location of xi in x + [xxi,j] = sort(xi(:)); + [dum,i] = sort([x;xxi]); + ui(i) = 1:length(i); + ui = (ui(length(x)+1:end) - (1:length(xxi)))'; + ui(j) = ui; + + % Map values in xi to index offset (ui) via linear interpolation + ui(ui<1) = 1; + ui(ui>length(x)-1) = length(x)-1; + ui = ui + (xi(:)-x(ui))./(x(ui+1)-x(ui)); + + x = (1:length(x)).'; + xi = ui; + else + uniform = 0; + end + end +end + +% +% Now do the interpolation based on the method flag +% +if method(1)=='n', % Nearest neighbor interpolation + yi = nearest(x,y,xi); + +elseif method(1)=='l', % Linear interpolation + if uniform + yi = linear(x,y,xi); + else + yi = interp1q(x,y,xi); + end + +elseif method(1)=='s', % Spline interpolation + yi = spline(x,y.',xi(:).').'; + +elseif method(1)=='c', % Cubic interpolation + if uniform + yi = cubic(x,y,xi); + else + d = find(xi < min(x) | xi > max(x)); + yi = spline(x,y.',xi(:).').'; + if min(size(yi))==1, yi(d) = NaN; else yi(d,:) = NaN; end + end + +else + error([deblank(method),' is an invalid method.']); + +end + +if (min(size(yi))==1) & (prod(siz)>1), yi = reshape(yi,siz); end + + +%------------------------------------------------------ +function F=linear(x,y,u) +%LINEAR Linear Interpolation of a 1-D function. +% F=LINEAR(Y,XI) returns the value of the 1-D function Y at the +% points XI using linear interpolation. length(F)=length(XI). XI is +% an index into the vector Y. Y is the value of the function +% evaluated uniformly on a interval. If Y is a matrix, then +% the interpolation is performed for each column of Y in which +% case F is length(XI)-by-size(Y,2). +% +% If Y is of length N then XI must contain values between 1 and N. +% The value NaN is returned if this is not the case. +% +% F = LINEAR(X,Y,XI) uses the vector X to specify the coordinates +% of the underlying interval. X must be equally spaced and +% monotonic. NaN's are returned for values of XI outside the +% coordinates in X. +% +% See also CUBIC, INTERP1. + +% Clay M. Thompson 7-4-91 + +if nargin==2, % No X specified. + u = y; y = x; + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + [nrows,ncols] = size(y); + +elseif nargin==3, % X specified. + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + if min(size(x))==1, x = x(:); end + [nrows,ncols] = size(y); + % Scale and shift u to be indices into Y. + if (min(size(x))~=1), error('X must be a vector.'); end + [m,n] = size(x); + if m ~= nrows, + error('The length of X must match the number of rows of Y.'); + end + u = 1 + (u-x(1))/(x(m)-x(1))*(nrows-1); + +else + error('Wrong number of input arguments.'); +end + +if isempty(u), F = []; return, end +if nrows<2, error('Y must have at least 2 rows.'); end + +siz = size(u); +u = u(:); % Make sure u is a vector +u = u(:,ones(1,ncols)); % Expand u +[m,n] = size(u); + +% Check for out of range values of u and set to 1 +uout = find(u<1 | u>nrows); +if ~isempty(uout), u(uout) = 1; end + +% Interpolation parameters, check for boundary value. +s = (u - floor(u)); +u = floor(u); +if isempty(u), d = u; else d = find(u==nrows); end +if length(d)>0, u(d) = u(d)-1; s(d) = s(d)+1; end + +% Now interpolate. +v = (0:n-1)*nrows; +ndx = u+v(ones(m,1),:); +F = ( y(ndx).*(1-s) + y(ndx+1).*s ); + +% Now set out of range values to NaN. +if ~isempty(uout), F(uout) = NaN; end + +if (min(size(F))==1) & (prod(siz)>1), F = reshape(F,siz); end + + +%------------------------------------------------------ +function F=cubic(x,y,u) +%CUBIC Cubic Interpolation of a 1-D function. +% YI=CUBIC(Y,XI) returns the value of the 1-D function Y at the +% points XI using cubic interpolation. length(YI)=length(XI). XI is +% an index into the vector Y. Y is the value of the function +% evaluated uniformly on a interval. If Y is a matrix, then +% the interpolation is performed for each column of Y in which +% case F is length(XI)-by-size(Y,2). +% +% If Y is of length N then XI must contain values between 1 and N. +% The value NaN is returned if this is not the case. +% +% YI = CUBIC(X,Y,XI) uses the vector X to specify the coordinates +% of the underlying interval. X must be equally spaced and +% monotonic. NaN's are returned for values of XI outside the +% coordinates in X. +% +% See also LINEAR, INTERP1. + +% Clay M. Thompson 7-4-91 + +% Based on "Cubic Convolution Interpolation for Digital Image +% Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and +% Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160. + +if nargin==2, % No X specified. + u = y; y = x; + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + [nrows,ncols] = size(y); + +elseif nargin==3, % X specified. + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + if min(size(x))==1, x = x(:); end + [nrows,ncols] = size(y); + % Scale and shift u to be indices into Y. + if (min(size(x))~=1), error('X must be a vector.'); end + [m,n] = size(x); + if m ~= nrows, + error('The length of X must match the number of rows of Y.'); + end + u = 1 + (u-x(1))/(x(m)-x(1))*(nrows-1); + +else + error('Wrong number of input arguments.'); +end + +if isempty(u), F = []; return, end +if nrows<3, error('Y must have at least 3 rows.'); end + +siz = size(u); u = u(:); % Make sure u is a vector. +u = u(:,ones(1,ncols)); % Expand u +[m,n] = size(u); + +% Check for out of range values of u and set to 1 +if isempty(u), uout = u; else uout = find(u<1 | u>nrows); end +if ~isempty(uout), u(uout) = 1; end + +% Interpolation parameters, check for boundary value. +s = (u - floor(u)); +u = floor(u); +if isempty(u), d = u; else d = find(u==nrows); end +if length(d)>0, u(d) = u(d)-1; s(d) = s(d)+1; end + +% Expand y so interpolation is valid at the boundary. +y = [3*y(1,:)-3*y(2,:)+y(3,:);y;3*y(nrows,:)-3*y(nrows-1,:)+y(nrows-2,:)]; +nrows = nrows + 2; + +% Now interpolate using computationally efficient algorithm. +s2 = s.*s; s3 = s.*s2; +v = (0:n-1)*nrows; +ndx = u+v(ones(m,1),:); +F = y(ndx).*(-s3+2*s2-s) + y(ndx+1).*(3*s3-5*s2+2) + ... + y(ndx+2).*(-3*s3+4*s2+s) + y(ndx+3).*(s3-s2); +F = F/2; + +% Now set out of range values to NaN. +if ~isempty(uout), F(uout) = NaN; end + +if (min(size(F))==1) & (prod(siz)>1), F = reshape(F,siz); end + + +%------------------------------------------------------ +function F = nearest(x,y,u) +%NEAREST Nearest Neighbor Interpolation of a 1-D function. +% YI=NEAREST(Y,XI) returns the value of the 1-D function Y at +% the points XI using nearest neighbor interpolation, +% length(YI)=length(XI). XI is an index into the vector Y. Y is +% the value of the function evaluated uniformly on a interval. If +% Y is a matrix, then the interpolation is performed for each +% column of Y in which case F is length(XI)-by-size(Y,2). +% +% If Y is of length N then XI must contain values between 1 and N. +% The value NaN is returned if this is not the case. +% +% YI = NEAREST(X,Y,XI) uses the vector X to specify the +% coordinates of the underlying interval. X must be equally spaced +% and monotonic. NaN's are returned for values of XI outside the +% coordinates in X. +% +% See also LINEAR, INTERP1. + +% Clay M. Thompson 7-4-91 + +if nargin==2, % No X specified. + u = y; y = x; + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + [nrows,ncols] = size(y); + +elseif nargin==3, % X specified. + % Check for vector problem. If so, make everything a column vector. + if min(size(y))==1, y = y(:); end + if min(size(x))==1, x = x(:); end + [nrows,ncols] = size(y); + % Scale and shift u to be indices into Y. + if (min(size(x))~=1), error('X must be a vector.'); end + [m,n] = size(x); + if m ~= nrows, + error('The length of X must match the number of rows of Y.'); + end + u = 1 + (u-x(1))/(x(m)-x(1))*(nrows-1); + +else + error('Wrong number of input arguments.'); +end + +if isempty(u), F = []; return, end +if nrows<2, error('Y must have at least 2 rows.'); end + +siz = size(u); u = u(:); % Make sure u is a vector. +u = u(:,ones(1,ncols)); % Expand u +[m,n] = size(u); + +% Check for out of range values of u and set to 1 +uout = find(u<.5 | u>=nrows+.5); +if ~isempty(uout), u(uout) = 1; end + +% Interpolation parameters +s = (u - round(u)); +u = round(u); + +% Now interpolate +v = (0:n-1)*nrows; +ndx = u+v(ones(m,1),:); +F = y(ndx); + +% Now set out of range values to NaN. +if ~isempty(uout), F(uout) = NaN; end + +if (min(size(F))==1) & (prod(siz)>1), F = reshape(F,siz); end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP2.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP2.M" index 79fce294f130db009681d95a81c5ce74b7861158..2c65b509baae00f118eee32429d20a7f1e99aa39 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP2.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/INTERP2.M" @@ -1,3 +1,555 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:89f0cae3601524a3e6cd6b6757e6859df524d58f85c05c38986343dc14fabc37 -size 18639 +function zi = interp2(varargin) +%¶þÔªº¯ÊýÍø¸ñÊý¾ÝµÄ²åÖµ +%ZI=interp2(X,Y,Z,XI,YI,'·½·¨') Çó¶þÔªº¯Êýz=f(x,y)µÄ²åÖµ. +% ÕâÀïX,Y,ZÊÇͬάÊý¾ØÕó±íʾÍø¸ñÊý¾Ý,XI,YI,ZIÊÇͬάÊý¾ØÕó±íʾ²åÖµµã. +%»òZI=interp2(x,y,z,xi,yi)ÆäÖÐ,x,xiΪÐÐÏòÁ¿,y,yiΪÁÐÏòÁ¿. +% 'bilinear',ʹÓÃË«ÏßÐÔ²åÖµ(ĬÈÏ) +% 'spline' ʹÓöþÔªÈý´ÎÑùÌõ²åÖµ. +% 'cubic' ʹÓöþÔªÈý´Î²åÖµ. +%ÀýÈç +% clear;close;x=0:4;y=2:4; +% Z=[82 81 80 82 84;79 63 61 65 81;84 84 82 85 86]; +% [X,Y]=meshgrid(x,y); +% subplot(2,1,1); +% mesh(X,Y,Z);title('RAW DATA'); +% xi=0:0.1:4;yi=2:0.2:4; +% [XI,YI]=meshgrid(xi,yi); +% zspline=interp2(x,y,z,XI,YI,'spline'); +% subplot(2,1,2); +% mesh(XI,YI,zspline); +% title('SPLINE'); +% +%INTERP2 2-D interpolation (table lookup). +% ZI = INTERP2(X,Y,Z,XI,YI) interpolates to find ZI, the values of the +% underlying 2-D function Z at the points in matrices XI and YI. +% Matrices X and Y specify the points at which the data Z is given. +% Out of range values are returned as NaN. +% +% XI can be a row vector, in which case it specifies a matrix with +% constant columns. Similarly, YI can be a column vector and it +% specifies a matrix with constant rows. +% +% ZI = INTERP2(Z,XI,YI) assumes X=1:N and Y=1:M where [M,N]=SIZE(Z). +% ZI = INTERP2(Z,NTIMES) expands Z by interleaving interpolates between +% every element, working recursively for NTIMES. INTERP2(Z) is the +% same as INTERP2(Z,1). +% +% ZI = INTERP2(...,'method') specifies alternate methods. The default +% is linear interpolation. Available methods are: +% +% 'nearest' - nearest neighbor interpolation +% 'linear' - bilinear interpolation +% 'cubic' - bicubic interpolation +% 'spline' - spline interpolation +% +% All the interpolation methods require that X and Y be monotonic and +% plaid (as if they were created using MESHGRID). X and Y can be +% non-uniformly spaced. For faster interpolation when X and Y are +% equally spaced and monotonic, use the methods '*linear', '*cubic', or +% '*nearest'. +% +% For example, to generate a coarse approximation of PEAKS and +% interpolate over a finer mesh: +% [x,y,z] = peaks(10); [xi,yi] = meshgrid(-3:.1:3,-3:.1:3); +% zi = interp2(x,y,z,xi,yi); mesh(xi,yi,zi) +% +% See also INTERP1, INTERP3, INTERPN, MESHGRID, GRIDDATA. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.26 $ + +error(nargchk(1,6,nargin)); + +bypass = 0; +uniform = 1; +if isstr(varargin{end}), + narg = nargin-1; + method = [varargin{end} ' ']; % Protect against short string. + if method(1)=='*', % Direct call bypass. + if method(2)=='l' | all(method(2:4)=='bil'), % bilinear interpolation. + zi = linear(varargin{1:end-1}); + return + + elseif method(2)=='c' | all(method(2:4)=='bic'), % bicubic interpolation + zi = cubic(varargin{1:end-1}); + return + + elseif method(2)=='n', % Nearest neighbor interpolation + zi = nearest(varargin{1:end-1}); + return + + elseif method(2)=='s', % spline interpolation + method = 'spline'; bypass = 1; + + else + error([deblank(method),' is an invalid method.']); + + end + elseif method(1)=='s', % Spline interpolation + method = 'spline'; bypass = 1; + end + +else + narg = nargin; + method = 'linear'; +end + +if narg==1, % interp2(z), % Expand Z + [nrows,ncols] = size(varargin{1}); + xi = 1:.5:ncols; yi = (1:.5:nrows)'; + x = 1:ncols; y = (1:nrows); + [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi); + +elseif narg==2. % interp2(z,n), Expand Z n times + [nrows,ncols] = size(varargin{1}); + ntimes = floor(varargin{2}(1)); + xi = 1:1/(2^ntimes):ncols; yi = (1:1/(2^ntimes):nrows)'; + x = 1:ncols; y = (1:nrows); + [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1},xi,yi); + +elseif narg==3, % interp2(z,xi,yi) + [nrows,ncols] = size(varargin{1}); + x = 1:ncols; y = (1:nrows); + [msg,x,y,z,xi,yi] = xyzchk(x,y,varargin{1:3}); + +elseif narg==4, + error('Wrong number of input arguments.'); + +elseif narg==5, % linear(x,y,z,xi,yi) + [msg,x,y,z,xi,yi] = xyzchk(varargin{1:5}); + +end + +if ~isempty(msg), error(msg); end + +% +% Check for plaid data. +% +xx = x(1,:); yy = y(:,1); +if (size(x,2)>1 & ~isequal(repmat(xx,size(x,1),1),x)) | ... + (size(y,1)>1 & ~isequal(repmat(yy,1,size(y,2)),y)), + error(sprintf(['X and Y must be matrices produced by MESHGRID. Use' ... + ' GRIDDATA instead \nof INTERP2 for scattered data.'])); +end + +% +% Check for non-equally spaced data. If so, map (x,y) and +% (xi,yi) to matrix (row,col) coordinate system. +% +if ~bypass, + xx = xx.'; % Make sure it's a column. + dx = diff(xx); dy = diff(yy); + xdiff = max(abs(diff(dx))); if isempty(xdiff), xdiff = 0; end + ydiff = max(abs(diff(dy))); if isempty(ydiff), ydiff = 0; end + if (xdiff > eps*max(abs(xx))) | (ydiff > eps*max(abs(yy))), + if any(dx < 0), % Flip orientation of data so x is increasing. + x = fliplr(x); y = fliplr(y); z = fliplr(z); + xx = flipud(xx); dx = -flipud(dx); + end + if any(dy < 0), % Flip orientation of data so y is increasing. + x = flipud(x); y = flipud(y); z = flipud(z); + yy = flipud(yy); dy = -flipud(dy); + end + + if any(dx<=0) | any(dy<=0), + error('X and Y must be monotonic vectors or matrices produced by MESHGRID.'); + end + + % Bypass mapping code for cubic + if method(1)~='c', + % Determine the nearest location of xi in x + [xxi,j] = sort(xi(:)); + [dum,i] = sort([xx;xxi]); + ui(i) = (1:length(i)); + ui = (ui(length(xx)+1:end)-(1:length(xxi)))'; + ui(j) = ui; + + % Map values in xi to index offset (ui) via linear interpolation + ui(ui<1) = 1; + ui(ui>length(xx)-1) = length(xx)-1; + ui = ui + (xi(:)-xx(ui))./(xx(ui+1)-xx(ui)); + + % Determine the nearest location of yi in y + [yyi,j] = sort(yi(:)); + [dum,i] = sort([yy;yyi(:)]); + vi(i) = (1:length(i)); + vi = (vi(length(yy)+1:end)-(1:length(yyi)))'; + vi(j) = vi; + + % Map values in yi to index offset (vi) via linear interpolation + vi(vi<1) = 1; + vi(vi>length(yy)-1) = length(yy)-1; + vi = vi + (yi(:)-yy(vi))./(yy(vi+1)-yy(vi)); + + [x,y] = meshgrid(1:size(x,2),1:size(y,1)); + xi(:) = ui; yi(:) = vi; + else + uniform = 0; + end + end +end + +% Now do the interpolation based on method. +method = [lower(method),' ']; % Protect against short string + +if method(1)=='l' | all(method(1:3)=='bil'), % bilinear interpolation. + zi = linear(x,y,z,xi,yi); + +elseif method(1)=='c' | all(method(1:3)=='bic'), % bicubic interpolation + if uniform + zi = cubic(x,y,z,xi,yi); + else + d = find(xi < min(x(:)) | xi > max(x(:)) | ... + yi < min(y(:)) | yi > max(y(:))); + zi = spline2(x,y,z,xi,yi); + zi(d) = NaN; + end + +elseif method(1)=='n', % Nearest neighbor interpolation + zi = nearest(x,y,z,xi,yi); + +elseif method(1)=='s', % Spline interpolation + zi = spline2(x,y,z,xi,yi); + +else + error([deblank(method),' is an invalid method.']); + +end + +%------------------------------------------------------ +function F = linear(arg1,arg2,arg3,arg4,arg5) +%LINEAR 2-D bilinear data interpolation. +% ZI = LINEAR(X,Y,Z,XI,YI) uses bilinear interpolation to +% find ZI, the values of the underlying 2-D function in Z at the points +% in matrices XI and YI. Matrices X and Y specify the points at which +% the data Z is given. X and Y can also be vectors specifying the +% abscissae for the matrix Z as for MESHGRID. In both cases, X +% and Y must be equally spaced and monotonic. +% +% Values of NaN are returned in ZI for values of XI and YI that are +% outside of the range of X and Y. +% +% If XI and YI are vectors, LINEAR returns vector ZI containing +% the interpolated values at the corresponding points (XI,YI). +% +% ZI = LINEAR(Z,XI,YI) assumes X = 1:N and Y = 1:M, where +% [M,N] = SIZE(Z). +% +% ZI = LINEAR(Z,NTIMES) returns the matrix Z expanded by interleaving +% bilinear interpolates between every element, working recursively +% for NTIMES. LINEAR(Z) is the same as LINEAR(Z,1). +% +% This function needs about 4 times SIZE(XI) memory to be available. +% +% See also INTERP2, CUBIC. + +% Clay M. Thompson 4-26-91, revised 7-3-91, 3-22-93 by CMT. + +if nargin==1, % linear(z), Expand Z + [nrows,ncols] = size(arg1); + s = 1:.5:ncols; sizs = size(s); + t = (1:.5:nrows)'; sizt = size(t); + s = s(ones(sizt),:); + t = t(:,ones(sizs)); + +elseif nargin==2, % linear(z,n), Expand Z n times + [nrows,ncols] = size(arg1); + ntimes = floor(arg2); + s = 1:1/(2^ntimes):ncols; sizs = size(s); + t = (1:1/(2^ntimes):nrows)'; sizt = size(t); + s = s(ones(sizt),:); + t = t(:,ones(sizs)); + +elseif nargin==3, % linear(z,s,t), No X or Y specified. + [nrows,ncols] = size(arg1); + s = arg2; t = arg3; + +elseif nargin==4, + error('Wrong number of input arguments.'); + +elseif nargin==5, % linear(x,y,z,s,t), X and Y specified. + [nrows,ncols] = size(arg3); + mx = prod(size(arg1)); my = prod(size(arg2)); + if any([mx my] ~= [ncols nrows]) & ... + ~isequal(size(arg1),size(arg2),size(arg3)) + error('The lengths of the X and Y vectors must match Z.'); + end + if any([nrows ncols]<[2 2]), error('Z must be at least 2-by-2.'); end + s = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1); + t = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1); + +end + +if any([nrows ncols]<[2 2]), error('Z must be at least 2-by-2.'); end +if ~isequal(size(s),size(t)), + error('XI and YI must be the same size.'); +end + +% Check for out of range values of s and set to 1 +sout = find((s<1)|(s>ncols)); +if length(sout)>0, s(sout) = ones(size(sout)); end + +% Check for out of range values of t and set to 1 +tout = find((t<1)|(t>nrows)); +if length(tout)>0, t(tout) = ones(size(tout)); end + +% Matrix element indexing +ndx = floor(t)+floor(s-1)*nrows; + +% Compute intepolation parameters, check for boundary value. +if isempty(s), d = s; else d = find(s==ncols); end +s(:) = (s - floor(s)); +if length(d)>0, s(d) = s(d)+1; ndx(d) = ndx(d)-nrows; end + +% Compute intepolation parameters, check for boundary value. +if isempty(t), d = t; else d = find(t==nrows); end +t(:) = (t - floor(t)); +if length(d)>0, t(d) = t(d)+1; ndx(d) = ndx(d)-1; end +d = []; + +% Now interpolate, reuse u and v to save memory. +if nargin==5, + F = ( arg3(ndx).*(1-t) + arg3(ndx+1).*t ).*(1-s) + ... + ( arg3(ndx+nrows).*(1-t) + arg3(ndx+(nrows+1)).*t ).*s; +else + F = ( arg1(ndx).*(1-t) + arg1(ndx+1).*t ).*(1-s) + ... + ( arg1(ndx+nrows).*(1-t) + arg1(ndx+(nrows+1)).*t ).*s; +end + +% Now set out of range values to NaN. +if length(sout)>0, F(sout) = NaN; end +if length(tout)>0, F(tout) = NaN; end + + + +%------------------------------------------------------ +function F = cubic(arg1,arg2,arg3,arg4,arg5) +%CUBIC 2-D bicubic data interpolation. +% CUBIC(...) is the same as LINEAR(....) except that it uses +% bicubic interpolation. +% +% This function needs about 7-8 times SIZE(XI) memory to be available. +% +% See also LINEAR. + +% Clay M. Thompson 4-26-91, revised 7-3-91, 3-22-93 by CMT. + +% Based on "Cubic Convolution Interpolation for Digital Image +% Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and +% Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160. + +if nargin==1, % cubic(z), Expand Z + [nrows,ncols] = size(arg1); + s = 1:.5:ncols; sizs = size(s); + t = (1:.5:nrows)'; sizt = size(t); + s = s(ones(sizt),:); + t = t(:,ones(sizs)); + +elseif nargin==2, % cubic(z,n), Expand Z n times + [nrows,ncols] = size(arg1); + ntimes = floor(arg2); + s = 1:1/(2^ntimes):ncols; sizs = size(s); + t = (1:1/(2^ntimes):nrows)'; sizt = size(t); + s = s(ones(sizt),:); + t = t(:,ones(sizs)); + +elseif nargin==3, % cubic(z,s,t), No X or Y specified. + [nrows,ncols] = size(arg1); + s = arg2; t = arg3; + +elseif nargin==4, + error('Wrong number of input arguments.'); + +elseif nargin==5, % cubic(x,y,z,s,t), X and Y specified. + [nrows,ncols] = size(arg3); + mx = prod(size(arg1)); my = prod(size(arg2)); + if any([mx my] ~= [ncols nrows]) & ... + ~isequal(size(arg1),size(arg2),size(arg3)) + error('The lengths of the X and Y vectors must match Z.'); + end + if any([nrows ncols]<[3 3]), error('Z must be at least 3-by-3.'); end + s = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1); + t = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1); + +end + +if any([nrows ncols]<[3 3]), error('Z must be at least 3-by-3.'); end +if ~isequal(size(s),size(t)), + error('XI and YI must be the same size.'); +end + +% Check for out of range values of s and set to 1 +sout = find((s<1)|(s>ncols)); +if length(sout)>0, s(sout) = ones(size(sout)); end + +% Check for out of range values of t and set to 1 +tout = find((t<1)|(t>nrows)); +if length(tout)>0, t(tout) = ones(size(tout)); end + +% Matrix element indexing +ndx = floor(t)+floor(s-1)*(nrows+2); + +% Compute intepolation parameters, check for boundary value. +if isempty(s), d = s; else d = find(s==ncols); end +s(:) = (s - floor(s)); +if length(d)>0, s(d) = s(d)+1; ndx(d) = ndx(d)-nrows-2; end + +% Compute intepolation parameters, check for boundary value. +if isempty(t), d = t; else d = find(t==nrows); end +t(:) = (t - floor(t)); +if length(d)>0, t(d) = t(d)+1; ndx(d) = ndx(d)-1; end +d = []; + +if nargin==5, + % Expand z so interpolation is valid at the boundaries. + zz = zeros(size(arg3)+2); + zz(1,2:ncols+1) = 3*arg3(1,:)-3*arg3(2,:)+arg3(3,:); + zz(2:nrows+1,2:ncols+1) = arg3; + zz(nrows+2,2:ncols+1) = 3*arg3(nrows,:)-3*arg3(nrows-1,:)+arg3(nrows-2,:); + zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4); + zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1); + nrows = nrows+2; ncols = ncols+2; +else + % Expand z so interpolation is valid at the boundaries. + zz = zeros(size(arg1)+2); + zz(1,2:ncols+1) = 3*arg1(1,:)-3*arg1(2,:)+arg1(3,:); + zz(2:nrows+1,2:ncols+1) = arg1; + zz(nrows+2,2:ncols+1) = 3*arg1(nrows,:)-3*arg1(nrows-1,:)+arg1(nrows-2,:); + zz(:,1) = 3*zz(:,2)-3*zz(:,3)+zz(:,4); + zz(:,ncols+2) = 3*zz(:,ncols+1)-3*zz(:,ncols)+zz(:,ncols-1); + nrows = nrows+2; ncols = ncols+2; +end + +% Now interpolate using computationally efficient algorithm. +t0 = ((2-t).*t-1).*t; +t1 = (3*t-5).*t.*t+2; +t2 = ((4-3*t).*t+1).*t; +t(:) = (t-1).*t.*t; +F = ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ... + .* (((2-s).*s-1).*s); +ndx(:) = ndx + nrows; +F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ... + .* ((3*s-5).*s.*s+2); +ndx(:) = ndx + nrows; +F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ... + .* (((4-3*s).*s+1).*s); +ndx(:) = ndx + nrows; +F(:) = F + ( zz(ndx).*t0 + zz(ndx+1).*t1 + zz(ndx+2).*t2 + zz(ndx+3).*t ) ... + .* ((s-1).*s.*s); +F(:) = F/4; + +% Now set out of range values to NaN. +if length(sout)>0, F(sout) = NaN; end +if length(tout)>0, F(tout) = NaN; end + + +%------------------------------------------------------ +function F = nearest(arg1,arg2,arg3,arg4,arg5) +%NEAREST 2-D Nearest neighbor interpolation. +% ZI = NEAREST(X,Y,Z,XI,YI) uses nearest neighbor interpolation to +% find ZI, the values of the underlying 2-D function in Z at the points +% in matrices XI and YI. Matrices X and Y specify the points at which +% the data Z is given. X and Y can also be vectors specifying the +% abscissae for the matrix Z as for MESHGRID. In both cases, X +% and Y must be equally spaced and monotonic. +% +% Values of NaN are returned in ZI for values of XI and YI that are +% outside of the range of X and Y. +% +% If XI and YI are vectors, NEAREST returns vector ZI containing +% the interpolated values at the corresponding points (XI,YI). +% +% ZI = NEAREST(Z,XI,YI) assumes X = 1:N and Y = 1:M, where +% [M,N] = SIZE(Z). +% +% F = NEAREST(Z,NTIMES) returns the matrix Z expanded by interleaving +% interpolates between every element. NEAREST(Z) is the same as +% NEAREST(Z,1). +% +% See also INTERP2, LINEAR, CUBIC. + +% Clay M. Thompson 4-26-91, revised 7-3-91 by CMT. + +if nargin==1, % nearest(z), Expand Z + [nrows,ncols] = size(arg1); + u = ones(2*nrows-1,1)*(1:.5:ncols); + v = (1:.5:nrows)'*ones(1,2*ncols-1); + +elseif nargin==2, % nearest(z,n), Expand Z n times + [nrows,ncols] = size(arg1); + ntimes = floor(arg2); + u = 1:1/(2^ntimes):ncols; sizu = size(u); + v = (1:1/(2^ntimes):nrows)'; sizv = size(v); + u = u(ones(sizv),:); + v = v(:,ones(sizu)); + +elseif nargin==3, % nearest(z,u,v) + [nrows,ncols] = size(arg1); + u = arg2; v = arg3; + +elseif nargin==4, + error('Wrong number of input arguments.'); + +elseif nargin==5, % nearest(x,y,z,u,v), X and Y specified. + [nrows,ncols] = size(arg3); + mx = prod(size(arg1)); my = prod(size(arg2)); + if any([mx my] ~= [ncols nrows]) & (size(arg1)~=size(arg3) | ... + size(arg2)~=size(arg3)), + error('The lengths of the X and Y vectors must match Z.'); + end + if all([nrows ncols]>[1 1]), + u = 1 + (arg4-arg1(1))/(arg1(mx)-arg1(1))*(ncols-1); + v = 1 + (arg5-arg2(1))/(arg2(my)-arg2(1))*(nrows-1); + else + u = 1 + (arg4-arg1(1)); + v = 1 + (arg5-arg2(1)); + end +end + +if size(u)~=size(v), error('XI and YI must be the same size.'); end + +% Check for out of range values of u and set to 1 +uout = (u<.5)|(u>=ncols+.5); +nuout = sum(uout(:)); +if any(uout(:)), u(uout) = ones(nuout,1); end + +% Check for out of range values of v and set to 1 +vout = (v<.5)|(v>=nrows+.5); +nvout = sum(vout(:)); +if any(vout(:)), v(vout) = ones(nvout,1); end + +% Interpolation parameters +s = (u - round(u)); t = (v - round(v)); +u = round(u); v = round(v); + +% Now interpolate +ndx = v+(u-1)*nrows; +if nargin==5, + F = arg3(ndx); +else + F = arg1(ndx); +end + +% Now set out of range values to NaN. +if any(uout(:)), F(uout) = NaN; end +if any(vout(:)), F(vout) = NaN; end + +%---------------------------------------------------------- +function F = spline2(varargin) +%2-D spline interpolation + +% Determine abscissa vectors +varargin{1} = varargin{1}(1,:); +varargin{2} = varargin{2}(:,1).'; + +% +% Check for plaid data. +% +xi = varargin{4}; yi = varargin{5}; +xxi = xi(1,:); yyi = yi(:,1); +if (size(xi,2)>1 & ~isequal(repmat(xxi,size(xi,1),1),xi)) | ... + (size(yi,1)>1 & ~isequal(repmat(yyi,1,size(yi,2)),yi)), + F = splncore(varargin(2:-1:1),varargin{3},varargin(5:-1:4)); +else + F = splncore(varargin(2:-1:1),varargin{3},{yyi(:).' xxi},'gridded'); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/LAGRANGE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/LAGRANGE.M" index 76145b5d8ad2276761759f88bdbf6062c534994b..1c2f413125c688256e1c698062543a10fe2bd8b9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/LAGRANGE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/LAGRANGE.M" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d1cd5bffd3aa8e9066c96a2c7f9b040d72242329669f2272fdf57362e484db77 -size 736 +function yy=lagrange(x,y,xx) +% Lagrange ²åÖµ +% yy=lagrange(x,y,xx)ÇóÊý¾Ý(x,y)Ëù±í´ïµÄº¯ÊýÔÚ²åÖµµãxx´¦µÄ²åÖµ +% ÒªÇóx,yΪͬάÊýÏòÁ¿ +%ÀýÈç Êý¾Ý +% x | 0.1 0.2 0.15 0.0 -0.2 0.3 +% --|------------------------------ +% y | 0.95 0.84 0.86 1.06 1.50 0.72 +% Çó½â +% clear;close; +% x=[0.1,0.2,0.15,0,-0.2,0.3]; +% y=[0.95,0.84,0.86,1.06,1.50,0.72]; +% xi=-0.2:0.01:0.3; +% yi=lagrange(x,y,xi); +% plot(x,y,'o',xi,yi,'k'); +% title('lagrange'); + +% L.J. Hu 8-20-1998 + +m=length(x);n=length(y); +if m~=n, error('ÏòÁ¿xÓëyµÄ³¤¶È±ØÐëÒ»ÖÂ');end +s=0; +for i=1:n + t=ones(1,length(xx)); + for j=1:n + if j~=i, + t=t.*(xx-x(j))/(x(i)-x(j)); + end + end + s=s+t*y(i); +end +yy=s; + + \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/POLYFIT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/POLYFIT.M" index d64ef4cc65caaabd09afe7d2ea0c364237f9a07d..ec1d050c7bab8ea00b2a5fed4ed472e0ae49c88f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/POLYFIT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/POLYFIT.M" @@ -1,3 +1,76 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:34532b9273c22125cb5687803de3c9741f8389c6040d8137050f95c6053310ee -size 2419 +function [p,S] = polyfit(x,y,n) +%p=polyfit(x,y,k)ÓÃk´Î¶àÏîʽÄâºÏÏòÁ¿Êý¾Ý(x,y) +%p·µ»Ø¶àÏîʽµÄ½µÃÝϵÊý.µ±k>=n-1ʱ,polyfitʵÏÖ¶àÏîʽ²åÖµ. +%ÀýÈç Óöþ´Î¶àÏîʽÄâºÏÊý¾Ý +% x | 0.1 0.2 0.15 0.0 -0.2 0.3 +% --|------------------------------ +% y | 0.95 0.84 0.86 1.06 1.50 0.72 +% Çó½â +% x=[0.1,0.2,0.15,0,-0.2,0.3]; +% y=[0.95,0.84,0.86,1.06,1.50,0.72]; +% p=polyfit(x,y,2) +% xi=-0.2:0.01:0.3; +% yi=polyval(p,xi); +% plot(x,y,'o',xi,yi,'k'); +% title('polyfit'); + +%POLYFIT Fit polynomial to data. +% POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of +% degree N that fits the data, P(X(I))~=Y(I), in a least-squares sense. +% +% [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a +% structure S for use with POLYVAL to obtain error estimates on +% predictions. If the errors in the data, Y, are independent normal +% with constant variance, POLYVAL will produce error bounds which +% contain at least 50% of the predictions. +% +% The structure S contains the Cholesky factor of the Vandermonde +% matrix (R), the degrees of freedom (df), and the norm of the +% residuals (normr) as fields. +% +% See also POLY, POLYVAL, ROOTS. + +% J.N. Little 4-21-85, 8-23-86; CBM, 12-27-91 BAJ, 5-7-93. +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.9 $ $Date: 1997/11/21 23:40:57 $ + +% The regression problem is formulated in matrix format as: +% +% y = V*p or +% +% 3 2 +% y = [x x x 1] [p3 +% p2 +% p1 +% p0] +% +% where the vector p contains the coefficients to be found. For a +% 7th order polynomial, matrix V would be: +% +% V = [x.^7 x.^6 x.^5 x.^4 x.^3 x.^2 x ones(size(x))]; + +if ~isequal(size(x),size(y)) + error('X and Y vectors must be the same size.') +end + +x = x(:); +y = y(:); + +% Construct Vandermonde matrix. +V(:,n+1) = ones(length(x),1); +for j = n:-1:1 + V(:,j) = x.*V(:,j+1); +end + +% Solve least squares problem, and save the Cholesky factor. +[Q,R] = qr(V,0); +p = R\(Q'*y); % Same as p = V\y; +r = y - V*p; +p = p.'; % Polynomial coefficients are row vectors by convention. + +% S is a structure containing three elements: the Cholesky factor of the +% Vandermonde matrix, the degrees of freedom and the norm of the residuals. + +S.R = R; +S.df = length(y) - (n+1); +S.normr = norm(r); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/SPLINE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/SPLINE.M" index a495b0f24a8f7ad16cd5af558b5187b96f37deec..956c1682fbcdd6dc4643bd49ef26e1f24b100c42 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/SPLINE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/SPLINE.M" @@ -1,3 +1,130 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:73510ace9a03489343d0f9922daacc11802acaaef90982e39f2046e06abe79f4 -size 4808 +function output = spline(x,y,xx) +%Èý´ÎÑùÌõ²åÖµ +%yi=spline(x,y,xi)µÈ¼ÛÓÚYI=interp(x,y,xi,'spline'), +% ¸ù¾ÝÊý¾Ý(x,y)¸ø³öÔÚxiµÄÏßÐÔ²åÖµ½á¹ûyi.. +% ʹÓÃ"·ÇŤ½á"¶ËµãÌõ¼þ, ¼´Ç¿ÆȵÚÒ»©p¶þ¶Ë¶àÏîʽÈý´ÎÏîϵÊýÏàͬ, +% ×îºóÒ»¶ÎºÍµ¹ÊýµÚ¶þ¶ÎÈý´ÎÏîϵÊýÏàͬ. +%pp=spline(x,y)·µ»ØÑùÌõ²åÖµµÄ·Ö¶Î¶àÏîʽ(ppÐÎʽ). +%[breaks,coefs]=unmkpp(pp)½«ppÐÎʽչ¿ª,ÆäÖÐbreaksΪ½áµã,coefsΪ¸÷¶Î¶àÏîʽϵÊý. +%yi=ppval(pp,xi),ppÐÎʽÔÚxiµÄº¯ÊýÖµ. +%Àý ¿¼ÂÇÊý¾Ý +% x | 1 2 4 5 +% ---|------------- +% y | 1 3 4 2 +% clear;close; +% x=[1 2 4 5];y=[1 3 4 2]; +% p=spline(x,y); +% xi=1:0.1:5;yi=ppval(p,xi); +% plot(x,y,'o',xi,yi,'k'); +% title('not-a-knot SPLINE'); +% [b,c]=unmkpp(p) +%ÁíÒ»¸öÀý×Ó¼ûÏÂÁÐÓ¢ÎIJ¿·Ö +% +%SPLINE Cubic spline data interpolation. +% YY = SPLINE(X,Y,XX) uses cubic spline interpolation +% to find a vector YY corresponding to XX. X and Y are the +% given data vectors and XX is the new abscissa vector. +% +% The ordinates Y may be vector-valued, in which case Y(:,j) is +% the j-th ordinate. +% +% PP = SPLINE(X,Y) returns the pp-form of the cubic spline +% interpolant instead, for later use with PPVAL, etc. +% +% Ordinarily, the not-a-knot end conditions are used. However, if +% Y contains two more ordinates than X has entries, then the first +% and last ordinate in Y are used as the endslopes for the cubic spline. +% +% Here's an example that generates a coarse sine curve, then +% samples the spline over a finer mesh: +% +% x = 0:10; y = sin(x); +% xx = 0:.25:10; +% yy = spline(x,y,xx); +% plot(x,y,'o',xx,yy) +% +% Here is an example that features a vector-valued spline, along with complete +% spline interpolation, i.e., fitting to given end slopes (instead of using the +% not-a-knot end condition); it uses SPLINE to generate a circle: +% +% circle = spline( 0:4, [0 1 0 -1 0 1 0; pi/2 0 1 0 -1 0 pi/2] ); +% xx = 0:.1:4; cc = ppval(circle, xx); plot(cc(1,:), cc(2,:)), axis equal +% +% See also INTERP1, PPVAL, SPLINES (The Spline Toolbox). + +% Carl de Boor 7-2-86 +% Revised 11-24-87 JNL, 6-16-92 CBM, 10-14-97 CB. +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.11 $ $Date: 1997/12/03 19:22:33 $ + +% Generate the cubic spline interpolant in pp form, depending on the +% number of data points (and usually using the not-a-knot end condition). + +output=[]; +n=length(x); +if n<2, error('There should be at least two data points.'), end + +if any(diff(x)<0), [x,ind]=sort(x); else, ind=1:n; end + +x=x(:); dx = diff(x); +if all(dx)==0, error('The data abscissae should be distinct.'), end + +[yd,yn] = size(y); % if Y happens to be a column matrix, change it to + % the expected row matrix. +if yn==1, yn=yd; y=reshape(y,1,yn); yd=1; end + +if yn==n + notaknot = 1; +elseif yn==n+2 + notaknot = 0; endslopes = y(:,[1 n+2]).'; y(:,[1 n+2])=[]; +else + error('Abscissa and ordinate vector should be of the same length.') +end + +yi=y(:,ind).'; dd = ones(1,yd); +dx = diff(x); divdif = diff(yi)./dx(:,dd); +if n==2 + if notaknot, % the interpolant is a straight line + pp=mkpp(x.',[divdif.' yi(1,:).'],yd); + else % the interpolant is the cubic Hermite polynomial + divdif2 = diff([endslopes(1,:);divdif;endslopes(2,:)])./dx([1 1],dd); + pp = mkpp(x,... + [(diff(divdif2)./dx(1,dd)).' ([2 -1]*divdif2).' ... + endslopes(1,:).' yi(1,:).'],yd); + end +elseif n==3¬aknot, % the interpolant is a parabola + yi(2:3,:)=divdif; + yi(3,:)=diff(divdif)/(x(3)-x(1)); + yi(2,:)=yi(2,:)-yi(3,:)*dx(1); + pp = mkpp([x(1),x(3)],yi([3 2 1],:).',yd); +else % set up the sparse, tridiagonal, linear system for the slopes at X . + b=zeros(n,yd); + b(2:n-1,:)=3*(dx(2:n-1,dd).*divdif(1:n-2,:)+dx(1:n-2,dd).*divdif(2:n-1,:)); + if notaknot + x31=x(3)-x(1);xn=x(n)-x(n-2); + b(1,:)=((dx(1)+2*x31)*dx(2)*divdif(1,:)+dx(1)^2*divdif(2,:))/x31; + b(n,:)=... + (dx(n-1)^2*divdif(n-2,:)+(2*xn+dx(n-1))*dx(n-2)*divdif(n-1,:))/xn; + else + x31 = 0; xn = 0; b([1 n],:) = dx([1 n-2],dd).*endslopes; + end + c = spdiags([ [dx(2:n-1);xn;0] ... + [dx(2);2*[dx(2:n-1)+dx(1:n-2)];dx(n-2)] ... + [0;x31;dx(1:n-2)] ],[-1 0 1],n,n); + + % sparse linear equation solution for the slopes + mmdflag = spparms('autommd'); + spparms('autommd',0); + s=c\b; + spparms('autommd',mmdflag); + % convert to pp form + c4=(s(1:n-1,:)+s(2:n,:)-2*divdif(1:n-1,:))./dx(:,dd); + c3=(divdif(1:n-1,:)-s(1:n-1,:))./dx(:,dd) - c4; + pp=mkpp(x.',... + reshape([(c4./dx(:,dd)).' c3.' s(1:n-1,:).' yi(1:n-1,:).'],(n-1)*yd,4),yd); +end +if nargin==2 + output=pp; +else + output=ppval(pp,xx); +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/\346\225\260\346\215\256\346\213\237\345\220\210.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/\346\225\260\346\215\256\346\213\237\345\220\210.txt" index 12424ec576b493d8be99ab4f97a0b305608df962..070ff8c43087d681108a283a8e05928e43306b45 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/\346\225\260\346\215\256\346\213\237\345\220\210.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\225\260\346\215\256\346\213\237\345\220\210/\346\225\260\346\215\256\346\213\237\345\220\210.txt" @@ -1,3 +1,11 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:df7ab4cbab6f5a2903260d8e25b8ef0934e5c2c9a1dbc4e095703e278e28d3bf -size 294 +% Êý¾ÝÄâºÏ +% interp1 - Ò»Ôªº¯Êý²åÖµ +% spline - ÑùÌõ²åÖµ +% polyfit - ¶àÏîʽ²åÖµ»òÄâºÏ +% curvefit - ÇúÏßÄâºÏ +% caspe - ¸÷Öֱ߽çÌõ¼þµÄÑùÌõ²åÖµ +% casps - ÑùÌõÄâºÏ(ûÓÐ) +% interp2 - ¶þÔªº¯Êý²åÖµ +% griddata - ²»¹æÔòÊý¾ÝµÄ¶þÔªº¯Êý²åÖµ +% *interp - ²»µ¥µ÷½Úµã²åÖµ +% *lagrange - À­¸ñÀÊÈÕ²åÖµ·¨ \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/FSOLVE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/FSOLVE.M" index fffc04c39a64253620bbaf996c648e97df299046..900f979ed6c7133635fa9ba9bd69f63e73fc67d4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/FSOLVE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/FSOLVE.M" @@ -1,3 +1,408 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:0bf5ca83b7d9b24d22b005322380802e00d7625d8d599380aec7096009268559 -size 15034 +function [x,FVAL,EXITFLAG,OUTPUT,JACOB] = fsolve(FUN,x,options,varargin) +%ÓÅ»¯¹¤¾ßÏ亯Êý,¿ÉÇó¶àÔª·ÇÏßÐÔ·½³Ì×éµÄʵ¸ù. Ó÷¨ÓëfzeroÀàËÆ¡£ +%Àý ÏÈдһ¸öMº¯Êýrooteg4fun.m +% function y=rooteg4fun(x) +% y(1)=4*x(1)-x(2)+exp(x(1))/10-1; +% y(2)=-x(1)+4*x(2)+x(1).^2/8; +% ʹÓà +% [x,f,h]=fsolve('rooteg4fun',[0,0]) %³õÖµx(1)=0,x(2)=0 +% x·µ»Ø½âÏòÁ¿£¬f·µ»ØÎó²îÏòÁ¿£¬h>0±íÃ÷Ëã·¨ÊÕÁ² +% ×¢Ò⣺·½³Ì±äÁ¿±ØÐëÆ´³ÉÒ»¸öÏòÁ¿±äÁ¿£¬¼´ÓÃx(1),x(2),... +% +%FSOLVE Solves nonlinear equations by a least squares method. +% +% FSOLVE solves equations of the form: +% +% F(X)=0 where F and X may be vectors or matrices. +% +% X=FSOLVE(FUN,X0) starts at the matrix X0 and tries to solve the +% equations described in FUN. FUN is usually an M-file which returns +% an evaluation of the equations for a particular value of X: F=FUN(X). +% +% X=FSOLVE(FUN,X0,OPTIONS) minimizes with the default optimization +% parameters replaced by values in the structure OPTIONS, an argument +% created with the OPTIMSET function. See OPTIMSET for details. Used +% options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, Jacobian, +% JacobPattern, LineSearchType, LevenbergMarquardt, MaxFunEvals, MaxIter, +% DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, +% TolPCG, TypicalX. Use the Jacobian option to specify that FUN may be called +% with two output arguments where the second, J, is the Jacobian matrix: +% [F,J] = feval(FUN,X). If FUN returns a vector (matrix) of m components when +% X has length n, then J is an m-by-n matrix where J(i,j) is the partial +% derivative of F(i) with respect to x(j). (Note that the Jacobian J is the +% transpose of the gradient of F.) +% +% X=FSOLVE(FUN,X0,OPTIONS,P1,P2,...) passes the problem-dependent +% parameters P1,P2,... directly to the function FUN: FUN(X,P1,P2,...). +% Pass an empty matrix for OPTIONS to use the default values. +% +% [X,FVAL]=FSOLVE(FUN,X0,...) returns the value of the objective function +% at X. +% +% [X,FVAL,EXITFLAG]=FSOLVE(FUN,X0,...) returns a string EXITFLAG that +% describes the exit condition of FSOLVE. +% If EXITFLAG is: +% > 0 then FSOLVE converged to a solution X. +% 0 then the maximum number of function evaluations was reached. +% < 0 then FSOLVE did not converge to a solution. +% +% [X,FVAL,EXITFLAG,OUTPUT]=FSOLVE(FUN,X0,...) returns a structure OUTPUT +% with the number of iterations taken in OUTPUT.iterations, the number of +% function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, +% the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order +% optimality (if used) in OUTPUT.firstorderopt. +% +% [X,FVAL,EXITFLAG,OUTPUT,JACOB]=FSOLVE(FUN,X0,...) returns the +% Jacobian of FUN at X. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.26 $ $Date: 1998/10/22 19:28:31 $ +% Andy Grace 7-9-90. + +% Grandfathered FSOLVE call for Optimization Toolbox versions prior to 2.0: +% [X,OPTIONS]=FSOLVE(FUN,X0,OPTIONS,GRADFUN,P1,P2,...) +% +% ------------Initialization---------------- + +defaultopt = optimset('display','final','LargeScale','on', ... + 'TolX',1e-6,'TolFun',1e-6,'DerivativeCheck','off',... + 'Jacobian','off','MaxFunEvals','100*numberOfVariables',... + 'Diagnostics','off',... + 'DiffMaxChange',1e-1,'DiffMinChange',1e-8,... + 'PrecondBandWidth',0,'TypicalX','ones(numberOfVariables,1)','MaxPCGIter','max(1,floor(numberOfVariables/2))', ... + 'TolPCG',0.1,'MaxIter',400,'JacobPattern',[], ... + 'LineSearchType','quadcubic','LevenbergMarq','off'); +% If just 'defaults' passed in, return the default options in X +if nargin==1 & nargout <= 1 & isequal(FUN,'defaults') + x = defaultopt; + return +end + +if nargin < 2, error('FSOLVE requires two input arguments');end +if nargin < 3, options=[]; end + +% These are added so that we can have the same code as in lsqnonlin which +% actually has upper and lower bounds. +LB = []; UB = []; + +%[x,FVAL,EXITFLAG,OUTPUT,JACOB] = fsolve(FUNin,x,options,varargin) +% Note: don't send varargin in as a comma separated list!! +numargin = nargin; numargout = nargout; +[calltype, GRADFUN, varargin] = parse_call(FUN,options,numargin,numargout,varargin); + +if isequal(calltype,'new') % fsolve version 2.* + + xstart=x(:); + numberOfVariables=length(xstart); + + large = 'large-scale'; + medium = 'medium-scale'; + + l = []; u = []; + + options = optimset(defaultopt,options); + switch optimget(options,'display') + case {'off','none'} + verbosity = 0; + case 'iter' + verbosity = 2; + case 'final' + verbosity = 1; + case 'testing' + verbosity = Inf; + otherwise + verbosity = 1; + end + diagnostics = isequal(optimget(options,'diagnostics','off'),'on'); + + gradflag = strcmp(optimget(options,'Jacobian'),'on'); + line_search = strcmp(optimget(options,'largescale','off'),'off'); % 0 means trust-region, 1 means line-search + + % Convert to inline function as needed + if ~isempty(FUN) % will detect empty string, empty matrix, empty cell array + [funfcn, msg] = fprefcnchk(FUN,'fsolve',length(varargin),gradflag); + else + errmsg = sprintf('%s\n%s', ... + 'FUN must be a function name, valid string expression, or inline object;', ... + ' or, FUN may be a cell array that contains these type of objects.'); + error(errmsg) + end + + x(:) = xstart; + switch funfcn{1} + case 'fun' + fuser = feval(funfcn{3},x,varargin{:}); + f = fuser(:); + nfun=length(f); + JAC = zeros(nfun,numberOfVariables); + case 'fungrad' + [fuser,JAC] = feval(funfcn{3},x,varargin{:}); + f = fuser(:); + nfun=length(f); + case 'fun_then_grad' + fuser = feval(funfcn{3},x,varargin{:}); + f = fuser(:); + JAC = feval(funfcn{4},x,varargin{:}); + nfun=length(f); + + otherwise + error('Undefined calltype in FSOLVE'); + end + + % check size of JAC + [Jrows, Jcols]=size(JAC); + if Jrows~=nfun | Jcols ~=numberOfVariables + errstr = sprintf('%s\n%s%d%s%d\n',... + 'User-defined Jacobian is not the correct size:',... + ' the Jacobian matrix should be ',nfun,'-by-',numberOfVariables); + error(errstr); + end + + YDATA = []; caller = 'fsolve'; + + % trustregion and enough equations (as many as variables) + if ~line_search & nfun >= numberOfVariables + OUTPUT.algorithm = large; + + % trust region and not enough equations -- switch to line_search + elseif ~line_search & nfun < numberOfVariables + warnstr = sprintf('%s\n%s\n', ... + 'Large-scale method requires at least as many equations as variables; ',... + ' switching to line-search method instead.'); + warning(warnstr); + OUTPUT.algorithm = medium; + + % line search and no bounds + elseif line_search & isempty(l) & isempty(u) + OUTPUT.algorithm = medium; + + % line search and bounds and enough equations, switch to trust region + elseif line_search & (~isempty(LB) | ~isempty(UB)) & nfun >= numberOfVariables + warnstr = sprintf('%s\n%s\n', ... + 'Line-search method does not handle bound constraints; ',... + ' switching to trust-region method instead.'); + warning(warnstr); + OUTPUT.algorithm = large; + + % can't handle this one: + elseif line_search & (~isempty(LB) | ~isempty(UB)) & nfun < numberOfVariables + errstr = sprintf('%s\n%s\n%s\n', ... + 'Line-search method does not handle bound constraints ',... + ' and trust-region method requires at least as many equations as variables; ',... + ' aborting.'); + error(errstr); + + end + + if diagnostics > 0 + % Do diagnostics on information so far + constflag = 0; gradconstflag = 0; non_eq=0;non_ineq=0;lin_eq=0;lin_ineq=0; + confcn{1}=[];c=[];ceq=[];cGRAD=[];ceqGRAD=[]; + hessflag = 0; HESS=[]; + msg = diagnose('fsolve',OUTPUT,gradflag,hessflag,constflag,gradconstflag,... + line_search,options,xstart,non_eq,... + non_ineq,lin_eq,lin_ineq,LB,UB,funfcn,confcn,f,JAC,HESS,c,ceq,cGRAD,ceqGRAD); + + end + + % Execute algorithm + if isequal(OUTPUT.algorithm, large) + if ~gradflag + Jstr = optimget(options,'JacobPattern',[]); + if isempty(Jstr) + % Put this code separate as it might generate OUT OF MEMORY error + Jstr = sparse(ones(Jrows,Jcols)); + end + else + Jstr = []; + end + l = []; u = []; computeLambda = 0; + [x,FVAL,LAMBDA,JACOB,EXITFLAG,OUTPUT]=... + snls(funfcn,x,l,u,verbosity,options,f,JAC,YDATA,caller,Jstr,computeLambda,varargin{:}); + else + [x,FVAL,JACOB,EXITFLAG,OUTPUT] = ... + nlsq(funfcn,x,verbosity,options,f,JAC,YDATA,caller,varargin{:}); + + end + + Resnorm = FVAL'*FVAL; % assumes FVAL still a vector + if Resnorm > 10*optimget(options,'TolFun',1e-4) & verbosity>0 + if verbosity > 0 + disp('Optimizer is stuck at a minimum that is not a root') + disp('Try again with a new starting guess') + end + EXITFLAG = -1; + end + + % Reset FVAL to shape of the user-function output, fuser + FVAL = reshape(FVAL,size(fuser)); + + % end FSOLVE 2.* +else % version 1.5 FSOLVE + + if length(options)<5; + options(5)=0; + end + % Switch methods making Gauss Newton the default method. + if options(5)==0; options(5)=1; else options(5)=0; end + + % Convert to inline function as needed. + if ~isempty(FUN) + [funfcn, msg] = fcnchk(FUN,length(varargin)); + if ~isempty(msg) + error(msg); + end + else + error('FUN must be a function name or valid expression.') + end + + if ~isempty(GRADFUN) + [gradfcn, msg] = fcnchk(GRADFUN,length(varargin)); + if ~isempty(msg) + error(msg); + end + else + gradfcn = []; + end + + [x,options] = nlsqold(funfcn,x,options,gradfcn,varargin{:}); + + if options(8)>10*options(3) & options(1)>0 + disp('Optimizer is stuck at a minimum that is not a root') + disp('Try again with a new starting guess') + end + + % Set the second output argument FVAL to be options as in old calling syntax + FVAL = options; + + % end fsolve version 1.5.* + +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function [calltype, GRADFUN, otherargs] = parse_call(FUN,options,numargin,numargout,otherargs) +% PARSE_CALL Determine which calling syntax is being used: the FSOLVE prior to 2.0, or +% in version 2.0 or later of the Toolbox. +% old call: [X,OPTIONS]=FSOLVE(FUN,X0,OPTIONS,GRADFUN,varargin) +% new call: [X,FVAL,EXITFLAG,OUTPUT,JACOB]=FSOLVE(FUN,X0,OPTIONS,varargin) + +if numargout > 2 % [X,FVAL,EXITFLAG,...]=FSOLVE (...) + calltype = 'new'; + GRADFUN = []; +elseif isa(FUN,'cell') % FUN == {...} + calltype = 'new'; + GRADFUN = []; +elseif ~isempty(options) & isa(options,'double') % OPTIONS == scalar or and array + calltype = 'old'; + if length(otherargs) > 0 + GRADFUN = otherargs{1}; + otherargs = otherargs(2:end); + else + GRADFUN = []; + end +elseif isa(options,'struct') % OPTIONS has fields + calltype = 'new'; + GRADFUN = []; +else % Ambiguous + warnstr = sprintf('%s\n%s\n%s\n',... + 'Cannot determine from calling sequence whether to use new (2.0 or later) FSOLVE ', ... + 'function or grandfathered FSOLVE function. Assuming new syntax; if call was grandfathered', ... + 'FSOLVE syntax, this may give unexpected results.'); + warning(warnstr) + calltype = 'new'; + GRADFUN = []; +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function [allfcns,msg] = fprefcnchk(funstr,caller,lenVarIn,gradflag) +%PREFCNCHK Pre- and post-process function expression for FUNCHK. +% [ALLFCNS,MSG] = PREFUNCHK(FUNSTR,CALLER,lenVarIn,GRADFLAG) takes +% the (nonempty) expression FUNSTR from CALLER with LenVarIn extra arguments, +% parses it according to what CALLER is, then returns a string or inline +% object in ALLFCNS. If an error occurs, this message is put in MSG. +% +% ALLFCNS is a cell array: +% ALLFCNS{1} contains a flag +% that says if the objective and gradients are together in one function +% (calltype=='fungrad') or in two functions (calltype='fun_then_grad') +% or there is no gradient (calltype=='fun'), etc. +% ALLFCNS{2} contains the string CALLER. +% ALLFCNS{3} contains the objective function +% ALLFCNS{4} contains the gradient function (transpose of Jacobian). +% +% NOTE: we assume FUNSTR is nonempty. +% Initialize +msg=''; +allfcns = {}; +funfcn = []; +gradfcn = []; + +if gradflag + calltype = 'fungrad'; +else + calltype = 'fun'; +end + +% {fun} +if isa(funstr, 'cell') & length(funstr)==1 + % take the cellarray apart: we know it is nonempty + if gradflag + calltype = 'fungrad';0 + end + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + error(msg); + end + + % {fun,[]} +elseif isa(funstr, 'cell') & length(funstr)==2 & isempty(funstr{2}) + if gradflag + calltype = 'fungrad'; + end + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + error(msg); + end + + % {fun, grad} +elseif isa(funstr, 'cell') & length(funstr)==2 % and ~isempty(funstr{2}) + + [funfcn, msg] = fcnchk(funstr{1},lenVarIn); + if ~isempty(msg) + error(msg); + end + [gradfcn, msg] = fcnchk(funstr{2},lenVarIn); + if ~isempty(msg) + error(msg); + end + calltype = 'fun_then_grad'; + if ~gradflag + warnstr = ... + sprintf('%s\n%s\n%s\n','Jacobian function provided but OPTIONS.Jacobian=''off'';', ... + ' ignoring Jacobian function and using finite-differencing.', ... + ' Rerun with OPTIONS.Jacobian=''on'' to use Jacobian function.'); + warning(warnstr); + calltype = 'fun'; + end + +elseif ~isa(funstr, 'cell') %Not a cell; is a string expression, function name string or inline object + [funfcn, msg] = fcnchk(funstr,lenVarIn); + if ~isempty(msg) + error(msg); + end + if gradflag % gradient and function in one function/M-file + gradfcn = funfcn; % Do this so graderr will print the correct name + end +else + errmsg = sprintf('%s\n%s', ... + 'FUN must be a function name, valid string expression, or inline object;', ... + ' or, FUN may be a cell array that contains these type of objects.'); + error(errmsg) +end + +allfcns{1} = calltype; +allfcns{2} = caller; +allfcns{3} = funfcn; +allfcns{4} = gradfcn; +allfcns{5}=[]; + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/INV.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/INV.M" index 067c52e5fdf6e6dca3789b55c4c1a3378e22a8a2..8cb7936319e46a81432c1f57767d8e8c26040081 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/INV.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/INV.M" @@ -1,3 +1,16 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:fb2a6893c5a077638d38e4da48833c7bdd1cf5a9ca515bad921112e30f1bcac2 -size 504 +%ÇóÄæ¾ØÕó +%Ó÷¨ B=inv(A) ÆäÖÐAΪÊýÖµ»ò·ûºÅ·½Õó,B·µ»ØAµÄÄæ +%ÀýÈç +% inv([1 2;3 4]) %ÊýÖµ +% syms a b c d;inv([[a,b;c,d]) %·ûºÅ +% +%INV Matrix inverse. +% INV(X) is the inverse of the square matrix X. +% A warning message is printed if X is badly scaled or +% nearly singular. +% +% See also SLASH, PINV, COND, CONDEST, NNLS, LSCOV. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.5 $ $Date: 1997/11/21 23:38:31 $ +% Built-in function. diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/NEWTON.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/NEWTON.M" index 1e4a782d5c6f57cc0e8da8e28196f70e8a8249e1..1f04b80ce49871d7f757edfb30302884e28d0172 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/NEWTON.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/NEWTON.M" @@ -1,3 +1,29 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:120e960c0b558b27aff63012832391ac331b305be0a319a3df4b1285d143f316 -size 824 +function x=newton(f_name,x0,tol) +% Purpose: Solve a nonlinear equation by Newton iteration +% Synopsis: x=newton('f_name',x0) +% x=newton('f_name',x0,tol) +% +% x: return a root of f(x)=0 near x0 +% f_name:name of the function f(x) that defines the equation +% x0: initial guess +% tol: tolerence(Default:1e-6) + +% L.J.Hu 1-8-1998 + +h=0.0001;M=500; +if nargin<3, tol=1e-6;end +x=x0;xb=x-999; +n=0; +while abs(x-xb)>tol + xb=x; + if n>M break;end + y=feval(f_name, x); + fprintf(' n=%3.0f, x=%12.5e, y=%12.5e, \n',n,x,y) + y_driv=(feval(f_name,x+h)-y)/h; + x=xb-y/y_driv; + n=n+1; +end +fprintf(' n=%3.0f, x=%12.5e, y=%12.5e, ',n,x,y) +if n>500, + fprintf('\n');disp('Warning: iterations exceeds the limitation, probable devergent'); +end \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/ROOTS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/ROOTS.M" index ffacedb24b3a87b952e41a12901c521d3cdb34d2..ff0121456c9ad962f61034501596d055377b03b3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/ROOTS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/ROOTS.M" @@ -1,3 +1,45 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:023350c5883030831c326ce86a46a71d9d6bb02d8dd195019e7ba42f9e9a272e -size 1108 +function r = roots(c) +%roots(p)¿ÉÇóµÃ¶àÏîʽpµÄËùÓи´¸ù. +%Àý x^3+2x^2-3=0 +% Çó½â +% roots([1 2 0 -3]) +% +%ROOTS Find polynomial roots. +% ROOTS(C) computes the roots of the polynomial whose coefficients +% are the elements of the vector C. If C has N+1 components, +% the polynomial is C(1)*X^N + ... + C(N)*X + C(N+1). +% +% See also POLY, RESIDUE, FZERO. + +% J.N. Little 3-17-86 +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.6 $ $Date: 1997/11/21 23:41:05 $ + +% ROOTS finds the eigenvalues of the associated companion matrix. + +if size(c,1)>1 & size(c,2)>1 + error('Must be a vector.') +end +c = c(:).'; +n = size(c,2); +r = zeros(0,1); + +inz = find(c); +if isempty(inz), + % All elements are zero + return +end + +% Strip leading zeros and throw away. +% Strip trailing zeros, but remember them as roots at zero. +nnz = length(inz); +c = c(inz(1):inz(nnz)); +r = zeros(n-inz(nnz),1); + +% Polynomial roots via a companion matrix +n = length(c); +if n > 1 + a = diag(ones(1,n-2),-1); + a(1,:) = -c(2:n) ./ c(1); + r = [r;eig(a)]; +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/SOLVE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/SOLVE.M" index 251b53c0ddc3d2b49ae78af6ae5ceb16597a2f63..f0c09005e33e40924c134020fd9f1d7746253c45 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/SOLVE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/SOLVE.M" @@ -1,3 +1,233 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:94eb7feac193f16cf93478145d81c6547c8e9dad2510ddaec7e50bc08fc40e75 -size 6501 +function varargout = solve(varargin) +%Çó¸÷ÖÖÀàÐÍ·½³Ì×éµÄ½âÎö½â, +%µ±ÕÒ²»µ½½âÎö½âʱ,½«×Ô¶¯Ñ°ÇóÔ­µã¸½½üµÄÒ»¸ö½üËƽâ, ²¢¿É´ïÈÎÒ⾫¶È. +%Ó÷¨ +% solve('·½³Ì1','·½³Ì2',...,'·½³ÌN','±äÁ¿1','±äÁ¿2',...,'±äÁ¿M') +%SOLVE Symbolic solution of algebraic equations. +% SOLVE('eqn1','eqn2',...,'eqnN') +% SOLVE('eqn1','eqn2',...,'eqnN','var1,var2,...,varN') +% SOLVE('eqn1','eqn2',...,'eqnN','var1','var2',...'varN') +% +% The eqns are symbolic expressions or strings specifying equations. The +% vars are symbolic variables or strings specifying the unknown variables. +% SOLVE seeks zeros of the expressions or solutions of the equations. +% If not specified, the unknowns in the system are determined by FINDSYM. +% If no analytical solution is found and the number of equations equals +% the number of dependent variables, a numeric solution is attempted. +% +% Three different types of output are possible. For one equation and one +% output, the resulting solution is returned, with multiple solutions to +% a nonlinear equation in a symbolic vector. For several equations and +% an equal number of outputs, the results are sorted in lexicographic +% order and assigned to the outputs. For several equations and a single +% output, a structure containing the solutions is returned. +% +% Examples: +% +% solve('p*sin(x) = r') chooses 'x' as the unknown and returns +% +% ans = +% asin(r/p) +% +% [x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0') returns +% +% x = +% [ 1] +% [ 3] +% +% y = +% [ 1] +% [ -3/2] +% +% S = solve('x^2*y^2 - 2*x - 1 = 0','x^2 - y^2 - 1 = 0') returns +% the solutions in a structure. +% +% S = +% x: [8x1 sym] +% y: [8x1 sym] +% +% [u,v] = solve('a*u^2 + v^2 = 0','u - v = 1') regards 'a' as a +% parameter and solves the two equations for u and v. +% +% S = solve('a*u^2 + v^2','u - v = 1','a,u') regards 'v' as a +% parameter, solves the two equations, and returns S.a and S.u. +% +% [a,u,v] = solve('a*u^2 + v^2','u - v = 1','a^2 - 5*a + 6') solves +% the three equations for a, u and v. +% +% [x,y] = solve('sin(x+y)-exp(x)*y = 0','x^2-y = 2') cannot find +% an analytic solution, so returns a numeric solution. +% +% See also DSOLVE. + +% Copyright (c) 1993-98 by The MathWorks, Inc. +% $Revision: 1.13 $ $Date: 1997/11/29 01:06:35 $ + +% Set the Explicit solution (for equations of order 4 or less) +% option on in the Maple Workspace. + +maple('_EnvExplicit := true;'); + +% Collect input arguments together in either equation or variable lists. + +eqns = []; +vars = []; +for k = 1:nargin + v = varargin{k}; + if all(isletter(v) | ('0'<=v & v<='9') | v == '_' | v == ',') + vars = [vars ',' v]; + else + [t,stat] = maple(v); + if stat + error(['''' v ''' is not a valid expression or equation.']) + end + eqns = [eqns ',' v]; + end +end + +if isempty(eqns) + warning('List of equations is empty.') + varargout = cell(1,nargout); + varargout{1} = sym([]); + return +else + eqns(1) = '{'; eqns(end+1) = '}'; +end +neqns = sum(commas(eqns)) + 1; + +% Determine default variables and sort variable list. + +if isempty(vars) + vars = ['[' findsym(sym(eqns),neqns) ']']; +else + vars(1) = '['; vars(end+1) = ']'; +end +v = vars; +[vars,stat] = maple('sort',v); +if stat + error(['''' v ''' is not a valid variable list.']) +end +vars(1) = '{'; vars(end) = '}'; +nvars = sum(commas(vars)) + 1; + +if neqns ~= nvars + warning([int2str(neqns) ' equations in ' int2str(nvars) ' variables.']) +end + +% Seek analytic solution. + +[R,stat] = maple('solve',eqns,vars); + +% If no analytic solution, seek numerical solution. + +if (isempty(R) & (nvars == neqns)) + [R,stat] = maple('fsolve',eqns,vars); +end + +if stat + error(R) +end + +% If still no solution, give up. + +if isempty(R) | findstr(R,'fsolve') + warning('Explicit solution could not be found.'); + varargout = cell(1,nargout); + varargout{1} = sym([]); + return +end + +% Expand any RootOf. + +while ~isempty(findstr(R,'RootOf')) + k = min(findstr(R,'RootOf')); + p = findstr(R,'{'); p = max(p(pk)); + s = R(p:q); + t = s(min(findstr(s,'RootOf'))+6:end); + e = min(find(cumsum((t=='(')-(t==')'))==0)); + if isempty(find(commas(t(2:e-1)))) + % RootOf with one argument, possibly an imbedded RootOf. + [s,stat] = maple('allvalues',s,'dependent'); + if stat + error(s) + end + else + % RootOf with a good estimate as the second argument. + s = maple('evalf',s); + end + R = [R(1:p-1) s R(q+1:end)]; +end + +% Parse the result. + +if nvars == 1 & nargout <= 1 + + % One variable and at most one output. + % Return a single scalar or vector sym. + + S = sym([]); + c = find(commas(R) | R == '}'); + for p = find(R == '=') + q = min(c(c>p)); + t = trim(R(p+1:q-1)); % The solution (xk) + S = [S; sym(t)]; + end + varargout{1} = S; + +else + + % Several variables. + % Create a skeleton structure. + + c = [1 find(commas(vars)) length(vars)]; + S = []; + for j = 1:nvars + v = trim(vars(c(j)+1:c(j+1)-1)); + S = setfield(S,v,[]); + end + + % Complete the structure. + + c = [1 find(commas(R) | R == '{' | R == '}') length(R)]; + for p = find(R == '=') + q = max(c(cp)); + t = trim(R(p+1:q-1)); % The solution (xk) + S = setfield(S,v,[getfield(S,v); sym(t)]); + end + + if nargout <= 1 + + % At most one output, return the structure. + varargout{1} = S; + + elseif nargout == nvars + + % Same number of outputs as variables. + % Match results in lexicographic order to outputs. + v = fieldnames(S); + for j = 1:nvars + varargout{j} = getfield(S,v{j}); + end + + else + error([int2str(nvars) ' variables does not match ' ... + int2str(nargout) ' outputs.']) + end +end + +%------------------------- + +function s = trim(s); +%TRIM TRIM(s) deletes any leading or trailing blanks. +while s(1) == ' ', s(1) = []; end +while s(end) == ' ', s(end) = []; end + +%------------------------- + +function c = commas(s) +%COMMAS COMMAS(s) is true for commas not inside parentheses. +p = cumsum((s == '(') - (s == ')')); +c = (s == ',') & (p == 0); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/\346\226\271\347\250\213\346\261\202\346\240\271.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/\346\226\271\347\250\213\346\261\202\346\240\271.txt" index 08280757e3a68d06333eeef6bd5dfbf70a8a4991..258a83f9f47591406a9ee66f8dbd314302aa2e0c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/\346\226\271\347\250\213\346\261\202\346\240\271.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\226\271\347\250\213\346\261\202\346\240\271/\346\226\271\347\250\213\346\261\202\346\240\271.txt" @@ -1,3 +1,7 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a0f8aa5c18e0dedb92efec7effbf070807c682889790883a2e12d99ff15dba5f -size 155 +% ·½³ÌÇó¸ù +% inv - Äæ¾ØÕó +% roots - ¶àÏîʽµÄ¸ù +% fzero - Ò»Ôªº¯ÊýÁãµã +% fsolve - ·ÇÏßÐÔ·½³Ì×é +% solve - ·ûºÅ·½³Ì½â +% *newton - Å£¶Ùµü´ú·¨½â·ÇÏßÐÔ·½³Ì \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\227\266\351\227\264\345\272\217\345\210\227\345\210\206\346\236\220\347\250\213\345\272\217.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\227\266\351\227\264\345\272\217\345\210\227\345\210\206\346\236\220\347\250\213\345\272\217.m" index 4d403080547991680062e9d33255d431ac3b1acc..3018fc0776dff3fdfbacf1cd271552e5f02a76a2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\227\266\351\227\264\345\272\217\345\210\227\345\210\206\346\236\220\347\250\213\345\272\217.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\227\266\351\227\264\345\272\217\345\210\227\345\210\206\346\236\220\347\250\213\345\272\217.m" @@ -1,3 +1,38 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:078d8b12b462f9463cafefa23aeb222e45d5664871212a959f70451e64eefad6 -size 804 +z=[16 12 15 10 9 17 11 16 10 14]; %ÈθøÒ»×éÊý¾Ý£¬Í¨¹ýÏÂÃ溯ÊýÇó½âÑù±¾¾ùÖµz1¡¢Ñù±¾×ÔЭ·½²îº¯Êýr¡¢Ñù±¾×ÔÏà¹Øº¯Êýp£¨SACF£©ºÍÑù±¾Æ«×ÔÏà¹Øº¯Êýq(SPACF) + +N=size(z); %size(A,1)·µ»Ø¾ØÕóAµÄÐÐÊý size(A,2)·µ»Ø¾ØÕóAµÄÁÐÊý +n=N(1,2); +z1=sum(z)/n; %Ñù±¾¾ùÖµz1 + +s0=0; +for i=1:n + s0=(z(i)-z1)^2+s0; +end +r0=s0/n; + +%%Ñù±¾×ÔЭ·½²îº¯Êýr +for k=1:(n-1) + nr(k)=0; + for t=1:(n-k) + nr(k)=(z(t)-z1)*(z(t+k)-z1)+nr(k); + end +end +r=nr./n; + +%%Ñù±¾×ÔÏà¹Øº¯Êýp +p=(r./r0)';%p=vpa((r./r0)',3); %vpa(n,m)¶Ôn±£ÁôСÊýµãºómλ + +%%Æ«×ÔÏà¹Øº¯Êýq +for m=1:(n-2) + q(1,1)=p(1); + D=0;T=0; + for h=1:m + D=p(m+1-h)*q(m,h)+D; + T=p(h)*q(m,h)+T; + end + q(m+1,m+1)=(p(m+1)-D)/(1-T); + for j=1:m + q(m+1,j)=q(m,j)-q(m+1,m+1)*q(m,m+1-j); + end +end +q diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/FUNTOOL.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/FUNTOOL.M" index 458fe90aec924b4905df2ec88b051b25ac7a01bc..55440a841a3d301422ae96552829cb0e9b2dfea7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/FUNTOOL.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/FUNTOOL.M" @@ -1,3 +1,488 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1bb69237928c0b00990367f0d18104c6a3e8ec1ffb1d9f854001f03a7dcbdfb9 -size 17087 +function funtool(keyword,varargin) +%ͼÐνçÃ溯Êý¼ÆËãÆ÷£¬ÄܽøÐк¯Êý¸÷Àà³õµÈÔËËã¡¢»ý·Ö¡¢Î¢·Ö¡¢×÷ͼ¡£ +%FUNTOOL A function calculator. +% FUNTOOL is an interactive graphing calculator that manipulates +% functions of a single variable. At any time, there are two functions +% displayed, f(x) and g(x). The result of most operations replaces f(x). +% +% The controls labeled 'f = ' and 'g = ' are editable text that may +% be changed at any time to install a new function. The control +% labeled 'x = ' may be changed to specify a new domain. The control +% labeled 'a = ' may be changed to specify a new value of a parameter. +% +% The top row of control buttons are unary function operators that +% involve only f(x). These operators are: +% df/dx - Symbolically differentiate f(x). +% int f - Symbolically integrate f(x). +% simple f - Simplify the symbolic expression, if possible. +% num f - Extract the numerator of a rational expression. +% den f - Extract the denominator of a rational expression. +% 1/f - Replace f(x) by 1/f(x). +% finv - Replace f(x) by its inverse function. +% +% The operators int(f) and finv may fail if the corresponding symbolic +% expressions do not exist in closed form. +% +% The second row of buttons translate and scale f(x) by the parameter 'a'. +% The operations are: +% f + a - Replace f(x) by f(x) + a. +% f - a - Replace f(x) by f(x) - a. +% f * a - Replace f(x) by f(x) * a. +% f / a - Replace f(x) by f(x) / a. +% f ^ a - Replace f(x) by f(x) ^ a. +% f(x+a) - Replace f(x) by f(x + a). +% f(x*a) - Replace f(x) by f(x * a). +% +% The third row of buttons are binary function operators that +% operate on both f(x) and g(x). The operations are: +% f + g - Replace f(x) by f(x) + g(x). +% f - g - Replace f(x) by f(x) - g(x). +% f * g - Replace f(x) by f(x) * g(x). +% f / g - Replace f(x) by f(x) / g(x). +% f(g) - Replace f(x) by f(g(x)). +% g = f - Replace g(x) by f(x). +% swap - Interchange f(x) and g(x). +% +% The first three buttons in the fourth row manage a list of functions. +% The Insert button places the current active function in the list. +% The Cycle button rotates the function list. +% The Delete button removes the active function from the list. +% The list of functions is named fxlist. A default fxlist containing +% several interesting functions is provided. +% +% The Reset button sets f, g, x, a and fxlist to their initial values. +% The Help button prints this help text. +% +% The Demo button poses the following challenge: Can you generate the +% function sin(x) without touching the keyboard, using just the mouse? +% The demo does it with a reset and then nine clicks. If you can do +% it with fewer clicks, please send e-mail to moler@mathworks.com. +% +% The Close button closes all three windows. +% +% See also EZPLOT. + +% Copyright (c) 1993-98 by The MathWorks, Inc. +% $Revision: 1.11 $ $Date: 1997/11/29 01:06:25 $ + +%Implementation Notes: +% f,g, and a are syms. +% x is a string. fxlist is a string matrix. +% +% The values of f, g, a, and x are stored in the UserData of the text +% objects "f", "g", "a", and "x", respectively. These text objects are +% tagged "fobj", "gobj", "aobj", and "xstr", respectively. +% fxlist is stored in the UserData of the control panel figure, which is +% tagged as "figp". +% The edit text boxes for f, g, x, and a are tagged "Sf", "Sg", "Sx", and +% "Sa", respectively. +% The initial values of f, g, x, a, and fxlist are stored in a structure +% called init that has fields .f, .g, .x, .a and .l. The structure is +% stored in the UserData of the Reset button. + +%%%%%%%%%%%%%%%%%%%%%%%%%% Initialization section. +if nargin == 0 + +init.f = 'x'; +init.g = '1'; +init.x = '[-2*pi, 2*pi]'; +init.a = '1/2'; +init.l = str2mat( ... + '1/(5+4*cos(x)); [-2*pi, 2*pi]', ... + 'cos(x^3)/(1+x^2); [-2*pi, 2*pi]', ... + 'x^4*(1-x)^4/(1+x^2); [0, 1]', ... + 'x^7-7*x^6+21*x^5-35*x^4+35*x^3-21*x^2+7*x-1; [0.985, 1.015]', ... + 'log(abs(sqrt(x))); [0, 2]', ... + 'tan(sin(x))-sin(tan(x)); [-pi, pi]'); + +f = sym(init.f); +g = sym(init.g); +a = sym(init.a); +x = init.x; +fxlist = init.l; + +% Macros +blanks = ' '; +p = .12*(1:7) - .02; +q = .60 - .14*(1:4); +r = [.10 .10]; + +% Position the two figures and the control panel. +figf = figure('units','normalized','pos',[.01 .50 .48 .48],... + 'menu','none','tag','figf'); +figg = figure('units','normalized','pos',[.50 .50 .48 .48],... + 'menu','none', 'tag','figg'); +figp = figure('units','normalized','pos',[.25 .05 .50 .40],'menu','none', ... + 'tag','figp',... + 'Color',get(0,'DefaultUIControlBackgroundColor'), ... + 'DefaultUIControlUnit','norm','UserData',fxlist); + +% Plot f(x) and g(x). +figure(figf) +ezplot(f,x,figf) +figure(figg) +ezplot(g,x,figg) + +% Control panel +figure(figp) +uicontrol('style','frame','pos',[0.01 0.60 0.98 0.38]); +uicontrol('style','frame','pos',[0.01 0.01 0.98 0.58]); +uicontrol('style','text','string','f = ','pos',[0.04 0.86 0.09 0.10],... + 'tag','fobj','UserData',f); +uicontrol('style','text','string','g = ','pos',[0.04 0.74 0.09 0.10],... + 'tag','gobj','UserData',g); +uicontrol('style','text','string','x = ','pos',[0.04 0.62 0.09 0.10],... + 'tag','xstr','UserData',x); +uicontrol('style','text','string','a = ','pos',[0.54 0.62 0.09 0.10],... + 'tag','aobj','UserData',a); +uicontrol('pos',[.12 .86 .82 .10],'style','edit','horiz','left', ... + 'backgroundcolor','white', ... + 'string', [blanks char(f)],'tag','Sf', ... + 'CallBack','funtool Sfcallback'); +uicontrol('pos',[.12 .74 .82 .10],'style','edit','horiz','left', ... + 'backgroundcolor','white', ... + 'string', [blanks char(g)], 'tag','Sg',... + 'CallBack','funtool Sgcallback'); +uicontrol('pos',[.12 .62 .32 .10],'style','edit','horiz','left', ... + 'backgroundcolor','white','string',[blanks x], 'tag','Sx',... + 'CallBack','funtool Sxcallback'); +uicontrol('pos',[.62 .62 .32 .10],'style','edit','horiz','left', ... + 'backgroundcolor','white', 'tag','Sa',... + 'string',[blanks char(a)],'CallBack','funtool Sacallback'); + +% Top row of unary operators. +uicontrol('pos',[p(1) q(1) r],'string','df/dx', ... + 'CallBack','funtool(''row1'',''diff'')'); +uicontrol('pos',[p(2) q(1) r],'string','int f', ... + 'CallBack','funtool(''row1'',''int'')'); +uicontrol('pos',[p(3) q(1) r],'string','simple f', ... + 'CallBack','funtool(''row1'',''simple'')'); +uicontrol('pos',[p(4) q(1) r],'string','num f', ... + 'CallBack','funtool(''row1'',''num'')'); +uicontrol('pos',[p(5) q(1) r],'string','den f', ... + 'CallBack','funtool(''row1'',''den'')'); +uicontrol('pos',[p(6) q(1) r],'string','1/f', ... + 'CallBack','funtool(''row1'',''1/f'')'); +uicontrol('pos',[p(7) q(1) r],'string','finv', ... + 'CallBack','funtool(''row1'',''finverse'')'); + +% Second row of unary operators. +uicontrol('pos',[p(1) q(2) r],'string','f+a', ... + 'CallBack','funtool(''row2'',''f+a'')'); +uicontrol('pos',[p(2) q(2) r],'string','f-a', ... + 'CallBack','funtool(''row2'',''f-a'')'); +uicontrol('pos',[p(3) q(2) r],'string','f*a', ... + 'CallBack','funtool(''row2'',''f*a'')'); +uicontrol('pos',[p(4) q(2) r],'string','f/a', ... + 'CallBack','funtool(''row2'',''f/a'')'); +uicontrol('pos',[p(5) q(2) r],'string','f^a', ... + 'CallBack','funtool(''row2'',''f^a'')'); +uicontrol('pos',[p(6) q(2) r],'string','f(x+a)', ... + 'CallBack','funtool(''row2'',''f(x+a)'')'); +uicontrol('pos',[p(7) q(2) r],'string','f(x*a)', ... + 'CallBack','funtool(''row2'',''f(x*a)'')'); + +% Third row, binary operators. +uicontrol('pos',[p(1) q(3) r],'string','f + g', ... + 'CallBack','funtool(''row3'',''f+g'')'); +uicontrol('pos',[p(2) q(3) r],'string','f - g', ... + 'CallBack','funtool(''row3'',''f-g'')'); +uicontrol('pos',[p(3) q(3) r],'string','f * g', ... + 'CallBack','funtool(''row3'',''f*g'')'); +uicontrol('pos',[p(4) q(3) r],'string','f / g', ... + 'CallBack','funtool(''row3'',''f/g'')'); +uicontrol('pos',[p(5) q(3) r],'string','f(g)', ... + 'CallBack','funtool(''row3'',''f(g)'')'); +uicontrol('pos',[p(6) q(3) r],'string','g = f', ... + 'CallBack','funtool(''row3'',''g=f'')'); +uicontrol('pos',[p(7) q(3) r],'string','swap', ... + 'CallBack','funtool(''row3'',''swap'')'); + +% Fourth row, auxilliary controls. +uicontrol('pos',[p(1) q(4) r],'string','Insert','CallBack','funtool Insert'); +uicontrol('pos',[p(2) q(4) r],'string','Cycle','CallBack','funtool Cycle'); +uicontrol('pos',[p(3) q(4) r],'string','Delete','CallBack','funtool Delete'); +uicontrol('pos',[p(4) q(4) r],'string','Reset','Tag','reset', ... + 'UserData', init, 'CallBack', 'funtool Reset'); +uicontrol('pos',[p(5) q(4) r],'string','Help', ... + 'CallBack','helpwin funtool'); +uicontrol('pos',[p(6) q(4) r],'string','Demo', ... + 'CallBack','funtool Demo'); +uicontrol('pos',[p(7) q(4) r],'string','Close', ... + 'CallBack','funtool close'); + +%%%%%%%%%%%%%%%%%%%%%%%%%% end of Initialization section + +else +switch keyword + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for top row of unary operators. +case 'row1' + figp = findobj(0,'tag','figp'); + fhndl = findobj(figp,'tag','fobj'); + f = get(fhndl,'UserData'); + x = get(findobj(figp,'tag','xstr'),'UserData'); + figf = findobj(0,'tag','figf'); + + switch varargin{1} + case 'diff' + f = diff(f); + case 'int' + f = int(f); + case 'simple' + f = simple(f); + case 'num' + [f,ans] = numden(f); + case 'den' + [ans,f] = numden(f); + case '1/f' + f = 1/f; + case 'finverse' + f = finverse(f); + end + + set(fhndl,'UserData',f); + ezplot(f,x,figf) + blanks = ' '; + set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for second row of unary operators. +case 'row2' + figp = findobj(0,'tag','figp'); + fhndl = findobj(figp,'tag','fobj'); + f = get(fhndl,'UserData'); + x = get(findobj(figp,'tag','xstr'),'UserData'); + a = get(findobj(figp,'tag','aobj'),'UserData'); + figf = findobj(0,'tag','figf'); + + switch varargin{1} + case 'f+a' + f = f+a; + case 'f-a' + f = f-a; + case 'f*a' + f = f*a; + case 'f/a' + f = f/a; + case 'f^a' + f = f^a; + case 'f(x+a)' + f = subs(f,sym('x'),sym('x')+a); + case 'f(x*a)', ... + f = subs(f,sym('x'),sym('x')*a); + end + + set(fhndl,'UserData',f); + ezplot(f,x,figf) + blanks = ' '; + set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for third row, binary operators. +case 'row3' + blanks = ' '; + + % Get variables. + figp = findobj(0,'tag','figp'); + fhndl = findobj(figp,'tag','fobj'); + ghndl = findobj(figp,'tag','gobj'); + f = get(fhndl,'UserData'); + g = get(ghndl,'UserData'); + x = get(findobj(figp,'tag','xstr'),'UserData'); + a = get(findobj(figp,'tag','aobj'),'UserData'); + figf = findobj(0,'tag','figf'); + figg = findobj(0,'tag','figg'); + + if strcmp(varargin{1}, 'g=f') + g = f; + set(ghndl,'UserData',g); + ezplot(g,x,figg) + set(findobj(figp,'tag','Sg'),'string',[blanks char(g)]); + + elseif strcmp(varargin{1}, 'swap') + h = f; f = g; g = h; + set(fhndl,'UserData',f); + ezplot(f,x,figf) + set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]); + set(ghndl,'UserData',g); + ezplot(g,x,figg) + set(findobj(figp,'tag','Sg'),'string',[blanks char(g)]); + + else + switch varargin{1} + case 'f+g' + f = f+g; + case 'f-g' + f = f-g; + case 'f*g' + f = f*g; + case 'f/g' + f = f/g; + case 'f(g)' + f = compose(f,g); + end + + set(fhndl,'UserData',f); + ezplot(f,x,figf) + set(findobj(figp,'tag','Sf'),'string',[blanks char(f)]); + end + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for F's edit text box. +case 'Sfcallback' + figp = findobj(0,'tag','figp'); + f = sym(get(gco,'string')); + fhndl = findobj(figp,'tag','fobj'); + set(fhndl,'UserData',f); + x = get(findobj(figp,'tag','xstr'),'UserData'); + figf = findobj(0,'tag','figf'); + ezplot(f,x,figf) + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for G's edit text box. +case 'Sgcallback' + figp = findobj(0,'tag','figp'); + g = sym(get(gco,'string')); + ghndl = findobj(figp,'tag','gobj'); + set(ghndl,'UserData',g); + x = get(findobj(figp,'tag','xstr'),'UserData'); + figg = findobj(0,'tag','figg'); + ezplot(g,x,figg) + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for A's edit text box. +case 'Sacallback' + a = sym(get(gco,'String')); + set(findobj(gcf,'tag','aobj'),'UserData',a); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for X's edit text box. +case 'Sxcallback' + + figp = findobj(0,'tag','figp'); + x = get(gco,'String'); + + % add brackets if needed + if isempty(x=='['), + x = ['[' x ']']; + blanks = ' '; + set(gco,'string',[blanks x]), + end; + set(findobj(figp,'tag','xstr'),'UserData',x); + + fhndl = findobj(figp,'tag','fobj'); + ghndl = findobj(figp,'tag','gobj'); + f = get(fhndl,'UserData'); + g = get(ghndl,'UserData'); + a = get(findobj(figp,'tag','aobj'),'UserData'); + figf = findobj(0,'tag','figf'); + figg = findobj(0,'tag','figg'); + + ezplot(f,x,figf) + ezplot(g,x,figg) + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Insert button. +case 'Insert' + f = get(findobj(gcf,'tag','fobj'),'UserData'); + x = get(findobj(gcf,'tag','xstr'),'UserData'); + fxlist = get(gcf,'UserData'); + fxlist = str2mat(fxlist,[char(f) '; ' x]); + set(gcf,'UserData',fxlist); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Cycle button. +case 'Cycle' + + % Get variables. + figp = gcf; + figf = findobj(0,'tag','figf'); + fxlist = get(figp,'UserData'); + + fx = fxlist(1,:); + fx(find(fx==' ')) = []; + k = find(fx == ';'); + fstr = fx(1:k-1); f = sym(fstr); + set(findobj(figp,'tag','fobj'),'UserData',f); + x = fx(k+1:length(fx)); + set(findobj(figp,'tag','xstr'),'UserData',x); + + blanks = ' '; + set(findobj(figp,'tag','Sx'),'string',[blanks x]); + set(findobj(figp,'tag','Sf'),'string',[blanks fstr]); + ezplot(f,x,figf); + k = [2:size(fxlist,1),1]; + fxlist = fxlist(k,:); + set(figp,'UserData',fxlist); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Delete button. +case 'Delete' + + % Get variables. + figp = gcf; + f = get(findobj(figp,'tag','fobj'),'UserData'); + x = get(findobj(figp,'tag','xstr'),'UserData'); + fxlist = get(figp,'UserData'); + + fx = [char(f) ';' x]; + fx(find(fx==' ')) = []; + for k = 1:size(fxlist,1), + element = fxlist(k,:); + element(find(element==' ')) = []; + if strcmp(fx,element) + fxlist(k,:) = []; + break + end + end; + if isempty(fxlist), fxlist = '0-0; [0,1]'; end + + set(figp,'UserData',fxlist); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Reset button. +case 'Reset' + blanks = ' '; + + % Get variables. + figp = gcf; + figf = findobj(0,'tag','figf'); + figg = findobj(0,'tag','figg'); + init = get(findobj(figp,'tag','reset'),'UserData'); + + set(findobj(figp,'tag','fobj'),'UserData',sym(init.f)); + set(findobj(figp,'tag','Sf'),'String',[blanks init.f]); + ezplot(sym(init.f),init.x,figf); + + set(findobj(figp,'tag','gobj'),'UserData',sym(init.g)); + set(findobj(figp,'tag','Sg'),'String',[blanks init.g]); + ezplot(sym(init.g),init.x,figg); + + set(findobj(figp,'tag','xstr'),'UserData',init.x); + set(findobj(figp,'tag','Sx'),'string',[blanks init.x]); + + set(findobj(figp,'tag','aobj'),'UserData',sym(init.a)); + set(findobj(figp,'tag','Sa'),'string',[blanks init.a]); + + set(figp,'UserData',init.l); + + % Reset all buttons to default bkgd color. + set(findobj(figp,'Style','pushbutton'),'BackgroundColor','default'); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Close button. +case 'close' + close(findobj(0,'tag','figf')); + close(findobj(0,'tag','figg')); + close(findobj(0,'tag','figp')); + +%%%%%%%%%%%%%%%%%%%%%%%%%% Callback for Demo button. +case 'Demo' + + % "B" is the vector of button handles in the control panel. + % "prog" is a "program" consisting of button codes. + + prog = {'Reset','f/a','int f','f + g','1/f', ... + 'int f','finv','int f','df/dx','num f'}; + B = findobj(gcf,'Style','pushbutton'); + for k = 1: length(prog) + currB = findobj(B,'String',prog{k}); + set(currB,'BackgroundColor','white'); + eval(get(currB,'Callback')); + pause(1) + set(currB,'BackgroundColor','default'); + end + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +end % switch statement for callbacks +end % end of FUNTOOL diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/MATHMODL.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/MATHMODL.M" index 24066c8e79bfe6b7bad16a39d7a0b2c694b5e576..ad45b916544760bfe31c7accba9b290d07bf6b48 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/MATHMODL.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/MATHMODL.M" @@ -1,3 +1,118 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ab2b15ec861edc859bf1572f89bfa1d8fbc8578c0831ec93704bc46a18ca22cc -size 4127 +clc;echo on; +%########################################################################## +% ±¾¹¤¾ßÏäÖ÷ҪΪѧϰÊýѧ½¨Ä£ºÍ²Î¼ÓÖйú´óѧÉúÊýѧ½¨Ä£¾ºÈüµÄͬѧ¶øÖÆ×÷¡£»ã¼¯ÁË +% Êýѧ½¨Ä£³£ÓõÄ×îÓÅ»¯¡¢Î¢·Ö·½³Ì¡¢Êý¾ÝÄâºÏ¡¢Í³¼ÆµÈ·½ÃæµÄ¼ÆË㹤¾ß£¬°üÀ¨ÎÒÃÇ×Ô +% ±àµÄ²¹³ä¹¤¾ß¡£¹¤¾ßÏ仹»ã¼¯ÁË96-99Öйú´óѧÉúÊýѧ½¨Ä£¾ºÈüÌâ½âMATLAB³ÌÐò¡£±¾ +% ¹¤¾ßÏäÒ²¿É¹©Ê¹ÓÃMATLAB×÷ÊýÖµ¼ÆËãµÄѧÉú¡¢½ÌʦºÍ¿Æ¼¼ÈËÔ±²Î¿¼¡£ +%########################################################################## +echo off +more(25) +echo on + +pause % Strike any key to continue (Note: use Ctrl-C to abort) + +type contents %ʹÓûسµ¼ü¿´ÏÂÐÐ +more off + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +clc + +%########################################################################## +% ÀýÒ»£ºÊ¹ÓÃÖÐÎÄ°ïÖú +%########################################################################## + +%(1)ÆäʵʹÓÃÖÐÎÄ°ïÖúºÍͨ³£Ê¹ÓÃÓ¢ÎÄ°ïÖúÊÇÒ»ÑùµÄ£¬ÀýÈçÄãÏëÖªµÀ plot µÄÓ÷¨£¬ÓÃÃüÁî +pause % Strike any key to continue (Note: use Ctrl-C to abort) +help plot +%ÒÔÉÏ×îÇ°¼¸ÐÐÊÇÖÐÎÄ°ïÖú£¬½ôËæÆäºóµÄÊÇÔ­ÏȵÄÓ¢ÎÄ°ïÖú¡£ + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +%(2)³ýÉÙÊýÓ¢ÎÄ°ïÖúÒÑÅäÀýÌâÍ⣬ÖÐÎÄ°ïÖú´ó¶à¶¼ÅäÓÐÖÐÎÄÀýÌ⣬ÀýÈçÑùÌõ²åÖµ spline +pause % Strike any key to continue (Note: use Ctrl-C to abort) +help spline + +%ÏÖÔÚʹÓà +pause % Strike any key to continue (Note: use Ctrl-C to abort) +clear;close; +x=[1 2 4 5];y=[1 3 4 2]; +p=spline(x,y); +xi=1:0.1:5;yi=ppval(p,xi); +plot(x,y,'o',xi,yi,'k'); +title('not-a-knot SPLINE'); +[b,c]=unmkpp(p) + +%(3)ÖÐÎÄ°ïÖúÖ»ÁгöÁË×î³£ÓõÄʹÓøñʽ£¬ÍêÈ«¸ñʽÇë²Î¿¼Ó¢ÎÄ°ïÖú¡£ + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +close;clc +%########################################################################## +% Àý¶þ£ºÑ§Ï°×îÓÅ»¯·½·¨ +%########################################################################## + +% MATLABÓÅ»¯¹¤¾ßÏäÓÐÒ»¸öѧϰ×îÓÅ»¯¼ÆËãµÄ½Ì³Ì¡£Ê¹ÓÃtutdemoÆô¶¯£¨ÕâÀïÊ¡ÂÔ£©¡£ +% Èç¹ûÄã¶ÔÆäÖÐÓ¢ÎÄÃüÁ̫¶®£¬ÇëʹÓÃÏàÓ¦µÄÖÐÎÄ°ïÖú +% +% ÀýÈçÏÂÁзÇÏßÐÔÔ¼ÊøÓÅ»¯·½·¨ constr +pause % Strike any key to continue (Note: use Ctrl-C to abort) +help constr + + +% ¸ù¾Ý°ïÖú£¬ÏÖÔÚÇëÄãÏÈÓÃMATLAB±à¼­Æ÷½«Ä£Ðͺ¯Êýд³ÉMº¯Êýoptfun2.m +% function [f,g]=optfun2(x) +% f=-x(1)*x(2)*x(3) +% g(1)=x(1)-x(2)-10; +% g(2)=x(1)-x(2)-2*x(3); +% g(3)=x(1)+2*x(2)+2*x(3)-72 +% È»ºóÔÚMATLABÃüÁî´°¿ÚÇó½â +pause % Strike any key to continue (Note: use Ctrl-C to abort) +x0=[10,10,10]; +options(13)=1; +[x,options]=constr('optfun2',x0,options,[-inf,10,-inf]',[inf,20,inf]); +x %×î´óÖµµã +-options(8) %Ä¿±êº¯Êý×î´óÖµ + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +clc +%########################################################################## +% ÀýÈý£º×Ա๤¾ß +%########################################################################## + +% ÎÒÃÇ×Ô±àÁËÐí¶àMATLABǷȱµÄÊýѧ½¨Ä£¹¤¾ß¡£ÈçÖØ»ý·Ö¡¢Ëæ»úÄ£Äâ¡¢ÀëÉ¢ÓÅ»¯µÈ¡£ÀýÈç +% ÏÂÁÐ×îСÉú³ÉÊ÷kruskalË㷨ʹÓÃÁËCMEX¼¼Êõ +pause % Strike any key to continue (Note: use Ctrl-C to abort) +help kruskal + +clear;map=[1 2 30;2 4 5;2 5 50;3 2 6;4 3 1;1 4 20;1 5 30] +[out,len]=kruskal(map) + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +close;clc; +%########################################################################## +% ÀýËÄ£ºÊýѧ½¨Ä£¾ºÈüÌâ½â³ÌÐò +%########################################################################## + +%ÎÒÃDZàдÁË96¡ª99Êýѧ½¨Ä£¾ºÈüһЩÓÅÐã½â´ðµÄMATLAB³ÌÐò +pause % Strike any key to continue (Note: use Ctrl-C to abort) +type jm98a1 +echo off +jm98a1 +echo on +pause % Strike any key to continue (Note: use Ctrl-C to abort) +type jm98a2 +echo off +jm98a2 +echo on +pause % Strike any key to continue (Note: use Ctrl-C to abort) +type jm98a1 +echo off +jm98a3 +echo on +pause % Strike any key to continue (Note: use Ctrl-C to abort) +clc +%########################################################################## +% Ô¸ÎÒÃǵŤ×÷ÄܶÔÄúÓÐËù°ïÖú¡£ +% »¶Ó­½»Á÷£¬Çë¶àÌáÒâ¼û¡£ +% Email: ljhu@dhu.edu.cn +% ²Î¼ÓÖÆ×÷£ººúÁ¼½£¡¢¶¡Ïþ¶«¡¢ÂíÔ£¡¢Â½Ëø¾ü¡¢ÀîΰÖÓ +%########################################################################## +echo off diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/TUTDEMO.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/TUTDEMO.M" index a5f1ae18e1df7e4b5bb62b785659d734be15ae92..e946c261aea455e710c48d89eeef9a532d7dbf53 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/TUTDEMO.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/TUTDEMO.M" @@ -1,3 +1,406 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5c1bde03305520ddf4490a47fb8317242874cdfed8143fbe10b9c29ae391034e -size 12464 +echo off +%ÓÅ»¯¹¤¾ßÏä¼òÃ÷½Ì³Ì +%TUTDEMO Tutorial for Optimization Toolbox. + +% Copyright (c) 1990-98 by The MathWorks, Inc. +% $Revision: 1.12 $ $Date: 1997/11/29 01:23:27 $ + +echo on; clc +%TUTDEMO Tutorial for Optimization Toolbox. +%########################################################################## +% +% This is a demonstration script-file for the OPTIMIZATION TOOLBOX +% It closely follows the Tutorial section of the users' guide +% +% It consists of: +% (1) unconstrained optimization example +% (2) constrained optimization example +% (3) constrained example using gradients +% (4) bounded example +% (5) equality constrained example +% (6) unconstrained example using user-supplied settings +% +% All the principles outlined in this demonstration apply to the other +% routines: attgoal, minimax, leastsq, fsolve. +% +% The routines differ from the Tutorial Section examples in the manual +% only in that M-files for the objective functions have not been coded +% up. Instead the expression form of the syntax has been used where +% functions to be minimized are expressed as MATLAB string variables. +% +%########################################################################## + +pause % Strike any key to continue (Note: use Ctrl-C to abort) +clc +%########################################################################## +% DEMO 1: UNCONSTRAINED PROBLEM +%-------------------------------------------------------------------------- +% +% Consider initially the problem of finding a minimum to the function: +% +% 2 2 +% f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% The function to be minimized is + +fun = 'exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1)'; + +pause % Strike any key to continue + +% Take a guess at the solution + +x0 = [-1 1]; + +pause % Strike any key to continue + +% Use default parameters + +options = []; + +pause % Strike any key to start the optimization + +[x, options] = fminu(fun, x0, options); + +% The optimizer has found a solution at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) +% Note: by entering the expression explicitly in a string using +% the variable 'x' we avoid having to write an M-file. + +pause % Strike any key for next demo +clc +%########################################################################## +% DEMO 2: CONSTRAINED PROBLEM +%-------------------------------------------------------------------------- +% +% Consider the above problem with two additional constraints: +% +% 2 2 +% minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +% subject to 1.5 + x(1).x(2) - x(1) - x(2) <= 0 +% - x(1).x(2) <= 10 +% +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% Objective Function and constraints + +funf = 'f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);'; +fung = 'g = [1.5 + x(1)*x(2) - x(1) - x(2); -x(1)*x(2) - 10];'; +fun = [funf fung]; + +pause % Strike any key to continue + +% Take a guess at the solution + +x0 = [-1 1]; + +pause % Strike any key to continue + +% Use default parameters + +options = []; + +pause % Strike any key to start the optimization + +[x, options] = constr(fun, x0, options); + +% A solution to this problem has been found at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% Both the constraints are active at the solution: +g = [1.5 + x(1)*x(2) - x(1) - x(2); - x(1)*x(2) - 10] +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) +pause % Strike any key for next demo +clc +%########################################################################## +% DEMO 3: BOUNDED EXAMPLE +%-------------------------------------------------------------------------- +% +% Consider the above problem with additional bound constraints: +% +% 2 2 +% minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +% subject to 1.5 + x(1).x(2) - x(1) - x(2) <= 0 +% - x(1).x(2) <= 10 +% +% and x(1) >= 0 +% x(2) >= 0 +% +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% Objective Function and constraints + +funf = 'f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);'; +fung = 'g = [1.5 + x(1)*x(2) - x(1) - x(2); -x(1)*x(2) - 10];'; +fun = [funf fung]; + +pause % Strike any key to continue + +% Again, make a guess at the solution + +x0 = [-1 1]; + +pause % Strike any key to continue + +% Use default parameters + +options = []; + +pause % Strike any key to continue + +% This time we will use the bounded syntax: +% X = CONSTR(`FUN', X0, OPTIONS, VLB, VUB) + +vlb = zeros(1,2); % Lower bounds X >= 0 +vub = []; % No upper bounds + +pause % Strike any key to start the optimization + +[x, options] = constr(fun, x0, options, vlb, vub); + +% The solution to this problem has been found at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% The constraint values at the solution are: +g = [1.5 + x(1)*x(2) - x(1) - x(2); - x(1)*x(2) - 10] +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) +pause % Strike any key for next demo +clc +%########################################################################## +% DEMO 4: USER-SUPPLIED GRADIENTS +%-------------------------------------------------------------------------- +% The above problem can be solved more efficiently and accurately if +% gradients are supplied by the user. This demo shows how this may be +% performed. +% +% Again the problem is: +% 2 2 +% minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +% subject to 1.5 + x(1).x(2) - x(1) - x(2) <= 0 +% - x(1).x(2) <= 10 +% +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% Objective function and constraints + +funf = 'f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);'; +fung = 'g = [1.5 + x(1)*x(2) - x(1) - x(2); -x(1)*x(2) - 10];'; +fun = [funf fung]; + +pause % Strike any key to continue + +% Make a guess at the solution: + +x0 = [-1 1]; + +pause % Strike any key to continue + +% Use default parameters + +options = []; + +pause % Strike any key to continue + +% Partial derivatives + +dfdx1 = 'exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1)+4*exp(x(1))*(2*x(1)+x(2));'; +dfdx2 = '4*exp(x(1))*(x(1)+x(2)+0.5);'; +dfdg = '[x(2)-1, -x(2); x(1)-1, -x(1)];'; +grad = ['df=[',dfdx1, dfdx2,']; dg=', dfdg]; + +pause % Strike any key to start the optimization + +[x, options] = constr(fun, x0, options, [], [], grad); + +% As before the solution to this problem has been found at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% Both the constraints are active at the solution: +g = [1.5 + x(1)*x(2) - x(1) - x(2); - x(1)*x(2) - 10] +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) + +pause % Strike any key for next demo +clc +%########################################################################## +% DEMO 5: EQUALITY CONSTRAINED EXAMPLE +%-------------------------------------------------------------------------- +% +% Consider the above problem with an additional equality constraint: +% +% 2 2 +% minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +% subject to x(1) + x(2) = 0 +% 1.5 + x(1).x(2) - x(1) - x(2) <= 0 +% - x(1).x(2) <= 10 +% +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% Objective function and constraints + +funf = 'f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);'; +fung = 'g = [x(1) + x(2); 1.5 + x(1)*x(2) - x(1) - x(2); -x(1)*x(2) - 10];'; +fun = [funf fung]; + +pause % Strike any key to continue + +% Again, make a guess at the solution + +x0 = [-1 1]; + +pause % Strike any key to continue + +% This time we will indicate the number of equality constraints +% by setting options(13) to the number of constraints. The equality +% constraints must be contained the in first few elements of g. + +% One equality constraint + +clear options +options(13) = 1; + +pause % Strike any key to start the optimization + +[x, options] = constr(fun, x0, options); + +% The solution to this problem has been found at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% The constraint values at the solution are: +g = [x(1) + x(2); 1.5 + x(1)*x(2) - x(1) - x(2); -x(1)*x(2) - 10] +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) + +pause % Strike any key for next demo +clc +%########################################################################## +% DEMO 6: CHANGING THE DEFAULT SETTINGS +%-------------------------------------------------------------------------- +% +% Consider the original unconstrained problem: +% +% 2 2 +% minimize f(x) = exp(x(1)) . (4x(1) + 2x(2) + 4x(1).x(2) + 2x(2) + 1) +% +% This time we will solve it more accurately by overriding the +% default termination criteria (OPTIONS(2) and OPTIONS(3)). +%-------------------------------------------------------------------------- +pause % Strike any key to continue + +% The function to be minimized is + +fun = 'exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1)'; + +pause % Strike any key to continue + +% Again, make a guess at the solution: + +x0 = [-1 1]; + +pause % Strike any key to continue + +% Override the default termination criteria: +clear options +options(2) = 1e-8; % Termination tolerance on X +options(3) = 1e-8; % Termination tolerance on F + +pause % Strike any key to start the optimization + +[x, options] = fminu(fun, x0, options); + +% The optimizer has found a solution at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) +% Note: warning messages may be displayed because of problems +% in the calculation of finite difference gradients at the +% solution point. They are an indication that tolerances are overly +% stringent, however, the optimizer always continues to make steps +% towards the solution. + +pause % Strike any key to continue + +% If we want a tabular display of each iteration we can set +% options(1) = 1 as follows: + +options = 1; % Set display parameter to on, the others to default. + +pause % Strike any key to start the optimization + +[x, options] = fminu(fun, x0, options); + +% The optimizer has found a solution at: +x +pause % Strike any key to continue + +% The function value at the solution is: +options(8) +pause % Strike any key to continue + +% The total number of function evaluations was: +options(10) +% At each major iteration the table displayed consists of: +% - number of function values +% - function value +% - step length used in the line search +% - gradient in the direction of search +% + +%------------------------------Demo End------------------------------------ +pause % Strike any key for main menu +echo off +disp('End of demo') diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/\346\274\224\347\244\272\347\250\213\345\272\217.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/\346\274\224\347\244\272\347\250\213\345\272\217.txt" index 40f3918a0bb19e9a077ff41a2039fcb7b8ab0357..5c19cc9d5fb302e5e83a3e82459f16438381d192 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/\346\274\224\347\244\272\347\250\213\345\272\217.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\346\274\224\347\244\272\347\250\213\345\272\217/\346\274\224\347\244\272\347\250\213\345\272\217.txt" @@ -1,3 +1,4 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3afc47781c9a7a8c173d8c9124850c3b093037c89bfc1e3aa9ee5b9a978e4793 -size 101 +% ÑÝʾ³ÌÐò +% funtool - º¯Êý¼ÆËãÆ÷ +% tutdemo - MATLABÓÅ»¯¹¤¾ßÏä½Ì³Ì +% mathmodl - Êýѧ½¨Ä£¹¤¾ßÏäÑÝʾ \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/BNB18.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/BNB18.M" index b84b09fe500fa3622d1f482f44b07e31d1d5b9cb..354793e5537af0006464ed5f3df3d4bd747fd299 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/BNB18.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/BNB18.M" @@ -1,3 +1,386 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:bb0b48805d4a64a38ca5fc13547abb07b62b6bcf5a465c5f2d25467d7e2253e3 -size 14681 +function [errmsg,Z,X,t,c,fail] = BNB18(fun,x0,xstat,xl,xu,A,B,Aeq,Beq,nonlcon,setts,options1,options2,maxSQPit,varargin); +%·ÇÏßÐÔÕûÊý¹æ»®Ä£ÐÍÇó½â·ÖÖ§¶¨½çµü´úËã·¨¡£ÔÚMATLAB5.3ÖÐʹÓã¬ÐèOptimization toolbox 2.0Ö§³Ö? +% Minimize F(x) +%subject to: xlb <= x <=xub +% A*x <= B +% Aeq*x=Beq +% C(x)<=0 +% Ceq(x)=0 +% +% x(i)¿ÉΪÁ¬Ðø±äÁ¿£¬ÕûÊý£¬»ò¹Ì¶¨Öµ +% ʹÓøñʽ +%[errmsg,Z,X]=BNB18('fun',x0,xstat,xl,xu,A,B,Aeq,Beq,'nonlcon',setts) +%fun£º MÎļþÃû£¬±íʾ×îС»¯Ä¿±êº¯Êýf=fun(x) +%x0: ÁÐÏòÁ¿£¬±íʾ±äÁ¿³õÖµ +%xstat£º ÁÐÏòÁ¿£¬xstat(i)=0±íʾx(i)ΪÁ¬Ðø±äÁ¿£¬1±íʾÕûÊý£¬2±íʾ¹Ì¶¨Öµ +%xl£º ÁÐÏòÁ¿£¬±íʾ±äÁ¿Ï½ç +%xu: ÁÐÏòÁ¿£¬±íʾ±äÁ¿ÉϽç +%A: ¾ØÕó, ±íʾÏßÐÔ²»µÈʽԼÊøϵÊý +%B: ÁÐÏòÁ¿, ±íʾÏßÐÔ²»µÈʽԼÊøÉϽç +%Aeq: ¾ØÕó, ±íʾÏßÐÔµÈʽԼÊøϵÊý +%Beg: ÁÐÏòÁ¿, ±íʾÏßÐÔ²»µÈʽԼÊøÓÒ¶ËÖµ +%nonlcon: MÎļþÃû£¬±íʾ·ÇÏßÐÔÔ¼Êøº¯Êý[C,Ceq]=nonlin(x),ÆäÖÐC(x)Ϊ²»µÈʽԼÊø, +% Ceq(x)ΪµÈʽԼÊø +%setts: Ëã·¨ÉèÖà +%errmsq: ·µ»Ø´íÎóÌáʾ +%Z: ·µ»ØÄ¿±êº¯Êý×îСֵ +%X: ·µ»Ø×îÓŽâ +% +%ÀýÌâ +% max x1*x2*x3 +% -x1+2*x2+2*x3>=0 +% x1+2*x2+2*x3<=72 +% 10<=x2<=20 +% x1-x2=10 +% ÏÈд Mº¯Êýdiscfun.m +% function f=discfun(x) +% f=-x(1)*x(2)*x(3); +%Çó½â +% clear;x0=[25,15,10]';xstat=[1 1 1]'; +% xl=[20 10 -10]';xu=[30 20 20]'; +% A=[1 -2 -2;1 2 2];B=[0 72]';Aeq=[1 -1 0];Beq=10; +% [err,Z,X]=BNB18('discfun',x0,xstat,xl,xu,A,B,Aeq,Beq); +% XMAX=X',ZMAX=-Z +% +% BNB18 Finds the constrained minimum of a function of several possibly integer variables. +% Usage: [errmsg,Z,X,t,c,fail] = +% BNB18(fun,x0,xstatus,xlb,xub,A,B,Aeq,Beq,nonlcon,settings,options1,options2,maxSQPiter,P1,P2,...) +% +% BNB solves problems of the form: +% Minimize F(x) subject to: xlb <= x0 <=xub +% A*x <= B Aeq*x=Beq +% C(x)<=0 Ceq(x)=0 +% x(i) is continuous for xstatus(i)=0 +% x(i) integer for xstatus(i)= 1 +% x(i) fixed for xstatus(i)=2 +% +% BNB uses: +% Optimization Toolbox Version 2.0 (R11) 09-Oct-1998 +% From this toolbox fmincon.m is called. For more info type help fmincon. +% +% fun is the function to be minimized and should return a scalar. F(x)=feval(fun,x). +% x0 is the starting point for x. x0 should be a column vector. +% xstatus is a column vector describing the status of every variable x(i). +% xlb and xub are column vectors with lower and upper bounds for x. +% A and Aeq are matrices for the linear constrains. +% B and Beq are column vectors for the linear constrains. +% nonlcon is the function for the nonlinear constrains. +% [C(x);Ceq(x)]=feval(nonlcon,x). Both C(x) and Ceq(x) should be column vectors. +% +% errmsg is a string containing an error message if BNB found an error in the input. +% Z is the scalar result of the minimization, X the values of the accompanying variables. +% t is the time elapsed while the algorithm BNB has run, c is the number of BNB cycles and +% fail is the number of unsolved leaf sub-problems. +% +% settings is a row vector with settings for BNB: +% settings(1) (standard 0) if 1: use phase 1 by relaxation. This sometimes makes the algorithm +% faster, because phase 1 means the algorithm first checks if there is a feasible solution +% for a sub-problem before trying to find a best solution. If there is no feasible solution BNB +% will not try to find a best solution. +% settings(2) (standard 0) if 1: if the sub-problem did not converge do not branch. If a sub- +% problem did not converge this means BNB did not find a solution for it. Normally BNB will +% branch the problem so it can try again to find a solution. +% A sub-problem that is a leaf of the branch-and-bound-three can not be branched. If such +% a problem does not converge it will be considered unfeasible and the parameter fail will be +% raised by one. +% settings(3) (standard 0) if 1: if 1 a sub-problem that did not converge but did return a feasible +% point will be considered convergent. This might be useful if fmincon is having a hard time with +% a certain problem but you do want some results. +% options1 and options2 are options structures for phase 1 and phase 2. +% For details about the options structure type help optimset. +% maxSQPiter is a global variable used by fmincon (if modified as described in bnb18.m). +% maxSQPiter is 1000 by default. +% P1,P2,... are parameters to be passed to fun and nonlcon. +% F(x)=feval(fun,x,P1,P2,...). [C(x);Ceq(x)]=feval(nonlcon,x,P1,P2,...). +% Type edit BNB18 for more info. + +% E.C. Kuipers +% e-mail E.C.Kuipers@cpedu.rug.nl +% FI-Lab +% Applied Physics +% Rijksuniversiteit Groningen + +% To get rid of bugs and to stop fmincon from hanging make the following chances: +% +% In optim/private/nlconst.m ($Revision: 1.20 $ $Date: 1998/08/24 13:46:15 $): +% Get EXITFLAG independent of verbosity. +% After the lines: disp(' less than 2*options.TolFun but constraints are not satisfied.') +% end +% EXITFLAG = -1; +% end +% end +% status=1; +% add the line: if (strncmp(howqp, 'i',1) & mg > 0), EXITFLAG = -1; end; +% +% In optim/private/qpsub.m ($Revision: 1.21 $ $Date: 1998/09/01 21:37:56 $): +% Stop qpsub from hanging. +% After the line: % Andy Grace 7-9-90. Mary Ann Branch 9-30-96. +% add the line: global maxSQPiter; +% and changed the line: maxSQPiters = Inf; +% to the line: if exist('maxSQPiter','var'), maxSQPiters = maxSQPiter; else maxSQPiters=inf; end; +% I guess there was a reason to put maxSQPiters at infinity, but this works fine for me. +global maxSQPiter; + +% STEP 0 CHECKING INPUT +Z=[]; X=[]; t=0; c=0; fail=0; +if nargin<2, errmsg='BNB needs at least 2 input arguments.'; return; end; +if isempty(fun), errmsg='No fun found.'; return; end; +if isempty(x0), errmsg='No x0 found.'; return; +elseif size(x0,2)>1, errmsg='x0 must be a column vector.'; return; end; +xstatus=zeros(size(x0)); +if nargin>2 & ~isempty(xstat) + if all(size(xstat)<=size(x0)) + xstatus(1:size(xstat))=xstat; + else errmsg='xstatus must be a column vector the same size as x0.'; return; + end; + if any(xstatus~=round(xstatus) | xstatus<0 | 23 & ~isempty(xl) + if all(size(xl)<=size(x0)) + xlb(1:size(xl,1))=xl; + else errmsg='xlb must be a column vector the same size as x0.'; return; + end; +end; +if any(x04 & ~isempty(xu) + if all(size(xu)<=size(x0)) + xub(1:size(xu,1))=xu; + else errmsg='xub must be a column vector the same size as x0.'; return; + end; +end; +if any(x0>xub) + errmsg='x0 must be in the range x0 <=xub.'; return; +elseif any(xstatus==1 & (~isfinite(xub) | xub~=round(xub))) + errmsg='xub(i) must be an integer if x(i) is an integer variabale.'; return; +end; +xub(find(xstatus==2))=x0(find(xstatus==2)); +if nargin>5 + if ~isempty(A) & size(A,2)~=size(x0,1), errmsg='Matrix A not correct.'; return; end; +else A=[]; end; +if nargin>6 + if ~isempty(B) & any(size(B)~=[size(A,1) 1]), errmsg='Column vector B not correct.'; return; end; +else B=[]; end; +if isempty(A) & ~isempty(B), errmsg='A and B should only be nonempty together.'; return; end; +if isempty(B) & ~isempty(A), B=zeros(size(A,1),1); end; +if nargin>7 & ~isempty(Aeq) + if size(Aeq,2)~=size(x0,1), errmsg='Matrix Aeq not correct.'; return; end; +else Aeq=[]; end; +if nargin>8 + if ~isempty(Beq) & any(size(Beq)~=[size(Aeq,1) 1]), errmsg='Column vector Beq not correct.'; return; end; +else Beq=[]; end; +if isempty(Aeq) & ~isempty(Beq), errmsg='Aeq and Beq should only be nonempty together'; return; end; +if isempty(Beq) & ~isempty(Aeq), Beq=zeros(size(Aeq,1),1); end; +if nargin<10, nonlcon=''; end; +settings = [0 0 0]; +if nargin>10 & ~isempty(setts) + if all(size(setts)<=size(settings)) + settings(setts~=0)=setts(setts~=0); + else errmsg='settings should be a row vector of length 3.'; return; end; +end; +if nargin<12, options1=[]; end; +options1=optimset(optimset('fmincon'),options1); +if nargin<13, options2=[]; end; +options2=optimset(optimset('fmincon'),options2); +if nargin<14, maxSQPiter=1000; +elseif isnumeric(maxSQPit) & all(size(maxSQPit))==1 & maxSQPit>0 & round(maxSQPit)==maxSQPit + maxSQPiter=maxSQPit; +else errmsg='maxSQPiter must be an integer >0'; return; end; +eval(['z=',fun,'(x0,varargin{:});'],'errmsg=''fun caused error.''; return;'); +if ~isempty(nonlcon) + eval(['[C, Ceq]=',nonlcon,'(x0,varargin{:});'],'errmsg=''nonlcon caused error.''; return;'); + if size(C,2)>1 | size(Ceq,2)>1, errmsg='C en Ceq must be column vectors.'; return; end; +end; + +% STEP 1 INITIALISATION +currentwarningstate=warning; +warning off; +tic; +lx = size(x0,1); +z_incumbent=inf; +x_incumbent=inf*ones(size(x0)); +I = ceil(sum(log2(xub(find(xstatus==1))-xlb(find(xstatus==1))+1))+size(find(xstatus==1),1)+1); +stackx0=zeros(lx,I); +stackx0(:,1)=x0; +stackxlb=zeros(lx,I); +stackxlb(:,1)=xlb; +stackxub=zeros(lx,I); +stackxub(:,1)=xub; +stacksize=1; +xchoice=zeros(size(x0)); +if ~isempty(Aeq) + j=0; + for i=1:size(Aeq,1) + if Beq(i)==1 & all(Aeq(i,:)==0 | Aeq(i,:)==1) + J=find(Aeq(i,:)==1); + if all(xstatus(J)~=0 & xchoice(J)==0 & xlb(J)==0 & xub(J)==1) + if all(xstatus(J)~=2) | all(x0(J(find(xstatus(J)==2)))==0) + j=j+1; + xchoice(J)=j; + if sum(x0(J))==0, errmsg='x0 not correct.'; return; end; + end; + end; + end; + end; +end; +errx=optimget(options2,'TolX'); +errcon=optimget(options2,'TolCon'); +fail=0; +c=0; + +% STEP 2 TERMINIATION +while stacksize>0 + c=c+1; + + % STEP 3 LOADING OF CSP + x0=stackx0(:,stacksize); + xlb=stackxlb(:,stacksize); + xub=stackxub(:,stacksize); + x0(find(x0xub))=xub(find(x0>xub)); + stacksize=stacksize-1; + + % STEP 4 RELAXATION + + % PHASE 1 + con=BNBCON(x0,A,B,Aeq,Beq,xlb,xub,nonlcon,varargin{:}); + if abs(con)>errcon & settings(1)~=0 + [x1 dummy feasflag]=fmincon('0',x0,A,B,Aeq,Beq,xlb,xub,nonlcon,options1,varargin{:}); + if settings(3) & feasflag==0 + con=BNBCON(x1,A,B,Aeq,Beq,xlb,xub,nonlcon,varargin{:}); + if con0 + [x z convflag]=fmincon(fun,x1,A,B,Aeq,Beq,xlb,xub,nonlcon,options2,varargin{:}); + if settings(3) & convflag==0 + con=BNBCON(x,A,B,Aeq,Beq,xlb,xub,nonlcon,varargin{:}); + if con=z_incumbent & convflag>0 + % FC 2 + separation=0; + elseif all(abs(round(x(K))-x(K))0 + % FC 3 + z_incumbent = z; + x_incumbent = x; + separation = 0; + end; + + % STEP 6 SELECTION + if separation == 1 & ~isempty(K) + dzsep=-1; + for i=1:size(K,1) + dxsepc = abs(round(x(K(i)))-x(K(i))); + if dxsepc>=errx | convflag==0 + xsepc = x; xsepc(K(i))=round(x(K(i))); + dzsepc = abs(feval(fun,xsepc,varargin{:})-z); + if dzsepc>dzsep + dzsep=dzsepc; + ixsep=K(i); + end; + end; + end; + + % STEP 7 SEPARATION + if xchoice(ixsep)==0 + + % XCHOICE==0 + branch=1; + domain=[xlb(ixsep) xub(ixsep)]; + while branch==1 + xboundary=(domain(1)+domain(2))/2; + if x(ixsep)=6 +% 2x1+3x2=9; +% x1, x2>=0ÇÒΪÕûÊý +%ÏȽ«x1+2x2>=6»¯Îª - x1 - 2x2<= -6 +%c=[1 4]; +%A=[2 1;-1 -2]; +%b=[8;-6]; +%Aeq=[2 3]; +%beq=9; +%[y,fval]=BranchBound(c,A,b,Aeq,beq) + + + +function [y,fval]=BranchBound(c,A,b,Aeq,beq) +NL=length(c); +UB=inf; +LB=-inf; +FN=[0]; +AA(1)={A}; +BB(1)={b}; +k=0; +flag=0; +while flag==0; + [x,fval,exitFlag]=linprog(c,A,b,Aeq,beq); + if (exitFlag == -2) | (fval >= UB) + FN(1)=[]; + if isempty(FN)==1 + flag=1; + else + k=FN(1); + A=AA{k}; + b=BB{k}; + end + else + for i=1:NL + if abs(x(i)-round(x(i)))>1e-7 + kk=FN(end); + FN=[FN,kk+1,kk+2]; + temp_A=zeros(1,NL); + temp_A(i)=1; + temp_A1=[A;temp_A]; + AA(kk+1)={temp_A1}; + b1=[b;fix(x(i))]; + BB(kk+1)={b1}; + temp_A2=[A;-temp_A]; + AA(kk+2)={temp_A2}; + b2=[b;-(fix(x(i))+1)]; + BB(kk+2)={b2}; + FN(1)=[]; + k=FN(1); + A=AA{k}; + b=BB{k}; + break; + end + end + if (i==NL) & (abs(x(i)-round(x(i)))<=1e-7) + UB=fval; + y=x; + FN(1)=[]; + if isempty(FN)==1 + flag=1; + else + k=FN(1); + A=AA{k}; + b=BB{k}; + end + end + end +end +y=round(y); +fval=c*y; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DIJKSTRA.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DIJKSTRA.M" index ccbdece460746995c6297c237c9f08098fcb3788..2157f08ec983ad7e942a5796eae7f7e1a291534f 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DIJKSTRA.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DIJKSTRA.M" @@ -1,3 +1,80 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:18c068d7b1b8862c6f6cc1b855c8c89a837808b4342e16589a66fca0adfe659a -size 1573 +function [p,v]=dijkstra(map,u1,u2) +%ÇóÍøÂç×î¶Ì·¾¶µÄdijkstraËã·¨ +%Ó÷¨: +% Ê×ÏÈÊäÈë¾ØÕó: +% map=[Æðµã1 ÖÕµã1 ±ß³¤1;Æðµã2 ÖÕµã2 ±ß³¤2;............;Æðµãn ÖÕµãn ±ß³¤n] +% ºÍu1,u2 +% ×¢Ò⣺ÕâÀïmapΪÎÞÏòͼ¡£ +% ÔÙÓÃ[p,v]=dijkstra(map,u1,u2)Çó×î¶Ì·¾¶ +%²ÎÊý˵Ã÷ +% map----3ÁÐÁÚ½Ó¾ØÕó,ÿÐбíʾһÌõ±ß. +% µÚÒ»ÁбíʾÆðµã,µÚ¶þÁбíʾÖÕµã,µÚÈýÁбíʾ±ß³¤ +% u1---ËùÇ󷾶Æðµã +% u2---ËùÇ󷾶ÖÕµã +% p---Êä³ö×î¶Ì·¾¶ +% v---×î¶Ì·¾¶µÄ×ܳ¤¶È +% +% +%ÀýÈç +% clear;map=[1 2 30;2 4 5;2 5 50;3 2 6;4 3 1;1 4 20;1 5 3] +% [p,v]=dijkstra(map,2,5) +% +%±¾Ëã·¨µ÷ÓÃÓÉVC++6.0³ÌÐòdijk.cÉú³ÉµÄMEXÎļþdijk.dllÇóµÃ×î¶Ì·¾¶ +% ±íʾÎÞÇî´óµÄÊýÖµÉϽç(ĬÈÏ10000) +% +%See also KRUSKAL,LPINT,DP,BNBGUI,BNB18, + +%By W. Z. Li, 2000 + +[m,n]=size(map); +mx=max(max(map(:,1:2))); +l=10000*ones(mx,mx); +for i=1:m + l(map(i,1),map(i,2))=map(i,3); + l(map(i,2),map(i,1))=map(i,3); + end; + [p,v]=dijk(l,u1,u2); +p=p(p~=0); + +%»­Í¼ +close; + set(gcf,'numbertitle','off'); + set(gcf,'name','Dijkstra'); + set(gca,'visible','off'); + axis square; + hold on; + + b=linspace(0,2*pi,mx+1); + b1=10*sin(b); + b2=10*cos(b); + plot(b1,b2,'ko'); + hh=char(49:48+mx); + for i=1:mx + text(b1(i)+0.5,b2(i),hh(i)); + end; + for j=1:m + for i=1:2 + c1(i)=b1(map(j,i)); + c2(i)=b2(map(j,i)); + end; + plot(c1,c2,':'); + end; + + kk=length(p); + k=0; + for i=1:kk + if(p(1,i)~=0) + k=k+1; + end; + end; + for i=1:k + d1(i)=b1(p(1,i)); + d2(i)=b2(p(1,i)); + h=plot(d1,d2,'r'); +end; + set(h,'linewidth',2); + legend(h,'´ÖÏß±íʾ×î¶Ì·'); + hold off + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DYNPROG.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DYNPROG.M" index 347fc38ac36887338347a83bd762d4924207d805..63d161dbe577b617709588c9c16ce6563e0f79cf 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DYNPROG.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/DYNPROG.M" @@ -1,3 +1,86 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ab9ef86cd6f10ff0289bf031250390694cfe9dbe36752b49d1019cf44f7df6b0 -size 3151 +function [p_opt,fval]=dynprog(x,DecisFun,ObjFun,TransFun) +% [p_opt,fval]=dynprog(x,DecisFun,ObjFun,TransFun) +% ×ÔÓÉʼ¶ËºÍÖն˵Ķ¯Ì¬¹æ»®,ÇóÖ¸±êº¯Êý×îСֵµÄÄæÐòËã·¨µÝ¹é +% ¼ÆËã³ÌÐò¡£xÊÇ״̬±äÁ¿£¬Ò»Áдú±íÒ»¸ö½×¶Î״̬£»M-º¯Êý +% DecisFun(k,x)Óɽ׶ÎkµÄ״̬±äÁ¿xÇó³öÏàÓ¦µÄÔÊÐí¾ö²ß±äÁ¿; +% M-º¯ÊýObjFun(k,x,u)Êǽ׶ÎÖ¸±êº¯Êý£¬M-º¯ÊýTransFun(k,x,u) +% ÊÇ״̬תÒƺ¯Êý,ÆäÖÐxÊǽ׶ÎkµÄij״̬±äÁ¿£¬uÊÇÏàÓ¦µÄ¾ö²ß±äÁ¿£» +% Êä³öp_optÓÉ4Áй¹³É£¬p_opt=[ÐòºÅ×é;×îÓŲßÂÔ×é;×îÓŹìÏß×é; +% Ö¸±êº¯ÊýÖµ×é]£»fvalÊÇÒ»¸öÁÐÏòÁ¿£¬¸÷ÔªËØ·Ö±ð±íʾp_opt¸÷ +% ×îÓŲßÂÔ×é¶ÔӦʼ¶Ë״̬xµÄ×îÓź¯ÊýÖµ£» +% +%Àý£¨²Î¿´ºúÁ¼½£µÈ±à¡¶ÊýѧʵÑé--ʹÓÃMATLAB¡·P180 +%ÏÈд3¸öº¯Êý +% eg13f1_2.m +% function u=DecisF_1(k,x) +% Ôڽ׶ÎkÓÉ״̬±äÁ¿xµÄÖµÇó³öÆäÏàÓ¦µÄ¾ö²ß±äÁ¿ËùÓеÄÈ¡Öµ +% c=[70,72,80,76];q=10*[6,7,12,6]; +% if q(k)-x<0,u=0:100; %¾ö²ß±äÁ¿²»ÄÜȡΪ¸ºÖµ +% else,u=q(k)-x:100;end; %²úÁ¿Âú×ãÐèÇóÇÒ²»³¬¹ý100 +% u=u(:); +% eg13f2_2.m +% function v=ObjF_1(k,x,u) +% ½×¶ÎkµÄÖ¸±êº¯Êý +% c=[70,72,80,76];v=c(k)*u+2*x; +% eg13f3_2.m +% function y=TransF_1(k,x,u) +% ״̬תÒÆ·½³Ì +% q=10*[6,7,12,6];y=x+u-q(k); +%µ÷ÓÃDynProg.m¼ÆËãÈçÏ£º +% clear;x=nan*ones(14,4);% xÊÇ10µÄ±¶Êý£¬×î´ó·¶Î§0¡Üx¡Ü130, +% %Òò´Ëx=0,1,...13£¬ËùÒÔx³õʼ»¯È¡14ÐУ¬nan±íʾÎÞÒâÒåÔªËØ +% x(1:7,1)=10*(0:6)'; % °´Ô¶¨ÒåxµÄ¿ÉÄÜÈ¡Öµ +% x(1:11,2)=10*(0:10)';x(1:12,3)=10*(2:13)'; +% x(1:7,4)=10*(0:6)'; +% [p,f]=dynprog(x,'eg13f1_2','eg13f2_2','eg13f3_2') + +% By X.D. Ding June 2000 + +k=length(x(1,:));f_opt=nan*ones(size(x));d_opt=f_opt; +t_vubm=inf*ones(size(x));x_isnan=~isnan(x);t_vub=inf; +% ¼ÆËãÖÕ¶ËÏà¹ØÖµ +tmp1=find(x_isnan(:,k));tmp2=length(tmp1); +for i=1:tmp2 + u=feval(DecisFun,k,x(i,k));tmp3=length(u); + for j=1:tmp3 + tmp=feval(ObjFun,k,x(tmp1(i),k),u(j)); + if tmp<=t_vub, + f_opt(i,k)=tmp;d_opt(i,k)=u(j);t_vub=tmp; +end;end;end +% ÄæÍƼÆËã¸÷½×¶ÎµÄµÝ¹éµ÷ÓóÌÐò +for ii=k-1:-1:1 + tmp10=find(x_isnan(:,ii));tmp20=length(tmp10); + for i=1:tmp20 + u=feval(DecisFun,ii,x(i,ii));tmp30=length(u); + for j=1:tmp30 + tmp00=feval(ObjFun,ii,x(tmp10(i),ii),u(j)); + tmp40=feval(TransFun,ii,x(tmp10(i),ii),u(j)); + tmp50=x(:,ii+1)-tmp40; + tmp60=find(tmp50==0); + if ~isempty(tmp60), + tmp00=tmp00+f_opt(tmp60(1),ii+1); + if tmp00<=t_vubm(i,ii) + f_opt(i,ii)=tmp00;d_opt(i,ii)=u(j); + t_vubm(i,ii)=tmp00; +end;end;end;end;end; +fval=f_opt(tmp1,1); +% ¼Ç¼×îÓžö²ß¡¢×îÓŹìÏߺÍÏàÓ¦Ö¸±êº¯ÊýÖµ +p_opt=[];tmpx=[];tmpd=[];tmpf=[]; +tmp0=find(x_isnan(:,1));tmp01=length(tmp0); +for i=1:tmp01, + tmpd(i)=d_opt(tmp0(i),1); + tmpx(i)=x(tmp0(i),1); + tmpf(i)=feval(ObjFun,1,tmpx(i),tmpd(i)); + p_opt(k*(i-1)+1,[1,2,3,4])=[1,tmpx(i),... +tmpd(i),tmpf(i)]; + for ii=2:k + tmpx(i)=feval(TransFun,ii-1,tmpx(i),tmpd(i)); + tmp1=x(:,ii)-tmpx(i);tmp2=find(tmp1==0); + if ~isempty(tmp2) + tmpd(i)=d_opt(tmp2(1),ii); + end; + tmpf(i)=feval(ObjFun,ii,tmpx(i),tmpd(i)); + p_opt(k*(i-1)+ii,[1,2,3,4])=[ii,tmpx(i),... +tmpd(i),tmpf(i)]; +end;end; + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/ENUM.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/ENUM.M" index def22292a5b44960e0adb2c007a660905c5c97ac..9588474476e41167e33ff7aaac97af2b1fe04741 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/ENUM.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/ENUM.M" @@ -1,3 +1,15 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:50c753cad7a440acb822c49fbc026051094b1b4528908c4411967e9c8de820ff -size 289 +%×îÓÅ»¯Ã¶¾Ù·¨Àý¡ª¡ªÂú×ãÒ»¶¨Ìõ¼þÇó×îÓŽâµÄÇî¾Ù·¨ +clear; +vmax=-inf; +for x2=10:20 + for x3=-5:16 + if x2+2*x3>=10&3*x2+2*x3<=62, + v=(x2+10)*x2*x3; + if v>vmax, + vmax=v;x20=x2;x30=x3; + end + end + end +end +x1=x20+10,x2=x20,x3=x30 +vmax diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.C" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.C" index 67f1b2dd84df0dcc955eab090fb5408497102e8b..8ad1affd4b3f878eddfd6c2f8ad9577312d28f82 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.C" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.C" @@ -1,3 +1,77 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:51076d8e27b21ae7adafbda3d31b544eced210229ff8aa605cc5c6dce6001431 -size 1633 +#include "mex.h" +#include "stdlib.h" +#include "iostream.h" +typedef struct TR +{double fromvex,endvex; + double length; +}edge; +void krusk(double *out,double *len,double *op,int mrows,int ncols) +{edge *T,*M,*N; + int i,j,v,u,c,p,d,max=10000; + edge k; + p=0; +T=(edge *)malloc(mrows*(mrows-1)*sizeof(struct TR)); +for(i=0;ifromvex=i+1; +(T+p)->endvex=j+1; +(T+p)->length=*(op+i*ncols+j); +p++; +} + +for(i=p-1;i>=0;--i) +{for(j=0;jlength>(T+j+1)->length) + {k=*(T+j); + *(T+j)=*(T+j+1); + *(T+j+1)=k; + } +} +} +N=(edge *)malloc(mrows*(mrows-1)*sizeof(struct TR)); +for(i=0;ifromvex!=(T+i)->endvex) + { *(M+d)=*(N+i); + d++; + if ((T+i)->endvex>(T+i)->fromvex) + { u=(T+i)->endvex;v=(T+i)->fromvex;} + else + {u=(T+i)->fromvex;v=(T+i)->endvex;} + c=u; + u=v; + for(j=0;jfromvex==c) + (T+j)->fromvex=v; + if ((T+j)->endvex==c) + (T+j)->endvex=v; + } + } + } +*len=0; +for(j=0;jfromvex; +*(out+j*2+1)=(M+j)->endvex; +*len=*len+(M+j)->length; +} +} + +void mexFunction(int nlhs,mxArray *plhs[],int nrhs,const mxArray *prhs[]) +{double *out; + double *op; + double *len; + int mrows,ncols; + op=mxGetPr(prhs[0]); + mrows=mxGetM(prhs[0]); + ncols=mxGetN(prhs[0]); + plhs[0]=mxCreateDoubleMatrix(2,mrows-1,mxREAL); + plhs[1]=mxCreateDoubleMatrix(1,1,mxREAL); +out=mxGetPr(plhs[0]); + len=mxGetPr(plhs[1]); +krusk(out,len,op,mrows,ncols); +} diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.DLL" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.DLL" index 5146eef1fb387361a2a41bf0e46129e21c173ee8..9dfab5f99981312486bc0c07b552b06dd3bf775f 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.DLL" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSK.DLL" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSKAL.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSKAL.M" index 172b6a207d409aeda2473b6197882a66ff3eacb7..1911b5d5534569d6e2367d2174ce696ef013743e 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSKAL.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/KRUSKAL.M" @@ -1,3 +1,70 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:d702409686b1c294214ebf5cd1e584d9fe9adec1629c50f85fcd87118e96bf47 -size 1479 +function [out,len]=kruskal(map) +%Çó×îСÉú³ÉÊ÷Ëã·¨,ͨ¹ýkruskalËã·¨Çó×îÓÅÊ÷,²¢¸ø³öÏàӦͼÏñ. +%Ó÷¨: +% Ê×ÏÈÊäÈë¾ØÕó: +% map=[Æðµã1 ÖÕµã1 ±ß³¤1;Æðµã2 ÖÕµã2 ±ß³¤2;............;Æðµãn ÖÕµãn ±ß³¤n] +% ÔÙÓÃ[out,len]=kruskal(map)Çó×îÓÅÊ÷ +%²ÎÊý˵Ã÷ +% map----3ÁÐÁÚ½Ó¾ØÕó,ÿÐбíʾһÌõ±ß.µÚÒ»ÁбíʾÆðµã,µÚ¶þÁбíʾÖÕµã,µÚÈýÁбíʾ±ß³¤ +% out---Êä³ö±ßÕó:[Æðµã ÖÕµã] +% len---Êä³ö×îÓÅÊ÷µÄ×ܳ¤¶È +% +%ÀýÈç +% clear;map=[1 2 30;2 4 5;2 5 50;3 2 6;4 3 1;1 4 20;1 5 30] +% [out,len]=kruskal(map) +% +%±¾Ëã·¨µ÷ÓÃÓÉVC++6.0³ÌÐòcrusal1.cÉú³ÉµÄMEXÎļþkruskal1.dllÇóµÃ×îСÉú³ÉÊ÷, +% ±íʾÎÞÇî´óµÄÊýÖµÉϽç(ĬÈÏ10000) +% +%See also DIJKSTRA,LPINT,DP,BNBGUI,BNB18, + +%By S. J. Lu 2000 + +mx=0; +[m,n]=size(map); +mx=max(max(map(:,1:2))); +op=10000*ones(mx,mx); +for i=1:m + op(map(i,1),map(i,2))=map(i,3); + op(map(i,2),map(i,1))=map(i,3); +end +[out,len]=krusk(op); +out=out'; + +% »­Í¼ +close; + set(gcf,'numbertitle','off'); + set(gcf,'name','Kruskal'); + set(gca,'visible','off'); + axis square; + hold on; + + b=linspace(0,2*pi,mx+1); + b1=10*sin(b); + b2=10*cos(b); + plot(b1,b2,'ko'); + + hh=char(49:48+mx); + for i=1:mx + text(b1(i)+1,b2(i),hh(i)); + end; + map + for j=1:m + for i=1:2 + c1(i)=b1(map(j,i)); + c2(i)=b2(map(j,i)); + end; + plot(c1,c2,':'); +end; + + k1=length(out); + for i=1:k1 + for j=1:2 + d1(j)=b1(out(i,j)); + d2(j)=b2(out(i,j)); + end + h=plot(d1,d2,'r'); + set(h,'linewidth',2); + end + legend(h,'´ÖÏßΪ×îÓÅÊ÷'); + hold off \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_e.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_e.m" index f4a90f2dec4c5e6d33ea9ff1662a33214a772684..36ab4db04171e67be5c7ebe83440c3b7f9603beb 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_e.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_e.m" @@ -1,3 +1,29 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b269ec89a87a56116eae777d7b5f74b8f3bb624b02ac240702d76b22b5fbdcd4 -size 749 +function [x,f]=L01p_e(c,A,b,N) +% [x,f]= L01p_e(c,A,b,N)ÓÃö¾Ù·¨Çó½âÏÂÁÐ +% 0-1ÏßÐԹ滮ÎÊÌâ +% min f=c'*x, s.t. A*x<=b,xµÄ·ÖÁ¿È«ÎªÕûÊý0»ò1, +% ÆäÖÐN±íʾԼÊøÌõ¼þ Ax ¡Ü bÖеÄÇ°N¸öÊǵÈʽ£¬N= 0ʱ¿ÉÒÔÊ¡ÂÔ¡£ +% ·µ»Ø½á¹ûxÊÇ×îÓŽ⣬fÊÇ×îÓŽ⴦µÄº¯ÊýÖµ¡£ +% +%Àý max f=3x1+5x2+2x3+4x4+2x5+3x6 +% s.t. 8x1+13x2+6x3+9x4+5x5+7x6<=24, x1,¡­,x6¾ùΪ0»ò1 +%Çó½â +% c=-[3,5,2,4,2,3];a=[8,13,6,9,5,7];b=24; +% x=l01p_e(c,a,b) + +% By X.D. Ding£¬ June 2000 + +if nargin<4,N=0;end +c=c(:);b=b(:); +[m,n]=size(A);x=[];f=abs(c')*ones(n,1);i=1; +while i<=2^n + B=de2bi(i-1,n)'; + t=A*B-b;t11=find(t(1:N,:)~=0); + t12=find(t(N+1:m,:)>0);t1=[t11;t12]; + if isempty(t1) + f=min([f,c'*B]); + if c'*B==f,x=B;end + end + i=i+1; +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_ie.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_ie.m" index ea72ca07c629c807121e31a63b193b48fdbf0fcf..fabf444a75c11fe9b028b6046bdaa8eb6b8d03b3 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_ie.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/L01p_ie.m" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:e1bf70edd623378030e5b1291a4130f1cdb8b4194d24ee6490c78a0967dfcb09 -size 963 +function [x,f]=L01p_ie(c,A,b,N) +% [x,f]= L01p_ie(c,A,b,N)ÓÃÒþö¾Ù·¨Çó½âÏÂÁÐ0-1ÏßÐԹ滮ÎÊÌâ +% min f=c'*x, s.t. A*x<=b£¬ xµÄ·ÖÁ¿È«ÎªÕûÊý0»ò1£¬ +% ÆäÖÐN±íʾԼÊøÌõ¼þ Ax ¡Ü bÖеÄÇ°N¸öÊǵÈʽ£¬N= 0ʱ¿ÉÒÔÊ¡ÂÔ¡£% ³ÌÐòÖÐÓõ½ÃüÁîB = de2bi(D)£¬Æä×÷ÓÃÊǽ«10½øÖÆÊýÏòÁ¿Dת»» +% ΪÏàÓ¦¶þ½øÖÆÊý°´Î»¹¹³ÉµÄÒÔ0£¬1ΪԪËصľØÕóB¡£ +% ´ËÃüÁîÔÚtoolbox communicationÖС£ +% ·µ»Ø½á¹ûxÊÇ×îÓŽ⣬fÊÇ×îÓŽ⴦µÄº¯ÊýÖµ¡£ +%Àý max f=3x1+5x2+2x3+4x4+2x5+3x6 +% s.t. 8x1+13x2+6x3+9x4+5x5+7x6<=24, x1,¡­,x6¾ùΪ0»ò1 +%Çó½â +% c=-[3,5,2,4,2,3];a=[8,13,6,9,5,7];b=24; +% x=1p_ie(c,a,b) + +% By X.D. Ding, June 2000 + +if nargin<4,N=0;end +c=c(:);b=b(:); +A=[-A(1:N,:);A];b=[-b(1:N);b]; +[m,n]=size(A);x=[];f=abs(c')*ones(n,1); +A=[c';A];b=[f;b];i=1; +while i<=2^n + B=de2bi(i-1,n)'; + j=1;t1=A(j,:)*B-b(j); + while(t1<=0&j0,j=1;end + end + if j==m+1 + x=B;f=c'*B; + b(1)=min([b(1),f]); + end + i=i+1; +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.M" index f773b5dc3fd8f6403596eb7b4604249405a1b55b..47684850ac5bd304f6c5e406066f78d143f70b00 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.M" @@ -1,3 +1,76 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:9f9c9cae824142527eed7569473f46bcf3bdef8d877c44bb229ca1c7cffe8e48 -size 2038 +function [x,y]=lpint(f,G,h,lb,ub,x,n,id) +%ÕûÊýÏßÐԹ滮·ÖÖ¦¶¨½ç·¨£¬¿ÉÇó½âÏßÐÔÈ«ÕûÊý»òÏßÐÔ»ìºÏÕûÊý¹æ»®¡£ +% y = min f'x subject to: Gx <= h xΪÕû +% x +%Ó÷¨ +% [x,y]=lpint(f,G,h) +% [x,y]=lpint(f,G,h,lb,ub) +% [x,y]=lpint(f,G,h,lb,ub,x) +% [x,y]=lpint(f,G,h,lb,ub,x,n) +% [x,y]=lpint(f,G,h,lb,ub,x,n,id) +%²ÎÊý˵Ã÷ +% x: ×îÓŽâÁÐÏòÁ¿ +% y: Ä¿±êº¯Êý×îСֵ +% f: Ä¿±êº¯ÊýϵÊýÁÐÏòÁ¿ +% G: Ô¼ÊøÌõ¼þϵÊý¾ØÕó +% h: Ô¼ÊøÌõ¼þÓÒ¶ËÁÐÏòÁ¿ +% lb: ½âµÄµÄϽçÁÐÏòÁ¿(Default: -inf) +% ub: ½âµÄµÄÉϽçÁÐÏòÁ¿(Default: inf) +% x: µü´ú³õÖµÁÐÏòÁ¿ +% n: µÈʽԼÊøÊý(Default: 0) +% id: ÕûÊý±äÁ¿Ö¸±êÁÐÏòÁ¿¡£1-ÕûÊý£¬0-ʵÊý(Default: 1) +%Àý2 min Z=x1+4x2 +% s.t. 2x1+x2<=8 +% x1+2x2>=6 +% x1, x2>=0ÇÒΪÕûÊý +%ÏȽ«x1+2x2>=6»¯Îª - x1 - 2x2<= -6 +%[x,y]=lpint([1;4],[2 1;-1 -2],[8;-6],[0;0]) + +% Y. MA & L.J. HU 1999 + +global upper opt c N x0 A b ID; +if nargin<8, id=ones(size(f));end +if nargin<7|isempty(n), n=0;end +if nargin<6, x=[];end +if nargin<5|isempty(ub), ub=inf*ones(size(f));end +if nargin<4|isempty(lb), lb=zeros(size(f));end + +upper=inf; +c=f;N=n;x0=x;A=G;b=h;ID=id; +temp=ILP(lb(:),ub(:)); +x=opt;y=upper; + +%ÒÔÏÂ×Óº¯Êý +function y=ILP(vlb,vub) +global upper opt c N x0 A b ID; + warning off; + [x,temp,how]=lp(c,A,b,vlb,vub,x0,N,-1); + if strcmp(how,'ok')~=1 + return; + end; + if c'*x-upper>0.00005 %in order to avoid error + return; + end; + + if max(abs(x.*ID-round(x.*ID)))<0.00005 + if upper-c'*x>0.00005 %in order to avoid error + opt=x'; + upper=c'*x; + return; + else + opt=[opt;x']; + return; + end; + end; + notintx=find(abs(x-round(x))>=0.00005); %in order to avoid error + intx=fix(x); + tempvlb=vlb; + tempvub=vub; + if vub(notintx(1,1),1)>=intx(notintx(1,1),1)+1 + tempvlb(notintx(1,1),1)=intx(notintx(1,1),1)+1; + temp=ILP(tempvlb,vub); + end; + if vlb(notintx(1,1),1)<=intx(notintx(1,1),1) + tempvub(notintx(1,1),1)=intx(notintx(1,1),1); + temp=ILP(vlb,tempvub); + end; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.asv" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.asv" index 2a24ec16a3075695591ed52e0931f90ae0358daf..3f44a3401fddf8da9ce1831779be4ce4c2cd7482 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.asv" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/LPINT.asv" @@ -1,3 +1,76 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8a7334421aa203651514515fd2b5254af22619b9357b8c5f0d40c109940bc05c -size 2048 +function [x,y]=lpint(f,G,h,lb,ub,x,n,id) +%ÕûÊýÏßÐԹ滮·ÖÖ¦¶¨½ç·¨£¬¿ÉÇó½âÏßÐÔÈ«ÕûÊý»òÏßÐÔ»ìºÏÕûÊý¹æ»®¡£ +% y = min f'x subject to: Gx <= h xΪÕû +% x +%Ó÷¨ +% [x,y]=lpint(f,G,h) +% [x,y]=lpint(f,G,h,lb,ub) +% [x,y]=lpint(f,G,h,lb,ub,x) +% [x,y]=lpint(f,G,h,lb,ub,x,n) +% [x,y]=lpint(f,G,h,lb,ub,x,n,id) +%²ÎÊý˵Ã÷ +% x: ×îÓŽâÁÐÏòÁ¿ +% y: Ä¿±êº¯Êý×îСֵ +% f: Ä¿±êº¯ÊýϵÊýÁÐÏòÁ¿ +% G: Ô¼ÊøÌõ¼þϵÊý¾ØÕó +% h: Ô¼ÊøÌõ¼þÓÒ¶ËÁÐÏòÁ¿ +% lb: ½âµÄµÄϽçÁÐÏòÁ¿(Default: -inf) +% ub: ½âµÄµÄÉϽçÁÐÏòÁ¿(Default: inf) +% x: µü´ú³õÖµÁÐÏòÁ¿ +% n: µÈʽԼÊøÊý(Default: 0) +% id: ÕûÊý±äÁ¿Ö¸±êÁÐÏòÁ¿¡£1-ÕûÊý£¬0-ʵÊý(Default: 1) +%Àý2 min Z=x1+4x2 +% s.t. 2x1+x2<=8 +% x1+2x2>=6 +% x1, x2>=0ÇÒΪÕûÊý +%ÏȽ«x1+2x2>=6»¯Îª - x1 - 2x2<= -6 +%[x,y]=lpint([1;4],[2 1;-1 -2],[8;-6],[0;0],[inf inf]) + +% Y. MA & L.J. HU 1999 + +global upper opt c N x0 A b ID; +if nargin<8, id=ones(size(f));end +if nargin<7|isempty(n), n=0;end +if nargin<6, x=[];end +if nargin<5|isempty(ub), ub=inf*ones(size(f));end +if nargin<4|isempty(lb), lb=zeros(size(f));end + +upper=inf; +c=f;N=n;x0=x;A=G;b=h;ID=id; +temp=ILP(lb(:),ub(:)); +x=opt;y=upper; + +%ÒÔÏÂ×Óº¯Êý +function y=ILP(vlb,vub) +global upper opt c N x0 A b ID; + warning off; + [x,temp,how]=lp(c,A,b,vlb,vub,x0,N,-1); + if strcmp(how,'ok')~=1 + return; + end; + if c'*x-upper>0.00005 %in order to avoid error + return; + end; + + if max(abs(x.*ID-round(x.*ID)))<0.00005 + if upper-c'*x>0.00005 %in order to avoid error + opt=x'; + upper=c'*x; + return; + else + opt=[opt;x']; + return; + end; + end; + notintx=find(abs(x-round(x))>=0.00005); %in order to avoid error + intx=fix(x); + tempvlb=vlb; + tempvub=vub; + if vub(notintx(1,1),1)>=intx(notintx(1,1),1)+1 + tempvlb(notintx(1,1),1)=intx(notintx(1,1),1)+1; + temp=ILP(tempvlb,vub); + end; + if vlb(notintx(1,1),1)<=intx(notintx(1,1),1) + tempvub(notintx(1,1),1)=intx(notintx(1,1),1); + temp=ILP(vlb,tempvub); + end; \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINROUTE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINROUTE.M" index dd5789c7fe62d769949805a5475d8b69a333024a..53d8717b9749ee751b7c81aa2b85b67f91e1e82a 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINROUTE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINROUTE.M" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:84b5f86cf921e1272927e9a644ecce7fba7166dda08475bd0b8e6763e24356d6 -size 1259 +function [S,D]=minRoute(i,m,W) +%ͼÓëÍøÂçÂÛÖÐÇó×î¶Ì·¾¶µÄDijkstraËã·¨ M-º¯Êý +%¸ñʽ [S,D]=minroute(i,n,W) +% iΪ×î¶Ì·¾¶µÄÆðʼµã,mΪͼ¶¥µãÊý,WΪͼµÄ´øȨÁÚ½Ó¾ØÕó£¬ +% ²»¹¹³É±ßµÄÁ½¶¥µãÖ®¼äµÄȨÓÃinf±íʾ¡£ÏÔʾ½á¹ûΪ£ºSµÄÿ +% Ò»ÁдÓÉϵ½Ï¼Ç¼ÁË´Óʼµãµ½ÖÕµãµÄ×î¶Ì·¾¶Ëù¾­¶¥µãµÄÐòºÅ£» +% DÊÇÒ»ÐÐÏòÁ¿£¬¼Ç¼ÁËSÖÐËùʾ·¾¶µÄ´óС; +%ÀýÈç +% clear;w=inf*ones(6);w(1,3)=10;w(1,5)=30; +% w(1,6)=100;w(2,3)=5;w(3,4)=50;w(4,6)=10; +% w(5,4)=20;w(5,6)=60; +% i=1;[s,d]=minroute(i,6,w) + +% By X.D. Ding June 2000 + +dd=[];tt=[];ss=[];ss(1,1)=i;V=1:m;V(i)=[];dd=[0;i]; +% ddµÄµÚ¶þÐÐÊÇÿ´ÎÇó³öµÄ×î¶Ì·¾¶µÄÖյ㣬µÚÒ»ÐÐÊÇ×î¶Ì·¾¶µÄÖµ +kk=2;[mdd,ndd]=size(dd); +while ~isempty(V) + [tmpd,j]=min(W(i,V));tmpj=V(j); + for k=2:ndd + [tmp1,jj]=min(dd(1,k)+W(dd(2,k),V)); + tmp2=V(jj);tt(k-1,:)=[tmp1,tmp2,jj]; + end + tmp=[tmpd,tmpj,j;tt];[tmp3,tmp4]=min(tmp(:,1)); + if tmp3==tmpd, ss(1:2,kk)=[i;tmp(tmp4,2)]; + else,tmp5=find(ss(:,tmp4)~=0);tmp6=length(tmp5); + if dd(2,tmp4)==ss(tmp6,tmp4) + ss(1:tmp6+1,kk)=[ss(tmp5,tmp4);tmp(tmp4,2)]; + else, ss(1:3,kk)=[i;dd(2,tmp4);tmp(tmp4,2)]; + end;end + dd=[dd,[tmp3;tmp(tmp4,2)]];V(tmp(tmp4,3))=[]; + [mdd,ndd]=size(dd);kk=kk+1; +end; S=ss; D=dd(1,:); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINTREEK.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINTREEK.M" index f4bfbe2dcdc3115ff44b84bd9c38773b021d0f57..587712fae91830f3f8d453772352f0a3a3674e61 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINTREEK.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MINTREEK.M" @@ -1,3 +1,48 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:ac4fe2d894552bfb172e78e835f1ded4f2aa0193094be013902e489d7250be19 -size 1824 +function [Wt,Pp]=mintreek(n,W) +%ͼÂÛÖÐ×îСÉú³ÉÊ÷KruskalËã·¨ ¼°»­Í¼³ÌÐò M-º¯Êý +%¸ñʽ [Wt,Pp]=mintreek(n,W)£ºnΪͼ¶¥µãÊý,WΪͼµÄ´øȨÁÚ½Ó¾Ø +% Õ󣬲»¹¹³É±ßµÄÁ½¶¥µãÖ®¼äµÄȨÓÃinf±íʾ¡£ÏÔʾ×îСÉú³ÉÊ÷µÄ±ß¼° +% ¶¥µã, WtΪ×îСÉú³ÉÊ÷µÄȨ,Pp(:,1:2)Ϊ×îСÉú³ÉÊ÷±ßµÄÁ½¶¥µã, +% Pp(:,3)Ϊ×îСÉú³ÉÊ÷µÄ±ßȨ,Pp(:,4)Ϊ×îСÉú³ÉÊ÷±ßµÄÐòºÅ; +%¸½Í¼,ºìÉ«Á¬ÏßΪ×îСÉú³ÉÊ÷µÄͼ; +%ÀýÈç +% n=6;w=inf*ones(6); +% w(1,[2,3,4])=[6,1,5];w(2,[3,5])=[5,3]; +% w(3,[4,5,6])=[5,6,4];w(4,6)=2;w(5,6)=6; +% [a,b]=mintreek(n,w) + +% By X.D. Ding June 2000 + +tmpa=find(W~=inf);[tmpb,tmpc]=find(W~=inf); +w=W(tmpa);e=[tmpb,tmpc]; %wÊÇWÖзÇinfÔªËØ°´Áй¹³ÉµÄÏòÁ¿ + %eµÄÿһÐÐÔªËرíʾһÌõ±ßµÄÁ½¸ö¶¥µãµÄÐòºÅ +[wa,wb]=sort(w);E=[e(wb,:),wa,wb];[nE,mE]=size(E); +temp=find(E(:,1)-E(:,2));E=E(temp,:); +P=E(1,:);k=length(E(:,1)); +while (rank(E)>0) + temp1=max(E(1,2),E(1,1));temp2=min(E(1,2),E(1,1)); + for i=1:k; + if (E(i,1)==temp1), E(i,1)=temp2; end; +if (E(i,2)==temp1), E(i,2)=temp2; end; + end; + a=find(E(:,1)-E(:,2));E=E(a,:); + if (rank(E)>0),P=[P;E(1,:)];k=length(E(:,1)); end; +end; +Wt=sum(P(:,3));Pp=[e(P(:,4),:),P(:,3:4)]; +for i=1:length(P(:,3)); %ÏÔʾ¶¥µãviÓë±ßej +disp([' ','e',num2str(P(i,4)),' ','(v',... +num2str(P(i,1)),' ','v',num2str(P(i,2)),')']); +end; +% ÒÔÏÂÊÇ»­Í¼³ÌÐò +axis equal; hold on +[x,y]=cylinder(1,n);xm=min(x(1,:)); ym=min(y(1,:)); +xx=max(x(1,:)); yy=max(y(1,:)); +axis([xm-abs(xm)*0.15,xx+abs(xx)*0.15,ym-abs(ym)*0.15, yy+abs(yy)*0.15]); plot(x(1,:),y(1,:),'ko') +for i=1:n; temp=[' v',int2str(i)]; + text(x(1,i),y(1,i),temp); end; +for i=1:nE; plot(x(1,e(i,:)),y(1,e(i,:)),'b'); end; +for i=1:length(P(:,4)); + plot(x(1,Pp(i,1:2)),y(1,Pp(i,1:2)),'r'); end; +text(-0.35,-1.2,['×îСÉú³ÉÊ÷µÄȨΪ',' ',num2str(Wt)]); +title('ºìÉ«Á¬ÏßΪ×îСÉú³ÉÊ÷'); axis('off');hold off + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MONTE.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MONTE.M" index c07998c2db4d58c757723f47bd66e755f2d86a83..9b5fe706b5c3dbed3a8ae74a5d56e750baa8e1f4 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MONTE.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/MONTE.M" @@ -1,3 +1,27 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:b88aa948c2dfc145f439de502a6d226970130e0e715b699ed3471b0089f5e2cf -size 664 +%MonteCarlo·¨½â×îÓÅ»¯µÄÀý +clear; +%É趨һ¸ö³õÖµ +vmax=-inf; + %specrndÉú³É¸ø¶¨·Ö²¼ÂɵÄËæ»úÊý + %r=specrnd(x,p)·µ»ØÒ»¸öÀ´×Ô·Ö²¼ÂÉP(x)=pµÄËæ»úÊý + %r=specrnd(x,p,m,n)·µ»Øm*nËæ»úÊý¾ØÕó + %pµÄĬÈÏֵΪµÈ¸ÅÂÊ + %ÀýÈç ·Ö²¼ÂÉ + % ¦Î 7 8 9 10 + % p 0.1 0.2 0.4 0.3 + %ÃüÁî specrnd([7 8 9 10],[0.1 0.2 0.4 0.3],10,10) + %²úÉú100¸öÄ£ÄâÊý¾Ý +x2=specrnd(10:20,[],1,5); +x3=specrnd(-5:16,[],1,5); +for i=1:5 + for j=1:5 + if x2(i)+2*x3(j)>=10&3*x2(i)+2*x3(j)<=62, + v=(x2(i)+10)*x2(i)*x3(j); + if v>vmax, + vmax=v;x20=x2(i);x30=x3(j); + end + end + end +end +x1=x20+10,x2=x20,x3=x30 +vmax diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/\347\246\273\346\225\243\344\274\230\345\214\226.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/\347\246\273\346\225\243\344\274\230\345\214\226.txt" index 197c6ba7dc828bef5b6517e511254703b10016a9..7f3157479df18209c94fc815eb925b3c3c9c39e7 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/\347\246\273\346\225\243\344\274\230\345\214\226.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\246\273\346\225\243\344\274\230\345\214\226/\347\246\273\346\225\243\344\274\230\345\214\226.txt" @@ -1,3 +1,13 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:65c41fea9d51379305392c8a90081e0957a8938e621758ff6a616746b87a0826 -size 427 +% ÀëÉ¢ÓÅ»¯ +% *enum - ö¾Ù·¨ +% *monte - ÃÉÌØ¿¨Âå·¨ +% *lpint (BranchBound)- ÏßÐÔÕûÊý¹æ»® +% *L01p_e - 0-1ÕûÊý¹æ»®Ã¶¾Ù·¨ +% *L01p_ie - 0-1ÕûÊý¹æ»®Òþö¾Ù·¨ +% *bnb18 - ·ÇÏßÐÔÕûÊý¹æ»®(ÔÚMATLAB5.3ʹÓÃ) +% *bnbgui - ·ÇÏßÐÔÕûÊý¹æ»®Í¼Ðι¤¾ß(ÔÚMATLAB5.3ʹÓÃ) +% *mintreek - ×îСÉú³ÉÊ÷kruskalËã·¨ +% *minroute - ×î¶Ì·dijkstraËã·¨ +% *krusk - ×îСÉú³ÉÊ÷kruskalËã·¨mex³ÌÐò +% *dijkstra - ×î¶Ì·dijkstraËã·¨mex³ÌÐò +% *dynprog - ¶¯Ì¬¹æ»® \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\200\222\346\216\250\345\205\263\347\263\273\345\274\217\347\232\204\344\275\234\345\233\276\347\250\213\345\272\217.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\200\222\346\216\250\345\205\263\347\263\273\345\274\217\347\232\204\344\275\234\345\233\276\347\250\213\345\272\217.m" index 8d5bf154d91b630e4aa09815ccc84e05eda9da1f..5ec631ecaba0843a6c4aadba8490159680b3b6bf 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\200\222\346\216\250\345\205\263\347\263\273\345\274\217\347\232\204\344\275\234\345\233\276\347\250\213\345\272\217.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\200\222\346\216\250\345\205\263\347\263\273\345\274\217\347\232\204\344\275\234\345\233\276\347\250\213\345\272\217.m" @@ -1,3 +1,6 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:3ffe690e26d2b145bf99ab0b417a724291781eddace52cd331a28fc6fb988e00 -size 143 +x(1)=1;x(2)=10; +hold on +for t=3:10 + x(t)=0.8*x(t-1)+1.5*x(t-2);%µÝÍƹØϵʽ£¬×¢ÒâMATLABÀïÏòÁ¿µÄϱ겻ÄÜ´ÓÁ㿪ʼ¡£ +end +plot(2:10,x(2:10)) \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/CHI2TEST.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/CHI2TEST.M" index 9de4a2a6029779d6655a139b0761a86008c29f57..282b91148624a725dde6cd3f6fd43d401fe239c1 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/CHI2TEST.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/CHI2TEST.M" @@ -1,3 +1,24 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:4aab34cde31937dcda527e4e93ccfd69004a7b6bfac154aa36fdffe27abbf753 -size 539 +function [h,sig]=chi2test(n,x,p,alpha) +%[h,sig]=chi2test(n,x,p,alpha) +% ·Ö²¼ÄâºÏ¶È¼ìÑé +% n: Êý¾Ý×ÜÊý +% x: ʵ¼Ê×éƵÊýÏòÁ¿ +% p: ÀíÂÛ×éƵÊýÏòÁ¿ +% h£º·µ»Ø1±íʾ¾Ü¾øH0£¬·µ»Ø0±íʾ½ÓÊÜH0¡£ +% sig£º·µ»Ø¼ìÑéͳ¼ÆÁ¿µÄÖµ£¬sig< alpha ʱh=1 + +% L.J. Hu 8-19-1999 + +if nargin<4,alpha=0.05;end +if min(size(x))~=1|min(size(p))~=1, + error('X,P must be vectors'); +end +kx=length(x);kp=length(p); +if kx~=kp, + error('Dimension of vectors must be agree'); +end + +chi2=sum((x-p).^2./p); +h=0; +sig=1-chi2cdf(chi2,kx-1); +if sig 1 + sigmai = sqrt((nu*s2/(nu-1)) - (r .^2 ./ ((nu-1) .* (1-hatdiag)))); + ser = sqrt(1-hatdiag) .* sigmai; +elseif nu == 1 + ser = sqrt(1-hatdiag) .* rmse; +end + +ti= r ./ ser; + +% Create confidence intervals for residuals. +Z=[(r-tval*ser) (r+tval*ser)]'; +rint=Z'; diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORT.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORT.M" index 166c89b335c9bf2984b6b1c68e47adf5fb6e0e5b..aa74c525b7849de2dc38f757bc3e6cf2beb355ca 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORT.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORT.M" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:27a6aca84604e51f8b98d0fbdeee51ffb0a46cb08d8a5d6f08f0d85fd86ce81d -size 1182 +%ÁÐ×´Êý¾ÝÉýÐòÅÅÁÐ +%ÀýÈç +% A=[11 4 0.2;22 3 0.5;0 3 0.4]; +% sort(A) +% +%SORT Sort in ascending order. +% For vectors, SORT(X) sorts the elements of X in ascending order. +% For matrices, SORT(X) sorts each column of X in ascending order. +% For N-D arrays, SORT(X) sorts the along the first non-singleton +% dimension of X. When X is a cell array of strings, SORT(X) sorts +% the strings in ASCII dictionary order. +% +% SORT(X,DIM) sorts along the dimension DIM. +% +% [Y,I] = SORT(X) also returns an index matrix I. If X is a +% vector, then Y = X(I). If X is an m-by-n matrix, then +% for j = 1:n, Y(:,j) = X(I(:,j),j); end +% +% When X is complex, the elements are sorted by ABS(X). Complex +% matches are further sorted by ANGLE(X). +% +% Example: If X = [3 7 5 +% 0 4 2] +% +% then sort(X,1) is [0 4 2 and sort(X,2) is [3 5 7 +% 3 7 5] 0 2 4]; +% +% See also SORTROWS, MIN, MAX, MEAN, MEDIAN. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 5.11 $ $Date: 1997/11/21 23:24:04 $ +% Built-in function. + +% Cell array implementation in @cell/sort.m diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORTROWS.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORTROWS.M" index 09d5ef5abfafb0abadb6b2764d9301d5383a8263..14ca79181aa427848ddf7c4a8979f567a664fa57 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORTROWS.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SORTROWS.M" @@ -1,3 +1,36 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2484f953e91f8bd7f9b4b2779be1e69cd021da846b2971b8a2ef74655ed8f657 -size 1256 +function [y,ndx] = sortrows(x,col) +%[Y,I]=sortrows(A,k)°´µÚkÁÐÉýÐòµÄÅÅÁÐ,ÏòÁ¿I·µ¸÷ÐеÄÔ­±àÖ·. +%ÀýÈç +% A=[11 4 0.2;22 3 0.5;0 3 0.4]; +% sortrows(A,3) +%SORTROWS Sort rows in ascending order. +% SORTROWS(X) sorts the rows of the matrix X in ascending order as a +% group. For ASCII strings, this is the familiar dictionary sort. +% When X is complex, the elements are sorted by ABS(X). Complex +% matches are further sorted by ANGLE(X). +% +% SORTROWS(X,COL) sorts the matrix based on the columns specified in +% the vector COL. For example, SORTROWS(X,[2 3]) sorts the rows of X +% by the second and third columns of X. +% +% [Y,I] = SORTROWS(X) also returns an index matrix I. If X is a +% vector, then Y = X(I). If X is an m-by-n matrix, then Y = X(I,:). +% +% See also SORT. + +% Copyright (c) 1984-98 by The MathWorks, Inc. +% $Revision: 1.9 $ $Date: 1997/11/21 23:24:05 $ + +if nargin<1, error('Not enough input arguments.'); end +if ndims(x)>2, error('X must be a 2-D matrix.'); end + +if nargin<2, col = 1:size(x,2); end +if isempty(x), y = x; ndx = []; return, end + +% Sort back to front +ndx = (1:size(x,1))'; +for i=length(col):-1:1, + [v,ind] = sort(x(ndx,col(i))); + ndx = ndx(ind); +end +y = x(ndx,:); diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SPECRND.M" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SPECRND.M" index b136a0bcf153581ed5e5e6f76477b3d23094750c..88d6f187e0d71429c4684ee75f8fd4e4f0fe24d0 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SPECRND.M" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/SPECRND.M" @@ -1,3 +1,38 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8d9768ac0c4be0dd78b27da821ddd51543ccaa9953207d7bb3d7169a7563ca42 -size 1035 +function r=specrnd(x,p,m,n) +% Éú³É¸ø¶¨·Ö²¼ÂɵÄËæ»úÊý +% r=specrnd(x,p)·µ»ØÒ»¸öÀ´×Ô·Ö²¼ÂÉP(x)=pµÄËæ»úÊý +% r=specrnd(x,p,m,n)·µ»Øm*nËæ»úÊý¾ØÕó +% pµÄĬÈÏֵΪµÈ¸ÅÂÊ +% ÀýÈç ·Ö²¼ÂÉ +% ¦Î 7 8 9 10 +% p 0.1 0.2 0.4 0.3 +% ÃüÁî specrnd([7 8 9 10],[0.1 0.2 0.4 0.3],10,10) +% ²úÉú100¸öÄ£ÄâÊý¾Ý + +% L. J. HU 9-10-1999 + +if nargin<4, n=1;end +if nargin<3, m=1;end +if nargin<2|isempty(p), p=1/length(x)*ones(size(x)); end; + +[mx,nx]=size(x);[mp,np]=size(p); +sx=min(mx,nx);sp=min(mp,np); +if (mx~=mp)|(nx~=np), + error('size must agree'); +end; +if (sx~=1)&(sx~=1),error('should be vector'); end; +x=x(:); +if any(x~=sort(x)), error('x should be acsend'); end; +if any((p<0)|(p>1)),error('p should be between 0 and 1'); end; +if abs(sum(p)-1)>1e-3,error('sum of p should be 1'); end; + +r=zeros(m,n);lx=max(mx,nx); +s=rand(m,n); +cp=cumsum(p); +k=find(s=cp(lx-1));r(k)=x(lx); +for i=2:(lx-1), + k=find((s>=cp(i-1))&(soutval*ones(n,1)*sigma); +if m>1, + data(any(outliers'),:)=[]; +else + data(find(outliers'),:)=[]; +end + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220.txt" index a76cfdb57e59bb2de46a4c357548f684ea1310f2..edea1177a4eb80dd6ca32922bc63a2aa9d09f903 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\225\260\345\255\246\345\273\272\346\250\241MATLAB\345\277\205\345\244\207\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\347\250\213\345\272\217\346\272\220\344\273\243\347\240\201/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220/\351\232\217\346\234\272\346\250\241\346\213\237\345\222\214\347\273\237\350\256\241\345\210\206\346\236\220.txt" @@ -1,3 +1,17 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:8611fd9722ae534e5a51e964ccbe5fb746a51ee9a2c7846be6499fdaec9e14dc -size 426 +%Ëæ»úÄ£ÄâºÍͳ¼Æ·ÖÎö +% max,min - ×î´ó£¬×îСֵ +% sum - ÇóºÍ +% mean - ¾ùÖµ +% std - ±ê×¼²î +% sort - ÅÅÐò£¨ÉýÐò£© +% sortrows - °´Ä³Ò»ÁÐÅÅÐò(ÉýÐò) +% rand - [0£¬1]Çø¼ä¾ùÔÈ·Ö²¼Ëæ»úÊý +% randn - ±ê×¼Õý̬·Ö²¼Ëæ»úÊý +% randperm - 1...n Ëæ»úÅÅÁÐ +% regress - ÏßÐԻعé +% classify - ͳ¼Æ¾ÛÀà +% *trim - »µÊý¾Ýìî³ý +% *specrnd - ¸ø¶¨·Ö²¼ÂÉËæ»úÊýÉú³É +% *randrow - ÕûÐÐËæ»úÅÅÁÐ +% *randmix - Ëæ»úÖû» +% *chi2test - ·Ö²¼ÄâºÏ¶È¿¨·½¼ìÑé \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\344\273\243\347\240\201\347\233\256\345\275\225.docx" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\344\273\243\347\240\201\347\233\256\345\275\225.docx" index c76891b6a836f693d6f188af39d38b7f2265cc50..f68e485e1e6fc2442293aab6470339a90c4e41b9 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\344\273\243\347\240\201\347\233\256\345\275\225.docx" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\344\273\243\347\240\201\347\233\256\345\275\225.docx" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\223\345\274\200\351\241\273\347\237\245.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\223\345\274\200\351\241\273\347\237\245.txt" index 5f86c79ecf8a8d58369b7c4c335ba9ca438c3502..32994e6f5523e35c49b4541fcf4d9489020cf214 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\223\345\274\200\351\241\273\347\237\245.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\223\345\274\200\351\241\273\347\237\245.txt" @@ -1,3 +1,5 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:a96a0edfdbd8d3eb8bfe91f8324a51c68ab515668f7334a9a5b22b62d5509793 -size 180 +P12-2ºÍP14-2µÄ´úÂëÖУ¬Ô­Ê¼µÄÊÇÔËÐв»ÆðÀ´µÄ£¬ÐèÒªµ¥¶À°²×°¹¤¾ßÏä¡£ +ÎÒ°ÑÏÂÔغóµÄ¹¤¾ßÏä·ÅÔÚÀïÃæÁË£¬»¹Óа²×°²½Ö裬Õâ¸öÄã¿ÉÒÔ×÷ΪÖصã +ÔÚÌÔ±¦µêÆÌչʾһÏ£¬ + +À©Õ¹³ÌÐòÕûÀí×ÔµÚ¶þ°æµÄ´úÂë \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/Kmeans results.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/Kmeans results.fig" index affe5d2aedca47dfbd38e0384acc10ca5d70af90..c21a866957ea0a82a5293c7e3ed32baba4c592d1 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/Kmeans results.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/Kmeans results.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/kmeans.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/kmeans.m" index 2fe4abcf98cb6006c15618fcc96b25ed245e84ae..5afbb254ba12980d07337988927e0ad0b7a1472c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/kmeans.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/Kmeans/kmeans.m" @@ -1,3 +1,54 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:58ec20371bd0841a9e37c3c5eb6ce467e65ec6d5880538420287c3ca785fd6a9 -size 1533 +% K-means Ëã·¨MATLABʵÏÖ +%-------------------------------------------------------------------------- +%% Êý¾Ý×¼±¸ºÍ³õʼ»¯ +clc +clear +x=[0 0;1 0; 0 1; 1 1;2 1;1 2; 2 2;3 2; 6 6; 7 6; 8 6; 6 7; 7 7; 8 7; 9 7 ; 7 8; 8 8; 9 8; 8 9 ; 9 9]; +z=zeros(2,2); +z1=zeros(2,2); +z=x(1:2, 1:2); +%% Ñ°ÕÒ¾ÛÀàÖÐÐÄ +while 1 + count=zeros(2,1); + allsum=zeros(2,2); + for i=1:20 % ¶Ôÿһ¸öÑù±¾i£¬¼ÆËãµ½2¸ö¾ÛÀàÖÐÐĵľàÀë + temp1=sqrt((z(1,1)-x(i,1)).^2+(z(1,2)-x(i,2)).^2); + temp2=sqrt((z(2,1)-x(i,1)).^2+(z(2,2)-x(i,2)).^2); + if(temp1=T + Com_num=K; + break; + end +end + +% Get the eigenvectors of the Com_num principal components +for j=1:Com_num + PV(:,j)=V(:,b+1-j); +end + +% Calculate the new socres of the orginal items +new_score=SA*PV; + +for i=1:a + total_score(i,2)=sum(new_score(i,:)); + total_score(i,1)=i; +end +new_score_s=sortrows(total_score,-2); + +% Displays result reports +disp('ÌØÕ÷Öµ¼°¹±Ï×ÂÊ£º') +DS +disp('·§ÖµT¶ÔÓ¦µÄÖ÷³É·ÖÊýÓëÌØÕ÷ÏòÁ¿£º') +Com_num +PV +disp('Ö÷³É·Ö·ÖÊý£º') +new_score +disp('Ö÷³É·Ö·ÖÊýÅÅÐò£º') +new_score_s + + + + + + + + + + + + + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246-cumcm2011B.doc" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246-cumcm2011B.doc" index e115df8a3c9b7e98e7e294558fa38798a49a4169..695f89837d11d7a2ed32d57ffe93988eec1b554f 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246-cumcm2011B.doc" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246-cumcm2011B.doc" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/ch15_p3_q1.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/ch15_p3_q1.m" index c7831a1441572864c608f132ef3b9eb329698cb5..462c6a081713398c20bff3b1b7faaecb32f1fa5c 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/ch15_p3_q1.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/ch15_p3_q1.m" @@ -1,3 +1,108 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:f5f8b6dda66a63bf3a4fb7e7cb591de322b692e7f54173a84b07fc8f89ffea00 -size 2838 +%% ×î¶Ì·¾¶µÄÇó½â£¬ÒÔ¼°ÏÖÓеĽ»Ñ²¾¯·þÎñƽ̨ÉèÖ÷½°¸µÄºÏÀíÐÔµÄÅÐ¶Ï +clc; clear all; close all +%% Êý¾Ý×¼±¸ +% È«Êн»Í¨ÍøÂçÖз¿Ú½Úµã½Úµã×ø±ê +A=xlsread('2011B_Table.xls', 'È«Êн»Í¨Â·¿Ú½ÚµãÊý¾Ý','A2:C583'); +% È«Êн»Í¨Â·Ïß +B=xlsread('2011B_Table.xls', 'È«Êн»Í¨Â·¿ÚµÄ·Ïß','A2:B929'); +% ÿ¸ö·¿Ú·¢°¸ÂÊ(´ÎÊý) +owl=xlsread('2011B_Table.xls', 'È«Êн»Í¨Â·¿Ú½ÚµãÊý¾Ý','E2:E93'); +%% ¼ÆËã×î¶Ì¾àÀë¾ØÕó +arn=size(A,1) +brn=size(B,1); +% ¹¹½¨¾àÀë¾ØÕó +D=ones(arn); +D(:)=inf; +for i=1:arn + D(i,i)=0; +end +for i=1:brn + m=B(i,1); % Æðµã±êºÅ + n=B(i,2); % ÖÕµã±êºÅ + d=sqrt((A(m,2)-A(n,2))^2+(A(m,3)-A(n,3))^2); + D(m,n)=d; + D(n,m)=d; +end +[dmin,path]=floyd(D); + +%% È·¶¨×î¼ÑÐÂÔö¾¯Ì¨Êý +alt_sta=21:92; +ppsl=1:20; +min_n=ones(1,5)*6; +%% ÆôÓÃË«ºË¼ÓËÙ¼ÆËã(¶àºË¼ÆËã»ú²Å¿ÉÒÔ²ÉÓÃ) +if matlabpool('size') == 0 + matlabpool open 2 +end +%% ¼ÆËã¸÷ÐÂÔö¾¯Ì¨ÊýÓë¶ÔÓ¦µÄ²»Âú×ã3·ÖÖÓ³ö¾¯µÄ·¿ÚÊý + apsn=4; + com_pat=nchoosek(alt_sta,apsn); + com_num=size(com_pat, 1); + avn=0; + bfair_f=inf; + for k1=1:com_num + npsl=[ppsl, com_pat(k1,:)]; % ¸üо¯Ì¨ÉèÖ÷½°¸ + % ¼ÆË㻹ÓжàÉÙ·¿Ú²»Âú×ã3·ÖÖÓ³ö¾¯ + SR=zeros(92,4); + for i=1:92 + i; + SR(i,1)=i; + SR(i,2)=0; + SR(i,3)=inf; + SR(i,4)=0; + for j=1:(20+apsn) + if SR(i,3)>dmin(i,npsl(j)) + SR(i,3)=dmin(i,npsl(j)); + SR(i,2)=npsl(j); + end + end + if SR(i,3)*100>3000 + SR(i,4)=1; + end + end + tun_num=sum(SR(:,4)); + + if tun_num==0 + avn=avn+1; + workload=zeros(1, 24); + for j=1:24 + for u=1:92 + if SR(u,2)==npsl(1,j) + workload(1,j)=workload(1,j)+owl(u,1); + end + end + end + fair_f=var(workload,1); + fair_r(avn,:)=[avn, fair_f, com_pat(k1,:)]; + + if fair_f 0 + matlabpool close +end +%% ÏÔʾ½á¹û +abpn=0; +for i=1:avn + if fair_r(i,2)==bfair_f + abpn=abpn+1; + abps(abpn,:)=[abpn, fair_r(i,2:end)]; + end +end +disp(['ËùÓпÉÐз½°¸Êý' num2str(avn)]); +disp(['×î¼Ñ·½°¸Êý' num2str(abpn)]); +disp('ËùÓÐ×î¼Ñ·½°¸:') +abps +disp('×î¼Ñ·½°¸¶ÔÓ¦µÄ¹¤×÷¾ùºâ¶È:') +bfair_f +plot(fair_r(:,1),fair_r(:,2),'-ko', 'LineWidth', 2); +set(gca,'linewidth',2) ; +xlabel('¿ÉÐз½°¸±àºÅ'); ylabel('¹¤×÷¾ùºâ¶È'); +title('¸÷¿ÉÐз½°¸µÄ¹¤×÷¾ùºâ¶È','fontsize',12); + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/floyd.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/floyd.m" index 579568991cc50497df798733ac3657d473adef23..76b10f31b6e31ae2c92f1b1e423c65eaabb619b9 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/floyd.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/floyd.m" @@ -1,3 +1,26 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:afddd01586bc32bbe18d4ef855449d1504ccca52374c80b31bc00bec39afa244 -size 563 +% floydËã·¨µÄº¯ÊýÎļþ +function [d,path]=floyd(a) +% floyd - ×î¶Ì·ÎÊÌâ +% a - ¾àÀë¾ØÕóÊÇÖ¸iµ½jÖ®¼äµÄ¾àÀ몢¿ÉÒÔÊÇÓÐÏòµÄ +% d - ×î¶Ì·µÄ¾àÀë +% path - ×î¶Ì·µÄ·¾¶ +[n,lie]=size(a); % nΪaµÄÐÐÊý +d=a; +path=zeros(n,n); +for i=1:n + for j=1:n + if d(i,j)~=inf + path(i,j)=j; %jÊÇiµÄºóÐøµã + end + end +end +for k=1:n + for i=1:n + for j=1:n + if d(i,j)>d(i,k)+d(k,j) + d(i,j)=d(i,k)+d(k,j); + path(i,j)=path(i,k); + end + end + end +end diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.fig" index ac813fbef93b3d9a4a6b2d9fa737c230b539c157..750c325a73aa135597f7b1266c9614511bbe17a8 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.txt" index 9ea9ac1d1a8ae22147aa47fdb13da791fad8ab31..06a2e9e9542e147ca643255f2af024535801442d 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/results.txt" @@ -1,3 +1,34 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1f6542a9eb1c1cb8803fdf773096e0fd9f807d2c3ca379a7e5ca0f6ed05be797 -size 1254 +arn = + + 582 + +Starting matlabpool using the 'local' profile ... connected to 2 workers. +Sending a stop signal to all the workers ... stopped. +ËùÓпÉÐз½°¸Êý72 +×î¼Ñ·½°¸Êý16 +ËùÓÐ×î¼Ñ·½°¸: + +abps = + + 1.0000 5.3844 28.0000 39.0000 48.0000 87.0000 + 2.0000 5.3844 28.0000 39.0000 48.0000 88.0000 + 3.0000 5.3844 28.0000 39.0000 48.0000 89.0000 + 4.0000 5.3844 28.0000 39.0000 48.0000 91.0000 + 5.0000 5.3844 28.0000 40.0000 48.0000 87.0000 + 6.0000 5.3844 28.0000 40.0000 48.0000 88.0000 + 7.0000 5.3844 28.0000 40.0000 48.0000 89.0000 + 8.0000 5.3844 28.0000 40.0000 48.0000 91.0000 + 9.0000 5.3844 29.0000 39.0000 48.0000 87.0000 + 10.0000 5.3844 29.0000 39.0000 48.0000 88.0000 + 11.0000 5.3844 29.0000 39.0000 48.0000 89.0000 + 12.0000 5.3844 29.0000 39.0000 48.0000 91.0000 + 13.0000 5.3844 29.0000 40.0000 48.0000 87.0000 + 14.0000 5.3844 29.0000 40.0000 48.0000 88.0000 + 15.0000 5.3844 29.0000 40.0000 48.0000 89.0000 + 16.0000 5.3844 29.0000 40.0000 48.0000 91.0000 + +×î¼Ñ·½°¸¶ÔÓ¦µÄ¹¤×÷¾ùºâ¶È: + +bfair_f = + + 5.3844 \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/\350\257\264\346\230\216.txt" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/\350\257\264\346\230\216.txt" index b03c24407bac2b5bf704180c4ba535742474e6a1..bf0b3bf16a5d0a77dcbee5ee9eccd0bcd06b3ad2 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/\350\257\264\346\230\216.txt" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\344\272\244\345\267\241\350\255\246\346\234\215\345\212\241\345\271\263\345\217\260\347\232\204\350\256\276\347\275\256\344\270\216\350\260\203\345\272\246\357\274\210CUMCM2011B\357\274\211/\347\250\213\345\272\217/\350\257\264\346\230\216.txt" @@ -1,3 +1,2 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:19074a8c5ab758ebdd1c63839912f9db28e87426430abd5a900bf67a4156af99 -size 207 +1£© ¸Ã³ÌÐòÐèÒªÖ´ÐÐ5-10·ÖÖÓ£¬¾ßÌåÖ÷Ҫȡ¾öÓÚµçÄÔÅäÖã» +2£© ±¾³ÌÐòÖÐʹÓÃÁ˲¢ÐмÆËã¼ÆË㣬ÊʺÏÓÚMATLAB2013a, Èç¹ûÔÚÆäËû°æ±¾Ö´Ðгö´í£¬¿ÉÒÔ×¢ÏúÏàÓ¦µÄ³ÌÐò¼´¿É£¬ÒòΪ²»Í¬°æ±¾µÄMATLAB, Æô¶¯²¢ÐмÆËã³ÌÐòµÄÃüÁî¿ÉÄܲ»Í¬¡£ \ No newline at end of file diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/2012A\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267.doc" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/2012A\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267.doc" index cdd374f2c3c1bb1b8c04662e481db54d99380416..0fa218eef8b4f1ba02b3ecb32697b45fe35daa2a 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/2012A\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267.doc" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/2012A\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267.doc" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/ch16_p1_Tmethod.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/ch16_p1_Tmethod.m" index da5c8f57ed1feaf6e46e0482fff2a3c66eee9cd2..ec7d4d940fb9112e87ee539ace4390627bae2486 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/ch16_p1_Tmethod.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/ch16_p1_Tmethod.m" @@ -1,3 +1,95 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:2b4add7b68c69285bf363a9a204c21d07dbc091f35c0275b9cb69fde9879fb36 -size 2299 +%% 2012A_question1_T evaluation +% ³ÌÐò15-1 +%-------------------------------------------------------------------------- +%% Êý¾Ý×¼±¸ +% Çå¿Õ»·¾³±äÁ¿ +clear all +clc + +%µ¼ÈëÊý¾Ý +X1=xlsread('2012A_T1_processed.xls', 'T1_red_grape', 'D3:M272'); +X2=xlsread('2012A_T1_processed.xls', 'T2_red_grape', 'D3:M272'); +X3=xlsread('2012A_T1_processed.xls', 'T1_white_grape', 'D3:M282'); +X4=xlsread('2012A_T1_processed.xls', 'T2_white_grape', 'D3:M282'); + +%% ºìÆÏÌѾÆT¼ìÑé¼ÆËã¹ý³Ì +[m1,n1]=size(X1); +K1=27; +% ¼ÆËãÿ¸öÑùÆ·µÄ×ÜµÃ·Ö +for i=1:K1 + for j=1:n1 + SX1(i,j)=sum(X1(10*i-9:10*i,j)); + SX2(i,j)=sum(X2(10*i-9:10*i,j)); + end +end +% ¼ÆËãÿ×éÑùÆ·µÃ·ÖµÄ¾ùÖµ +for i=1:K1 + Mean1(i)=mean(SX1(i,:)); + Mean2(i)=mean(SX2(i,:)); +end +% ¼ÆËã¼ìÑéÖµ +for i=1:K1 + S1(1,i)=(sum((SX1(i,:)-Mean1(i)).^2)+sum((SX2(i,:)-Mean2(i)).^2))/(n1*(n1-1)); + T1(1,i)=(Mean1(i)-Mean2(i))/(sqrt(S1(1,i))); +end +AT_R=abs(T1); +M_AT_R=mean(AT_R); +%% °×ÆÏÌѾÆT¼ìÑé¼ÆËã¹ý³Ì +[m2,n2]=size(X3); +K2=28; +% ¼ÆËãÿ¸öÑùÆ·µÄ×ÜµÃ·Ö +for i=1:K2 + for j=1:n2 + SX3(i,j)=sum(X3(10*i-9:10*i,j)); + SX4(i,j)=sum(X4(10*i-9:10*i,j)); + end +end +% ¼ÆËãÿ×éÑùÆ·µÃ·ÖµÄ¾ùÖµ +for i=1:K2 + Mean3(i)=mean(SX3(i,:)); + Mean4(i)=mean(SX4(i,:)); +end +% ¼ÆËã¼ìÑéÖµ +for i=1:K2 + S2(1,i)=(sum((SX3(i,:)-Mean3(i)).^2)+sum((SX4(i,:)-Mean4(i)).^2))/(n2*(n2-1)); + T2(1,i)=(Mean3(i)-Mean4(i))/(sqrt(S2(1,i))); +end +AT_W=abs(T2); +M_AT_W=mean(AT_W); +%% ½á¹ûÏÔʾÓë±È½Ï +a=2.102; % T(0.05,2,18)=2.101 +b=2.878; % T(0.01,2,18)=2.878 +set(gca,'linewidth',2) +% ºì¾Æ½á¹û +for i=1:K1 + Ta1(i)=a; + Tb1(i)=b; +end +t1=1:K1; +subplot(2,1,1); +plot(t1,AT_R,'*k-',t1,Ta1,'r-',t1,Tb1,'-.b', 'LineWidth', 2) +title('ºì¾ÆÏÔÖøÐÔ¼ìÑé½á¹û','fontsize',14) +legend('T¼ìÑéÖµ', 'T(0.05)Öµ', 'T(0.01)Öµ') +xlabel('ÑùÆ·ºÅ'), ylabel('T¼ìÑéÖµ') + +% °×¾Æ½á¹û +for i=1:K2 + Ta2(i)=a; + Tb2(i)=b; +end +t2=1:K2; +subplot(2,1,2); +plot(t2,AT_W,'*k-',t2,Ta2,'r-',t2,Tb2,'-.b', 'LineWidth', 2) +title('°×¾ÆÏÔÖøÐÔ¼ìÑé½á¹û','fontsize',14) +legend('T¼ìÑéÖµ', 'T(0.05)Öµ', 'T(0.01)Öµ') +xlabel('ÑùÆ·ºÅ'), ylabel('T¼ìÑéÖµ') +% ÏÔʾƽ¾ù¼ìÑé½á¹û +disp(['Á½×éÆ·¾Æʦ¶Ôºì¾ÆµÄƽ¾ùÏÔÖøÐÔT¼ìÑéÖµ:' num2str(M_AT_R)]); +disp(['Á½×éÆ·¾Æʦ¶Ô°×¾ÆµÄƽ¾ùÏÔÖøÐÔT¼ìÑéÖµ:' num2str(M_AT_W)]); + + + + + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/results.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/results.fig" index 0cf755def3ef38e08daa494c2b1282ce50430f0b..76f79b3e3ff03a495c0079c6e02c6c67f9b8ed5c 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/results.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/1\350\221\241\350\220\204\351\205\222\345\271\263\345\235\207\346\230\276\350\221\227\346\200\247T\346\243\200\351\252\214\345\200\274/results.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/ch16_P2.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/ch16_P2.m" index 533415d3f3d51bf58009da16b9e7742e5d5950bd..74cb7c22aef8af951dc896f8f018e3cebbbf3b25 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/ch16_P2.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/ch16_P2.m" @@ -1,3 +1,56 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:659261fa55f7023e61f4a0fa6cbf505b9013bdd749e7e3555577ffc065770043 -size 1320 +%% 2012A_question1_T evaluation +% ³ÌÐò16-2 +%-------------------------------------------------------------------------- +%% Êý¾Ý×¼±¸ +% Çå¿Õ»·¾³±äÁ¿ +clear all +clc + +%µ¼ÈëÊý¾Ý(°×ÆÏÌѾÆ) +% X1=xlsread('2012A_T1_processed.xls', 'T1_white_grape', 'D3:M282'); +% X2=xlsread('2012A_T1_processed.xls', 'T2_white_grape', 'D3:M282'); +%µ¼ÈëÊý¾Ý(ºìÆÏÌѾÆ) +X1=xlsread('2012A_T1_processed.xls', 'T1_red_grape', 'D3:M272'); +X2=xlsread('2012A_T1_processed.xls', 'T2_red_grape', 'D3:M272'); + +%% ¼ÆËãÿ×éÆ·¾Æʦ¶Ôÿ¸öÑùÆ·µÄ·½²î +[m,n]=size(X1); +K=27; +% K=28 °×ÆÏÌÑ¾Æ +% ¼ÆËãÿ¸öÑùÆ·µÄ×ÜµÃ·Ö +for i=1:K + for j=1:n + SX1(i,j)=sum(X1(10*i-9:10*i,j)); + SX2(i,j)=sum(X2(10*i-9:10*i,j)); + end + u0(i)=mean([SX1(i,:), SX2(i,:)]); +end +% ¼ÆËã·½²î +for i=1:K + SD1(i,:)=(SX1(i,:)-u0(i)).*(SX1(i,:)-u0(i)); + SD2(i,:)=(SX2(i,:)-u0(i)).*(SX2(i,:)-u0(i)); +end + +%% ½á¹ûÏÔʾÓë±È½Ï +for i=1:K + TSD(1,i)=sum(SD1(i,:)); + TSD(2,i)=sum(SD2(i,:)); +end +t=1:K; +plot(t,TSD(1,:),'*k-',t,TSD(2,:),'ok--', 'LineWidth', 2) +set(gca,'linewidth',2); +legend('Ò»×é·½²î','¶þ×é·½²î') +xlabel('ºìÆÏÌѾÆÑùÆ·±àºÅ'); ylabel('ºìÆÏÌѾÆÆÀ¼Û·½²î'); +TSD1=sum(TSD(1,:)); +TSD2=sum(TSD(2,:)); +disp(['Ò»×é¶Ô°×ÆÏÌѾÆ×Ü·½²î:' num2str(TSD1)]); +disp(['¶þ×é¶Ô°×ÆÏÌѾÆ×Ü·½²î:' num2str(TSD2)]); + + + + + + + + + diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/results.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/results.fig" index 9145077d904e4a7186a74ae85477a2dd4bc7f601..6dccc6ef2a4ea4ad649a8a4baefa07e4a57ebbf1 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/results.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/2\350\221\241\350\220\204\351\205\222\346\200\273\346\226\271\345\267\256/results.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/ch16_p3.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/ch16_p3.m" index 6d0a0e4110bed1c7eb74b906ae745f58cce8bc79..bedd9a052815beda2ea456eb3ef08f74f4705931 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/ch16_p3.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/ch16_p3.m" @@ -1,3 +1,94 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:5816f9d70834926e45eef7cbdc73e74a30068764ba4f9f6b4314324cf2e02910 -size 2760 +%% ÓþÛÀ෨ȷ¶¨ÆÏÌѾƷּ¶ +clc, clear all, close all +%% ÐèÒª¾ÛÀàµÄÊý¾Ý +% ºìÆÏÌѾÆÖÊÁ¿ÆÀ·ÖÊý¾Ý +A=[79.95 75 80.45 78.15 76.25 71.95 75.85 71.85 76.65 77.05... + 71.85 67.84 69.9 74.55 75.4 70.65 79.55 74.9 74.3 77.2... + 77.8 75.2 76.65 74.7 78.3 77.8 70.9 80.45]; +% °×ÆÏÌѾÆÖÊÁ¿ÆÀ·ÖÊý¾Ý +% A=[79.95 75 80.45 78.15 76.25 71.95 75.85 71.85 76.65 77.05... +% 71.85 67.85 69.9 74.55 75.4 70.65 79.55 74.9 74.3 77.2... +% 77.8 75.2 76.65 74.7 78.3 77.8 70.9] +%% ÓÃk-Means¾ÛÀ෨ȷ¶¨×î¼ÑµÄ¾ÛÀàÊý +X=A'; +numC=7; +for i=1:numC + kidx = kmeans(X,i); + silh = silhouette(X,kidx); %¼ÆËãÂÖÀªÖµ + silh_m(i) = mean(silh); %¼ÆËãƽ¾ùÂÖÀªÖµ +end + +figure +plot(1:numC,silh_m,'ko-', 'linewidth',2) +set(gca,'linewidth',2); +xlabel('Àà±ðÊý') +ylabel('ƽ¾ùÂÖÀªÖµ') +title(' ²»Í¬Àà±ð¶ÔÓ¦µÄƽ¾ùÂÖÀªÖµ') + +% »æÖÆ2ÖÁ5ÀàʱµÄÂÖÀªÖµ·Ö²¼Í¼ + figure + set(gca,'linewidth',2); +for i=2:5 + kidx = kmeans(X,i); + subplot(2,2,i-1); + [~,h] = silhouette(X,kidx); + set(gca,'linewidth',2); + title([num2str(i), 'ÀàʱµÄÂÖÀªÖµ ' ]) + snapnow + xlabel('ÂÖÀªÖµ'); + ylabel('Àà±ðÊý'); +end + +%% K-means¾ÛÀà¹ý³Ì£¬²¢½«½á¹ûÏÔʾ³öÀ´ +[idx,ctr]=kmeans(A',4); % ÓÃK-means·¨¾ÛÀà +% ÌáȡͬһÀà±ðµÄÑùÆ·ºÅ +c1=find(idx==1); c2=find(idx==2); +c3=find(idx==3); c4=find(idx==4); +figure +F1 = plot(find(idx==1), A(idx==1),'k:*', ... + find(idx==2), A(idx==2),'k:o', ... + find(idx==3), A(idx==3),'k:p', ... + find(idx==4), A(idx==4),'k:d'); +set(gca,'linewidth',2); +set(F1,'linewidth',2, 'MarkerSize',8); +xlabel('±àºÅ','fontsize',12); +ylabel('µÃ·Ö','fontsize',12); +title('Kmeans·½·¨¾ÛÀà½á¹û') +disp('¾ÛÀà½á¹û£º'); +disp(['µÚ1Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(1)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c1')]); +disp(['µÚ2Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(2)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c2')]); +disp(['µÚ3Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(3)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c3')]); +disp(['µÚ4Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(4)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c4')]); + +%% ²ã´Î¾ÛÀà +X=A'; +Y=pdist(X); %¼ÆËãÑùÆ·¼äµÄŷʽ¾àÀë +Z=linkage(Y, 'average'); % ÀûÓÃÀàƽ¾ù·¨´´½¨ÏµÍ³¾ÛÀàÊ÷ +cn=size(X); +clabel=1:cn; +clabel=clabel'; +figure +F2 = dendrogram(Z); % »æÖƾÛÀàÊ÷ÐÎͼ +set(gca,'linewidth',2); +title('²ã´Î¾ÛÀà·¨¾ÛÀà½á¹û') +set(F2,'linewidth',2); +ylabel('±ê×¼¾àÀë'); +%% Fuzzy C-means¾ÛÀà +X=A'; +[center,U] = fcm(X,4); +Cid1 = find(U(1,:) ==max(U)); +Cid2 = find(U(2,:) ==max(U)); +Cid3 = find(U(3,:) ==max(U)); +Cid4 = find(U(4,:) ==max(U)); +figure +F3=plot(Cid1, A(Cid1),'k:*', ... + Cid2, A(Cid2),'k:o', ... + Cid3, A(Cid3),'k:p', ... + Cid4, A(Cid4),'k:d'); + +set(gca,'linewidth',2); +set(F3,'linewidth',2, 'MarkerSize',8); +xlabel('±àºÅ'); +ylabel('µÃ·Ö'); +title('Fuzzy C-means·½·¨¾ÛÀà½á¹û') +%% 2012ÄêÈ«¹úÈüAÌâµÚ¶þÎÊÇó½âʾÀý³ÌÐò diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result1.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result1.fig" index a6f054aa03c999e75e1015949aa429bc96734d93..7edb56f4ca670bab6f1712cfcf5d1509c32f7ba6 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result1.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result1.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result2.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result2.fig" index e1338c3ac4d4dc21a493dbd0fd08d2e742de3bd1..4b7a8c0ddaa3b3a3ea458ea2c586871379deaed4 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result2.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result2.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result3.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result3.fig" index a70cfba36ea28f13d6abc136e1e9d17edcd8423a..79bbb77651530963b5db627162e78bcbdb096a03 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result3.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result3.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result4.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result4.fig" index 1680fbf6bbec29b962c34bc2a15497c24ffd5fee..eb72eca9150b4a791fe047db30f67981ec439c67 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result4.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result4.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result5.fig" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result5.fig" index 7a0308336e9f764115757d85f35cfe42c33576ac..49dcf014be4b77dff2c7aeb1590a1290ed1bf12a 100644 Binary files "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result5.fig" and "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/3\350\201\232\347\261\273\346\263\225\347\241\256\345\256\232\350\221\241\350\220\204\351\205\222\345\210\206\347\272\247/result5.fig" differ diff --git "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/4-PCA-kmeans\346\226\271\346\263\225\345\256\236\347\216\260\345\257\271\350\221\241\350\220\204\347\232\204\347\220\206\345\214\226\346\214\207\346\240\207\350\277\233\350\241\214\350\201\232\347\261\273/ch16_P4.m" "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/4-PCA-kmeans\346\226\271\346\263\225\345\256\236\347\216\260\345\257\271\350\221\241\350\220\204\347\232\204\347\220\206\345\214\226\346\214\207\346\240\207\350\277\233\350\241\214\350\201\232\347\261\273/ch16_P4.m" index 229c3de4d2cd698b7d0981b8821291ec818b09e9..b648a5f8645e8d1a39295cf721c83445f45f49f6 100644 --- "a/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/4-PCA-kmeans\346\226\271\346\263\225\345\256\236\347\216\260\345\257\271\350\221\241\350\220\204\347\232\204\347\220\206\345\214\226\346\214\207\346\240\207\350\277\233\350\241\214\350\201\232\347\261\273/ch16_P4.m" +++ "b/matlab\346\225\260\345\255\246\345\273\272\346\250\241\347\256\227\346\263\225/\346\272\220\347\250\213\345\272\217_Maltab\345\234\250\346\225\260\345\255\246\345\273\272\346\250\241\344\270\255\347\232\204\345\272\224\347\224\250\357\274\210\350\257\246\347\273\206\346\263\250\351\207\212\357\274\211/\346\211\251\345\261\225\347\250\213\345\272\217/\347\234\237\351\242\230--\350\221\241\350\220\204\351\205\222\347\232\204\350\257\204\344\273\267\357\274\210CUMCM2012A\357\274\211/\344\273\243\347\240\201/4-PCA-kmeans\346\226\271\346\263\225\345\256\236\347\216\260\345\257\271\350\221\241\350\220\204\347\232\204\347\220\206\345\214\226\346\214\207\346\240\207\350\277\233\350\241\214\350\201\232\347\261\273/ch16_P4.m" @@ -1,3 +1,69 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:1b711efde3c0a537f8da674f5c474e6c4600e39f274b7a57c230c29e89db5eac -size 2187 +%% PCA-kmeans·½·¨ÊµÏÖ¶ÔÆÏÌѵÄÀí»¯Ö¸±ê½øÐоÛÀà +%-------------------------------------------------------------------------- +%% Êý¾Ýµ¼Èë¼°´¦Àí +clc, clear all, close all +% A=xlsread('2012A_Table2.xls','ÆÏÌѾÆÖ¸±ê»ã×Ü', 'C3:J29');% ºìÆÏÌÑ¾Æ +A=xlsread('2012A_Table2.xls','ÆÏÌѾÆÖ¸±ê»ã×Ü', 'C33:J60');% °×ÆÏÌÑ¾Æ + +% Êý¾Ý±ê×¼»¯´¦Àí +a=size(A,1); +b=size(A,2); +for i=1:b + SA(:,i)=(A(:,i)-mean(A(:,i)))/std(A(:,i)); +end + +%% ¼ÆËãÏà¹ØϵÊý¾ØÕóµÄÌØÕ÷ÖµºÍÌØÕ÷ÏòÁ¿ +CM=corrcoef(SA); % ¼ÆËãÏà¹ØϵÊý¾ØÕó(correlation matrix) +[V, D]=eig(CM); % ¼ÆËãÌØÕ÷ÖµºÍÌØÕ÷ÏòÁ¿ + +for j=1:b + DS(j,1)=D(b+1-j, b+1-j); % ¶ÔÌØÕ÷Öµ°´½µÐò½øÐÐÅÅÐò +end +for i=1:b + DS(i,2)=DS(i,1)/sum(DS(:,1)); %¹±Ï×ÂÊ + DS(i,3)=sum(DS(1:i,1))/sum(DS(:,1)); %ÀÛ»ý¹±Ï×ÂÊ +end + +%% Ñ¡ÔñÖ÷³É·Ö¼°¶ÔÓ¦µÄÌØÕ÷ÏòÁ¿ +T=0.8; % Ö÷³É·ÖÐÅÏ¢±£ÁôÂÊ. +for K=1:b + if DS(K,3)>=T + Com_num=K; + break; + end +end + +% ÌáÈ¡Ö÷³É·Ö¶ÔÓ¦µÄÌØÕ÷ÏòÁ¿ +for j=1:Com_num + PV(:,j)=V(:,b+1-j); +end + +%% ¼ÆËã¸÷ÆÀ¼Û¶ÔÏóµÄÖ÷³É·ÖµÃ·Ö +new_score=SA*PV; +for i=1:a + total_score(i,1)=sum(new_score(i,:)); + total_score(i,2)=i; +end +result_report=[new_score, total_score]; % ½«¸÷Ö÷³É·ÖµÃ·ÖÓë×Ü·Ö·ÅÔÚͬһ¸ö¾ØÕóÖÐ +result_report=sortrows(result_report,(K+2)); % °´×Ü·Ö½µÐòÅÅÐò + +%% Kmeans¾ÛÀ༰½á¹û±¨¸æ +A=result_report(:,(K+1)); +[idx,ctr]=kmeans(A,4); +[m,n]=size(A); +t1=ones(1,n)*30; +c1=find(idx==1); c2=find(idx==2); c3=find(idx==3); c4=find(idx==4); +h=plot(t1,A,'ko',c1,A(idx==1),'k--*', c2,A(idx==2),'k--s', c3,A(idx==3),'k--d', c4,A(idx==4),'k--p'); +xlabel('°×ÆÏÌѾÆÑùÆ·±àºÅ','fontsize',12); +ylabel('Ö÷³É·ÖµÃ·Ö','fontsize',12); +title('°×ÆÏÌѾÆÀí»¯Ö¸±ê¾ÛÀàͼ','fontsize',12) +set(h, 'MarkerSize',8, 'MarkerFaceColor','k'); +set(gca,'linewidth',2) ; + +disp('Ö÷³É·ÖµÃ·Ö(×îºó1ÁÐΪÑù±¾±àºÅ£¬µ¹ÊýµÚ2ÁÐΪ×Ü·Ö£¬Ç°ÃæΪ¸÷Ö÷³É·ÖµÃ·Ö)') +result_report +disp('·ÖÀà½á¹û£º'); +disp(['µÚ1Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(1)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c1')]); +disp(['µÚ2Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(2)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c2')]); +disp(['µÚ3Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(3)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c3')]); +disp(['µÚ4Àà:' ,'ÖÐÐĵ㣺',num2str(ctr(4)),' ','¸ÃÀàÑùÆ·±àºÅ£º', num2str(c4')]);