File size: 3,974 Bytes
ed7d493 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 | function [ pert_coeffs,power_coeffs ] = GetInitial( order,derivs,choose,nyss,nxss,n_x,n_x1 )
%This function transforms a pertrubation solution to an initial guess for Taylor
%Projection. Two types of guess are available: pert_coeffs includes
%correction for volatility. power_coeffs does not include correction for
%volatility.
%
% � Copyright, Oren Levintal, June 13, 2016.
if order==1
[GH0,GH1]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)]);
pert_coeffs=[GH0,GH1];
if nargout==2
[GH0,GH1]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)]);
power_coeffs=[GH0,GH1];
end
elseif order==2
[GH0,GH1,GH2]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2);
[U2,~]=create_UW(n_x,2);
pert_coeffs=[GH0,GH1,GH2*U2];
if nargout==2
[GH0,GH1,GH2]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2);
power_coeffs=[GH0,GH1,GH2*U2];
end
elseif order==3
[GH0,GH1,GH2,GH3]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3));
[U2,~]=create_UW(n_x,2);
[U3,~]=create_UW(n_x,3);
pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3];
if nargout==2
[GH0,GH1,GH2,GH3]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3));
power_coeffs=[GH0,GH1,GH2*U2,GH3*U3];
end
elseif order==4
[GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
[derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4));
[U2,~]=create_UW(n_x,2);
[U3,~]=create_UW(n_x,3);
[U4,~]=create_UW(n_x,4);
pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
if nargout==2
[GH0,GH1,GH2,GH3,GH4]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
[derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4));
power_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4];
end
elseif order==5
[GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;1],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
[derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx(choose,:);derivs.hxxxxx(1:n_x1,:)]/factorial(5));
[U2,~]=create_UW(n_x,2);
[U3,~]=create_UW(n_x,3);
[U4,~]=create_UW(n_x,4);
[U5,~]=create_UW(n_x,5);
pert_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
if nargout==2
[GH0,GH1,GH2,GH3,GH4,GH5]=shiftpoly([nxss;0],[nxss;0],1:n_x,[nyss;nxss(1:n_x1,:)],[derivs.gx(choose,:);derivs.hx(1:n_x1,:)],...
[derivs.gxx(choose,:);derivs.hxx(1:n_x1,:)]/2,[derivs.gxxx(choose,:);derivs.hxxx(1:n_x1,:)]/factorial(3),...
[derivs.gxxxx(choose,:);derivs.hxxxx(1:n_x1,:)]/factorial(4),[derivs.gxxxxx(choose,:);derivs.hxxxxx(1:n_x1,:)]/factorial(5));
power_coeffs=[GH0,GH1,GH2*U2,GH3*U3,GH4*U4,GH5*U5];
end
end
pert_coeffs=pert_coeffs(:);
if nargout==2
power_coeffs=power_coeffs(:);
end
end
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