| //Translated by Jose Antonio De Santiago-Castillo. | |
| //E-mail:JAntonioDeSantiago@gmail.com | |
| //Website: www.DotNumerics.com | |
| // | |
| //Fortran to C# Translation. | |
| //Translated by: | |
| //F2CSharp Version 0.72 (Dicember 7, 2009) | |
| //Code Optimizations: , assignment operator, for-loop: array indexes | |
| // | |
| using System; | |
| using DotNumerics.FortranLibrary; | |
| namespace DotNumerics.LinearAlgebra.CSLapack | |
| { | |
| /// <summary> | |
| /// -- LAPACK routine (version 3.1) -- | |
| /// Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. | |
| /// November 2006 | |
| /// Purpose | |
| /// ======= | |
| /// | |
| /// DGEBD2 reduces a real general m by n matrix A to upper or lower | |
| /// bidiagonal form B by an orthogonal transformation: Q' * A * P = B. | |
| /// | |
| /// If m .GE. n, B is upper bidiagonal; if m .LT. n, B is lower bidiagonal. | |
| /// | |
| ///</summary> | |
| public class DGEBD2 | |
| { | |
| DLARF _dlarf; DLARFG _dlarfg; XERBLA _xerbla; | |
| const double ZERO = 0.0E+0; const double ONE = 1.0E+0; | |
| public DGEBD2(DLARF dlarf, DLARFG dlarfg, XERBLA xerbla) | |
| { | |
| this._dlarf = dlarf; this._dlarfg = dlarfg; this._xerbla = xerbla; | |
| } | |
| public DGEBD2() | |
| { | |
| LSAME lsame = new LSAME(); | |
| XERBLA xerbla = new XERBLA(); | |
| DLAMC3 dlamc3 = new DLAMC3(); | |
| DLAPY2 dlapy2 = new DLAPY2(); | |
| DNRM2 dnrm2 = new DNRM2(); | |
| DSCAL dscal = new DSCAL(); | |
| DGEMV dgemv = new DGEMV(lsame, xerbla); | |
| DGER dger = new DGER(xerbla); | |
| DLARF dlarf = new DLARF(dgemv, dger, lsame); | |
| DLAMC1 dlamc1 = new DLAMC1(dlamc3); | |
| DLAMC4 dlamc4 = new DLAMC4(dlamc3); | |
| DLAMC5 dlamc5 = new DLAMC5(dlamc3); | |
| DLAMC2 dlamc2 = new DLAMC2(dlamc3, dlamc1, dlamc4, dlamc5); | |
| DLAMCH dlamch = new DLAMCH(lsame, dlamc2); | |
| DLARFG dlarfg = new DLARFG(dlamch, dlapy2, dnrm2, dscal); | |
| this._dlarf = dlarf; this._dlarfg = dlarfg; this._xerbla = xerbla; | |
| } | |
| /// <summary> | |
| /// Purpose | |
| /// ======= | |
| /// | |
| /// DGEBD2 reduces a real general m by n matrix A to upper or lower | |
| /// bidiagonal form B by an orthogonal transformation: Q' * A * P = B. | |
| /// | |
| /// If m .GE. n, B is upper bidiagonal; if m .LT. n, B is lower bidiagonal. | |
| /// | |
| ///</summary> | |
| /// <param name="M"> | |
| /// (input) INTEGER | |
| /// The number of rows in the matrix A. M .GE. 0. | |
| ///</param> | |
| /// <param name="N"> | |
| /// (input) INTEGER | |
| /// The number of columns in the matrix A. N .GE. 0. | |
| ///</param> | |
| /// <param name="A"> | |
| /// (input/output) DOUBLE PRECISION array, dimension (LDA,N) | |
| /// On entry, the m by n general matrix to be reduced. | |
| /// On exit, | |
| /// if m .GE. n, the diagonal and the first superdiagonal are | |
| /// overwritten with the upper bidiagonal matrix B; the | |
| /// elements below the diagonal, with the array TAUQ, represent | |
| /// the orthogonal matrix Q as a product of elementary | |
| /// reflectors, and the elements above the first superdiagonal, | |
| /// with the array TAUP, represent the orthogonal matrix P as | |
| /// a product of elementary reflectors; | |
| /// if m .LT. n, the diagonal and the first subdiagonal are | |
| /// overwritten with the lower bidiagonal matrix B; the | |
| /// elements below the first subdiagonal, with the array TAUQ, | |
| /// represent the orthogonal matrix Q as a product of | |
| /// elementary reflectors, and the elements above the diagonal, | |
| /// with the array TAUP, represent the orthogonal matrix P as | |
| /// a product of elementary reflectors. | |
| /// See Further Details. | |
| ///</param> | |
| /// <param name="LDA"> | |
| /// (input) INTEGER | |
| /// The leading dimension of the array A. LDA .GE. max(1,M). | |
| ///</param> | |
| /// <param name="D"> | |
| /// (output) DOUBLE PRECISION array, dimension (min(M,N)) | |
| /// The diagonal elements of the bidiagonal matrix B: | |
| /// D(i) = A(i,i). | |
| ///</param> | |
| /// <param name="E"> | |
| /// (output) DOUBLE PRECISION array, dimension (min(M,N)-1) | |
| /// The off-diagonal elements of the bidiagonal matrix B: | |
| /// if m .GE. n, E(i) = A(i,i+1) for i = 1,2,...,n-1; | |
| /// if m .LT. n, E(i) = A(i+1,i) for i = 1,2,...,m-1. | |
| ///</param> | |
| /// <param name="TAUQ"> | |
| /// (output) DOUBLE PRECISION array dimension (min(M,N)) | |
| /// The scalar factors of the elementary reflectors which | |
| /// represent the orthogonal matrix Q. See Further Details. | |
| ///</param> | |
| /// <param name="TAUP"> | |
| /// (output) DOUBLE PRECISION array, dimension (min(M,N)) | |
| /// The scalar factors of the elementary reflectors which | |
| /// represent the orthogonal matrix P. See Further Details. | |
| ///</param> | |
| /// <param name="WORK"> | |
| /// (workspace) DOUBLE PRECISION array, dimension (max(M,N)) | |
| ///</param> | |
| /// <param name="INFO"> | |
| /// (output) INTEGER | |
| /// = 0: successful exit. | |
| /// .LT. 0: if INFO = -i, the i-th argument had an illegal value. | |
| ///</param> | |
| public void Run(int M, int N, ref double[] A, int offset_a, int LDA, ref double[] D, int offset_d, ref double[] E, int offset_e | |
| , ref double[] TAUQ, int offset_tauq, ref double[] TAUP, int offset_taup, ref double[] WORK, int offset_work, ref int INFO) | |
| { | |
| int I = 0; | |
| int o_a = -1 - LDA + offset_a; int o_d = -1 + offset_d; int o_e = -1 + offset_e; int o_tauq = -1 + offset_tauq; | |
| int o_taup = -1 + offset_taup; int o_work = -1 + offset_work; | |
| // * | |
| // * -- LAPACK routine (version 3.1) -- | |
| // * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. | |
| // * November 2006 | |
| // * | |
| // * .. Scalar Arguments .. | |
| // * .. | |
| // * .. Array Arguments .. | |
| // * .. | |
| // * | |
| // * Purpose | |
| // * ======= | |
| // * | |
| // * DGEBD2 reduces a real general m by n matrix A to upper or lower | |
| // * bidiagonal form B by an orthogonal transformation: Q' * A * P = B. | |
| // * | |
| // * If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. | |
| // * | |
| // * Arguments | |
| // * ========= | |
| // * | |
| // * M (input) INTEGER | |
| // * The number of rows in the matrix A. M >= 0. | |
| // * | |
| // * N (input) INTEGER | |
| // * The number of columns in the matrix A. N >= 0. | |
| // * | |
| // * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) | |
| // * On entry, the m by n general matrix to be reduced. | |
| // * On exit, | |
| // * if m >= n, the diagonal and the first superdiagonal are | |
| // * overwritten with the upper bidiagonal matrix B; the | |
| // * elements below the diagonal, with the array TAUQ, represent | |
| // * the orthogonal matrix Q as a product of elementary | |
| // * reflectors, and the elements above the first superdiagonal, | |
| // * with the array TAUP, represent the orthogonal matrix P as | |
| // * a product of elementary reflectors; | |
| // * if m < n, the diagonal and the first subdiagonal are | |
| // * overwritten with the lower bidiagonal matrix B; the | |
| // * elements below the first subdiagonal, with the array TAUQ, | |
| // * represent the orthogonal matrix Q as a product of | |
| // * elementary reflectors, and the elements above the diagonal, | |
| // * with the array TAUP, represent the orthogonal matrix P as | |
| // * a product of elementary reflectors. | |
| // * See Further Details. | |
| // * | |
| // * LDA (input) INTEGER | |
| // * The leading dimension of the array A. LDA >= max(1,M). | |
| // * | |
| // * D (output) DOUBLE PRECISION array, dimension (min(M,N)) | |
| // * The diagonal elements of the bidiagonal matrix B: | |
| // * D(i) = A(i,i). | |
| // * | |
| // * E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) | |
| // * The off-diagonal elements of the bidiagonal matrix B: | |
| // * if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; | |
| // * if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. | |
| // * | |
| // * TAUQ (output) DOUBLE PRECISION array dimension (min(M,N)) | |
| // * The scalar factors of the elementary reflectors which | |
| // * represent the orthogonal matrix Q. See Further Details. | |
| // * | |
| // * TAUP (output) DOUBLE PRECISION array, dimension (min(M,N)) | |
| // * The scalar factors of the elementary reflectors which | |
| // * represent the orthogonal matrix P. See Further Details. | |
| // * | |
| // * WORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) | |
| // * | |
| // * INFO (output) INTEGER | |
| // * = 0: successful exit. | |
| // * < 0: if INFO = -i, the i-th argument had an illegal value. | |
| // * | |
| // * Further Details | |
| // * =============== | |
| // * | |
| // * The matrices Q and P are represented as products of elementary | |
| // * reflectors: | |
| // * | |
| // * If m >= n, | |
| // * | |
| // * Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) | |
| // * | |
| // * Each H(i) and G(i) has the form: | |
| // * | |
| // * H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' | |
| // * | |
| // * where tauq and taup are real scalars, and v and u are real vectors; | |
| // * v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); | |
| // * u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); | |
| // * tauq is stored in TAUQ(i) and taup in TAUP(i). | |
| // * | |
| // * If m < n, | |
| // * | |
| // * Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) | |
| // * | |
| // * Each H(i) and G(i) has the form: | |
| // * | |
| // * H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' | |
| // * | |
| // * where tauq and taup are real scalars, and v and u are real vectors; | |
| // * v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); | |
| // * u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); | |
| // * tauq is stored in TAUQ(i) and taup in TAUP(i). | |
| // * | |
| // * The contents of A on exit are illustrated by the following examples: | |
| // * | |
| // * m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): | |
| // * | |
| // * ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) | |
| // * ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) | |
| // * ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) | |
| // * ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) | |
| // * ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) | |
| // * ( v1 v2 v3 v4 v5 ) | |
| // * | |
| // * where d and e denote diagonal and off-diagonal elements of B, vi | |
| // * denotes an element of the vector defining H(i), and ui an element of | |
| // * the vector defining G(i). | |
| // * | |
| // * ===================================================================== | |
| // * | |
| // * .. Parameters .. | |
| // * .. | |
| // * .. Local Scalars .. | |
| // * .. | |
| // * .. External Subroutines .. | |
| // * .. | |
| // * .. Intrinsic Functions .. | |
| // INTRINSIC MAX, MIN; | |
| // * .. | |
| // * .. Executable Statements .. | |
| // * | |
| // * Test the input parameters | |
| // * | |
| INFO = 0; | |
| if (M < 0) | |
| { | |
| INFO = - 1; | |
| } | |
| else | |
| { | |
| if (N < 0) | |
| { | |
| INFO = - 2; | |
| } | |
| else | |
| { | |
| if (LDA < Math.Max(1, M)) | |
| { | |
| INFO = - 4; | |
| } | |
| } | |
| } | |
| if (INFO < 0) | |
| { | |
| this._xerbla.Run("DGEBD2", - INFO); | |
| return; | |
| } | |
| // * | |
| if (M >= N) | |
| { | |
| // * | |
| // * Reduce to upper bidiagonal form | |
| // * | |
| for (I = 1; I <= N; I++) | |
| { | |
| // * | |
| // * Generate elementary reflector H(i) to annihilate A(i+1:m,i) | |
| // * | |
| this._dlarfg.Run(M - I + 1, ref A[I+I * LDA + o_a], ref A, Math.Min(I + 1, M)+I * LDA + o_a, 1, ref TAUQ[I + o_tauq]); | |
| D[I + o_d] = A[I+I * LDA + o_a]; | |
| A[I+I * LDA + o_a] = ONE; | |
| // * | |
| // * Apply H(i) to A(i:m,i+1:n) from the left | |
| // * | |
| if (I < N) | |
| { | |
| this._dlarf.Run("Left", M - I + 1, N - I, A, I+I * LDA + o_a, 1, TAUQ[I + o_tauq] | |
| , ref A, I+(I + 1) * LDA + o_a, LDA, ref WORK, offset_work); | |
| } | |
| A[I+I * LDA + o_a] = D[I + o_d]; | |
| // * | |
| if (I < N) | |
| { | |
| // * | |
| // * Generate elementary reflector G(i) to annihilate | |
| // * A(i,i+2:n) | |
| // * | |
| this._dlarfg.Run(N - I, ref A[I+(I + 1) * LDA + o_a], ref A, I+Math.Min(I + 2, N) * LDA + o_a, LDA, ref TAUP[I + o_taup]); | |
| E[I + o_e] = A[I+(I + 1) * LDA + o_a]; | |
| A[I+(I + 1) * LDA + o_a] = ONE; | |
| // * | |
| // * Apply G(i) to A(i+1:m,i+1:n) from the right | |
| // * | |
| this._dlarf.Run("Right", M - I, N - I, A, I+(I + 1) * LDA + o_a, LDA, TAUP[I + o_taup] | |
| , ref A, I + 1+(I + 1) * LDA + o_a, LDA, ref WORK, offset_work); | |
| A[I+(I + 1) * LDA + o_a] = E[I + o_e]; | |
| } | |
| else | |
| { | |
| TAUP[I + o_taup] = ZERO; | |
| } | |
| } | |
| } | |
| else | |
| { | |
| // * | |
| // * Reduce to lower bidiagonal form | |
| // * | |
| for (I = 1; I <= M; I++) | |
| { | |
| // * | |
| // * Generate elementary reflector G(i) to annihilate A(i,i+1:n) | |
| // * | |
| this._dlarfg.Run(N - I + 1, ref A[I+I * LDA + o_a], ref A, I+Math.Min(I + 1, N) * LDA + o_a, LDA, ref TAUP[I + o_taup]); | |
| D[I + o_d] = A[I+I * LDA + o_a]; | |
| A[I+I * LDA + o_a] = ONE; | |
| // * | |
| // * Apply G(i) to A(i+1:m,i:n) from the right | |
| // * | |
| if (I < M) | |
| { | |
| this._dlarf.Run("Right", M - I, N - I + 1, A, I+I * LDA + o_a, LDA, TAUP[I + o_taup] | |
| , ref A, I + 1+I * LDA + o_a, LDA, ref WORK, offset_work); | |
| } | |
| A[I+I * LDA + o_a] = D[I + o_d]; | |
| // * | |
| if (I < M) | |
| { | |
| // * | |
| // * Generate elementary reflector H(i) to annihilate | |
| // * A(i+2:m,i) | |
| // * | |
| this._dlarfg.Run(M - I, ref A[I + 1+I * LDA + o_a], ref A, Math.Min(I + 2, M)+I * LDA + o_a, 1, ref TAUQ[I + o_tauq]); | |
| E[I + o_e] = A[I + 1+I * LDA + o_a]; | |
| A[I + 1+I * LDA + o_a] = ONE; | |
| // * | |
| // * Apply H(i) to A(i+1:m,i+1:n) from the left | |
| // * | |
| this._dlarf.Run("Left", M - I, N - I, A, I + 1+I * LDA + o_a, 1, TAUQ[I + o_tauq] | |
| , ref A, I + 1+(I + 1) * LDA + o_a, LDA, ref WORK, offset_work); | |
| A[I + 1+I * LDA + o_a] = E[I + o_e]; | |
| } | |
| else | |
| { | |
| TAUQ[I + o_tauq] = ZERO; | |
| } | |
| } | |
| } | |
| return; | |
| // * | |
| // * End of DGEBD2 | |
| // * | |
| } | |
| } | |
| } | |