| //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 auxiliary routine (version 3.1) -- | |
| /// Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. | |
| /// November 2006 | |
| /// Purpose | |
| /// ======= | |
| /// | |
| /// DLABRD reduces the first NB rows and columns of a real general | |
| /// m by n matrix A to upper or lower bidiagonal form by an orthogonal | |
| /// transformation Q' * A * P, and returns the matrices X and Y which | |
| /// are needed to apply the transformation to the unreduced part of A. | |
| /// | |
| /// If m .GE. n, A is reduced to upper bidiagonal form; if m .LT. n, to lower | |
| /// bidiagonal form. | |
| /// | |
| /// This is an auxiliary routine called by DGEBRD | |
| /// | |
| ///</summary> | |
| public class DLABRD | |
| { | |
| DGEMV _dgemv; DLARFG _dlarfg; DSCAL _dscal; | |
| const double ZERO = 0.0E0; const double ONE = 1.0E0; | |
| public DLABRD(DGEMV dgemv, DLARFG dlarfg, DSCAL dscal) | |
| { | |
| this._dgemv = dgemv; this._dlarfg = dlarfg; this._dscal = dscal; | |
| } | |
| public DLABRD() | |
| { | |
| 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); | |
| 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._dgemv = dgemv; this._dlarfg = dlarfg; this._dscal = dscal; | |
| } | |
| /// <summary> | |
| /// Purpose | |
| /// ======= | |
| /// | |
| /// DLABRD reduces the first NB rows and columns of a real general | |
| /// m by n matrix A to upper or lower bidiagonal form by an orthogonal | |
| /// transformation Q' * A * P, and returns the matrices X and Y which | |
| /// are needed to apply the transformation to the unreduced part of A. | |
| /// | |
| /// If m .GE. n, A is reduced to upper bidiagonal form; if m .LT. n, to lower | |
| /// bidiagonal form. | |
| /// | |
| /// This is an auxiliary routine called by DGEBRD | |
| /// | |
| ///</summary> | |
| /// <param name="M"> | |
| /// (input) INTEGER | |
| /// The number of rows in the matrix A. | |
| ///</param> | |
| /// <param name="N"> | |
| /// (input) INTEGER | |
| /// The number of columns in the matrix A. | |
| ///</param> | |
| /// <param name="NB"> | |
| /// (input) INTEGER | |
| /// The number of leading rows and columns of A to be reduced. | |
| ///</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, the first NB rows and columns of the matrix are | |
| /// overwritten; the rest of the array is unchanged. | |
| /// If m .GE. n, elements on and below the diagonal in the first NB | |
| /// columns, with the array TAUQ, represent the orthogonal | |
| /// matrix Q as a product of elementary reflectors; and | |
| /// elements above the diagonal in the first NB rows, with the | |
| /// array TAUP, represent the orthogonal matrix P as a product | |
| /// of elementary reflectors. | |
| /// If m .LT. n, elements below the diagonal in the first NB | |
| /// columns, with the array TAUQ, represent the orthogonal | |
| /// matrix Q as a product of elementary reflectors, and | |
| /// elements on and above the diagonal in the first NB rows, | |
| /// 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 (NB) | |
| /// The diagonal elements of the first NB rows and columns of | |
| /// the reduced matrix. D(i) = A(i,i). | |
| ///</param> | |
| /// <param name="E"> | |
| /// (output) DOUBLE PRECISION array, dimension (NB) | |
| /// The off-diagonal elements of the first NB rows and columns of | |
| /// the reduced matrix. | |
| ///</param> | |
| /// <param name="TAUQ"> | |
| /// (output) DOUBLE PRECISION array dimension (NB) | |
| /// 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 (NB) | |
| /// The scalar factors of the elementary reflectors which | |
| /// represent the orthogonal matrix P. See Further Details. | |
| ///</param> | |
| /// <param name="X"> | |
| /// (output) DOUBLE PRECISION array, dimension (LDX,NB) | |
| /// The m-by-nb matrix X required to update the unreduced part | |
| /// of A. | |
| ///</param> | |
| /// <param name="LDX"> | |
| /// (input) INTEGER | |
| /// The leading dimension of the array X. LDX .GE. M. | |
| ///</param> | |
| /// <param name="Y"> | |
| /// (output) DOUBLE PRECISION array, dimension (LDY,NB) | |
| /// The n-by-nb matrix Y required to update the unreduced part | |
| /// of A. | |
| ///</param> | |
| /// <param name="LDY"> | |
| /// (input) INTEGER | |
| /// The leading dimension of the array Y. LDY .GE. N. | |
| ///</param> | |
| public void Run(int M, int N, int NB, 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[] X, int offset_x, int LDX, ref double[] Y, int offset_y | |
| , int LDY) | |
| { | |
| 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_x = -1 - LDX + offset_x; int o_y = -1 - LDY + offset_y; | |
| // * | |
| // * -- LAPACK auxiliary routine (version 3.1) -- | |
| // * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. | |
| // * November 2006 | |
| // * | |
| // * .. Scalar Arguments .. | |
| // * .. | |
| // * .. Array Arguments .. | |
| // * .. | |
| // * | |
| // * Purpose | |
| // * ======= | |
| // * | |
| // * DLABRD reduces the first NB rows and columns of a real general | |
| // * m by n matrix A to upper or lower bidiagonal form by an orthogonal | |
| // * transformation Q' * A * P, and returns the matrices X and Y which | |
| // * are needed to apply the transformation to the unreduced part of A. | |
| // * | |
| // * If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower | |
| // * bidiagonal form. | |
| // * | |
| // * This is an auxiliary routine called by DGEBRD | |
| // * | |
| // * Arguments | |
| // * ========= | |
| // * | |
| // * M (input) INTEGER | |
| // * The number of rows in the matrix A. | |
| // * | |
| // * N (input) INTEGER | |
| // * The number of columns in the matrix A. | |
| // * | |
| // * NB (input) INTEGER | |
| // * The number of leading rows and columns of A to be reduced. | |
| // * | |
| // * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) | |
| // * On entry, the m by n general matrix to be reduced. | |
| // * On exit, the first NB rows and columns of the matrix are | |
| // * overwritten; the rest of the array is unchanged. | |
| // * If m >= n, elements on and below the diagonal in the first NB | |
| // * columns, with the array TAUQ, represent the orthogonal | |
| // * matrix Q as a product of elementary reflectors; and | |
| // * elements above the diagonal in the first NB rows, with the | |
| // * array TAUP, represent the orthogonal matrix P as a product | |
| // * of elementary reflectors. | |
| // * If m < n, elements below the diagonal in the first NB | |
| // * columns, with the array TAUQ, represent the orthogonal | |
| // * matrix Q as a product of elementary reflectors, and | |
| // * elements on and above the diagonal in the first NB rows, | |
| // * 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 (NB) | |
| // * The diagonal elements of the first NB rows and columns of | |
| // * the reduced matrix. D(i) = A(i,i). | |
| // * | |
| // * E (output) DOUBLE PRECISION array, dimension (NB) | |
| // * The off-diagonal elements of the first NB rows and columns of | |
| // * the reduced matrix. | |
| // * | |
| // * TAUQ (output) DOUBLE PRECISION array dimension (NB) | |
| // * The scalar factors of the elementary reflectors which | |
| // * represent the orthogonal matrix Q. See Further Details. | |
| // * | |
| // * TAUP (output) DOUBLE PRECISION array, dimension (NB) | |
| // * The scalar factors of the elementary reflectors which | |
| // * represent the orthogonal matrix P. See Further Details. | |
| // * | |
| // * X (output) DOUBLE PRECISION array, dimension (LDX,NB) | |
| // * The m-by-nb matrix X required to update the unreduced part | |
| // * of A. | |
| // * | |
| // * LDX (input) INTEGER | |
| // * The leading dimension of the array X. LDX >= M. | |
| // * | |
| // * Y (output) DOUBLE PRECISION array, dimension (LDY,NB) | |
| // * The n-by-nb matrix Y required to update the unreduced part | |
| // * of A. | |
| // * | |
| // * LDY (input) INTEGER | |
| // * The leading dimension of the array Y. LDY >= N. | |
| // * | |
| // * Further Details | |
| // * =============== | |
| // * | |
| // * The matrices Q and P are represented as products of elementary | |
| // * reflectors: | |
| // * | |
| // * Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) | |
| // * | |
| // * 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. | |
| // * | |
| // * If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in | |
| // * A(i:m,i); u(1:i) = 0, u(i+1) = 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). | |
| // * | |
| // * If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in | |
| // * A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in | |
| // * A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). | |
| // * | |
| // * The elements of the vectors v and u together form the m-by-nb matrix | |
| // * V and the nb-by-n matrix U' which are needed, with X and Y, to apply | |
| // * the transformation to the unreduced part of the matrix, using a block | |
| // * update of the form: A := A - V*Y' - X*U'. | |
| // * | |
| // * The contents of A on exit are illustrated by the following examples | |
| // * with nb = 2: | |
| // * | |
| // * m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): | |
| // * | |
| // * ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) | |
| // * ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) | |
| // * ( v1 v2 a a a ) ( v1 1 a a a a ) | |
| // * ( v1 v2 a a a ) ( v1 v2 a a a a ) | |
| // * ( v1 v2 a a a ) ( v1 v2 a a a a ) | |
| // * ( v1 v2 a a a ) | |
| // * | |
| // * where a denotes an element of the original matrix which is unchanged, | |
| // * 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 MIN; | |
| // * .. | |
| // * .. Executable Statements .. | |
| // * | |
| // * Quick return if possible | |
| // * | |
| if (M <= 0 || N <= 0) return; | |
| // * | |
| if (M >= N) | |
| { | |
| // * | |
| // * Reduce to upper bidiagonal form | |
| // * | |
| for (I = 1; I <= NB; I++) | |
| { | |
| // * | |
| // * Update A(i:m,i) | |
| // * | |
| this._dgemv.Run("No transpose", M - I + 1, I - 1, - ONE, A, I+1 * LDA + o_a, LDA | |
| , Y, I+1 * LDY + o_y, LDY, ONE, ref A, I+I * LDA + o_a, 1); | |
| this._dgemv.Run("No transpose", M - I + 1, I - 1, - ONE, X, I+1 * LDX + o_x, LDX | |
| , A, 1+I * LDA + o_a, 1, ONE, ref A, I+I * LDA + o_a, 1); | |
| // * | |
| // * Generate reflection Q(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]; | |
| if (I < N) | |
| { | |
| A[I+I * LDA + o_a] = ONE; | |
| // * | |
| // * Compute Y(i+1:n,i) | |
| // * | |
| this._dgemv.Run("Transpose", M - I + 1, N - I, ONE, A, I+(I + 1) * LDA + o_a, LDA | |
| , A, I+I * LDA + o_a, 1, ZERO, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", M - I + 1, I - 1, ONE, A, I+1 * LDA + o_a, LDA | |
| , A, I+I * LDA + o_a, 1, ZERO, ref Y, 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("No transpose", N - I, I - 1, - ONE, Y, I + 1+1 * LDY + o_y, LDY | |
| , Y, 1+I * LDY + o_y, 1, ONE, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", M - I + 1, I - 1, ONE, X, I+1 * LDX + o_x, LDX | |
| , A, I+I * LDA + o_a, 1, ZERO, ref Y, 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", I - 1, N - I, - ONE, A, 1+(I + 1) * LDA + o_a, LDA | |
| , Y, 1+I * LDY + o_y, 1, ONE, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dscal.Run(N - I, TAUQ[I + o_tauq], ref Y, I + 1+I * LDY + o_y, 1); | |
| // * | |
| // * Update A(i,i+1:n) | |
| // * | |
| this._dgemv.Run("No transpose", N - I, I, - ONE, Y, I + 1+1 * LDY + o_y, LDY | |
| , A, I+1 * LDA + o_a, LDA, ONE, ref A, I+(I + 1) * LDA + o_a, LDA); | |
| this._dgemv.Run("Transpose", I - 1, N - I, - ONE, A, 1+(I + 1) * LDA + o_a, LDA | |
| , X, I+1 * LDX + o_x, LDX, ONE, ref A, I+(I + 1) * LDA + o_a, LDA); | |
| // * | |
| // * Generate reflection P(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; | |
| // * | |
| // * Compute X(i+1:m,i) | |
| // * | |
| this._dgemv.Run("No transpose", M - I, N - I, ONE, A, I + 1+(I + 1) * LDA + o_a, LDA | |
| , A, I+(I + 1) * LDA + o_a, LDA, ZERO, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("Transpose", N - I, I, ONE, Y, I + 1+1 * LDY + o_y, LDY | |
| , A, I+(I + 1) * LDA + o_a, LDA, ZERO, ref X, 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", M - I, I, - ONE, A, I + 1+1 * LDA + o_a, LDA | |
| , X, 1+I * LDX + o_x, 1, ONE, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", I - 1, N - I, ONE, A, 1+(I + 1) * LDA + o_a, LDA | |
| , A, I+(I + 1) * LDA + o_a, LDA, ZERO, ref X, 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", M - I, I - 1, - ONE, X, I + 1+1 * LDX + o_x, LDX | |
| , X, 1+I * LDX + o_x, 1, ONE, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dscal.Run(M - I, TAUP[I + o_taup], ref X, I + 1+I * LDX + o_x, 1); | |
| } | |
| } | |
| } | |
| else | |
| { | |
| // * | |
| // * Reduce to lower bidiagonal form | |
| // * | |
| for (I = 1; I <= NB; I++) | |
| { | |
| // * | |
| // * Update A(i,i:n) | |
| // * | |
| this._dgemv.Run("No transpose", N - I + 1, I - 1, - ONE, Y, I+1 * LDY + o_y, LDY | |
| , A, I+1 * LDA + o_a, LDA, ONE, ref A, I+I * LDA + o_a, LDA); | |
| this._dgemv.Run("Transpose", I - 1, N - I + 1, - ONE, A, 1+I * LDA + o_a, LDA | |
| , X, I+1 * LDX + o_x, LDX, ONE, ref A, I+I * LDA + o_a, LDA); | |
| // * | |
| // * Generate reflection P(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]; | |
| if (I < M) | |
| { | |
| A[I+I * LDA + o_a] = ONE; | |
| // * | |
| // * Compute X(i+1:m,i) | |
| // * | |
| this._dgemv.Run("No transpose", M - I, N - I + 1, ONE, A, I + 1+I * LDA + o_a, LDA | |
| , A, I+I * LDA + o_a, LDA, ZERO, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("Transpose", N - I + 1, I - 1, ONE, Y, I+1 * LDY + o_y, LDY | |
| , A, I+I * LDA + o_a, LDA, ZERO, ref X, 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", M - I, I - 1, - ONE, A, I + 1+1 * LDA + o_a, LDA | |
| , X, 1+I * LDX + o_x, 1, ONE, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", I - 1, N - I + 1, ONE, A, 1+I * LDA + o_a, LDA | |
| , A, I+I * LDA + o_a, LDA, ZERO, ref X, 1+I * LDX + o_x, 1); | |
| this._dgemv.Run("No transpose", M - I, I - 1, - ONE, X, I + 1+1 * LDX + o_x, LDX | |
| , X, 1+I * LDX + o_x, 1, ONE, ref X, I + 1+I * LDX + o_x, 1); | |
| this._dscal.Run(M - I, TAUP[I + o_taup], ref X, I + 1+I * LDX + o_x, 1); | |
| // * | |
| // * Update A(i+1:m,i) | |
| // * | |
| this._dgemv.Run("No transpose", M - I, I - 1, - ONE, A, I + 1+1 * LDA + o_a, LDA | |
| , Y, I+1 * LDY + o_y, LDY, ONE, ref A, I + 1+I * LDA + o_a, 1); | |
| this._dgemv.Run("No transpose", M - I, I, - ONE, X, I + 1+1 * LDX + o_x, LDX | |
| , A, 1+I * LDA + o_a, 1, ONE, ref A, I + 1+I * LDA + o_a, 1); | |
| // * | |
| // * Generate reflection Q(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; | |
| // * | |
| // * Compute Y(i+1:n,i) | |
| // * | |
| this._dgemv.Run("Transpose", M - I, N - I, ONE, A, I + 1+(I + 1) * LDA + o_a, LDA | |
| , A, I + 1+I * LDA + o_a, 1, ZERO, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", M - I, I - 1, ONE, A, I + 1+1 * LDA + o_a, LDA | |
| , A, I + 1+I * LDA + o_a, 1, ZERO, ref Y, 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("No transpose", N - I, I - 1, - ONE, Y, I + 1+1 * LDY + o_y, LDY | |
| , Y, 1+I * LDY + o_y, 1, ONE, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", M - I, I, ONE, X, I + 1+1 * LDX + o_x, LDX | |
| , A, I + 1+I * LDA + o_a, 1, ZERO, ref Y, 1+I * LDY + o_y, 1); | |
| this._dgemv.Run("Transpose", I, N - I, - ONE, A, 1+(I + 1) * LDA + o_a, LDA | |
| , Y, 1+I * LDY + o_y, 1, ONE, ref Y, I + 1+I * LDY + o_y, 1); | |
| this._dscal.Run(N - I, TAUQ[I + o_tauq], ref Y, I + 1+I * LDY + o_y, 1); | |
| } | |
| } | |
| } | |
| return; | |
| // * | |
| // * End of DLABRD | |
| // * | |
| } | |
| } | |
| } | |