"atomic bomb" commit. Reorganized OpenCV directory structure
This commit is contained in:
Vadim Pisarevsky
291
3rdparty/lapack/dgebd2.c
vendored
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291
3rdparty/lapack/dgebd2.c
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#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer *
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lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
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taup, doublereal *work, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__;
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extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *,
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doublereal *), dlarfg_(integer *, doublereal *,
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doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DGEBD2 reduces a real general m by n matrix A to upper or lower */
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/* bidiagonal form B by an orthogonal transformation: Q' * A * P = B. */
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/* If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. */
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/* Arguments */
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/* ========= */
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/* M (input) INTEGER */
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/* The number of rows in the matrix A. M >= 0. */
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/* N (input) INTEGER */
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/* The number of columns in the matrix A. N >= 0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the m by n general matrix to be reduced. */
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/* On exit, */
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/* if m >= n, the diagonal and the first superdiagonal are */
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/* overwritten with the upper bidiagonal matrix B; the */
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/* elements below the diagonal, with the array TAUQ, represent */
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/* the orthogonal matrix Q as a product of elementary */
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/* reflectors, and the elements above the first superdiagonal, */
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/* with the array TAUP, represent the orthogonal matrix P as */
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/* a product of elementary reflectors; */
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/* if m < n, the diagonal and the first subdiagonal are */
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/* overwritten with the lower bidiagonal matrix B; the */
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/* elements below the first subdiagonal, with the array TAUQ, */
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/* represent the orthogonal matrix Q as a product of */
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/* elementary reflectors, and the elements above the diagonal, */
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/* with the array TAUP, represent the orthogonal matrix P as */
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/* a product of elementary reflectors. */
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/* See Further Details. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,M). */
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/* D (output) DOUBLE PRECISION array, dimension (min(M,N)) */
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/* The diagonal elements of the bidiagonal matrix B: */
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/* D(i) = A(i,i). */
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/* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
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/* The off-diagonal elements of the bidiagonal matrix B: */
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/* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; */
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/* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. */
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/* TAUQ (output) DOUBLE PRECISION array dimension (min(M,N)) */
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/* The scalar factors of the elementary reflectors which */
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/* represent the orthogonal matrix Q. See Further Details. */
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/* TAUP (output) DOUBLE PRECISION array, dimension (min(M,N)) */
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/* The scalar factors of the elementary reflectors which */
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/* represent the orthogonal matrix P. See Further Details. */
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/* WORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */
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/* INFO (output) INTEGER */
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/* = 0: successful exit. */
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* Further Details */
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/* =============== */
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/* The matrices Q and P are represented as products of elementary */
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/* reflectors: */
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/* If m >= n, */
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/* Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) */
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/* Each H(i) and G(i) has the form: */
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/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */
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/* where tauq and taup are real scalars, and v and u are real vectors; */
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/* v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i); */
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/* u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n); */
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/* tauq is stored in TAUQ(i) and taup in TAUP(i). */
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/* If m < n, */
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/* Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) */
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/* Each H(i) and G(i) has the form: */
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/* H(i) = I - tauq * v * v' and G(i) = I - taup * u * u' */
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/* where tauq and taup are real scalars, and v and u are real vectors; */
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/* v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); */
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/* u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); */
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/* tauq is stored in TAUQ(i) and taup in TAUP(i). */
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/* The contents of A on exit are illustrated by the following examples: */
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/* m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): */
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/* ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) */
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/* ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) */
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/* ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) */
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/* ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) */
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/* ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) */
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/* ( v1 v2 v3 v4 v5 ) */
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/* where d and e denote diagonal and off-diagonal elements of B, vi */
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/* denotes an element of the vector defining H(i), and ui an element of */
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/* the vector defining G(i). */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--d__;
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--e;
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--tauq;
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--taup;
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--work;
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/* Function Body */
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*info = 0;
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if (*m < 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*m)) {
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*info = -4;
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}
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if (*info < 0) {
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i__1 = -(*info);
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xerbla_("DGEBD2", &i__1);
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return 0;
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}
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if (*m >= *n) {
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/* Reduce to upper bidiagonal form */
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
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i__2 = *m - i__ + 1;
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/* Computing MIN */
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i__3 = i__ + 1;
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dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ *
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a_dim1], &c__1, &tauq[i__]);
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d__[i__] = a[i__ + i__ * a_dim1];
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a[i__ + i__ * a_dim1] = 1.;
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/* Apply H(i) to A(i:m,i+1:n) from the left */
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if (i__ < *n) {
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i__2 = *m - i__ + 1;
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i__3 = *n - i__;
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dlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
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tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]
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);
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}
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a[i__ + i__ * a_dim1] = d__[i__];
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if (i__ < *n) {
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/* Generate elementary reflector G(i) to annihilate */
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/* A(i,i+2:n) */
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i__2 = *n - i__;
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/* Computing MIN */
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i__3 = i__ + 2;
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dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(
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i__3, *n)* a_dim1], lda, &taup[i__]);
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e[i__] = a[i__ + (i__ + 1) * a_dim1];
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a[i__ + (i__ + 1) * a_dim1] = 1.;
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/* Apply G(i) to A(i+1:m,i+1:n) from the right */
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i__2 = *m - i__;
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i__3 = *n - i__;
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dlarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1],
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lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
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lda, &work[1]);
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a[i__ + (i__ + 1) * a_dim1] = e[i__];
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} else {
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taup[i__] = 0.;
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}
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/* L10: */
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}
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} else {
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/* Reduce to lower bidiagonal form */
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */
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i__2 = *n - i__ + 1;
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/* Computing MIN */
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i__3 = i__ + 1;
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dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)*
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a_dim1], lda, &taup[i__]);
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d__[i__] = a[i__ + i__ * a_dim1];
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a[i__ + i__ * a_dim1] = 1.;
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/* Apply G(i) to A(i+1:m,i:n) from the right */
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if (i__ < *m) {
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i__2 = *m - i__;
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i__3 = *n - i__ + 1;
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dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &
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taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
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}
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a[i__ + i__ * a_dim1] = d__[i__];
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if (i__ < *m) {
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/* Generate elementary reflector H(i) to annihilate */
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/* A(i+2:m,i) */
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i__2 = *m - i__;
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/* Computing MIN */
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i__3 = i__ + 2;
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dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+
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i__ * a_dim1], &c__1, &tauq[i__]);
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e[i__] = a[i__ + 1 + i__ * a_dim1];
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a[i__ + 1 + i__ * a_dim1] = 1.;
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/* Apply H(i) to A(i+1:m,i+1:n) from the left */
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i__2 = *m - i__;
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i__3 = *n - i__;
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dlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
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c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
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lda, &work[1]);
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a[i__ + 1 + i__ * a_dim1] = e[i__];
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} else {
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tauq[i__] = 0.;
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}
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/* L20: */
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}
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}
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return 0;
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/* End of DGEBD2 */
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} /* dgebd2_ */
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