--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+
+/* Subroutine */ int dgebd2_(integer *m, integer *n, doublereal *a, integer *
+ lda, doublereal *d__, doublereal *e, doublereal *tauq, doublereal *
+ taup, doublereal *work, integer *info)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3;
+
+ /* Local variables */
+ integer i__;
+ extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
+ doublereal *, integer *, doublereal *, doublereal *, integer *,
+ doublereal *), dlarfg_(integer *, doublereal *,
+ doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
+
+
+/* -- 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 .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Test the input parameters */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --d__;
+ --e;
+ --tauq;
+ --taup;
+ --work;
+
+ /* Function Body */
+ *info = 0;
+ if (*m < 0) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*lda < max(1,*m)) {
+ *info = -4;
+ }
+ if (*info < 0) {
+ i__1 = -(*info);
+ xerbla_("DGEBD2", &i__1);
+ return 0;
+ }
+
+ if (*m >= *n) {
+
+/* Reduce to upper bidiagonal form */
+
+ i__1 = *n;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
+
+ i__2 = *m - i__ + 1;
+/* Computing MIN */
+ i__3 = i__ + 1;
+ dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3, *m)+ i__ *
+ a_dim1], &c__1, &tauq[i__]);
+ d__[i__] = a[i__ + i__ * a_dim1];
+ a[i__ + i__ * a_dim1] = 1.;
+
+/* Apply H(i) to A(i:m,i+1:n) from the left */
+
+ if (i__ < *n) {
+ i__2 = *m - i__ + 1;
+ i__3 = *n - i__;
+ dlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
+ tauq[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]
+);
+ }
+ a[i__ + i__ * a_dim1] = d__[i__];
+
+ if (i__ < *n) {
+
+/* Generate elementary reflector G(i) to annihilate */
+/* A(i,i+2:n) */
+
+ i__2 = *n - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ dlarfg_(&i__2, &a[i__ + (i__ + 1) * a_dim1], &a[i__ + min(
+ i__3, *n)* a_dim1], lda, &taup[i__]);
+ e[i__] = a[i__ + (i__ + 1) * a_dim1];
+ a[i__ + (i__ + 1) * a_dim1] = 1.;
+
+/* Apply G(i) to A(i+1:m,i+1:n) from the right */
+
+ i__2 = *m - i__;
+ i__3 = *n - i__;
+ dlarf_("Right", &i__2, &i__3, &a[i__ + (i__ + 1) * a_dim1],
+ lda, &taup[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
+ lda, &work[1]);
+ a[i__ + (i__ + 1) * a_dim1] = e[i__];
+ } else {
+ taup[i__] = 0.;
+ }
+/* L10: */
+ }
+ } else {
+
+/* Reduce to lower bidiagonal form */
+
+ i__1 = *m;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Generate elementary reflector G(i) to annihilate A(i,i+1:n) */
+
+ i__2 = *n - i__ + 1;
+/* Computing MIN */
+ i__3 = i__ + 1;
+ dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)*
+ a_dim1], lda, &taup[i__]);
+ d__[i__] = a[i__ + i__ * a_dim1];
+ a[i__ + i__ * a_dim1] = 1.;
+
+/* Apply G(i) to A(i+1:m,i:n) from the right */
+
+ if (i__ < *m) {
+ i__2 = *m - i__;
+ i__3 = *n - i__ + 1;
+ dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &
+ taup[i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
+ }
+ a[i__ + i__ * a_dim1] = d__[i__];
+
+ if (i__ < *m) {
+
+/* Generate elementary reflector H(i) to annihilate */
+/* A(i+2:m,i) */
+
+ i__2 = *m - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ dlarfg_(&i__2, &a[i__ + 1 + i__ * a_dim1], &a[min(i__3, *m)+
+ i__ * a_dim1], &c__1, &tauq[i__]);
+ e[i__] = a[i__ + 1 + i__ * a_dim1];
+ a[i__ + 1 + i__ * a_dim1] = 1.;
+
+/* Apply H(i) to A(i+1:m,i+1:n) from the left */
+
+ i__2 = *m - i__;
+ i__3 = *n - i__;
+ dlarf_("Left", &i__2, &i__3, &a[i__ + 1 + i__ * a_dim1], &
+ c__1, &tauq[i__], &a[i__ + 1 + (i__ + 1) * a_dim1],
+ lda, &work[1]);
+ a[i__ + 1 + i__ * a_dim1] = e[i__];
+ } else {
+ tauq[i__] = 0.;
+ }
+/* L20: */
+ }
+ }
+ return 0;
+
+/* End of DGEBD2 */
+
+} /* dgebd2_ */
projects / opencv / blobdiff