--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__3 = 3;
+static integer c__2 = 2;
+static real c_b21 = -1.f;
+static real c_b22 = 1.f;
+
+/* Subroutine */ int sgebrd_(integer *m, integer *n, real *a, integer *lda,
+ real *d__, real *e, real *tauq, real *taup, real *work, integer *
+ lwork, integer *info)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
+
+ /* Local variables */
+ integer i__, j, nb, nx;
+ real ws;
+ integer nbmin, iinfo;
+ extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *,
+ integer *, real *, real *, integer *, real *, integer *, real *,
+ real *, integer *);
+ integer minmn;
+ extern /* Subroutine */ int sgebd2_(integer *, integer *, real *, integer
+ *, real *, real *, real *, real *, real *, integer *), slabrd_(
+ integer *, integer *, integer *, real *, integer *, real *, real *
+, real *, real *, real *, integer *, real *, integer *), xerbla_(
+ char *, integer *);
+ extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
+ integer *, integer *);
+ integer ldwrkx, ldwrky, lwkopt;
+ logical lquery;
+
+
+/* -- LAPACK routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SGEBRD reduces a general real M-by-N matrix A to upper or lower */
+/* bidiagonal form B by an orthogonal transformation: Q**T * 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) REAL 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) REAL array, dimension (min(M,N)) */
+/* The diagonal elements of the bidiagonal matrix B: */
+/* D(i) = A(i,i). */
+
+/* E (output) REAL 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) REAL array dimension (min(M,N)) */
+/* The scalar factors of the elementary reflectors which */
+/* represent the orthogonal matrix Q. See Further Details. */
+
+/* TAUP (output) REAL array, dimension (min(M,N)) */
+/* The scalar factors of the elementary reflectors which */
+/* represent the orthogonal matrix P. See Further Details. */
+
+/* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */
+/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
+
+/* LWORK (input) INTEGER */
+/* The length of the array WORK. LWORK >= max(1,M,N). */
+/* For optimum performance LWORK >= (M+N)*NB, where NB */
+/* is the optimal blocksize. */
+
+/* If LWORK = -1, then a workspace query is assumed; the routine */
+/* only calculates the optimal size of the WORK array, returns */
+/* this value as the first entry of the WORK array, and no error */
+/* message related to LWORK is issued by XERBLA. */
+
+/* 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 .. */
+/* .. */
+/* .. External 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;
+/* Computing MAX */
+ i__1 = 1, i__2 = ilaenv_(&c__1, "SGEBRD", " ", m, n, &c_n1, &c_n1);
+ nb = max(i__1,i__2);
+ lwkopt = (*m + *n) * nb;
+ work[1] = (real) lwkopt;
+ lquery = *lwork == -1;
+ if (*m < 0) {
+ *info = -1;
+ } else if (*n < 0) {
+ *info = -2;
+ } else if (*lda < max(1,*m)) {
+ *info = -4;
+ } else /* if(complicated condition) */ {
+/* Computing MAX */
+ i__1 = max(1,*m);
+ if (*lwork < max(i__1,*n) && ! lquery) {
+ *info = -10;
+ }
+ }
+ if (*info < 0) {
+ i__1 = -(*info);
+ xerbla_("SGEBRD", &i__1);
+ return 0;
+ } else if (lquery) {
+ return 0;
+ }
+
+/* Quick return if possible */
+
+ minmn = min(*m,*n);
+ if (minmn == 0) {
+ work[1] = 1.f;
+ return 0;
+ }
+
+ ws = (real) max(*m,*n);
+ ldwrkx = *m;
+ ldwrky = *n;
+
+ if (nb > 1 && nb < minmn) {
+
+/* Set the crossover point NX. */
+
+/* Computing MAX */
+ i__1 = nb, i__2 = ilaenv_(&c__3, "SGEBRD", " ", m, n, &c_n1, &c_n1);
+ nx = max(i__1,i__2);
+
+/* Determine when to switch from blocked to unblocked code. */
+
+ if (nx < minmn) {
+ ws = (real) ((*m + *n) * nb);
+ if ((real) (*lwork) < ws) {
+
+/* Not enough work space for the optimal NB, consider using */
+/* a smaller block size. */
+
+ nbmin = ilaenv_(&c__2, "SGEBRD", " ", m, n, &c_n1, &c_n1);
+ if (*lwork >= (*m + *n) * nbmin) {
+ nb = *lwork / (*m + *n);
+ } else {
+ nb = 1;
+ nx = minmn;
+ }
+ }
+ }
+ } else {
+ nx = minmn;
+ }
+
+ i__1 = minmn - nx;
+ i__2 = nb;
+ for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
+
+/* Reduce rows and columns i:i+nb-1 to bidiagonal form and return */
+/* the matrices X and Y which are needed to update the unreduced */
+/* part of the matrix */
+
+ i__3 = *m - i__ + 1;
+ i__4 = *n - i__ + 1;
+ slabrd_(&i__3, &i__4, &nb, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[
+ i__], &tauq[i__], &taup[i__], &work[1], &ldwrkx, &work[ldwrkx
+ * nb + 1], &ldwrky);
+
+/* Update the trailing submatrix A(i+nb:m,i+nb:n), using an update */
+/* of the form A := A - V*Y' - X*U' */
+
+ i__3 = *m - i__ - nb + 1;
+ i__4 = *n - i__ - nb + 1;
+ sgemm_("No transpose", "Transpose", &i__3, &i__4, &nb, &c_b21, &a[i__
+ + nb + i__ * a_dim1], lda, &work[ldwrkx * nb + nb + 1], &
+ ldwrky, &c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
+ i__3 = *m - i__ - nb + 1;
+ i__4 = *n - i__ - nb + 1;
+ sgemm_("No transpose", "No transpose", &i__3, &i__4, &nb, &c_b21, &
+ work[nb + 1], &ldwrkx, &a[i__ + (i__ + nb) * a_dim1], lda, &
+ c_b22, &a[i__ + nb + (i__ + nb) * a_dim1], lda);
+
+/* Copy diagonal and off-diagonal elements of B back into A */
+
+ if (*m >= *n) {
+ i__3 = i__ + nb - 1;
+ for (j = i__; j <= i__3; ++j) {
+ a[j + j * a_dim1] = d__[j];
+ a[j + (j + 1) * a_dim1] = e[j];
+/* L10: */
+ }
+ } else {
+ i__3 = i__ + nb - 1;
+ for (j = i__; j <= i__3; ++j) {
+ a[j + j * a_dim1] = d__[j];
+ a[j + 1 + j * a_dim1] = e[j];
+/* L20: */
+ }
+ }
+/* L30: */
+ }
+
+/* Use unblocked code to reduce the remainder of the matrix */
+
+ i__2 = *m - i__ + 1;
+ i__1 = *n - i__ + 1;
+ sgebd2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], &
+ tauq[i__], &taup[i__], &work[1], &iinfo);
+ work[1] = ws;
+ return 0;
+
+/* End of SGEBRD */
+
+} /* sgebrd_ */
projects / opencv / blobdiff