--- /dev/null
+#include "clapack.h"
+
+/* Table of constant values */
+
+static real c_b4 = -1.f;
+static real c_b5 = 1.f;
+static integer c__1 = 1;
+static real c_b16 = 0.f;
+
+/* Subroutine */ int slabrd_(integer *m, integer *n, integer *nb, real *a,
+ integer *lda, real *d__, real *e, real *tauq, real *taup, real *x,
+ integer *ldx, real *y, integer *ldy)
+{
+ /* System generated locals */
+ integer a_dim1, a_offset, x_dim1, x_offset, y_dim1, y_offset, i__1, i__2,
+ i__3;
+
+ /* Local variables */
+ integer i__;
+ extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *),
+ sgemv_(char *, integer *, integer *, real *, real *, integer *,
+ real *, integer *, real *, real *, integer *), slarfg_(
+ integer *, real *, real *, integer *, real *);
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLABRD 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 SGEBRD */
+
+/* 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) REAL 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) REAL array, dimension (NB) */
+/* The diagonal elements of the first NB rows and columns of */
+/* the reduced matrix. D(i) = A(i,i). */
+
+/* E (output) REAL array, dimension (NB) */
+/* The off-diagonal elements of the first NB rows and columns of */
+/* the reduced matrix. */
+
+/* TAUQ (output) REAL array dimension (NB) */
+/* The scalar factors of the elementary reflectors which */
+/* represent the orthogonal matrix Q. See Further Details. */
+
+/* TAUP (output) REAL array, dimension (NB) */
+/* The scalar factors of the elementary reflectors which */
+/* represent the orthogonal matrix P. See Further Details. */
+
+/* X (output) REAL 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) REAL 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 .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Quick return if possible */
+
+ /* Parameter adjustments */
+ a_dim1 = *lda;
+ a_offset = 1 + a_dim1;
+ a -= a_offset;
+ --d__;
+ --e;
+ --tauq;
+ --taup;
+ x_dim1 = *ldx;
+ x_offset = 1 + x_dim1;
+ x -= x_offset;
+ y_dim1 = *ldy;
+ y_offset = 1 + y_dim1;
+ y -= y_offset;
+
+ /* Function Body */
+ if (*m <= 0 || *n <= 0) {
+ return 0;
+ }
+
+ if (*m >= *n) {
+
+/* Reduce to upper bidiagonal form */
+
+ i__1 = *nb;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Update A(i:m,i) */
+
+ i__2 = *m - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + a_dim1], lda,
+ &y[i__ + y_dim1], ldy, &c_b5, &a[i__ + i__ * a_dim1], &
+ c__1);
+ i__2 = *m - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + x_dim1], ldx,
+ &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[i__ + i__ *
+ a_dim1], &c__1);
+
+/* Generate reflection Q(i) to annihilate A(i+1:m,i) */
+
+ i__2 = *m - i__ + 1;
+/* Computing MIN */
+ i__3 = i__ + 1;
+ slarfg_(&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];
+ if (i__ < *n) {
+ a[i__ + i__ * a_dim1] = 1.f;
+
+/* Compute Y(i+1:n,i) */
+
+ i__2 = *m - i__ + 1;
+ i__3 = *n - i__;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + (i__ + 1) *
+ a_dim1], lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &
+ y[i__ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *m - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + a_dim1],
+ lda, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
+ y_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
+ y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
+ i__ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *m - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &x[i__ + x_dim1],
+ ldx, &a[i__ + i__ * a_dim1], &c__1, &c_b16, &y[i__ *
+ y_dim1 + 1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5,
+ &y[i__ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *n - i__;
+ sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
+
+/* Update A(i,i+1:n) */
+
+ i__2 = *n - i__;
+ sgemv_("No transpose", &i__2, &i__, &c_b4, &y[i__ + 1 +
+ y_dim1], ldy, &a[i__ + a_dim1], lda, &c_b5, &a[i__ + (
+ i__ + 1) * a_dim1], lda);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &x[i__ + x_dim1], ldx, &c_b5, &a[
+ i__ + (i__ + 1) * a_dim1], lda);
+
+/* Generate reflection P(i) to annihilate A(i,i+2:n) */
+
+ i__2 = *n - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ slarfg_(&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.f;
+
+/* Compute X(i+1:m,i) */
+
+ i__2 = *m - i__;
+ i__3 = *n - i__;
+ sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__
+ + 1) * a_dim1], lda, &a[i__ + (i__ + 1) * a_dim1],
+ lda, &c_b16, &x[i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = *n - i__;
+ sgemv_("Transpose", &i__2, &i__, &c_b5, &y[i__ + 1 + y_dim1],
+ ldy, &a[i__ + (i__ + 1) * a_dim1], lda, &c_b16, &x[
+ i__ * x_dim1 + 1], &c__1);
+ i__2 = *m - i__;
+ sgemv_("No transpose", &i__2, &i__, &c_b4, &a[i__ + 1 +
+ a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
+ i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__;
+ sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[(i__ + 1) *
+ a_dim1 + 1], lda, &a[i__ + (i__ + 1) * a_dim1], lda, &
+ c_b16, &x[i__ * x_dim1 + 1], &c__1);
+ i__2 = *m - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
+ x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
+ i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = *m - i__;
+ sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
+ }
+/* L10: */
+ }
+ } else {
+
+/* Reduce to lower bidiagonal form */
+
+ i__1 = *nb;
+ for (i__ = 1; i__ <= i__1; ++i__) {
+
+/* Update A(i,i:n) */
+
+ i__2 = *n - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + y_dim1], ldy,
+ &a[i__ + a_dim1], lda, &c_b5, &a[i__ + i__ * a_dim1],
+ lda);
+ i__2 = i__ - 1;
+ i__3 = *n - i__ + 1;
+ sgemv_("Transpose", &i__2, &i__3, &c_b4, &a[i__ * a_dim1 + 1],
+ lda, &x[i__ + x_dim1], ldx, &c_b5, &a[i__ + i__ * a_dim1],
+ lda);
+
+/* Generate reflection P(i) to annihilate A(i,i+1:n) */
+
+ i__2 = *n - i__ + 1;
+/* Computing MIN */
+ i__3 = i__ + 1;
+ slarfg_(&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];
+ if (i__ < *m) {
+ a[i__ + i__ * a_dim1] = 1.f;
+
+/* Compute X(i+1:m,i) */
+
+ i__2 = *m - i__;
+ i__3 = *n - i__ + 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + i__ *
+ a_dim1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &
+ x[i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = *n - i__ + 1;
+ i__3 = i__ - 1;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &y[i__ + y_dim1],
+ ldy, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
+ x_dim1 + 1], &c__1);
+ i__2 = *m - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
+ a_dim1], lda, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
+ i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = i__ - 1;
+ i__3 = *n - i__ + 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b5, &a[i__ * a_dim1 +
+ 1], lda, &a[i__ + i__ * a_dim1], lda, &c_b16, &x[i__ *
+ x_dim1 + 1], &c__1);
+ i__2 = *m - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &x[i__ + 1 +
+ x_dim1], ldx, &x[i__ * x_dim1 + 1], &c__1, &c_b5, &x[
+ i__ + 1 + i__ * x_dim1], &c__1);
+ i__2 = *m - i__;
+ sscal_(&i__2, &taup[i__], &x[i__ + 1 + i__ * x_dim1], &c__1);
+
+/* Update A(i+1:m,i) */
+
+ i__2 = *m - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &a[i__ + 1 +
+ a_dim1], lda, &y[i__ + y_dim1], ldy, &c_b5, &a[i__ +
+ 1 + i__ * a_dim1], &c__1);
+ i__2 = *m - i__;
+ sgemv_("No transpose", &i__2, &i__, &c_b4, &x[i__ + 1 +
+ x_dim1], ldx, &a[i__ * a_dim1 + 1], &c__1, &c_b5, &a[
+ i__ + 1 + i__ * a_dim1], &c__1);
+
+/* Generate reflection Q(i) to annihilate A(i+2:m,i) */
+
+ i__2 = *m - i__;
+/* Computing MIN */
+ i__3 = i__ + 2;
+ slarfg_(&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.f;
+
+/* Compute Y(i+1:n,i) */
+
+ i__2 = *m - i__;
+ i__3 = *n - i__;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + (i__ +
+ 1) * a_dim1], lda, &a[i__ + 1 + i__ * a_dim1], &c__1,
+ &c_b16, &y[i__ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *m - i__;
+ i__3 = i__ - 1;
+ sgemv_("Transpose", &i__2, &i__3, &c_b5, &a[i__ + 1 + a_dim1],
+ lda, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
+ i__ * y_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ i__3 = i__ - 1;
+ sgemv_("No transpose", &i__2, &i__3, &c_b4, &y[i__ + 1 +
+ y_dim1], ldy, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[
+ i__ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *m - i__;
+ sgemv_("Transpose", &i__2, &i__, &c_b5, &x[i__ + 1 + x_dim1],
+ ldx, &a[i__ + 1 + i__ * a_dim1], &c__1, &c_b16, &y[
+ i__ * y_dim1 + 1], &c__1);
+ i__2 = *n - i__;
+ sgemv_("Transpose", &i__, &i__2, &c_b4, &a[(i__ + 1) * a_dim1
+ + 1], lda, &y[i__ * y_dim1 + 1], &c__1, &c_b5, &y[i__
+ + 1 + i__ * y_dim1], &c__1);
+ i__2 = *n - i__;
+ sscal_(&i__2, &tauq[i__], &y[i__ + 1 + i__ * y_dim1], &c__1);
+ }
+/* L20: */
+ }
+ }
+ return 0;
+
+/* End of SLABRD */
+
+} /* slabrd_ */
projects / opencv / blobdiff