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/* ../../../dependencies/lapack/src/dgebd2.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.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, i__4;
/* Local variables */
static integer i__;
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, ftnlen), dlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *), xerbla_(char *, integer *,
ftnlen);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* February 29, 1992 */
/* .. 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, (ftnlen)6);
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 */
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], (
ftnlen)4);
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], (ftnlen)5);
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 */
i__2 = *m - i__;
i__3 = *n - i__ + 1;
/* Computing MIN */
i__4 = i__ + 1;
dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &taup[
i__], &a[min(i__4,*m) + i__ * a_dim1], lda, &work[1], (
ftnlen)5);
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], (ftnlen)4);
a[i__ + 1 + i__ * a_dim1] = e[i__];
} else {
tauq[i__] = 0.;
}
/* L20: */
}
}
return 0;
/* End of DGEBD2 */
} /* dgebd2_ */
|
