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/* sgebrd.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"
#include "blaswrap.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 3.2) -- */
/* 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_ */
|
