sgebrd.c

/* 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 "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 3.2) -- */
/*     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_ */