opencv/3rdparty/lapack/ssytrd.c

/* ssytrd.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_b22 = -1.f;
static real c_b23 = 1.f;

/* Subroutine */ int ssytrd_(char *uplo, integer *n, real *a, integer *lda, 
	real *d__, real *e, real *tau, real *work, integer *lwork, integer *
	info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer i__, j, nb, kk, nx, iws;
    extern logical lsame_(char *, char *);
    integer nbmin, iinfo;
    logical upper;
    extern /* Subroutine */ int ssytd2_(char *, integer *, real *, integer *, 
	    real *, real *, real *, integer *), ssyr2k_(char *, char *
, integer *, integer *, real *, real *, integer *, real *, 
	    integer *, real *, real *, integer *), xerbla_(
	    char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int slatrd_(char *, integer *, integer *, real *, 
	    integer *, real *, real *, real *, integer *);
    integer ldwork, 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 */
/*  ======= */

/*  SSYTRD reduces a real symmetric matrix A to real symmetric */
/*  tridiagonal form T by an orthogonal similarity transformation: */
/*  Q**T * A * Q = T. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, the symmetric matrix A.  If UPLO = 'U', the leading */
/*          N-by-N upper triangular part of A contains the upper */
/*          triangular part of the matrix A, and the strictly lower */
/*          triangular part of A is not referenced.  If UPLO = 'L', the */
/*          leading N-by-N lower triangular part of A contains the lower */
/*          triangular part of the matrix A, and the strictly upper */
/*          triangular part of A is not referenced. */
/*          On exit, if UPLO = 'U', the diagonal and first superdiagonal */
/*          of A are overwritten by the corresponding elements of the */
/*          tridiagonal matrix T, and the elements above the first */
/*          superdiagonal, with the array TAU, represent the orthogonal */
/*          matrix Q as a product of elementary reflectors; if UPLO */
/*          = 'L', the diagonal and first subdiagonal of A are over- */
/*          written by the corresponding elements of the tridiagonal */
/*          matrix T, and the elements below the first subdiagonal, with */
/*          the array TAU, represent the orthogonal matrix Q as a product */
/*          of elementary reflectors. See Further Details. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A.  LDA >= max(1,N). */

/*  D       (output) REAL array, dimension (N) */
/*          The diagonal elements of the tridiagonal matrix T: */
/*          D(i) = A(i,i). */

/*  E       (output) REAL array, dimension (N-1) */
/*          The off-diagonal elements of the tridiagonal matrix T: */
/*          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. */

/*  TAU     (output) REAL array, dimension (N-1) */
/*          The scalar factors of the elementary reflectors (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 dimension of the array WORK.  LWORK >= 1. */
/*          For optimum performance LWORK >= 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 */
/*  =============== */

/*  If UPLO = 'U', the matrix Q is represented as a product of elementary */
/*  reflectors */

/*     Q = H(n-1) . . . H(2) H(1). */

/*  Each H(i) has the form */

/*     H(i) = I - tau * v * v' */

/*  where tau is a real scalar, and v is a real vector with */
/*  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in */
/*  A(1:i-1,i+1), and tau in TAU(i). */

/*  If UPLO = 'L', the matrix Q is represented as a product of elementary */
/*  reflectors */

/*     Q = H(1) H(2) . . . H(n-1). */

/*  Each H(i) has the form */

/*     H(i) = I - tau * v * v' */

/*  where tau is a real scalar, and v is a real vector with */
/*  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), */
/*  and tau in TAU(i). */

/*  The contents of A on exit are illustrated by the following examples */
/*  with n = 5: */

/*  if UPLO = 'U':                       if UPLO = 'L': */

/*    (  d   e   v2  v3  v4 )              (  d                  ) */
/*    (      d   e   v3  v4 )              (  e   d              ) */
/*    (          d   e   v4 )              (  v1  e   d          ) */
/*    (              d   e  )              (  v1  v2  e   d      ) */
/*    (                  d  )              (  v1  v2  v3  e   d  ) */

/*  where d and e denote diagonal and off-diagonal elements of T, and vi */
/*  denotes an element of the vector defining H(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;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    lquery = *lwork == -1;
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < max(1,*n)) {
	*info = -4;
    } else if (*lwork < 1 && ! lquery) {
	*info = -9;
    }

    if (*info == 0) {

/*        Determine the block size. */

	nb = ilaenv_(&c__1, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
	lwkopt = *n * nb;
	work[1] = (real) lwkopt;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SSYTRD", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	work[1] = 1.f;
	return 0;
    }

    nx = *n;
    iws = 1;
    if (nb > 1 && nb < *n) {

/*        Determine when to cross over from blocked to unblocked code */
/*        (last block is always handled by unblocked code). */

/* Computing MAX */
	i__1 = nb, i__2 = ilaenv_(&c__3, "SSYTRD", uplo, n, &c_n1, &c_n1, &
		c_n1);
	nx = max(i__1,i__2);
	if (nx < *n) {

/*           Determine if workspace is large enough for blocked code. */

	    ldwork = *n;
	    iws = ldwork * nb;
	    if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  determine the */
/*              minimum value of NB, and reduce NB or force use of */
/*              unblocked code by setting NX = N. */

/* Computing MAX */
		i__1 = *lwork / ldwork;
		nb = max(i__1,1);
		nbmin = ilaenv_(&c__2, "SSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
		if (nb < nbmin) {
		    nx = *n;
		}
	    }
	} else {
	    nx = *n;
	}
    } else {
	nb = 1;
    }

    if (upper) {

/*        Reduce the upper triangle of A. */
/*        Columns 1:kk are handled by the unblocked method. */

	kk = *n - (*n - nx + nb - 1) / nb * nb;
	i__1 = kk + 1;
	i__2 = -nb;
	for (i__ = *n - nb + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += 
		i__2) {

/*           Reduce columns i:i+nb-1 to tridiagonal form and form the */
/*           matrix W which is needed to update the unreduced part of */
/*           the matrix */

	    i__3 = i__ + nb - 1;
	    slatrd_(uplo, &i__3, &nb, &a[a_offset], lda, &e[1], &tau[1], &
		    work[1], &ldwork);

/*           Update the unreduced submatrix A(1:i-1,1:i-1), using an */
/*           update of the form:  A := A - V*W' - W*V' */

	    i__3 = i__ - 1;
	    ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ * a_dim1 
		    + 1], lda, &work[1], &ldwork, &c_b23, &a[a_offset], lda);

/*           Copy superdiagonal elements back into A, and diagonal */
/*           elements into D */

	    i__3 = i__ + nb - 1;
	    for (j = i__; j <= i__3; ++j) {
		a[j - 1 + j * a_dim1] = e[j - 1];
		d__[j] = a[j + j * a_dim1];
/* L10: */
	    }
/* L20: */
	}

/*        Use unblocked code to reduce the last or only block */

	ssytd2_(uplo, &kk, &a[a_offset], lda, &d__[1], &e[1], &tau[1], &iinfo);
    } else {

/*        Reduce the lower triangle of A */

	i__2 = *n - nx;
	i__1 = nb;
	for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ += i__1) {

/*           Reduce columns i:i+nb-1 to tridiagonal form and form the */
/*           matrix W which is needed to update the unreduced part of */
/*           the matrix */

	    i__3 = *n - i__ + 1;
	    slatrd_(uplo, &i__3, &nb, &a[i__ + i__ * a_dim1], lda, &e[i__], &
		    tau[i__], &work[1], &ldwork);

/*           Update the unreduced submatrix A(i+ib:n,i+ib:n), using */
/*           an update of the form:  A := A - V*W' - W*V' */

	    i__3 = *n - i__ - nb + 1;
	    ssyr2k_(uplo, "No transpose", &i__3, &nb, &c_b22, &a[i__ + nb + 
		    i__ * a_dim1], lda, &work[nb + 1], &ldwork, &c_b23, &a[
		    i__ + nb + (i__ + nb) * a_dim1], lda);

/*           Copy subdiagonal elements back into A, and diagonal */
/*           elements into D */

	    i__3 = i__ + nb - 1;
	    for (j = i__; j <= i__3; ++j) {
		a[j + 1 + j * a_dim1] = e[j];
		d__[j] = a[j + j * a_dim1];
/* L30: */
	    }
/* L40: */
	}

/*        Use unblocked code to reduce the last or only block */

	i__1 = *n - i__ + 1;
	ssytd2_(uplo, &i__1, &a[i__ + i__ * a_dim1], lda, &d__[i__], &e[i__], 
		&tau[i__], &iinfo);
    }

    work[1] = (real) lwkopt;
    return 0;

/*     End of SSYTRD */

} /* ssytrd_ */