starpu-max/min-dgels/base/SRC/dsyev.c

/* dsyev.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__0 = 0;
static doublereal c_b17 = 1.;

/* Subroutine */ int _starpu_dsyev_(char *jobz, char *uplo, integer *n, doublereal *a, 
	 integer *lda, doublereal *w, doublereal *work, integer *lwork, 
	integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;
    doublereal d__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    integer nb;
    doublereal eps;
    integer inde;
    doublereal anrm;
    integer imax;
    doublereal rmin, rmax;
    extern /* Subroutine */ int _starpu_dscal_(integer *, doublereal *, doublereal *, 
	    integer *);
    doublereal sigma;
    extern logical _starpu_lsame_(char *, char *);
    integer iinfo;
    logical lower, wantz;
    extern doublereal _starpu_dlamch_(char *);
    integer iscale;
    extern /* Subroutine */ int _starpu_dlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *);
    doublereal safmin;
    extern integer _starpu_ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *);
    extern /* Subroutine */ int _starpu_xerbla_(char *, integer *);
    doublereal bignum;
    integer indtau;
    extern /* Subroutine */ int _starpu_dsterf_(integer *, doublereal *, doublereal *, 
	     integer *);
    extern doublereal _starpu_dlansy_(char *, char *, integer *, doublereal *, 
	    integer *, doublereal *);
    integer indwrk;
    extern /* Subroutine */ int _starpu_dorgtr_(char *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), _starpu_dsteqr_(char *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    _starpu_dsytrd_(char *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, integer *, integer *);
    integer llwork;
    doublereal smlnum;
    integer lwkopt;
    logical lquery;


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DSYEV computes all eigenvalues and, optionally, eigenvectors of a */
/*  real symmetric matrix A. */

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

/*  JOBZ    (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only; */
/*          = 'V':  Compute eigenvalues and eigenvectors. */

/*  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) DOUBLE PRECISION 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.  If UPLO = 'L', */
/*          the leading N-by-N lower triangular part of A contains */
/*          the lower triangular part of the matrix A. */
/*          On exit, if JOBZ = 'V', then if INFO = 0, A contains the */
/*          orthonormal eigenvectors of the matrix A. */
/*          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') */
/*          or the upper triangle (if UPLO='U') of A, including the */
/*          diagonal, is destroyed. */

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

/*  W       (output) DOUBLE PRECISION array, dimension (N) */
/*          If INFO = 0, the eigenvalues in ascending order. */

/*  WORK    (workspace/output) DOUBLE PRECISION 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(1,3*N-1). */
/*          For optimal efficiency, LWORK >= (NB+2)*N, */
/*          where NB is the blocksize for DSYTRD returned by ILAENV. */

/*          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 */
/*          > 0:  if INFO = i, the algorithm failed to converge; i */
/*                off-diagonal elements of an intermediate tridiagonal */
/*                form did not converge to zero. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --w;
    --work;

    /* Function Body */
    wantz = _starpu_lsame_(jobz, "V");
    lower = _starpu_lsame_(uplo, "L");
    lquery = *lwork == -1;

    *info = 0;
    if (! (wantz || _starpu_lsame_(jobz, "N"))) {
	*info = -1;
    } else if (! (lower || _starpu_lsame_(uplo, "U"))) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < max(1,*n)) {
	*info = -5;
    }

    if (*info == 0) {
	nb = _starpu_ilaenv_(&c__1, "DSYTRD", uplo, n, &c_n1, &c_n1, &c_n1);
/* Computing MAX */
	i__1 = 1, i__2 = (nb + 2) * *n;
	lwkopt = max(i__1,i__2);
	work[1] = (doublereal) lwkopt;

/* Computing MAX */
	i__1 = 1, i__2 = *n * 3 - 1;
	if (*lwork < max(i__1,i__2) && ! lquery) {
	    *info = -8;
	}
    }

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

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

    if (*n == 1) {
	w[1] = a[a_dim1 + 1];
	work[1] = 2.;
	if (wantz) {
	    a[a_dim1 + 1] = 1.;
	}
	return 0;
    }

/*     Get machine constants. */

    safmin = _starpu_dlamch_("Safe minimum");
    eps = _starpu_dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

/*     Scale matrix to allowable range, if necessary. */

    anrm = _starpu_dlansy_("M", uplo, n, &a[a_offset], lda, &work[1]);
    iscale = 0;
    if (anrm > 0. && anrm < rmin) {
	iscale = 1;
	sigma = rmin / anrm;
    } else if (anrm > rmax) {
	iscale = 1;
	sigma = rmax / anrm;
    }
    if (iscale == 1) {
	_starpu_dlascl_(uplo, &c__0, &c__0, &c_b17, &sigma, n, n, &a[a_offset], lda, 
		info);
    }

/*     Call DSYTRD to reduce symmetric matrix to tridiagonal form. */

    inde = 1;
    indtau = inde + *n;
    indwrk = indtau + *n;
    llwork = *lwork - indwrk + 1;
    _starpu_dsytrd_(uplo, n, &a[a_offset], lda, &w[1], &work[inde], &work[indtau], &
	    work[indwrk], &llwork, &iinfo);

/*     For eigenvalues only, call DSTERF.  For eigenvectors, first call */
/*     DORGTR to generate the orthogonal matrix, then call DSTEQR. */

    if (! wantz) {
	_starpu_dsterf_(n, &w[1], &work[inde], info);
    } else {
	_starpu_dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &
		llwork, &iinfo);
	_starpu_dsteqr_(jobz, n, &w[1], &work[inde], &a[a_offset], lda, &work[indtau], 
		 info);
    }

/*     If matrix was scaled, then rescale eigenvalues appropriately. */

    if (iscale == 1) {
	if (*info == 0) {
	    imax = *n;
	} else {
	    imax = *info - 1;
	}
	d__1 = 1. / sigma;
	_starpu_dscal_(&imax, &d__1, &w[1], &c__1);
    }

/*     Set WORK(1) to optimal workspace size. */

    work[1] = (doublereal) lwkopt;

    return 0;

/*     End of DSYEV */

} /* _starpu_dsyev_ */