dsyev.c

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/* 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 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 dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal sigma;
    extern logical lsame_(char *, char *);
    integer iinfo;
    logical lower, wantz;
    extern doublereal dlamch_(char *);
    integer iscale;
    extern /* Subroutine */ int dlascl_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, integer *, doublereal *, 
            integer *, integer *);
    doublereal safmin;
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal bignum;
    integer indtau;
    extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, 
             integer *);
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
            integer *, doublereal *);
    integer indwrk;
    extern /* Subroutine */ int dorgtr_(char *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *, integer *), dsteqr_(char *, integer *, doublereal *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *), 
            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 = lsame_(jobz, "V");
    lower = lsame_(uplo, "L");
    lquery = *lwork == -1;

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

    if (*info == 0) {
        nb = 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);
        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 = dlamch_("Safe minimum");
    eps = dlamch_("Precision");
    smlnum = safmin / eps;
    bignum = 1. / smlnum;
    rmin = sqrt(smlnum);
    rmax = sqrt(bignum);

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

    anrm = 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) {
        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;
    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) {
        dsterf_(n, &w[1], &work[inde], info);
    } else {
        dorgtr_(uplo, n, &a[a_offset], lda, &work[indtau], &work[indwrk], &
                llwork, &iinfo);
        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;
        dscal_(&imax, &d__1, &w[1], &c__1);
    }

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

    work[1] = (doublereal) lwkopt;

    return 0;

/*     End of DSYEV */

} /* dsyev_ */