dstevd.c

Go to the documentation of this file.

/* dstevd.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;

/* Subroutine */ int dstevd_(char *jobz, integer *n, doublereal *d__, 
        doublereal *e, doublereal *z__, integer *ldz, doublereal *work, 
        integer *lwork, integer *iwork, integer *liwork, integer *info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1;
    doublereal d__1;

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

    /* Local variables */
    doublereal eps, rmin, rmax, tnrm;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal sigma;
    extern logical lsame_(char *, char *);
    integer lwmin;
    logical wantz;
    extern doublereal dlamch_(char *);
    integer iscale;
    extern /* Subroutine */ int dstedc_(char *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            integer *, integer *, integer *);
    doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal bignum;
    extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
    extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *, 
             integer *);
    integer liwmin;
    doublereal smlnum;
    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 */
/*  ======= */

/*  DSTEVD computes all eigenvalues and, optionally, eigenvectors of a */
/*  real symmetric tridiagonal matrix. If eigenvectors are desired, it */
/*  uses a divide and conquer algorithm. */

/*  The divide and conquer algorithm makes very mild assumptions about */
/*  floating point arithmetic. It will work on machines with a guard */
/*  digit in add/subtract, or on those binary machines without guard */
/*  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/*  Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/*  without guard digits, but we know of none. */

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

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

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

/*  D       (input/output) DOUBLE PRECISION array, dimension (N) */
/*          On entry, the n diagonal elements of the tridiagonal matrix */
/*          A. */
/*          On exit, if INFO = 0, the eigenvalues in ascending order. */

/*  E       (input/output) DOUBLE PRECISION array, dimension (N-1) */
/*          On entry, the (n-1) subdiagonal elements of the tridiagonal */
/*          matrix A, stored in elements 1 to N-1 of E. */
/*          On exit, the contents of E are destroyed. */

/*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, N) */
/*          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal */
/*          eigenvectors of the matrix A, with the i-th column of Z */
/*          holding the eigenvector associated with D(i). */
/*          If JOBZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1, and if */
/*          JOBZ = 'V', LDZ >= max(1,N). */

/*  WORK    (workspace/output) DOUBLE PRECISION array, */
/*                                         dimension (LWORK) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. */
/*          If JOBZ  = 'N' or N <= 1 then LWORK must be at least 1. */
/*          If JOBZ  = 'V' and N > 1 then LWORK must be at least */
/*                         ( 1 + 4*N + N**2 ). */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal sizes of the WORK and IWORK */
/*          arrays, returns these values as the first entries of the WORK */
/*          and IWORK arrays, and no error message related to LWORK or */
/*          LIWORK is issued by XERBLA. */

/*  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK. */
/*          If JOBZ  = 'N' or N <= 1 then LIWORK must be at least 1. */
/*          If JOBZ  = 'V' and N > 1 then LIWORK must be at least 3+5*N. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK and */
/*          IWORK arrays, returns these values as the first entries of */
/*          the WORK and IWORK arrays, and no error message related to */
/*          LWORK or LIWORK 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 E did not converge to zero. */

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --work;
    --iwork;

    /* Function Body */
    wantz = lsame_(jobz, "V");
    lquery = *lwork == -1 || *liwork == -1;

    *info = 0;
    liwmin = 1;
    lwmin = 1;
    if (*n > 1 && wantz) {
/* Computing 2nd power */
        i__1 = *n;
        lwmin = (*n << 2) + 1 + i__1 * i__1;
        liwmin = *n * 5 + 3;
    }

    if (! (wantz || lsame_(jobz, "N"))) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*ldz < 1 || wantz && *ldz < *n) {
        *info = -6;
    }

    if (*info == 0) {
        work[1] = (doublereal) lwmin;
        iwork[1] = liwmin;

        if (*lwork < lwmin && ! lquery) {
            *info = -8;
        } else if (*liwork < liwmin && ! lquery) {
            *info = -10;
        }
    }

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

/*     Quick return if possible */

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

    if (*n == 1) {
        if (wantz) {
            z__[z_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. */

    iscale = 0;
    tnrm = dlanst_("M", n, &d__[1], &e[1]);
    if (tnrm > 0. && tnrm < rmin) {
        iscale = 1;
        sigma = rmin / tnrm;
    } else if (tnrm > rmax) {
        iscale = 1;
        sigma = rmax / tnrm;
    }
    if (iscale == 1) {
        dscal_(n, &sigma, &d__[1], &c__1);
        i__1 = *n - 1;
        dscal_(&i__1, &sigma, &e[1], &c__1);
    }

/*     For eigenvalues only, call DSTERF.  For eigenvalues and */
/*     eigenvectors, call DSTEDC. */

    if (! wantz) {
        dsterf_(n, &d__[1], &e[1], info);
    } else {
        dstedc_("I", n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], lwork, 
                &iwork[1], liwork, info);
    }

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

    if (iscale == 1) {
        d__1 = 1. / sigma;
        dscal_(n, &d__1, &d__[1], &c__1);
    }

    work[1] = (doublereal) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of DSTEVD */

} /* dstevd_ */