cstedc.c

Go to the documentation of this file.

/* cstedc.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__9 = 9;
static integer c__0 = 0;
static integer c__2 = 2;
static real c_b17 = 0.f;
static real c_b18 = 1.f;
static integer c__1 = 1;

/* Subroutine */ int cstedc_(char *compz, integer *n, real *d__, real *e, 
        complex *z__, integer *ldz, complex *work, integer *lwork, real *
        rwork, integer *lrwork, integer *iwork, integer *liwork, integer *
        info)
{
    /* System generated locals */
    integer z_dim1, z_offset, i__1, i__2, i__3, i__4;
    real r__1, r__2;

    /* Builtin functions */
    double log(doublereal);
    integer pow_ii(integer *, integer *);
    double sqrt(doublereal);

    /* Local variables */
    integer i__, j, k, m;
    real p;
    integer ii, ll, lgn;
    real eps, tiny;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int cswap_(integer *, complex *, integer *, 
            complex *, integer *);
    integer lwmin;
    extern /* Subroutine */ int claed0_(integer *, integer *, real *, real *, 
            complex *, integer *, complex *, integer *, real *, integer *, 
            integer *);
    integer start;
    extern /* Subroutine */ int clacrm_(integer *, integer *, complex *, 
            integer *, real *, integer *, complex *, integer *, real *);
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
            *, integer *, complex *, integer *), xerbla_(char *, 
            integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    integer finish;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
            real *, integer *, integer *, real *, integer *, integer *), sstedc_(char *, integer *, real *, real *, real *, 
            integer *, real *, integer *, integer *, integer *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
            real *, integer *);
    integer liwmin, icompz;
    extern /* Subroutine */ int csteqr_(char *, integer *, real *, real *, 
            complex *, integer *, real *, integer *);
    real orgnrm;
    extern doublereal slanst_(char *, integer *, real *, real *);
    extern /* Subroutine */ int ssterf_(integer *, real *, real *, integer *);
    integer lrwmin;
    logical lquery;
    integer smlsiz;
    extern /* Subroutine */ int ssteqr_(char *, integer *, real *, real *, 
            real *, integer *, real *, integer *);


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

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

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

/*  CSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
/*  symmetric tridiagonal matrix using the divide and conquer method. */
/*  The eigenvectors of a full or band complex Hermitian matrix can also */
/*  be found if CHETRD or CHPTRD or CHBTRD has been used to reduce this */
/*  matrix to tridiagonal form. */

/*  This code 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.  See SLAED3 for details. */

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

/*  COMPZ   (input) CHARACTER*1 */
/*          = 'N':  Compute eigenvalues only. */
/*          = 'I':  Compute eigenvectors of tridiagonal matrix also. */
/*          = 'V':  Compute eigenvectors of original Hermitian matrix */
/*                  also.  On entry, Z contains the unitary matrix used */
/*                  to reduce the original matrix to tridiagonal form. */

/*  N       (input) INTEGER */
/*          The dimension of the symmetric tridiagonal matrix.  N >= 0. */

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

/*  E       (input/output) REAL array, dimension (N-1) */
/*          On entry, the subdiagonal elements of the tridiagonal matrix. */
/*          On exit, E has been destroyed. */

/*  Z       (input/output) COMPLEX array, dimension (LDZ,N) */
/*          On entry, if COMPZ = 'V', then Z contains the unitary */
/*          matrix used in the reduction to tridiagonal form. */
/*          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
/*          orthonormal eigenvectors of the original Hermitian matrix, */
/*          and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
/*          of the symmetric tridiagonal matrix. */
/*          If  COMPZ = 'N', then Z is not referenced. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z.  LDZ >= 1. */
/*          If eigenvectors are desired, then LDZ >= max(1,N). */

/*  WORK    (workspace/output) COMPLEX    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. */
/*          If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. */
/*          If COMPZ = 'V' and N > 1, LWORK must be at least N*N. */
/*          Note that for COMPZ = 'V', then if N is less than or */
/*          equal to the minimum divide size, usually 25, then LWORK need */
/*          only be 1. */

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

/*  RWORK   (workspace/output) REAL array, dimension (MAX(1,LRWORK)) */
/*          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */

/*  LRWORK  (input) INTEGER */
/*          The dimension of the array RWORK. */
/*          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. */
/*          If COMPZ = 'V' and N > 1, LRWORK must be at least */
/*                         1 + 3*N + 2*N*lg N + 3*N**2 , */
/*                         where lg( N ) = smallest integer k such */
/*                         that 2**k >= N. */
/*          If COMPZ = 'I' and N > 1, LRWORK must be at least */
/*                         1 + 4*N + 2*N**2 . */
/*          Note that for COMPZ = 'I' or 'V', then if N is less than or */
/*          equal to the minimum divide size, usually 25, then LRWORK */
/*          need only be max(1,2*(N-1)). */

/*          If LRWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK 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 COMPZ = 'N' or N <= 1, LIWORK must be at least 1. */
/*          If COMPZ = 'V' or N > 1,  LIWORK must be at least */
/*                                    6 + 6*N + 5*N*lg N. */
/*          If COMPZ = 'I' or N > 1,  LIWORK must be at least */
/*                                    3 + 5*N . */
/*          Note that for COMPZ = 'I' or 'V', then if N is less than or */
/*          equal to the minimum divide size, usually 25, then LIWORK */
/*          need only be 1. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the optimal sizes of the WORK, RWORK */
/*          and IWORK arrays, returns these values as the first entries */
/*          of the WORK, RWORK and IWORK arrays, and no error message */
/*          related to LWORK or LRWORK 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:  The algorithm failed to compute an eigenvalue while */
/*                working on the submatrix lying in rows and columns */
/*                INFO/(N+1) through mod(INFO,N+1). */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Jeff Rutter, Computer Science Division, University of California */
/*     at Berkeley, USA */

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

/*     .. 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;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;

    if (lsame_(compz, "N")) {
        icompz = 0;
    } else if (lsame_(compz, "V")) {
        icompz = 1;
    } else if (lsame_(compz, "I")) {
        icompz = 2;
    } else {
        icompz = -1;
    }
    if (icompz < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
        *info = -6;
    }

    if (*info == 0) {

/*        Compute the workspace requirements */

        smlsiz = ilaenv_(&c__9, "CSTEDC", " ", &c__0, &c__0, &c__0, &c__0);
        if (*n <= 1 || icompz == 0) {
            lwmin = 1;
            liwmin = 1;
            lrwmin = 1;
        } else if (*n <= smlsiz) {
            lwmin = 1;
            liwmin = 1;
            lrwmin = *n - 1 << 1;
        } else if (icompz == 1) {
            lgn = (integer) (log((real) (*n)) / log(2.f));
            if (pow_ii(&c__2, &lgn) < *n) {
                ++lgn;
            }
            if (pow_ii(&c__2, &lgn) < *n) {
                ++lgn;
            }
            lwmin = *n * *n;
/* Computing 2nd power */
            i__1 = *n;
            lrwmin = *n * 3 + 1 + (*n << 1) * lgn + i__1 * i__1 * 3;
            liwmin = *n * 6 + 6 + *n * 5 * lgn;
        } else if (icompz == 2) {
            lwmin = 1;
/* Computing 2nd power */
            i__1 = *n;
            lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1);
            liwmin = *n * 5 + 3;
        }
        work[1].r = (real) lwmin, work[1].i = 0.f;
        rwork[1] = (real) lrwmin;
        iwork[1] = liwmin;

        if (*lwork < lwmin && ! lquery) {
            *info = -8;
        } else if (*lrwork < lrwmin && ! lquery) {
            *info = -10;
        } else if (*liwork < liwmin && ! lquery) {
            *info = -12;
        }
    }

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

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }
    if (*n == 1) {
        if (icompz != 0) {
            i__1 = z_dim1 + 1;
            z__[i__1].r = 1.f, z__[i__1].i = 0.f;
        }
        return 0;
    }

/*     If the following conditional clause is removed, then the routine */
/*     will use the Divide and Conquer routine to compute only the */
/*     eigenvalues, which requires (3N + 3N**2) real workspace and */
/*     (2 + 5N + 2N lg(N)) integer workspace. */
/*     Since on many architectures SSTERF is much faster than any other */
/*     algorithm for finding eigenvalues only, it is used here */
/*     as the default. If the conditional clause is removed, then */
/*     information on the size of workspace needs to be changed. */

/*     If COMPZ = 'N', use SSTERF to compute the eigenvalues. */

    if (icompz == 0) {
        ssterf_(n, &d__[1], &e[1], info);
        goto L70;
    }

/*     If N is smaller than the minimum divide size (SMLSIZ+1), then */
/*     solve the problem with another solver. */

    if (*n <= smlsiz) {

        csteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1], 
                info);

    } else {

/*        If COMPZ = 'I', we simply call SSTEDC instead. */

        if (icompz == 2) {
            slaset_("Full", n, n, &c_b17, &c_b18, &rwork[1], n);
            ll = *n * *n + 1;
            i__1 = *lrwork - ll + 1;
            sstedc_("I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, &
                    iwork[1], liwork, info);
            i__1 = *n;
            for (j = 1; j <= i__1; ++j) {
                i__2 = *n;
                for (i__ = 1; i__ <= i__2; ++i__) {
                    i__3 = i__ + j * z_dim1;
                    i__4 = (j - 1) * *n + i__;
                    z__[i__3].r = rwork[i__4], z__[i__3].i = 0.f;
/* L10: */
                }
/* L20: */
            }
            goto L70;
        }

/*        From now on, only option left to be handled is COMPZ = 'V', */
/*        i.e. ICOMPZ = 1. */

/*        Scale. */

        orgnrm = slanst_("M", n, &d__[1], &e[1]);
        if (orgnrm == 0.f) {
            goto L70;
        }

        eps = slamch_("Epsilon");

        start = 1;

/*        while ( START <= N ) */

L30:
        if (start <= *n) {

/*           Let FINISH be the position of the next subdiagonal entry */
/*           such that E( FINISH ) <= TINY or FINISH = N if no such */
/*           subdiagonal exists.  The matrix identified by the elements */
/*           between START and FINISH constitutes an independent */
/*           sub-problem. */

            finish = start;
L40:
            if (finish < *n) {
                tiny = eps * sqrt((r__1 = d__[finish], dabs(r__1))) * sqrt((
                        r__2 = d__[finish + 1], dabs(r__2)));
                if ((r__1 = e[finish], dabs(r__1)) > tiny) {
                    ++finish;
                    goto L40;
                }
            }

/*           (Sub) Problem determined.  Compute its size and solve it. */

            m = finish - start + 1;
            if (m > smlsiz) {

/*              Scale. */

                orgnrm = slanst_("M", &m, &d__[start], &e[start]);
                slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[
                        start], &m, info);
                i__1 = m - 1;
                i__2 = m - 1;
                slascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[
                        start], &i__2, info);

                claed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 + 
                        1], ldz, &work[1], n, &rwork[1], &iwork[1], info);
                if (*info > 0) {
                    *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info %
                             (m + 1) + start - 1;
                    goto L70;
                }

/*              Scale back. */

                slascl_("G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[
                        start], &m, info);

            } else {
                ssteqr_("I", &m, &d__[start], &e[start], &rwork[1], &m, &
                        rwork[m * m + 1], info);
                clacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, &
                        work[1], n, &rwork[m * m + 1]);
                clacpy_("A", n, &m, &work[1], n, &z__[start * z_dim1 + 1], 
                        ldz);
                if (*info > 0) {
                    *info = start * (*n + 1) + finish;
                    goto L70;
                }
            }

            start = finish + 1;
            goto L30;
        }

/*        endwhile */

/*        If the problem split any number of times, then the eigenvalues */
/*        will not be properly ordered.  Here we permute the eigenvalues */
/*        (and the associated eigenvectors) into ascending order. */

        if (m != *n) {

/*           Use Selection Sort to minimize swaps of eigenvectors */

            i__1 = *n;
            for (ii = 2; ii <= i__1; ++ii) {
                i__ = ii - 1;
                k = i__;
                p = d__[i__];
                i__2 = *n;
                for (j = ii; j <= i__2; ++j) {
                    if (d__[j] < p) {
                        k = j;
                        p = d__[j];
                    }
/* L50: */
                }
                if (k != i__) {
                    d__[k] = d__[i__];
                    d__[i__] = p;
                    cswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 
                            + 1], &c__1);
                }
/* L60: */
            }
        }
    }

L70:
    work[1].r = (real) lwmin, work[1].i = 0.f;
    rwork[1] = (real) lrwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of CSTEDC */

} /* cstedc_ */