zlaed0.c

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/* zlaed0.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 integer c__1 = 1;

/* Subroutine */ int zlaed0_(integer *qsiz, integer *n, doublereal *d__, 
        doublereal *e, doublecomplex *q, integer *ldq, doublecomplex *qstore, 
        integer *ldqs, doublereal *rwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2;
    doublereal d__1;

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

    /* Local variables */
    integer i__, j, k, ll, iq, lgn, msd2, smm1, spm1, spm2;
    doublereal temp;
    integer curr, iperm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    integer indxq, iwrem, iqptr, tlvls;
    extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *, 
            doublecomplex *, integer *), zlaed7_(integer *, integer *, 
            integer *, integer *, integer *, integer *, doublereal *, 
            doublecomplex *, integer *, doublereal *, integer *, doublereal *, 
             integer *, integer *, integer *, integer *, integer *, 
            doublereal *, doublecomplex *, doublereal *, integer *, integer *)
            ;
    integer igivcl;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int zlacrm_(integer *, integer *, doublecomplex *, 
             integer *, doublereal *, integer *, doublecomplex *, integer *, 
            doublereal *);
    integer igivnm, submat, curprb, subpbs, igivpt;
    extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *);
    integer curlvl, matsiz, iprmpt, smlsiz;


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

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

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

/*  Using the divide and conquer method, ZLAED0 computes all eigenvalues */
/*  of a symmetric tridiagonal matrix which is one diagonal block of */
/*  those from reducing a dense or band Hermitian matrix and */
/*  corresponding eigenvectors of the dense or band matrix. */

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

/*  QSIZ   (input) INTEGER */
/*         The dimension of the unitary matrix used to reduce */
/*         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1. */

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

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

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

/*  Q      (input/output) COMPLEX*16 array, dimension (LDQ,N) */
/*         On entry, Q must contain an QSIZ x N matrix whose columns */
/*         unitarily orthonormal. It is a part of the unitary matrix */
/*         that reduces the full dense Hermitian matrix to a */
/*         (reducible) symmetric tridiagonal matrix. */

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

/*  IWORK  (workspace) INTEGER array, */
/*         the dimension of IWORK must be at least */
/*                      6 + 6*N + 5*N*lg N */
/*                      ( lg( N ) = smallest integer k */
/*                                  such that 2^k >= N ) */

/*  RWORK  (workspace) DOUBLE PRECISION array, */
/*                               dimension (1 + 3*N + 2*N*lg N + 3*N**2) */
/*                        ( lg( N ) = smallest integer k */
/*                                    such that 2^k >= N ) */

/*  QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N) */
/*         Used to store parts of */
/*         the eigenvector matrix when the updating matrix multiplies */
/*         take place. */

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

/*  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). */

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

/*  Warning:      N could be as big as QSIZ! */

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    --e;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    qstore_dim1 = *ldqs;
    qstore_offset = 1 + qstore_dim1;
    qstore -= qstore_offset;
    --rwork;
    --iwork;

    /* Function Body */
    *info = 0;

/*     IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN */
/*        INFO = -1 */
/*     ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) */
/*    $        THEN */
    if (*qsiz < max(0,*n)) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*ldq < max(1,*n)) {
        *info = -6;
    } else if (*ldqs < max(1,*n)) {
        *info = -8;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("ZLAED0", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    smlsiz = ilaenv_(&c__9, "ZLAED0", " ", &c__0, &c__0, &c__0, &c__0);

/*     Determine the size and placement of the submatrices, and save in */
/*     the leading elements of IWORK. */

    iwork[1] = *n;
    subpbs = 1;
    tlvls = 0;
L10:
    if (iwork[subpbs] > smlsiz) {
        for (j = subpbs; j >= 1; --j) {
            iwork[j * 2] = (iwork[j] + 1) / 2;
            iwork[(j << 1) - 1] = iwork[j] / 2;
/* L20: */
        }
        ++tlvls;
        subpbs <<= 1;
        goto L10;
    }
    i__1 = subpbs;
    for (j = 2; j <= i__1; ++j) {
        iwork[j] += iwork[j - 1];
/* L30: */
    }

/*     Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */
/*     using rank-1 modifications (cuts). */

    spm1 = subpbs - 1;
    i__1 = spm1;
    for (i__ = 1; i__ <= i__1; ++i__) {
        submat = iwork[i__] + 1;
        smm1 = submat - 1;
        d__[smm1] -= (d__1 = e[smm1], abs(d__1));
        d__[submat] -= (d__1 = e[smm1], abs(d__1));
/* L40: */
    }

    indxq = (*n << 2) + 3;

/*     Set up workspaces for eigenvalues only/accumulate new vectors */
/*     routine */

    temp = log((doublereal) (*n)) / log(2.);
    lgn = (integer) temp;
    if (pow_ii(&c__2, &lgn) < *n) {
        ++lgn;
    }
    if (pow_ii(&c__2, &lgn) < *n) {
        ++lgn;
    }
    iprmpt = indxq + *n + 1;
    iperm = iprmpt + *n * lgn;
    iqptr = iperm + *n * lgn;
    igivpt = iqptr + *n + 2;
    igivcl = igivpt + *n * lgn;

    igivnm = 1;
    iq = igivnm + (*n << 1) * lgn;
/* Computing 2nd power */
    i__1 = *n;
    iwrem = iq + i__1 * i__1 + 1;
/*     Initialize pointers */
    i__1 = subpbs;
    for (i__ = 0; i__ <= i__1; ++i__) {
        iwork[iprmpt + i__] = 1;
        iwork[igivpt + i__] = 1;
/* L50: */
    }
    iwork[iqptr] = 1;

/*     Solve each submatrix eigenproblem at the bottom of the divide and */
/*     conquer tree. */

    curr = 0;
    i__1 = spm1;
    for (i__ = 0; i__ <= i__1; ++i__) {
        if (i__ == 0) {
            submat = 1;
            matsiz = iwork[1];
        } else {
            submat = iwork[i__] + 1;
            matsiz = iwork[i__ + 1] - iwork[i__];
        }
        ll = iq - 1 + iwork[iqptr + curr];
        dsteqr_("I", &matsiz, &d__[submat], &e[submat], &rwork[ll], &matsiz, &
                rwork[1], info);
        zlacrm_(qsiz, &matsiz, &q[submat * q_dim1 + 1], ldq, &rwork[ll], &
                matsiz, &qstore[submat * qstore_dim1 + 1], ldqs, &rwork[iwrem]
);
/* Computing 2nd power */
        i__2 = matsiz;
        iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
        ++curr;
        if (*info > 0) {
            *info = submat * (*n + 1) + submat + matsiz - 1;
            return 0;
        }
        k = 1;
        i__2 = iwork[i__ + 1];
        for (j = submat; j <= i__2; ++j) {
            iwork[indxq + j] = k;
            ++k;
/* L60: */
        }
/* L70: */
    }

/*     Successively merge eigensystems of adjacent submatrices */
/*     into eigensystem for the corresponding larger matrix. */

/*     while ( SUBPBS > 1 ) */

    curlvl = 1;
L80:
    if (subpbs > 1) {
        spm2 = subpbs - 2;
        i__1 = spm2;
        for (i__ = 0; i__ <= i__1; i__ += 2) {
            if (i__ == 0) {
                submat = 1;
                matsiz = iwork[2];
                msd2 = iwork[1];
                curprb = 0;
            } else {
                submat = iwork[i__] + 1;
                matsiz = iwork[i__ + 2] - iwork[i__];
                msd2 = matsiz / 2;
                ++curprb;
            }

/*     Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */
/*     into an eigensystem of size MATSIZ.  ZLAED7 handles the case */
/*     when the eigenvectors of a full or band Hermitian matrix (which */
/*     was reduced to tridiagonal form) are desired. */

/*     I am free to use Q as a valuable working space until Loop 150. */

            zlaed7_(&matsiz, &msd2, qsiz, &tlvls, &curlvl, &curprb, &d__[
                    submat], &qstore[submat * qstore_dim1 + 1], ldqs, &e[
                    submat + msd2 - 1], &iwork[indxq + submat], &rwork[iq], &
                    iwork[iqptr], &iwork[iprmpt], &iwork[iperm], &iwork[
                    igivpt], &iwork[igivcl], &rwork[igivnm], &q[submat * 
                    q_dim1 + 1], &rwork[iwrem], &iwork[subpbs + 1], info);
            if (*info > 0) {
                *info = submat * (*n + 1) + submat + matsiz - 1;
                return 0;
            }
            iwork[i__ / 2 + 1] = iwork[i__ + 2];
/* L90: */
        }
        subpbs /= 2;
        ++curlvl;
        goto L80;
    }

/*     end while */

/*     Re-merge the eigenvalues/vectors which were deflated at the final */
/*     merge step. */

    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
        j = iwork[indxq + i__];
        rwork[i__] = d__[j];
        zcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1]
, &c__1);
/* L100: */
    }
    dcopy_(n, &rwork[1], &c__1, &d__[1], &c__1);

    return 0;

/*     End of ZLAED0 */

} /* zlaed0_ */