dlaed0.c

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/* dlaed0.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 doublereal c_b23 = 1.;
static doublereal c_b24 = 0.;
static integer c__1 = 1;

/* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, 
        doublereal *d__, doublereal *e, doublereal *q, integer *ldq, 
        doublereal *qstore, integer *ldqs, doublereal *work, 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, iq, lgn, msd2, smm1, spm1, spm2;
    doublereal temp;
    integer curr;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *);
    integer iperm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    integer indxq, iwrem;
    extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, 
             integer *, integer *, doublereal *, integer *, doublereal *, 
            integer *, integer *);
    integer iqptr;
    extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, 
            integer *, integer *, integer *, doublereal *, doublereal *, 
            integer *, integer *, doublereal *, integer *, doublereal *, 
            integer *, integer *, integer *, integer *, integer *, doublereal 
            *, doublereal *, integer *, integer *);
    integer tlvls;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *);
    integer igivcl;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    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 */
/*  ======= */

/*  DLAED0 computes all eigenvalues and corresponding eigenvectors of a */
/*  symmetric tridiagonal matrix using the divide and conquer method. */

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

/*  ICOMPQ  (input) INTEGER */
/*          = 0:  Compute eigenvalues only. */
/*          = 1:  Compute eigenvectors of original dense symmetric matrix */
/*                also.  On entry, Q contains the orthogonal matrix used */
/*                to reduce the original matrix to tridiagonal form. */
/*          = 2:  Compute eigenvalues and eigenvectors of tridiagonal */
/*                matrix. */

/*  QSIZ   (input) INTEGER */
/*         The dimension of the orthogonal 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 main diagonal of the tridiagonal matrix. */
/*         On exit, its eigenvalues. */

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

/*  Q      (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */
/*         On entry, Q must contain an N-by-N orthogonal matrix. */
/*         If ICOMPQ = 0    Q is not referenced. */
/*         If ICOMPQ = 1    On entry, Q is a subset of the columns of the */
/*                          orthogonal matrix used to reduce the full */
/*                          matrix to tridiagonal form corresponding to */
/*                          the subset of the full matrix which is being */
/*                          decomposed at this time. */
/*         If ICOMPQ = 2    On entry, Q will be the identity matrix. */
/*                          On exit, Q contains the eigenvectors of the */
/*                          tridiagonal matrix. */

/*  LDQ    (input) INTEGER */
/*         The leading dimension of the array Q.  If eigenvectors are */
/*         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1. */

/*  QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N) */
/*         Referenced only when ICOMPQ = 1.  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.  If ICOMPQ = 1, */
/*         then  LDQS >= max(1,N).  In any case,  LDQS >= 1. */

/*  WORK   (workspace) DOUBLE PRECISION array, */
/*         If ICOMPQ = 0 or 1, the dimension of WORK must be at least */
/*                     1 + 3*N + 2*N*lg N + 2*N**2 */
/*                     ( lg( N ) = smallest integer k */
/*                                 such that 2^k >= N ) */
/*         If ICOMPQ = 2, the dimension of WORK must be at least */
/*                     4*N + N**2. */

/*  IWORK  (workspace) INTEGER array, */
/*         If ICOMPQ = 0 or 1, 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 ) */
/*         If ICOMPQ = 2, the dimension of IWORK must be at least */
/*                        3 + 5*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). */

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

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

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

/*     .. 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;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 2) {
        *info = -1;
    } else if (*icompq == 1 && *qsiz < max(0,*n)) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*ldq < max(1,*n)) {
        *info = -7;
    } else if (*ldqs < max(1,*n)) {
        *info = -9;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DLAED0", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

    smlsiz = ilaenv_(&c__9, "DLAED0", " ", &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;
    if (*icompq != 2) {

/*        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__];
        }
        if (*icompq == 2) {
            dsteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat + 
                    submat * q_dim1], ldq, &work[1], info);
            if (*info != 0) {
                goto L130;
            }
        } else {
            dsteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + 
                    iwork[iqptr + curr]], &matsiz, &work[1], info);
            if (*info != 0) {
                goto L130;
            }
            if (*icompq == 1) {
                dgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * 
                        q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], 
                         &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], 
                        ldqs);
            }
/* Computing 2nd power */
            i__2 = matsiz;
            iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2;
            ++curr;
        }
        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. */
/*     DLAED1 is used only for the full eigensystem of a tridiagonal */
/*     matrix. */
/*     DLAED7 handles the cases in which eigenvalues only or eigenvalues */
/*     and eigenvectors of a full symmetric matrix (which was reduced to */
/*     tridiagonal form) are desired. */

            if (*icompq == 2) {
                dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], 
                        ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], &
                        msd2, &work[1], &iwork[subpbs + 1], info);
            } else {
                dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[
                        submat], &qstore[submat * qstore_dim1 + 1], ldqs, &
                        iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, &
                        work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm]
, &iwork[igivpt], &iwork[igivcl], &work[igivnm], &
                        work[iwrem], &iwork[subpbs + 1], info);
            }
            if (*info != 0) {
                goto L130;
            }
            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. */

    if (*icompq == 1) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            j = iwork[indxq + i__];
            work[i__] = d__[j];
            dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 
                    + 1], &c__1);
/* L100: */
        }
        dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
    } else if (*icompq == 2) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            j = iwork[indxq + i__];
            work[i__] = d__[j];
            dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1);
/* L110: */
        }
        dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
        dlacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq);
    } else {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            j = iwork[indxq + i__];
            work[i__] = d__[j];
/* L120: */
        }
        dcopy_(n, &work[1], &c__1, &d__[1], &c__1);
    }
    goto L140;

L130:
    *info = submat * (*n + 1) + submat + matsiz - 1;

L140:
    return 0;

/*     End of DLAED0 */

} /* dlaed0_ */