dlaeda.c

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/* dlaeda.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__2 = 2;
static integer c__1 = 1;
static doublereal c_b24 = 1.;
static doublereal c_b26 = 0.;

/* Subroutine */ int dlaeda_(integer *n, integer *tlvls, integer *curlvl, 
        integer *curpbm, integer *prmptr, integer *perm, integer *givptr, 
        integer *givcol, doublereal *givnum, doublereal *q, integer *qptr, 
        doublereal *z__, doublereal *ztemp, integer *info)
{
    /* System generated locals */
    integer i__1, i__2, i__3;

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

    /* Local variables */
    integer i__, k, mid, ptr;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *);
    integer curr, bsiz1, bsiz2, psiz1, psiz2, zptr1;
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *), dcopy_(integer *, 
            doublereal *, integer *, doublereal *, integer *), xerbla_(char *, 
             integer *);


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

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

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

/*  DLAEDA computes the Z vector corresponding to the merge step in the */
/*  CURLVLth step of the merge process with TLVLS steps for the CURPBMth */
/*  problem. */

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

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

/*  TLVLS  (input) INTEGER */
/*         The total number of merging levels in the overall divide and */
/*         conquer tree. */

/*  CURLVL (input) INTEGER */
/*         The current level in the overall merge routine, */
/*         0 <= curlvl <= tlvls. */

/*  CURPBM (input) INTEGER */
/*         The current problem in the current level in the overall */
/*         merge routine (counting from upper left to lower right). */

/*  PRMPTR (input) INTEGER array, dimension (N lg N) */
/*         Contains a list of pointers which indicate where in PERM a */
/*         level's permutation is stored.  PRMPTR(i+1) - PRMPTR(i) */
/*         indicates the size of the permutation and incidentally the */
/*         size of the full, non-deflated problem. */

/*  PERM   (input) INTEGER array, dimension (N lg N) */
/*         Contains the permutations (from deflation and sorting) to be */
/*         applied to each eigenblock. */

/*  GIVPTR (input) INTEGER array, dimension (N lg N) */
/*         Contains a list of pointers which indicate where in GIVCOL a */
/*         level's Givens rotations are stored.  GIVPTR(i+1) - GIVPTR(i) */
/*         indicates the number of Givens rotations. */

/*  GIVCOL (input) INTEGER array, dimension (2, N lg N) */
/*         Each pair of numbers indicates a pair of columns to take place */
/*         in a Givens rotation. */

/*  GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) */
/*         Each number indicates the S value to be used in the */
/*         corresponding Givens rotation. */

/*  Q      (input) DOUBLE PRECISION array, dimension (N**2) */
/*         Contains the square eigenblocks from previous levels, the */
/*         starting positions for blocks are given by QPTR. */

/*  QPTR   (input) INTEGER array, dimension (N+2) */
/*         Contains a list of pointers which indicate where in Q an */
/*         eigenblock is stored.  SQRT( QPTR(i+1) - QPTR(i) ) indicates */
/*         the size of the block. */

/*  Z      (output) DOUBLE PRECISION array, dimension (N) */
/*         On output this vector contains the updating vector (the last */
/*         row of the first sub-eigenvector matrix and the first row of */
/*         the second sub-eigenvector matrix). */

/*  ZTEMP  (workspace) DOUBLE PRECISION array, dimension (N) */

/*  INFO   (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

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

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

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

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

/*     Test the input parameters. */

    /* Parameter adjustments */
    --ztemp;
    --z__;
    --qptr;
    --q;
    givnum -= 3;
    givcol -= 3;
    --givptr;
    --perm;
    --prmptr;

    /* Function Body */
    *info = 0;

    if (*n < 0) {
        *info = -1;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DLAEDA", &i__1);
        return 0;
    }

/*     Quick return if possible */

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

/*     Determine location of first number in second half. */

    mid = *n / 2 + 1;

/*     Gather last/first rows of appropriate eigenblocks into center of Z */

    ptr = 1;

/*     Determine location of lowest level subproblem in the full storage */
/*     scheme */

    i__1 = *curlvl - 1;
    curr = ptr + *curpbm * pow_ii(&c__2, curlvl) + pow_ii(&c__2, &i__1) - 1;

/*     Determine size of these matrices.  We add HALF to the value of */
/*     the SQRT in case the machine underestimates one of these square */
/*     roots. */

    bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + .5);
    bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])) + 
            .5);
    i__1 = mid - bsiz1 - 1;
    for (k = 1; k <= i__1; ++k) {
        z__[k] = 0.;
/* L10: */
    }
    dcopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], &
            c__1);
    dcopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1);
    i__1 = *n;
    for (k = mid + bsiz2; k <= i__1; ++k) {
        z__[k] = 0.;
/* L20: */
    }

/*     Loop thru remaining levels 1 -> CURLVL applying the Givens */
/*     rotations and permutation and then multiplying the center matrices */
/*     against the current Z. */

    ptr = pow_ii(&c__2, tlvls) + 1;
    i__1 = *curlvl - 1;
    for (k = 1; k <= i__1; ++k) {
        i__2 = *curlvl - k;
        i__3 = *curlvl - k - 1;
        curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - 
                1;
        psiz1 = prmptr[curr + 1] - prmptr[curr];
        psiz2 = prmptr[curr + 2] - prmptr[curr + 1];
        zptr1 = mid - psiz1;

/*       Apply Givens at CURR and CURR+1 */

        i__2 = givptr[curr + 1] - 1;
        for (i__ = givptr[curr]; i__ <= i__2; ++i__) {
            drot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, &
                    z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[(
                    i__ << 1) + 1], &givnum[(i__ << 1) + 2]);
/* L30: */
        }
        i__2 = givptr[curr + 2] - 1;
        for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) {
            drot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[
                    mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << 
                    1) + 1], &givnum[(i__ << 1) + 2]);
/* L40: */
        }
        psiz1 = prmptr[curr + 1] - prmptr[curr];
        psiz2 = prmptr[curr + 2] - prmptr[curr + 1];
        i__2 = psiz1 - 1;
        for (i__ = 0; i__ <= i__2; ++i__) {
            ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1];
/* L50: */
        }
        i__2 = psiz2 - 1;
        for (i__ = 0; i__ <= i__2; ++i__) {
            ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - 
                    1];
/* L60: */
        }

/*        Multiply Blocks at CURR and CURR+1 */

/*        Determine size of these matrices.  We add HALF to the value of */
/*        the SQRT in case the machine underestimates one of these */
/*        square roots. */

        bsiz1 = (integer) (sqrt((doublereal) (qptr[curr + 1] - qptr[curr])) + 
                .5);
        bsiz2 = (integer) (sqrt((doublereal) (qptr[curr + 2] - qptr[curr + 1])
                ) + .5);
        if (bsiz1 > 0) {
            dgemv_("T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, &
                    ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1);
        }
        i__2 = psiz1 - bsiz1;
        dcopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1);
        if (bsiz2 > 0) {
            dgemv_("T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, &
                    ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1);
        }
        i__2 = psiz2 - bsiz2;
        dcopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], &
                c__1);

        i__2 = *tlvls - k;
        ptr += pow_ii(&c__2, &i__2);
/* L70: */
    }

    return 0;

/*     End of DLAEDA */

} /* dlaeda_ */