/* slaeda.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 real c_b24 = 1.f;
static real c_b26 = 0.f;
/* Subroutine */ int slaeda_(integer *n, integer *tlvls, integer *curlvl,
integer *curpbm, integer *prmptr, integer *perm, integer *givptr,
integer *givcol, real *givnum, real *q, integer *qptr, real *z__,
real *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, curr;
extern /* Subroutine */ int srot_(integer *, real *, integer *, real *,
integer *, real *, real *);
integer bsiz1, bsiz2, psiz1, psiz2, zptr1;
extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *,
real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, 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 */
/* ======= */
/* SLAEDA 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) REAL array, dimension (2, N lg N) */
/* Each number indicates the S value to be used in the */
/* corresponding Givens rotation. */
/* Q (input) REAL 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) REAL 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) REAL 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_("SLAEDA", &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((real) (qptr[curr + 1] - qptr[curr])) + .5f);
bsiz2 = (integer) (sqrt((real) (qptr[curr + 2] - qptr[curr + 1])) + .5f);
i__1 = mid - bsiz1 - 1;
for (k = 1; k <= i__1; ++k) {
z__[k] = 0.f;
/* L10: */
}
scopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], &
c__1);
scopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1);
i__1 = *n;
for (k = mid + bsiz2; k <= i__1; ++k) {
z__[k] = 0.f;
/* 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__) {
srot_(&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__) {
srot_(&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((real) (qptr[curr + 1] - qptr[curr])) + .5f);
bsiz2 = (integer) (sqrt((real) (qptr[curr + 2] - qptr[curr + 1])) +
.5f);
if (bsiz1 > 0) {
sgemv_("T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, &
ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1);
}
i__2 = psiz1 - bsiz1;
scopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1);
if (bsiz2 > 0) {
sgemv_("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;
scopy_(&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 SLAEDA */
} /* slaeda_ */