352 lines
9.4 KiB
C
352 lines
9.4 KiB
C
/* -- translated by f2c (version 20100827).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* Table of constant values */
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static int c__1 = 1;
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static float c_b8 = -1.f;
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static float c_b9 = 1.f;
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/** SSYTRF_REC2 computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
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*
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* This routine is a minor modification of LAPACK's slasyf.
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* It serves as an unblocked kernel in the recursive algorithms.
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* The blocked BLAS Level 3 updates were removed and moved to the
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* recursive algorithm.
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* */
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/* Subroutine */ void RELAPACK_ssytrf_rec2(char *uplo, int *n, int *
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nb, int *kb, float *a, int *lda, int *ipiv, float *w,
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int *ldw, int *info, ftnlen uplo_len)
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{
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/* System generated locals */
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int a_dim1, a_offset, w_dim1, w_offset, i__1, i__2;
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float r__1, r__2, r__3;
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/* Builtin functions */
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double sqrt(double);
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/* Local variables */
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static int j, k;
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static float t, r1, d11, d21, d22;
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static int jj, kk, jp, kp, kw, kkw, imax, jmax;
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static float alpha;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int sscal_(int *, float *, float *, int *),
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sgemv_(char *, int *, int *, float *, float *, int *,
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float *, int *, float *, float *, int *, ftnlen);
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static int kstep;
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extern /* Subroutine */ int scopy_(int *, float *, int *, float *,
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int *), sswap_(int *, float *, int *, float *, int *
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);
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static float absakk;
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extern int isamax_(int *, float *, int *);
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static float colmax, rowmax;
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--ipiv;
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w_dim1 = *ldw;
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w_offset = 1 + w_dim1;
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w -= w_offset;
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/* Function Body */
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*info = 0;
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alpha = (sqrt(17.f) + 1.f) / 8.f;
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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k = *n;
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L10:
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kw = *nb + k - *n;
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if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
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goto L30;
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}
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scopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
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if (k < *n) {
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i__1 = *n - k;
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sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1],
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lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b9, &w[kw *
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w_dim1 + 1], &c__1, (ftnlen)12);
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}
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kstep = 1;
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absakk = (r__1 = w[k + kw * w_dim1], dabs(r__1));
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if (k > 1) {
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i__1 = k - 1;
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imax = isamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
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colmax = (r__1 = w[imax + kw * w_dim1], dabs(r__1));
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} else {
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colmax = 0.f;
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}
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if (dmax(absakk,colmax) == 0.f) {
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if (*info == 0) {
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*info = k;
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}
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kp = k;
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} else {
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if (absakk >= alpha * colmax) {
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kp = k;
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} else {
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scopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
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w_dim1 + 1], &c__1);
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i__1 = k - imax;
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scopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
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1 + (kw - 1) * w_dim1], &c__1);
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if (k < *n) {
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i__1 = *n - k;
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sgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) *
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a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
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ldw, &c_b9, &w[(kw - 1) * w_dim1 + 1], &c__1, (
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ftnlen)12);
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}
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i__1 = k - imax;
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jmax = imax + isamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
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&c__1);
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rowmax = (r__1 = w[jmax + (kw - 1) * w_dim1], dabs(r__1));
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if (imax > 1) {
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i__1 = imax - 1;
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jmax = isamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
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/* Computing MAX */
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r__2 = rowmax, r__3 = (r__1 = w[jmax + (kw - 1) * w_dim1],
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dabs(r__1));
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rowmax = dmax(r__2,r__3);
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}
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if (absakk >= alpha * colmax * (colmax / rowmax)) {
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kp = k;
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} else if ((r__1 = w[imax + (kw - 1) * w_dim1], dabs(r__1)) >=
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alpha * rowmax) {
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kp = imax;
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scopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
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w_dim1 + 1], &c__1);
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} else {
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kp = imax;
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kstep = 2;
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}
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}
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kk = k - kstep + 1;
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kkw = *nb + kk - *n;
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if (kp != kk) {
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a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
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i__1 = kk - 1 - kp;
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scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
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1) * a_dim1], lda);
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if (kp > 1) {
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i__1 = kp - 1;
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scopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
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+ 1], &c__1);
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}
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if (k < *n) {
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i__1 = *n - k;
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sswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
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+ 1) * a_dim1], lda);
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}
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i__1 = *n - kk + 1;
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sswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
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w_dim1], ldw);
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}
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if (kstep == 1) {
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scopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
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c__1);
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r1 = 1.f / a[k + k * a_dim1];
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i__1 = k - 1;
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sscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
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} else {
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if (k > 2) {
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d21 = w[k - 1 + kw * w_dim1];
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d11 = w[k + kw * w_dim1] / d21;
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d22 = w[k - 1 + (kw - 1) * w_dim1] / d21;
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t = 1.f / (d11 * d22 - 1.f);
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d21 = t / d21;
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i__1 = k - 2;
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for (j = 1; j <= i__1; ++j) {
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a[j + (k - 1) * a_dim1] = d21 * (d11 * w[j + (kw - 1)
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* w_dim1] - w[j + kw * w_dim1]);
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a[j + k * a_dim1] = d21 * (d22 * w[j + kw * w_dim1] -
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w[j + (kw - 1) * w_dim1]);
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/* L20: */
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}
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}
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a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1];
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a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1];
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a[k + k * a_dim1] = w[k + kw * w_dim1];
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}
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}
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if (kstep == 1) {
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ipiv[k] = kp;
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} else {
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ipiv[k] = -kp;
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ipiv[k - 1] = -kp;
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}
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k -= kstep;
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goto L10;
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L30:
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j = k + 1;
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L60:
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jj = j;
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jp = ipiv[j];
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if (jp < 0) {
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jp = -jp;
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++j;
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}
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++j;
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if (jp != jj && j <= *n) {
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i__1 = *n - j + 1;
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sswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
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}
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if (j < *n) {
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goto L60;
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}
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*kb = *n - k;
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} else {
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k = 1;
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L70:
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if ((k >= *nb && *nb < *n) || k > *n) {
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goto L90;
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}
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i__1 = *n - k + 1;
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scopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
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i__1 = *n - k + 1;
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i__2 = k - 1;
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sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[k
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+ w_dim1], ldw, &c_b9, &w[k + k * w_dim1], &c__1, (ftnlen)12);
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kstep = 1;
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absakk = (r__1 = w[k + k * w_dim1], dabs(r__1));
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if (k < *n) {
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i__1 = *n - k;
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imax = k + isamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
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colmax = (r__1 = w[imax + k * w_dim1], dabs(r__1));
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} else {
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colmax = 0.f;
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}
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if (dmax(absakk,colmax) == 0.f) {
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if (*info == 0) {
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*info = k;
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}
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kp = k;
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} else {
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if (absakk >= alpha * colmax) {
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kp = k;
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} else {
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i__1 = imax - k;
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scopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
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w_dim1], &c__1);
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i__1 = *n - imax + 1;
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scopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
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1) * w_dim1], &c__1);
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i__1 = *n - k + 1;
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i__2 = k - 1;
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sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1],
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lda, &w[imax + w_dim1], ldw, &c_b9, &w[k + (k + 1) *
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w_dim1], &c__1, (ftnlen)12);
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i__1 = imax - k;
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jmax = k - 1 + isamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
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;
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rowmax = (r__1 = w[jmax + (k + 1) * w_dim1], dabs(r__1));
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if (imax < *n) {
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i__1 = *n - imax;
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jmax = imax + isamax_(&i__1, &w[imax + 1 + (k + 1) *
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w_dim1], &c__1);
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/* Computing MAX */
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r__2 = rowmax, r__3 = (r__1 = w[jmax + (k + 1) * w_dim1],
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dabs(r__1));
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rowmax = dmax(r__2,r__3);
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}
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if (absakk >= alpha * colmax * (colmax / rowmax)) {
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kp = k;
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} else if ((r__1 = w[imax + (k + 1) * w_dim1], dabs(r__1)) >=
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alpha * rowmax) {
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kp = imax;
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i__1 = *n - k + 1;
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scopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
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w_dim1], &c__1);
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} else {
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kp = imax;
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kstep = 2;
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}
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}
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kk = k + kstep - 1;
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if (kp != kk) {
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a[kp + kp * a_dim1] = a[kk + kk * a_dim1];
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i__1 = kp - kk - 1;
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scopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
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1) * a_dim1], lda);
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if (kp < *n) {
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i__1 = *n - kp;
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scopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
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+ kp * a_dim1], &c__1);
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}
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if (k > 1) {
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i__1 = k - 1;
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sswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
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}
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sswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
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}
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if (kstep == 1) {
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i__1 = *n - k + 1;
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scopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
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c__1);
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if (k < *n) {
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r1 = 1.f / a[k + k * a_dim1];
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i__1 = *n - k;
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sscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
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}
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} else {
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if (k < *n - 1) {
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d21 = w[k + 1 + k * w_dim1];
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d11 = w[k + 1 + (k + 1) * w_dim1] / d21;
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d22 = w[k + k * w_dim1] / d21;
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t = 1.f / (d11 * d22 - 1.f);
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d21 = t / d21;
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i__1 = *n;
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for (j = k + 2; j <= i__1; ++j) {
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a[j + k * a_dim1] = d21 * (d11 * w[j + k * w_dim1] -
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w[j + (k + 1) * w_dim1]);
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a[j + (k + 1) * a_dim1] = d21 * (d22 * w[j + (k + 1) *
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w_dim1] - w[j + k * w_dim1]);
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/* L80: */
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}
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}
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a[k + k * a_dim1] = w[k + k * w_dim1];
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a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1];
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a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1];
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}
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}
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if (kstep == 1) {
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ipiv[k] = kp;
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} else {
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ipiv[k] = -kp;
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ipiv[k + 1] = -kp;
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}
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k += kstep;
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goto L70;
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L90:
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j = k - 1;
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L120:
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jj = j;
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jp = ipiv[j];
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if (jp < 0) {
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jp = -jp;
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--j;
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}
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--j;
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if (jp != jj && j >= 1) {
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sswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
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}
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if (j > 1) {
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goto L120;
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}
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*kb = k - 1;
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}
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return;
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}
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