521 lines
15 KiB
C
521 lines
15 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 complex c_b1 = {1.f,0.f};
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static blasint c__1 = 1;
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/** CHETRF_REC2 computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kau fman diagonal pivoting method
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*
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* This routine is a minor modification of LAPACK's clahef.
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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_chetrf_rec2(char *uplo, blasint *n, blasint *
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nb, blasint *kb, complex *a, blasint *lda, blasint *ipiv, complex *w,
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int *ldw, blasint *info, ftnlen uplo_len)
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{
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/* System generated locals */
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blasint a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
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float r__1, r__2, r__3, r__4;
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complex q__1, q__2, q__3, q__4;
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/* Builtin functions */
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double sqrt(double), r_imag(complex *);
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void r_cnjg(complex *, complex *), c_div(complex *, complex *, complex *);
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/* Local variables */
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static blasint j, k;
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static float t, r1;
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static complex d11, d21, d22;
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static blasint 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 */ blasint cgemv_(char *, blasint *, blasint *, complex *
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, complex *, blasint *, complex *, blasint *, complex *, complex *
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, blasint *, ftnlen), ccopy_(int *, complex *, blasint *,
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complex *, blasint *), cswap_(int *, complex *, blasint *,
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complex *, blasint *);
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static blasint kstep;
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static float absakk;
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extern /* Subroutine */ blasint clacgv_(int *, complex *, blasint *);
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extern blasint icamax_(int *, complex *, blasint *);
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extern /* Subroutine */ blasint csscal_(int *, float *, complex *, int
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*);
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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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kstep = 1;
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i__1 = k - 1;
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ccopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
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i__1 = k + kw * w_dim1;
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i__2 = k + k * a_dim1;
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r__1 = a[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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if (k < *n) {
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i__1 = *n - k;
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q__1.r = -1.f, q__1.i = -0.f;
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cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1],
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lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
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w_dim1 + 1], &c__1, (ftnlen)12);
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i__1 = k + kw * w_dim1;
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i__2 = k + kw * w_dim1;
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r__1 = w[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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}
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i__1 = k + kw * w_dim1;
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absakk = (r__1 = w[i__1].r, dabs(r__1));
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if (k > 1) {
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i__1 = k - 1;
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imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
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i__1 = imax + kw * w_dim1;
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colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
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+ kw * w_dim1]), dabs(r__2));
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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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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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r__1 = a[i__2].r;
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a[i__1].r = r__1, a[i__1].i = 0.f;
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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 - 1;
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ccopy_(&i__1, &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 = imax + (kw - 1) * w_dim1;
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i__2 = imax + imax * a_dim1;
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r__1 = a[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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i__1 = k - imax;
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ccopy_(&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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i__1 = k - imax;
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clacgv_(&i__1, &w[imax + 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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q__1.r = -1.f, q__1.i = -0.f;
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cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) *
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a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
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ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
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ftnlen)12);
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i__1 = imax + (kw - 1) * w_dim1;
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i__2 = imax + (kw - 1) * w_dim1;
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r__1 = w[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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}
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i__1 = k - imax;
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jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
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&c__1);
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i__1 = jmax + (kw - 1) * w_dim1;
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rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
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jmax + (kw - 1) * w_dim1]), dabs(r__2));
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if (imax > 1) {
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i__1 = imax - 1;
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jmax = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
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/* Computing MAX */
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i__1 = jmax + (kw - 1) * w_dim1;
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r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
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r__2 = r_imag(&w[jmax + (kw - 1) * w_dim1]), dabs(
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r__2));
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rowmax = dmax(r__3,r__4);
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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(complicated condition) */ {
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i__1 = imax + (kw - 1) * w_dim1;
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if ((r__1 = w[i__1].r, dabs(r__1)) >= alpha * rowmax) {
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kp = imax;
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ccopy_(&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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}
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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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i__1 = kp + kp * a_dim1;
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i__2 = kk + kk * a_dim1;
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r__1 = a[i__2].r;
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a[i__1].r = r__1, a[i__1].i = 0.f;
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i__1 = kk - 1 - kp;
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ccopy_(&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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i__1 = kk - 1 - kp;
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clacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
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if (kp > 1) {
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i__1 = kp - 1;
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ccopy_(&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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cswap_(&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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cswap_(&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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ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
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c__1);
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if (k > 1) {
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i__1 = k + k * a_dim1;
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r1 = 1.f / a[i__1].r;
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i__1 = k - 1;
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csscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
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i__1 = k - 1;
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clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
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}
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} else {
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if (k > 2) {
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i__1 = k - 1 + kw * w_dim1;
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d21.r = w[i__1].r, d21.i = w[i__1].i;
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r_cnjg(&q__2, &d21);
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c_div(&q__1, &w[k + kw * w_dim1], &q__2);
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d11.r = q__1.r, d11.i = q__1.i;
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c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
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d22.r = q__1.r, d22.i = q__1.i;
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q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
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d22.i + d11.i * d22.r;
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t = 1.f / (q__1.r - 1.f);
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q__2.r = t, q__2.i = 0.f;
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c_div(&q__1, &q__2, &d21);
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d21.r = q__1.r, d21.i = q__1.i;
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i__1 = k - 2;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j + (k - 1) * a_dim1;
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i__3 = j + (kw - 1) * w_dim1;
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q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
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q__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
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.r;
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i__4 = j + kw * w_dim1;
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q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
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.i;
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q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
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d21.r * q__2.i + d21.i * q__2.r;
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a[i__2].r = q__1.r, a[i__2].i = q__1.i;
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i__2 = j + k * a_dim1;
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r_cnjg(&q__2, &d21);
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i__3 = j + kw * w_dim1;
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q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
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q__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
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.r;
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i__4 = j + (kw - 1) * w_dim1;
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q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
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.i;
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q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i =
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q__2.r * q__3.i + q__2.i * q__3.r;
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a[i__2].r = q__1.r, a[i__2].i = q__1.i;
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/* L20: */
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}
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}
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i__1 = k - 1 + (k - 1) * a_dim1;
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i__2 = k - 1 + (kw - 1) * w_dim1;
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a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
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i__1 = k - 1 + k * a_dim1;
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i__2 = k - 1 + kw * w_dim1;
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a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
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i__1 = k + k * a_dim1;
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i__2 = k + kw * w_dim1;
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a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
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i__1 = k - 1;
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clacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
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i__1 = k - 2;
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clacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
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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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cswap_(&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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kstep = 1;
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i__1 = k + k * w_dim1;
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i__2 = k + k * a_dim1;
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r__1 = a[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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if (k < *n) {
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i__1 = *n - k;
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ccopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k *
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w_dim1], &c__1);
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}
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i__1 = *n - k + 1;
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i__2 = k - 1;
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q__1.r = -1.f, q__1.i = -0.f;
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cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &w[k
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+ w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
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i__1 = k + k * w_dim1;
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i__2 = k + k * w_dim1;
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r__1 = w[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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i__1 = k + k * w_dim1;
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absakk = (r__1 = w[i__1].r, dabs(r__1));
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if (k < *n) {
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i__1 = *n - k;
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imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
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i__1 = imax + k * w_dim1;
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colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax
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+ k * w_dim1]), dabs(r__2));
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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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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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r__1 = a[i__2].r;
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a[i__1].r = r__1, a[i__1].i = 0.f;
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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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ccopy_(&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 = imax - k;
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clacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
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i__1 = imax + (k + 1) * w_dim1;
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i__2 = imax + imax * a_dim1;
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r__1 = a[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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if (imax < *n) {
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i__1 = *n - imax;
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ccopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[
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imax + 1 + (k + 1) * w_dim1], &c__1);
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}
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i__1 = *n - k + 1;
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i__2 = k - 1;
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q__1.r = -1.f, q__1.i = -0.f;
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cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1],
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lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
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w_dim1], &c__1, (ftnlen)12);
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i__1 = imax + (k + 1) * w_dim1;
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i__2 = imax + (k + 1) * w_dim1;
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r__1 = w[i__2].r;
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w[i__1].r = r__1, w[i__1].i = 0.f;
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i__1 = imax - k;
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jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
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;
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i__1 = jmax + (k + 1) * w_dim1;
|
|
rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[
|
|
jmax + (k + 1) * w_dim1]), dabs(r__2));
|
|
if (imax < *n) {
|
|
i__1 = *n - imax;
|
|
jmax = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) *
|
|
w_dim1], &c__1);
|
|
/* Computing MAX */
|
|
i__1 = jmax + (k + 1) * w_dim1;
|
|
r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + (
|
|
r__2 = r_imag(&w[jmax + (k + 1) * w_dim1]), dabs(
|
|
r__2));
|
|
rowmax = dmax(r__3,r__4);
|
|
}
|
|
if (absakk >= alpha * colmax * (colmax / rowmax)) {
|
|
kp = k;
|
|
} else /* if(complicated condition) */ {
|
|
i__1 = imax + (k + 1) * w_dim1;
|
|
if ((r__1 = w[i__1].r, dabs(r__1)) >= alpha * rowmax) {
|
|
kp = imax;
|
|
i__1 = *n - k + 1;
|
|
ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
|
|
k * w_dim1], &c__1);
|
|
} else {
|
|
kp = imax;
|
|
kstep = 2;
|
|
}
|
|
}
|
|
}
|
|
kk = k + kstep - 1;
|
|
if (kp != kk) {
|
|
i__1 = kp + kp * a_dim1;
|
|
i__2 = kk + kk * a_dim1;
|
|
r__1 = a[i__2].r;
|
|
a[i__1].r = r__1, a[i__1].i = 0.f;
|
|
i__1 = kp - kk - 1;
|
|
ccopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
|
|
1) * a_dim1], lda);
|
|
i__1 = kp - kk - 1;
|
|
clacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
|
|
if (kp < *n) {
|
|
i__1 = *n - kp;
|
|
ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
|
|
+ kp * a_dim1], &c__1);
|
|
}
|
|
if (k > 1) {
|
|
i__1 = k - 1;
|
|
cswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
|
|
}
|
|
cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
|
|
}
|
|
if (kstep == 1) {
|
|
i__1 = *n - k + 1;
|
|
ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
|
|
c__1);
|
|
if (k < *n) {
|
|
i__1 = k + k * a_dim1;
|
|
r1 = 1.f / a[i__1].r;
|
|
i__1 = *n - k;
|
|
csscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
|
|
i__1 = *n - k;
|
|
clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
|
|
}
|
|
} else {
|
|
if (k < *n - 1) {
|
|
i__1 = k + 1 + k * w_dim1;
|
|
d21.r = w[i__1].r, d21.i = w[i__1].i;
|
|
c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
|
|
d11.r = q__1.r, d11.i = q__1.i;
|
|
r_cnjg(&q__2, &d21);
|
|
c_div(&q__1, &w[k + k * w_dim1], &q__2);
|
|
d22.r = q__1.r, d22.i = q__1.i;
|
|
q__1.r = d11.r * d22.r - d11.i * d22.i, q__1.i = d11.r *
|
|
d22.i + d11.i * d22.r;
|
|
t = 1.f / (q__1.r - 1.f);
|
|
q__2.r = t, q__2.i = 0.f;
|
|
c_div(&q__1, &q__2, &d21);
|
|
d21.r = q__1.r, d21.i = q__1.i;
|
|
i__1 = *n;
|
|
for (j = k + 2; j <= i__1; ++j) {
|
|
i__2 = j + k * a_dim1;
|
|
r_cnjg(&q__2, &d21);
|
|
i__3 = j + k * w_dim1;
|
|
q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
|
|
q__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
|
|
.r;
|
|
i__4 = j + (k + 1) * w_dim1;
|
|
q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4]
|
|
.i;
|
|
q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i =
|
|
q__2.r * q__3.i + q__2.i * q__3.r;
|
|
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
|
|
i__2 = j + (k + 1) * a_dim1;
|
|
i__3 = j + (k + 1) * w_dim1;
|
|
q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
|
|
q__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
|
|
.r;
|
|
i__4 = j + k * w_dim1;
|
|
q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4]
|
|
.i;
|
|
q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i =
|
|
d21.r * q__2.i + d21.i * q__2.r;
|
|
a[i__2].r = q__1.r, a[i__2].i = q__1.i;
|
|
/* L80: */
|
|
}
|
|
}
|
|
i__1 = k + k * a_dim1;
|
|
i__2 = k + k * w_dim1;
|
|
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
|
|
i__1 = k + 1 + k * a_dim1;
|
|
i__2 = k + 1 + k * w_dim1;
|
|
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
|
|
i__1 = k + 1 + (k + 1) * a_dim1;
|
|
i__2 = k + 1 + (k + 1) * w_dim1;
|
|
a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
|
|
i__1 = *n - k;
|
|
clacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
|
|
i__1 = *n - k - 1;
|
|
clacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1);
|
|
}
|
|
}
|
|
if (kstep == 1) {
|
|
ipiv[k] = kp;
|
|
} else {
|
|
ipiv[k] = -kp;
|
|
ipiv[k + 1] = -kp;
|
|
}
|
|
k += kstep;
|
|
goto L70;
|
|
L90:
|
|
j = k - 1;
|
|
L120:
|
|
jj = j;
|
|
jp = ipiv[j];
|
|
if (jp < 0) {
|
|
jp = -jp;
|
|
--j;
|
|
}
|
|
--j;
|
|
if (jp != jj && j >= 1) {
|
|
cswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
|
|
}
|
|
if (j >= 1) {
|
|
goto L120;
|
|
}
|
|
*kb = k - 1;
|
|
}
|
|
return;
|
|
}
|