|
- /* -- translated by f2c (version 20100827).
- 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"
-
- /* Table of constant values */
-
- static doublecomplex c_b1 = {1.,0.};
- static blasint c__1 = 1;
-
- /** ZSYTRF_ROOK_REC2 computes a partial factorization of a complex symmetric matrix using the bounded Bunch-K aufman ("rook") diagonal pivoting method.
- *
- * This routine is a minor modification of LAPACK's zlasyf_rook.
- * It serves as an unblocked kernel in the recursive algorithms.
- * The blocked BLAS Level 3 updates were removed and moved to the
- * recursive algorithm.
- * */
- /* Subroutine */ void RELAPACK_zsytrf_rook_rec2(char *uplo, blasint *n,
- int *nb, blasint *kb, doublecomplex *a, blasint *lda, blasint *
- ipiv, doublecomplex *w, blasint *ldw, blasint *info, ftnlen uplo_len)
- {
- /* System generated locals */
- blasint a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
- double d__1, d__2;
- doublecomplex z__1, z__2, z__3, z__4;
-
- /* Builtin functions */
- double sqrt(double), d_imag(doublecomplex *);
- void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
-
- /* Local variables */
- static blasint j, k, p;
- static doublecomplex t, r1, d11, d12, d21, d22;
- static blasint ii, jj, kk, kp, kw, jp1, jp2, kkw;
- static logical done;
- static blasint imax, jmax;
- static double alpha;
- extern logical lsame_(char *, char *, ftnlen, ftnlen);
- static double dtemp, sfmin;
- extern /* Subroutine */ blasint zscal_(int *, doublecomplex *,
- doublecomplex *, blasint *);
- static blasint itemp, kstep;
- extern /* Subroutine */ blasint zgemv_(char *, blasint *, blasint *,
- doublecomplex *, doublecomplex *, blasint *, doublecomplex *,
- blasint *, doublecomplex *, doublecomplex *, blasint *, ftnlen),
- zcopy_(int *, doublecomplex *, blasint *, doublecomplex *,
- blasint *), zswap_(int *, doublecomplex *, blasint *,
- doublecomplex *, blasint *);
- extern double dlamch_(char *, ftnlen);
- static double absakk, colmax;
- extern blasint izamax_(int *, doublecomplex *, blasint *);
- static double rowmax;
-
- /* Parameter adjustments */
- a_dim1 = *lda;
- a_offset = 1 + a_dim1;
- a -= a_offset;
- --ipiv;
- w_dim1 = *ldw;
- w_offset = 1 + w_dim1;
- w -= w_offset;
-
- /* Function Body */
- *info = 0;
- alpha = (sqrt(17.) + 1.) / 8.;
- sfmin = dlamch_("S", (ftnlen)1);
- if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
- k = *n;
- L10:
- kw = *nb + k - *n;
- if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
- goto L30;
- }
- kstep = 1;
- p = k;
- zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
- if (k < *n) {
- i__1 = *n - k;
- z__1.r = -1., z__1.i = -0.;
- zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
- lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
- w_dim1 + 1], &c__1, (ftnlen)12);
- }
- i__1 = k + kw * w_dim1;
- absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + kw *
- w_dim1]), abs(d__2));
- if (k > 1) {
- i__1 = k - 1;
- imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
- i__1 = imax + kw * w_dim1;
- colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
- kw * w_dim1]), abs(d__2));
- } else {
- colmax = 0.;
- }
- if (max(absakk,colmax) == 0.) {
- if (*info == 0) {
- *info = k;
- }
- kp = k;
- zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
- } else {
- if (! (absakk < alpha * colmax)) {
- kp = k;
- } else {
- done = FALSE_;
- L12:
- zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
- w_dim1 + 1], &c__1);
- i__1 = k - imax;
- zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
- 1 + (kw - 1) * w_dim1], &c__1);
- if (k < *n) {
- i__1 = *n - k;
- z__1.r = -1., z__1.i = -0.;
- zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
- a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
- ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
- ftnlen)12);
- }
- if (imax != k) {
- i__1 = k - imax;
- jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) *
- w_dim1], &c__1);
- i__1 = jmax + (kw - 1) * w_dim1;
- rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
- w[jmax + (kw - 1) * w_dim1]), abs(d__2));
- } else {
- rowmax = 0.;
- }
- if (imax > 1) {
- i__1 = imax - 1;
- itemp = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
- i__1 = itemp + (kw - 1) * w_dim1;
- dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
- itemp + (kw - 1) * w_dim1]), abs(d__2));
- if (dtemp > rowmax) {
- rowmax = dtemp;
- jmax = itemp;
- }
- }
- i__1 = imax + (kw - 1) * w_dim1;
- if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
- + (kw - 1) * w_dim1]), abs(d__2)) < alpha * rowmax)) {
- kp = imax;
- zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
- w_dim1 + 1], &c__1);
- done = TRUE_;
- } else if (p == jmax || rowmax <= colmax) {
- kp = imax;
- kstep = 2;
- done = TRUE_;
- } else {
- p = imax;
- colmax = rowmax;
- imax = jmax;
- zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
- w_dim1 + 1], &c__1);
- }
- if (! done) {
- goto L12;
- }
- }
- kk = k - kstep + 1;
- kkw = *nb + kk - *n;
- if (kstep == 2 && p != k) {
- i__1 = k - p;
- zcopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) *
- a_dim1], lda);
- zcopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &
- c__1);
- i__1 = *n - k + 1;
- zswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1],
- lda);
- i__1 = *n - kk + 1;
- zswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1],
- ldw);
- }
- if (kp != kk) {
- i__1 = kp + k * a_dim1;
- i__2 = kk + k * a_dim1;
- a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
- i__1 = k - 1 - kp;
- zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
- 1) * a_dim1], lda);
- zcopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &
- c__1);
- i__1 = *n - kk + 1;
- zswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1],
- lda);
- i__1 = *n - kk + 1;
- zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
- w_dim1], ldw);
- }
- if (kstep == 1) {
- zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
- c__1);
- if (k > 1) {
- i__1 = k + k * a_dim1;
- if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
- k * a_dim1]), abs(d__2)) >= sfmin) {
- z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
- r1.r = z__1.r, r1.i = z__1.i;
- i__1 = k - 1;
- zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
- } else /* if(complicated condition) */ {
- i__1 = k + k * a_dim1;
- if (a[i__1].r != 0. || a[i__1].i != 0.) {
- i__1 = k - 1;
- for (ii = 1; ii <= i__1; ++ii) {
- i__2 = ii + k * a_dim1;
- z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
- a_dim1]);
- a[i__2].r = z__1.r, a[i__2].i = z__1.i;
- /* L14: */
- }
- }
- }
- }
- } else {
- if (k > 2) {
- i__1 = k - 1 + kw * w_dim1;
- d12.r = w[i__1].r, d12.i = w[i__1].i;
- z_div(&z__1, &w[k + kw * w_dim1], &d12);
- d11.r = z__1.r, d11.i = z__1.i;
- z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d12);
- d22.r = z__1.r, d22.i = z__1.i;
- z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
- d22.i + d11.i * d22.r;
- z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
- z_div(&z__1, &c_b1, &z__2);
- t.r = z__1.r, t.i = z__1.i;
- i__1 = k - 2;
- for (j = 1; j <= i__1; ++j) {
- i__2 = j + (k - 1) * a_dim1;
- i__3 = j + (kw - 1) * w_dim1;
- z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
- z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
- .r;
- i__4 = j + kw * w_dim1;
- z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
- .i;
- z_div(&z__2, &z__3, &d12);
- z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
- z__2.i + t.i * z__2.r;
- a[i__2].r = z__1.r, a[i__2].i = z__1.i;
- i__2 = j + k * a_dim1;
- i__3 = j + kw * w_dim1;
- z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
- z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
- .r;
- i__4 = j + (kw - 1) * w_dim1;
- z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
- .i;
- z_div(&z__2, &z__3, &d12);
- z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
- z__2.i + t.i * z__2.r;
- a[i__2].r = z__1.r, a[i__2].i = z__1.i;
- /* L20: */
- }
- }
- i__1 = k - 1 + (k - 1) * a_dim1;
- i__2 = k - 1 + (kw - 1) * 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 + kw * w_dim1;
- a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
- i__1 = k + k * a_dim1;
- i__2 = k + kw * w_dim1;
- a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
- }
- }
- if (kstep == 1) {
- ipiv[k] = kp;
- } else {
- ipiv[k] = -p;
- ipiv[k - 1] = -kp;
- }
- k -= kstep;
- goto L10;
- L30:
- j = k + 1;
- L60:
- kstep = 1;
- jp1 = 1;
- jj = j;
- jp2 = ipiv[j];
- if (jp2 < 0) {
- jp2 = -jp2;
- ++j;
- jp1 = -ipiv[j];
- kstep = 2;
- }
- ++j;
- if (jp2 != jj && j <= *n) {
- i__1 = *n - j + 1;
- zswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
- ;
- }
- jj = j - 1;
- if (jp1 != jj && kstep == 2) {
- i__1 = *n - j + 1;
- zswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda)
- ;
- }
- if (j <= *n) {
- goto L60;
- }
- *kb = *n - k;
- } else {
- k = 1;
- L70:
- if ((k >= *nb && *nb < *n) || k > *n) {
- goto L90;
- }
- kstep = 1;
- p = k;
- i__1 = *n - k + 1;
- zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
- if (k > 1) {
- i__1 = *n - k + 1;
- i__2 = k - 1;
- z__1.r = -1., z__1.i = -0.;
- zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &
- w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (
- ftnlen)12);
- }
- i__1 = k + k * w_dim1;
- absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + k *
- w_dim1]), abs(d__2));
- if (k < *n) {
- i__1 = *n - k;
- imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
- i__1 = imax + k * w_dim1;
- colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
- k * w_dim1]), abs(d__2));
- } else {
- colmax = 0.;
- }
- if (max(absakk,colmax) == 0.) {
- if (*info == 0) {
- *info = k;
- }
- kp = k;
- i__1 = *n - k + 1;
- zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
- c__1);
- } else {
- if (! (absakk < alpha * colmax)) {
- kp = k;
- } else {
- done = FALSE_;
- L72:
- i__1 = imax - k;
- zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
- w_dim1], &c__1);
- i__1 = *n - imax + 1;
- zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
- 1) * w_dim1], &c__1);
- if (k > 1) {
- i__1 = *n - k + 1;
- i__2 = k - 1;
- z__1.r = -1., z__1.i = -0.;
- zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1]
- , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k +
- 1) * w_dim1], &c__1, (ftnlen)12);
- }
- if (imax != k) {
- i__1 = imax - k;
- jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &
- c__1);
- i__1 = jmax + (k + 1) * w_dim1;
- rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&
- w[jmax + (k + 1) * w_dim1]), abs(d__2));
- } else {
- rowmax = 0.;
- }
- if (imax < *n) {
- i__1 = *n - imax;
- itemp = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
- w_dim1], &c__1);
- i__1 = itemp + (k + 1) * w_dim1;
- dtemp = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
- itemp + (k + 1) * w_dim1]), abs(d__2));
- if (dtemp > rowmax) {
- rowmax = dtemp;
- jmax = itemp;
- }
- }
- i__1 = imax + (k + 1) * w_dim1;
- if (! ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax
- + (k + 1) * w_dim1]), abs(d__2)) < alpha * rowmax)) {
- kp = imax;
- i__1 = *n - k + 1;
- zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
- w_dim1], &c__1);
- done = TRUE_;
- } else if (p == jmax || rowmax <= colmax) {
- kp = imax;
- kstep = 2;
- done = TRUE_;
- } else {
- p = imax;
- colmax = rowmax;
- imax = jmax;
- i__1 = *n - k + 1;
- zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k *
- w_dim1], &c__1);
- }
- if (! done) {
- goto L72;
- }
- }
- kk = k + kstep - 1;
- if (kstep == 2 && p != k) {
- i__1 = p - k;
- zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1],
- lda);
- i__1 = *n - p + 1;
- zcopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], &
- c__1);
- zswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda);
- zswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw);
- }
- if (kp != kk) {
- i__1 = kp + k * a_dim1;
- i__2 = kk + k * a_dim1;
- a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
- i__1 = kp - k - 1;
- zcopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1)
- * a_dim1], lda);
- i__1 = *n - kp + 1;
- zcopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp *
- a_dim1], &c__1);
- zswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
- zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
- }
- if (kstep == 1) {
- i__1 = *n - k + 1;
- zcopy_(&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;
- if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k +
- k * a_dim1]), abs(d__2)) >= sfmin) {
- z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
- r1.r = z__1.r, r1.i = z__1.i;
- i__1 = *n - k;
- zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
- } else /* if(complicated condition) */ {
- i__1 = k + k * a_dim1;
- if (a[i__1].r != 0. || a[i__1].i != 0.) {
- i__1 = *n;
- for (ii = k + 1; ii <= i__1; ++ii) {
- i__2 = ii + k * a_dim1;
- z_div(&z__1, &a[ii + k * a_dim1], &a[k + k *
- a_dim1]);
- a[i__2].r = z__1.r, a[i__2].i = z__1.i;
- /* L74: */
- }
- }
- }
- }
- } else {
- if (k < *n - 1) {
- i__1 = k + 1 + k * w_dim1;
- d21.r = w[i__1].r, d21.i = w[i__1].i;
- z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
- d11.r = z__1.r, d11.i = z__1.i;
- z_div(&z__1, &w[k + k * w_dim1], &d21);
- d22.r = z__1.r, d22.i = z__1.i;
- z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
- d22.i + d11.i * d22.r;
- z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
- z_div(&z__1, &c_b1, &z__2);
- t.r = z__1.r, t.i = z__1.i;
- i__1 = *n;
- for (j = k + 2; j <= i__1; ++j) {
- i__2 = j + k * a_dim1;
- i__3 = j + k * w_dim1;
- z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
- z__4.i = d11.r * w[i__3].i + d11.i * w[i__3]
- .r;
- i__4 = j + (k + 1) * w_dim1;
- z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
- .i;
- z_div(&z__2, &z__3, &d21);
- z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
- z__2.i + t.i * z__2.r;
- a[i__2].r = z__1.r, a[i__2].i = z__1.i;
- i__2 = j + (k + 1) * a_dim1;
- i__3 = j + (k + 1) * w_dim1;
- z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
- z__4.i = d22.r * w[i__3].i + d22.i * w[i__3]
- .r;
- i__4 = j + k * w_dim1;
- z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4]
- .i;
- z_div(&z__2, &z__3, &d21);
- z__1.r = t.r * z__2.r - t.i * z__2.i, z__1.i = t.r *
- z__2.i + t.i * z__2.r;
- a[i__2].r = z__1.r, a[i__2].i = z__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;
- }
- }
- if (kstep == 1) {
- ipiv[k] = kp;
- } else {
- ipiv[k] = -p;
- ipiv[k + 1] = -kp;
- }
- k += kstep;
- goto L70;
- L90:
- j = k - 1;
- L120:
- kstep = 1;
- jp1 = 1;
- jj = j;
- jp2 = ipiv[j];
- if (jp2 < 0) {
- jp2 = -jp2;
- --j;
- jp1 = -ipiv[j];
- kstep = 2;
- }
- --j;
- if (jp2 != jj && j >= 1) {
- zswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda);
- }
- jj = j + 1;
- if (jp1 != jj && kstep == 2) {
- zswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda);
- }
- if (j >= 1) {
- goto L120;
- }
- *kb = k - 1;
- }
- return;
- }
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