440 lines
18 KiB
C++
440 lines
18 KiB
C++
#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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static integer c__1 = 1;
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int zhetf2_(char *uplo, integer *n, doublecomplex *a, integer *lda, integer *ipiv, integer *info,
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ftnlen uplo_len)
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{
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
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doublereal d__1, d__2, d__3, d__4;
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doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
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double sqrt(doublereal), d_lmp_imag(doublecomplex *);
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void d_lmp_cnjg(doublecomplex *, doublecomplex *);
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doublereal d__;
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integer i__, j, k;
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doublecomplex t;
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doublereal r1, d11;
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doublecomplex d12;
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doublereal d22;
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doublecomplex d21;
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integer kk, kp;
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doublecomplex wk;
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doublereal tt;
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doublecomplex wkm1, wkp1;
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integer imax, jmax;
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extern int zher_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *,
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integer *, ftnlen);
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doublereal alpha;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer kstep;
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logical upper;
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extern int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *);
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extern doublereal dlapy2_(doublereal *, doublereal *);
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doublereal absakk;
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extern logical disnan_(doublereal *);
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extern int xerbla_(char *, integer *, ftnlen),
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zdscal_(integer *, doublereal *, doublecomplex *, integer *);
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doublereal colmax;
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extern integer izamax_(integer *, doublecomplex *, integer *);
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doublereal rowmax;
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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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*info = 0;
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upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
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if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1, *n)) {
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*info = -4;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"ZHETF2", &i__1, (ftnlen)6);
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return 0;
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}
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alpha = (sqrt(17.) + 1.) / 8.;
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if (upper) {
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k = *n;
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L10:
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if (k < 1) {
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goto L90;
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}
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kstep = 1;
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i__1 = k + k * a_dim1;
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absakk = (d__1 = a[i__1].r, abs(d__1));
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if (k > 1) {
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i__1 = k - 1;
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imax = izamax_(&i__1, &a[k * a_dim1 + 1], &c__1);
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i__1 = imax + k * a_dim1;
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colmax =
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(d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + k * a_dim1]), abs(d__2));
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} else {
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colmax = 0.;
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}
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if (max(absakk, colmax) == 0. || disnan_(&absakk)) {
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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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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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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 = k - imax;
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jmax = imax + izamax_(&i__1, &a[imax + (imax + 1) * a_dim1], lda);
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i__1 = imax + jmax * a_dim1;
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rowmax = (d__1 = a[i__1].r, abs(d__1)) +
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(d__2 = d_lmp_imag(&a[imax + jmax * a_dim1]), abs(d__2));
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if (imax > 1) {
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i__1 = imax - 1;
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jmax = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
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i__1 = jmax + imax * a_dim1;
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d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) +
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(d__2 = d_lmp_imag(&a[jmax + imax * a_dim1]), abs(d__2));
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rowmax = max(d__3, d__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 {
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i__1 = imax + imax * a_dim1;
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if ((d__1 = a[i__1].r, abs(d__1)) >= alpha * rowmax) {
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kp = imax;
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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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if (kp != kk) {
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i__1 = kp - 1;
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zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
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i__1 = kk - 1;
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for (j = kp + 1; j <= i__1; ++j) {
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d_lmp_cnjg(&z__1, &a[j + kk * a_dim1]);
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t.r = z__1.r, t.i = z__1.i;
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i__2 = j + kk * a_dim1;
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d_lmp_cnjg(&z__1, &a[kp + j * a_dim1]);
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a[i__2].r = z__1.r, a[i__2].i = z__1.i;
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i__2 = kp + j * a_dim1;
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a[i__2].r = t.r, a[i__2].i = t.i;
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}
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i__1 = kp + kk * a_dim1;
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d_lmp_cnjg(&z__1, &a[kp + kk * a_dim1]);
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a[i__1].r = z__1.r, a[i__1].i = z__1.i;
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i__1 = kk + kk * a_dim1;
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r1 = a[i__1].r;
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i__1 = kk + kk * a_dim1;
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i__2 = kp + kp * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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i__1 = kp + kp * a_dim1;
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a[i__1].r = r1, a[i__1].i = 0.;
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if (kstep == 2) {
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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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i__1 = k - 1 + k * a_dim1;
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t.r = a[i__1].r, t.i = a[i__1].i;
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i__1 = k - 1 + k * a_dim1;
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i__2 = kp + k * a_dim1;
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a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
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i__1 = kp + k * a_dim1;
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a[i__1].r = t.r, a[i__1].i = t.i;
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}
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} else {
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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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if (kstep == 2) {
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i__1 = k - 1 + (k - 1) * a_dim1;
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i__2 = k - 1 + (k - 1) * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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}
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}
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if (kstep == 1) {
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i__1 = k + k * a_dim1;
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r1 = 1. / a[i__1].r;
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i__1 = k - 1;
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d__1 = -r1;
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zher_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1);
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i__1 = k - 1;
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zdscal_(&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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i__1 = k - 1 + k * a_dim1;
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d__1 = a[i__1].r;
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d__2 = d_lmp_imag(&a[k - 1 + k * a_dim1]);
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d__ = dlapy2_(&d__1, &d__2);
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i__1 = k - 1 + (k - 1) * a_dim1;
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d22 = a[i__1].r / d__;
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i__1 = k + k * a_dim1;
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d11 = a[i__1].r / d__;
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tt = 1. / (d11 * d22 - 1.);
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i__1 = k - 1 + k * a_dim1;
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z__1.r = a[i__1].r / d__, z__1.i = a[i__1].i / d__;
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d12.r = z__1.r, d12.i = z__1.i;
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d__ = tt / d__;
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for (j = k - 2; j >= 1; --j) {
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i__1 = j + (k - 1) * a_dim1;
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z__3.r = d11 * a[i__1].r, z__3.i = d11 * a[i__1].i;
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d_lmp_cnjg(&z__5, &d12);
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i__2 = j + k * a_dim1;
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z__4.r = z__5.r * a[i__2].r - z__5.i * a[i__2].i,
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z__4.i = z__5.r * a[i__2].i + z__5.i * a[i__2].r;
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z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
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z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i;
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wkm1.r = z__1.r, wkm1.i = z__1.i;
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i__1 = j + k * a_dim1;
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z__3.r = d22 * a[i__1].r, z__3.i = d22 * a[i__1].i;
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i__2 = j + (k - 1) * a_dim1;
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z__4.r = d12.r * a[i__2].r - d12.i * a[i__2].i,
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z__4.i = d12.r * a[i__2].i + d12.i * a[i__2].r;
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z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
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z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i;
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wk.r = z__1.r, wk.i = z__1.i;
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for (i__ = j; i__ >= 1; --i__) {
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i__1 = i__ + j * a_dim1;
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i__2 = i__ + j * a_dim1;
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i__3 = i__ + k * a_dim1;
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d_lmp_cnjg(&z__4, &wk);
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z__3.r = a[i__3].r * z__4.r - a[i__3].i * z__4.i,
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z__3.i = a[i__3].r * z__4.i + a[i__3].i * z__4.r;
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z__2.r = a[i__2].r - z__3.r, z__2.i = a[i__2].i - z__3.i;
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i__4 = i__ + (k - 1) * a_dim1;
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d_lmp_cnjg(&z__6, &wkm1);
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z__5.r = a[i__4].r * z__6.r - a[i__4].i * z__6.i,
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z__5.i = a[i__4].r * z__6.i + a[i__4].i * z__6.r;
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z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i;
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a[i__1].r = z__1.r, a[i__1].i = z__1.i;
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}
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i__1 = j + k * a_dim1;
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a[i__1].r = wk.r, a[i__1].i = wk.i;
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i__1 = j + (k - 1) * a_dim1;
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a[i__1].r = wkm1.r, a[i__1].i = wkm1.i;
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i__1 = j + j * a_dim1;
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i__2 = j + j * a_dim1;
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d__1 = a[i__2].r;
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z__1.r = d__1, z__1.i = 0.;
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a[i__1].r = z__1.r, a[i__1].i = z__1.i;
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}
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}
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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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} else {
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k = 1;
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L50:
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if (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 * a_dim1;
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absakk = (d__1 = a[i__1].r, abs(d__1));
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if (k < *n) {
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i__1 = *n - k;
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imax = k + izamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1);
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i__1 = imax + k * a_dim1;
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colmax =
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(d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + k * a_dim1]), abs(d__2));
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} else {
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colmax = 0.;
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}
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if (max(absakk, colmax) == 0. || disnan_(&absakk)) {
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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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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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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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jmax = k - 1 + izamax_(&i__1, &a[imax + k * a_dim1], lda);
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i__1 = imax + jmax * a_dim1;
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rowmax = (d__1 = a[i__1].r, abs(d__1)) +
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(d__2 = d_lmp_imag(&a[imax + jmax * a_dim1]), abs(d__2));
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if (imax < *n) {
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i__1 = *n - imax;
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jmax = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1);
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i__1 = jmax + imax * a_dim1;
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d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) +
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(d__2 = d_lmp_imag(&a[jmax + imax * a_dim1]), abs(d__2));
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rowmax = max(d__3, d__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 {
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i__1 = imax + imax * a_dim1;
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if ((d__1 = a[i__1].r, abs(d__1)) >= alpha * rowmax) {
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kp = imax;
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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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if (kp != kk) {
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if (kp < *n) {
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i__1 = *n - kp;
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zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1);
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}
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i__1 = kp - 1;
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for (j = kk + 1; j <= i__1; ++j) {
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d_lmp_cnjg(&z__1, &a[j + kk * a_dim1]);
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t.r = z__1.r, t.i = z__1.i;
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i__2 = j + kk * a_dim1;
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d_lmp_cnjg(&z__1, &a[kp + j * a_dim1]);
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a[i__2].r = z__1.r, a[i__2].i = z__1.i;
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i__2 = kp + j * a_dim1;
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a[i__2].r = t.r, a[i__2].i = t.i;
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}
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i__1 = kp + kk * a_dim1;
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d_lmp_cnjg(&z__1, &a[kp + kk * a_dim1]);
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a[i__1].r = z__1.r, a[i__1].i = z__1.i;
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i__1 = kk + kk * a_dim1;
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r1 = a[i__1].r;
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i__1 = kk + kk * a_dim1;
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i__2 = kp + kp * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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i__1 = kp + kp * a_dim1;
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a[i__1].r = r1, a[i__1].i = 0.;
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if (kstep == 2) {
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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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i__1 = k + 1 + k * a_dim1;
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t.r = a[i__1].r, t.i = a[i__1].i;
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i__1 = k + 1 + k * a_dim1;
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i__2 = kp + k * a_dim1;
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a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
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i__1 = kp + k * a_dim1;
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a[i__1].r = t.r, a[i__1].i = t.i;
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}
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} else {
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i__1 = k + k * a_dim1;
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i__2 = k + k * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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if (kstep == 2) {
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i__1 = k + 1 + (k + 1) * a_dim1;
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i__2 = k + 1 + (k + 1) * a_dim1;
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d__1 = a[i__2].r;
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a[i__1].r = d__1, a[i__1].i = 0.;
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}
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}
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if (kstep == 1) {
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if (k < *n) {
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i__1 = k + k * a_dim1;
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r1 = 1. / a[i__1].r;
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i__1 = *n - k;
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d__1 = -r1;
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zher_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &c__1,
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&a[k + 1 + (k + 1) * a_dim1], lda, (ftnlen)1);
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i__1 = *n - k;
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zdscal_(&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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i__1 = k + 1 + k * a_dim1;
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d__1 = a[i__1].r;
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d__2 = d_lmp_imag(&a[k + 1 + k * a_dim1]);
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d__ = dlapy2_(&d__1, &d__2);
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i__1 = k + 1 + (k + 1) * a_dim1;
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d11 = a[i__1].r / d__;
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i__1 = k + k * a_dim1;
|
|
d22 = a[i__1].r / d__;
|
|
tt = 1. / (d11 * d22 - 1.);
|
|
i__1 = k + 1 + k * a_dim1;
|
|
z__1.r = a[i__1].r / d__, z__1.i = a[i__1].i / d__;
|
|
d21.r = z__1.r, d21.i = z__1.i;
|
|
d__ = tt / d__;
|
|
i__1 = *n;
|
|
for (j = k + 2; j <= i__1; ++j) {
|
|
i__2 = j + k * a_dim1;
|
|
z__3.r = d11 * a[i__2].r, z__3.i = d11 * a[i__2].i;
|
|
i__3 = j + (k + 1) * a_dim1;
|
|
z__4.r = d21.r * a[i__3].r - d21.i * a[i__3].i,
|
|
z__4.i = d21.r * a[i__3].i + d21.i * a[i__3].r;
|
|
z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
|
|
z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i;
|
|
wk.r = z__1.r, wk.i = z__1.i;
|
|
i__2 = j + (k + 1) * a_dim1;
|
|
z__3.r = d22 * a[i__2].r, z__3.i = d22 * a[i__2].i;
|
|
d_lmp_cnjg(&z__5, &d21);
|
|
i__3 = j + k * a_dim1;
|
|
z__4.r = z__5.r * a[i__3].r - z__5.i * a[i__3].i,
|
|
z__4.i = z__5.r * a[i__3].i + z__5.i * a[i__3].r;
|
|
z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i;
|
|
z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i;
|
|
wkp1.r = z__1.r, wkp1.i = z__1.i;
|
|
i__2 = *n;
|
|
for (i__ = j; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * a_dim1;
|
|
i__4 = i__ + j * a_dim1;
|
|
i__5 = i__ + k * a_dim1;
|
|
d_lmp_cnjg(&z__4, &wk);
|
|
z__3.r = a[i__5].r * z__4.r - a[i__5].i * z__4.i,
|
|
z__3.i = a[i__5].r * z__4.i + a[i__5].i * z__4.r;
|
|
z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i - z__3.i;
|
|
i__6 = i__ + (k + 1) * a_dim1;
|
|
d_lmp_cnjg(&z__6, &wkp1);
|
|
z__5.r = a[i__6].r * z__6.r - a[i__6].i * z__6.i,
|
|
z__5.i = a[i__6].r * z__6.i + a[i__6].i * z__6.r;
|
|
z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i;
|
|
a[i__3].r = z__1.r, a[i__3].i = z__1.i;
|
|
}
|
|
i__2 = j + k * a_dim1;
|
|
a[i__2].r = wk.r, a[i__2].i = wk.i;
|
|
i__2 = j + (k + 1) * a_dim1;
|
|
a[i__2].r = wkp1.r, a[i__2].i = wkp1.i;
|
|
i__2 = j + j * a_dim1;
|
|
i__3 = j + j * a_dim1;
|
|
d__1 = a[i__3].r;
|
|
z__1.r = d__1, z__1.i = 0.;
|
|
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (kstep == 1) {
|
|
ipiv[k] = kp;
|
|
} else {
|
|
ipiv[k] = -kp;
|
|
ipiv[k + 1] = -kp;
|
|
}
|
|
k += kstep;
|
|
goto L50;
|
|
}
|
|
L90:
|
|
return 0;
|
|
}
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|