Files
lammps/lib/linalg/zlahef.cpp
2024-11-09 04:14:11 -05:00

521 lines
22 KiB
C++

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"
static doublecomplex c_b1 = {1., 0.};
static integer c__1 = 1;
int zlahef_(char *uplo, integer *n, integer *nb, integer *kb, doublecomplex *a, integer *lda,
integer *ipiv, doublecomplex *w, integer *ldw, integer *info, ftnlen uplo_len)
{
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4, i__5;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2, z__3, z__4;
double sqrt(doublereal), d_lmp_imag(doublecomplex *);
void d_lmp_cnjg(doublecomplex *, doublecomplex *),
z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *);
integer j, k;
doublereal t, r1;
doublecomplex d11, d21, d22;
integer jb, jj, kk, jp, kp, kw, kkw, imax, jmax;
doublereal alpha;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, ftnlen, ftnlen);
integer kstep;
extern int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *,
ftnlen),
zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *),
zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *);
doublereal absakk;
extern int zdscal_(integer *, doublereal *, doublecomplex *, integer *);
doublereal colmax;
extern int zlacgv_(integer *, doublecomplex *, integer *);
extern integer izamax_(integer *, doublecomplex *, integer *);
doublereal rowmax;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
w_dim1 = *ldw;
w_offset = 1 + w_dim1;
w -= w_offset;
*info = 0;
alpha = (sqrt(17.) + 1.) / 8.;
if (lsame_(uplo, (char *)"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;
i__1 = k - 1;
zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
i__1 = k + kw * w_dim1;
i__2 = k + k * a_dim1;
d__1 = a[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
if (k < *n) {
i__1 = *n - k;
z__1.r = -1., z__1.i = -0.;
zgemv_((char *)"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;
i__2 = k + kw * w_dim1;
d__1 = w[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
}
i__1 = k + kw * w_dim1;
absakk = (d__1 = w[i__1].r, abs(d__1));
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_lmp_imag(&w[imax + kw * w_dim1]), abs(d__2));
} else {
colmax = 0.;
}
if (max(absakk, colmax) == 0.) {
if (*info == 0) {
*info = k;
}
kp = k;
i__1 = k + k * a_dim1;
i__2 = k + k * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
} else {
if (absakk >= alpha * colmax) {
kp = k;
} else {
i__1 = imax - 1;
zcopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
i__1 = imax + (kw - 1) * w_dim1;
i__2 = imax + imax * a_dim1;
d__1 = a[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
i__1 = k - imax;
zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax + 1 + (kw - 1) * w_dim1],
&c__1);
i__1 = k - imax;
zlacgv_(&i__1, &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_((char *)"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);
i__1 = imax + (kw - 1) * w_dim1;
i__2 = imax + (kw - 1) * w_dim1;
d__1 = w[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
}
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_lmp_imag(&w[jmax + (kw - 1) * w_dim1]), abs(d__2));
if (imax > 1) {
i__1 = imax - 1;
jmax = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
i__1 = jmax + (kw - 1) * w_dim1;
d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) +
(d__2 = d_lmp_imag(&w[jmax + (kw - 1) * w_dim1]), abs(d__2));
rowmax = max(d__3, d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
kp = k;
} else {
i__1 = imax + (kw - 1) * w_dim1;
if ((d__1 = w[i__1].r, abs(d__1)) >= alpha * rowmax) {
kp = imax;
zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
} else {
kp = imax;
kstep = 2;
}
}
}
kk = k - kstep + 1;
kkw = *nb + kk - *n;
if (kp != kk) {
i__1 = kp + kp * a_dim1;
i__2 = kk + kk * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
i__1 = kk - 1 - kp;
zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda);
i__1 = kk - 1 - kp;
zlacgv_(&i__1, &a[kp + (kp + 1) * a_dim1], lda);
if (kp > 1) {
i__1 = kp - 1;
zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
}
if (k < *n) {
i__1 = *n - k;
zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k + 1) * 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;
r1 = 1. / a[i__1].r;
i__1 = k - 1;
zdscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
i__1 = k - 1;
zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
}
} else {
if (k > 2) {
i__1 = k - 1 + kw * w_dim1;
d21.r = w[i__1].r, d21.i = w[i__1].i;
d_lmp_cnjg(&z__2, &d21);
z_lmp_div(&z__1, &w[k + kw * w_dim1], &z__2);
d11.r = z__1.r, d11.i = z__1.i;
z_lmp_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
d22.r = z__1.r, d22.i = z__1.i;
z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r * d22.i + d11.i * d22.r;
t = 1. / (z__1.r - 1.);
z__2.r = t, z__2.i = 0.;
z_lmp_div(&z__1, &z__2, &d21);
d21.r = z__1.r, d21.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__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
z__3.i = d11.r * w[i__3].i + d11.i * w[i__3].r;
i__4 = j + kw * w_dim1;
z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i,
z__1.i = d21.r * z__2.i + d21.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
i__2 = j + k * a_dim1;
d_lmp_cnjg(&z__2, &d21);
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__1.r = z__2.r * z__3.r - z__2.i * z__3.i,
z__1.i = z__2.r * z__3.i + z__2.i * z__3.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
}
}
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;
i__1 = k - 1;
zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1);
i__1 = k - 2;
zlacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
}
}
if (kstep == 1) {
ipiv[k] = kp;
} else {
ipiv[k] = -kp;
ipiv[k - 1] = -kp;
}
k -= kstep;
goto L10;
L30:
i__1 = -(*nb);
for (j = (k - 1) / *nb * *nb + 1; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
i__2 = *nb, i__3 = k - j + 1;
jb = min(i__2, i__3);
i__2 = j + jb - 1;
for (jj = j; jj <= i__2; ++jj) {
i__3 = jj + jj * a_dim1;
i__4 = jj + jj * a_dim1;
d__1 = a[i__4].r;
a[i__3].r = d__1, a[i__3].i = 0.;
i__3 = jj - j + 1;
i__4 = *n - k;
z__1.r = -1., z__1.i = -0.;
zgemv_((char *)"No transpose", &i__3, &i__4, &z__1, &a[j + (k + 1) * a_dim1], lda,
&w[jj + (kw + 1) * w_dim1], ldw, &c_b1, &a[j + jj * a_dim1], &c__1,
(ftnlen)12);
i__3 = jj + jj * a_dim1;
i__4 = jj + jj * a_dim1;
d__1 = a[i__4].r;
a[i__3].r = d__1, a[i__3].i = 0.;
}
i__2 = j - 1;
i__3 = *n - k;
z__1.r = -1., z__1.i = -0.;
zgemm_((char *)"No transpose", (char *)"Transpose", &i__2, &jb, &i__3, &z__1, &a[(k + 1) * a_dim1 + 1],
lda, &w[j + (kw + 1) * w_dim1], ldw, &c_b1, &a[j * a_dim1 + 1], lda, (ftnlen)12,
(ftnlen)9);
}
j = k + 1;
L60:
jj = j;
jp = ipiv[j];
if (jp < 0) {
jp = -jp;
++j;
}
++j;
if (jp != jj && j <= *n) {
i__1 = *n - j + 1;
zswap_(&i__1, &a[jp + 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;
i__1 = k + k * w_dim1;
i__2 = k + k * a_dim1;
d__1 = a[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
if (k < *n) {
i__1 = *n - k;
zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k * w_dim1], &c__1);
}
i__1 = *n - k + 1;
i__2 = k - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_((char *)"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;
i__2 = k + k * w_dim1;
d__1 = w[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
i__1 = k + k * w_dim1;
absakk = (d__1 = w[i__1].r, abs(d__1));
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_lmp_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 = k + k * a_dim1;
i__2 = k + k * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
} else {
if (absakk >= alpha * colmax) {
kp = k;
} else {
i__1 = imax - k;
zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) * w_dim1], &c__1);
i__1 = imax - k;
zlacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1);
i__1 = imax + (k + 1) * w_dim1;
i__2 = imax + imax * a_dim1;
d__1 = a[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
if (imax < *n) {
i__1 = *n - imax;
zcopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1,
&w[imax + 1 + (k + 1) * w_dim1], &c__1);
}
i__1 = *n - k + 1;
i__2 = k - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_((char *)"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);
i__1 = imax + (k + 1) * w_dim1;
i__2 = imax + (k + 1) * w_dim1;
d__1 = w[i__2].r;
w[i__1].r = d__1, w[i__1].i = 0.;
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_lmp_imag(&w[jmax + (k + 1) * w_dim1]), abs(d__2));
if (imax < *n) {
i__1 = *n - imax;
jmax = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) * w_dim1], &c__1);
i__1 = jmax + (k + 1) * w_dim1;
d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) +
(d__2 = d_lmp_imag(&w[jmax + (k + 1) * w_dim1]), abs(d__2));
rowmax = max(d__3, d__4);
}
if (absakk >= alpha * colmax * (colmax / rowmax)) {
kp = k;
} else {
i__1 = imax + (k + 1) * w_dim1;
if ((d__1 = w[i__1].r, abs(d__1)) >= 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);
} else {
kp = imax;
kstep = 2;
}
}
}
kk = k + kstep - 1;
if (kp != kk) {
i__1 = kp + kp * a_dim1;
i__2 = kk + kk * a_dim1;
d__1 = a[i__2].r;
a[i__1].r = d__1, a[i__1].i = 0.;
i__1 = kp - kk - 1;
zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk + 1) * a_dim1], lda);
i__1 = kp - kk - 1;
zlacgv_(&i__1, &a[kp + (kk + 1) * a_dim1], lda);
if (kp < *n) {
i__1 = *n - kp;
zcopy_(&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;
zswap_(&i__1, &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;
r1 = 1. / a[i__1].r;
i__1 = *n - k;
zdscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
i__1 = *n - k;
zlacgv_(&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;
z_lmp_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
d11.r = z__1.r, d11.i = z__1.i;
d_lmp_cnjg(&z__2, &d21);
z_lmp_div(&z__1, &w[k + k * w_dim1], &z__2);
d22.r = z__1.r, d22.i = z__1.i;
z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r * d22.i + d11.i * d22.r;
t = 1. / (z__1.r - 1.);
z__2.r = t, z__2.i = 0.;
z_lmp_div(&z__1, &z__2, &d21);
d21.r = z__1.r, d21.i = z__1.i;
i__1 = *n;
for (j = k + 2; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
d_lmp_cnjg(&z__2, &d21);
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__1.r = z__2.r * z__3.r - z__2.i * z__3.i,
z__1.i = z__2.r * z__3.i + z__2.i * z__3.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__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
z__3.i = d22.r * w[i__3].i + d22.i * w[i__3].r;
i__4 = j + k * w_dim1;
z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i;
z__1.r = d21.r * z__2.r - d21.i * z__2.i,
z__1.i = d21.r * z__2.i + d21.i * z__2.r;
a[i__2].r = z__1.r, a[i__2].i = z__1.i;
}
}
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;
zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
i__1 = *n - k - 1;
zlacgv_(&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:
i__1 = *n;
i__2 = *nb;
for (j = k; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
i__3 = *nb, i__4 = *n - j + 1;
jb = min(i__3, i__4);
i__3 = j + jb - 1;
for (jj = j; jj <= i__3; ++jj) {
i__4 = jj + jj * a_dim1;
i__5 = jj + jj * a_dim1;
d__1 = a[i__5].r;
a[i__4].r = d__1, a[i__4].i = 0.;
i__4 = j + jb - jj;
i__5 = k - 1;
z__1.r = -1., z__1.i = -0.;
zgemv_((char *)"No transpose", &i__4, &i__5, &z__1, &a[jj + a_dim1], lda, &w[jj + w_dim1],
ldw, &c_b1, &a[jj + jj * a_dim1], &c__1, (ftnlen)12);
i__4 = jj + jj * a_dim1;
i__5 = jj + jj * a_dim1;
d__1 = a[i__5].r;
a[i__4].r = d__1, a[i__4].i = 0.;
}
if (j + jb <= *n) {
i__3 = *n - j - jb + 1;
i__4 = k - 1;
z__1.r = -1., z__1.i = -0.;
zgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, &z__1, &a[j + jb + a_dim1],
lda, &w[j + w_dim1], ldw, &c_b1, &a[j + jb + j * a_dim1], lda, (ftnlen)12,
(ftnlen)9);
}
}
j = k - 1;
L120:
jj = j;
jp = ipiv[j];
if (jp < 0) {
jp = -jp;
--j;
}
--j;
if (jp != jj && j >= 1) {
zswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
}
if (j > 1) {
goto L120;
}
*kb = k - 1;
}
return 0;
}
#ifdef __cplusplus
}
#endif