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lammps/lib/linalg/dbdsqr.cpp

523 lines
18 KiB
C++

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"
static doublereal c_b15 = -.125;
static integer c__1 = 1;
static doublereal c_b49 = 1.;
static doublereal c_b72 = -1.;
int dbdsqr_(char *uplo, integer *n, integer *ncvt, integer *nru, integer *ncc, doublereal *d__,
doublereal *e, doublereal *vt, integer *ldvt, doublereal *u, integer *ldu,
doublereal *c__, integer *ldc, doublereal *work, integer *info, ftnlen uplo_len)
{
integer c_dim1, c_offset, u_dim1, u_offset, vt_dim1, vt_offset, i__1, i__2;
doublereal d__1, d__2, d__3, d__4;
double pow_lmp_dd(doublereal *, doublereal *), sqrt(doublereal), d_lmp_sign(doublereal *, doublereal *);
integer iterdivn;
doublereal f, g, h__;
integer i__, j, m;
doublereal r__;
integer maxitdivn;
doublereal cs;
integer ll;
doublereal sn, mu;
integer nm1, nm12, nm13, lll;
doublereal eps, sll, tol, abse;
integer idir;
doublereal abss;
integer oldm;
doublereal cosl;
integer isub, iter;
doublereal unfl, sinl, cosr, smin, smax, sinr;
extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *),
dlas2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *),
dscal_(integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
doublereal oldcs;
extern int dlasr_(char *, char *, char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, ftnlen, ftnlen, ftnlen);
integer oldll;
doublereal shift, sigmn, oldsn;
extern int dswap_(integer *, doublereal *, integer *, doublereal *, integer *);
doublereal sminl, sigmx;
logical lower;
extern int dlasq1_(integer *, doublereal *, doublereal *, doublereal *, integer *),
dlasv2_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *);
extern doublereal dlamch_(char *, ftnlen);
extern int dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *),
xerbla_(char *, integer *, ftnlen);
doublereal sminoa, thresh;
logical rotate;
doublereal tolmul;
--d__;
--e;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
*info = 0;
lower = lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1);
if (!lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && !lower) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ncvt < 0) {
*info = -3;
} else if (*nru < 0) {
*info = -4;
} else if (*ncc < 0) {
*info = -5;
} else if (*ncvt == 0 && *ldvt < 1 || *ncvt > 0 && *ldvt < max(1, *n)) {
*info = -9;
} else if (*ldu < max(1, *nru)) {
*info = -11;
} else if (*ncc == 0 && *ldc < 1 || *ncc > 0 && *ldc < max(1, *n)) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DBDSQR", &i__1, (ftnlen)6);
return 0;
}
if (*n == 0) {
return 0;
}
if (*n == 1) {
goto L160;
}
rotate = *ncvt > 0 || *nru > 0 || *ncc > 0;
if (!rotate) {
dlasq1_(n, &d__[1], &e[1], &work[1], info);
if (*info != 2) {
return 0;
}
*info = 0;
}
nm1 = *n - 1;
nm12 = nm1 + nm1;
nm13 = nm12 + nm1;
idir = 0;
eps = dlamch_((char *)"Epsilon", (ftnlen)7);
unfl = dlamch_((char *)"Safe minimum", (ftnlen)12);
if (lower) {
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
dlartg_(&d__[i__], &e[i__], &cs, &sn, &r__);
d__[i__] = r__;
e[i__] = sn * d__[i__ + 1];
d__[i__ + 1] = cs * d__[i__ + 1];
work[i__] = cs;
work[nm1 + i__] = sn;
}
if (*nru > 0) {
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, n, &work[1], &work[*n], &u[u_offset], ldu, (ftnlen)1,
(ftnlen)1, (ftnlen)1);
}
if (*ncc > 0) {
dlasr_((char *)"L", (char *)"V", (char *)"F", n, ncc, &work[1], &work[*n], &c__[c_offset], ldc, (ftnlen)1,
(ftnlen)1, (ftnlen)1);
}
}
d__3 = 100., d__4 = pow_lmp_dd(&eps, &c_b15);
d__1 = 10., d__2 = min(d__3, d__4);
tolmul = max(d__1, d__2);
tol = tolmul * eps;
smax = 0.;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__2 = smax, d__3 = (d__1 = d__[i__], abs(d__1));
smax = max(d__2, d__3);
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
d__2 = smax, d__3 = (d__1 = e[i__], abs(d__1));
smax = max(d__2, d__3);
}
sminl = 0.;
if (tol >= 0.) {
sminoa = abs(d__[1]);
if (sminoa == 0.) {
goto L50;
}
mu = sminoa;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
mu = (d__2 = d__[i__], abs(d__2)) * (mu / (mu + (d__1 = e[i__ - 1], abs(d__1))));
sminoa = min(sminoa, mu);
if (sminoa == 0.) {
goto L50;
}
}
L50:
sminoa /= sqrt((doublereal)(*n));
d__1 = tol * sminoa, d__2 = *n * (*n * unfl) * 6;
thresh = max(d__1, d__2);
} else {
d__1 = abs(tol) * smax, d__2 = *n * (*n * unfl) * 6;
thresh = max(d__1, d__2);
}
maxitdivn = *n * 6;
iterdivn = 0;
iter = -1;
oldll = -1;
oldm = -1;
m = *n;
L60:
if (m <= 1) {
goto L160;
}
if (iter >= *n) {
iter -= *n;
++iterdivn;
if (iterdivn >= maxitdivn) {
goto L200;
}
}
if (tol < 0. && (d__1 = d__[m], abs(d__1)) <= thresh) {
d__[m] = 0.;
}
smax = (d__1 = d__[m], abs(d__1));
smin = smax;
i__1 = m - 1;
for (lll = 1; lll <= i__1; ++lll) {
ll = m - lll;
abss = (d__1 = d__[ll], abs(d__1));
abse = (d__1 = e[ll], abs(d__1));
if (tol < 0. && abss <= thresh) {
d__[ll] = 0.;
}
if (abse <= thresh) {
goto L80;
}
smin = min(smin, abss);
d__1 = max(smax, abss);
smax = max(d__1, abse);
}
ll = 0;
goto L90;
L80:
e[ll] = 0.;
if (ll == m - 1) {
--m;
goto L60;
}
L90:
++ll;
if (ll == m - 1) {
dlasv2_(&d__[m - 1], &e[m - 1], &d__[m], &sigmn, &sigmx, &sinr, &cosr, &sinl, &cosl);
d__[m - 1] = sigmx;
e[m - 1] = 0.;
d__[m] = sigmn;
if (*ncvt > 0) {
drot_(ncvt, &vt[m - 1 + vt_dim1], ldvt, &vt[m + vt_dim1], ldvt, &cosr, &sinr);
}
if (*nru > 0) {
drot_(nru, &u[(m - 1) * u_dim1 + 1], &c__1, &u[m * u_dim1 + 1], &c__1, &cosl, &sinl);
}
if (*ncc > 0) {
drot_(ncc, &c__[m - 1 + c_dim1], ldc, &c__[m + c_dim1], ldc, &cosl, &sinl);
}
m += -2;
goto L60;
}
if (ll > oldm || m < oldll) {
if ((d__1 = d__[ll], abs(d__1)) >= (d__2 = d__[m], abs(d__2))) {
idir = 1;
} else {
idir = 2;
}
}
if (idir == 1) {
if ((d__2 = e[m - 1], abs(d__2)) <= abs(tol) * (d__1 = d__[m], abs(d__1)) ||
tol < 0. && (d__3 = e[m - 1], abs(d__3)) <= thresh) {
e[m - 1] = 0.;
goto L60;
}
if (tol >= 0.) {
mu = (d__1 = d__[ll], abs(d__1));
sminl = mu;
i__1 = m - 1;
for (lll = ll; lll <= i__1; ++lll) {
if ((d__1 = e[lll], abs(d__1)) <= tol * mu) {
e[lll] = 0.;
goto L60;
}
mu = (d__2 = d__[lll + 1], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1))));
sminl = min(sminl, mu);
}
}
} else {
if ((d__2 = e[ll], abs(d__2)) <= abs(tol) * (d__1 = d__[ll], abs(d__1)) ||
tol < 0. && (d__3 = e[ll], abs(d__3)) <= thresh) {
e[ll] = 0.;
goto L60;
}
if (tol >= 0.) {
mu = (d__1 = d__[m], abs(d__1));
sminl = mu;
i__1 = ll;
for (lll = m - 1; lll >= i__1; --lll) {
if ((d__1 = e[lll], abs(d__1)) <= tol * mu) {
e[lll] = 0.;
goto L60;
}
mu = (d__2 = d__[lll], abs(d__2)) * (mu / (mu + (d__1 = e[lll], abs(d__1))));
sminl = min(sminl, mu);
}
}
}
oldll = ll;
oldm = m;
d__1 = eps, d__2 = tol * .01;
if (tol >= 0. && *n * tol * (sminl / smax) <= max(d__1, d__2)) {
shift = 0.;
} else {
if (idir == 1) {
sll = (d__1 = d__[ll], abs(d__1));
dlas2_(&d__[m - 1], &e[m - 1], &d__[m], &shift, &r__);
} else {
sll = (d__1 = d__[m], abs(d__1));
dlas2_(&d__[ll], &e[ll], &d__[ll + 1], &shift, &r__);
}
if (sll > 0.) {
d__1 = shift / sll;
if (d__1 * d__1 < eps) {
shift = 0.;
}
}
}
iter = iter + m - ll;
if (shift == 0.) {
if (idir == 1) {
cs = 1.;
oldcs = 1.;
i__1 = m - 1;
for (i__ = ll; i__ <= i__1; ++i__) {
d__1 = d__[i__] * cs;
dlartg_(&d__1, &e[i__], &cs, &sn, &r__);
if (i__ > ll) {
e[i__ - 1] = oldsn * r__;
}
d__1 = oldcs * r__;
d__2 = d__[i__ + 1] * sn;
dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]);
work[i__ - ll + 1] = cs;
work[i__ - ll + 1 + nm1] = sn;
work[i__ - ll + 1 + nm12] = oldcs;
work[i__ - ll + 1 + nm13] = oldsn;
}
h__ = d__[m] * cs;
d__[m] = h__ * oldcs;
e[m - 1] = h__ * oldsn;
if (*ncvt > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*nru > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1],
&u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*ncc > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1],
&c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if ((d__1 = e[m - 1], abs(d__1)) <= thresh) {
e[m - 1] = 0.;
}
} else {
cs = 1.;
oldcs = 1.;
i__1 = ll + 1;
for (i__ = m; i__ >= i__1; --i__) {
d__1 = d__[i__] * cs;
dlartg_(&d__1, &e[i__ - 1], &cs, &sn, &r__);
if (i__ < m) {
e[i__] = oldsn * r__;
}
d__1 = oldcs * r__;
d__2 = d__[i__ - 1] * sn;
dlartg_(&d__1, &d__2, &oldcs, &oldsn, &d__[i__]);
work[i__ - ll] = cs;
work[i__ - ll + nm1] = -sn;
work[i__ - ll + nm12] = oldcs;
work[i__ - ll + nm13] = -oldsn;
}
h__ = d__[ll] * cs;
d__[ll] = h__ * oldcs;
e[ll] = h__ * oldsn;
if (*ncvt > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1],
&vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*nru > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*ncc > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if ((d__1 = e[ll], abs(d__1)) <= thresh) {
e[ll] = 0.;
}
}
} else {
if (idir == 1) {
f = ((d__1 = d__[ll], abs(d__1)) - shift) *
(d_lmp_sign(&c_b49, &d__[ll]) + shift / d__[ll]);
g = e[ll];
i__1 = m - 1;
for (i__ = ll; i__ <= i__1; ++i__) {
dlartg_(&f, &g, &cosr, &sinr, &r__);
if (i__ > ll) {
e[i__ - 1] = r__;
}
f = cosr * d__[i__] + sinr * e[i__];
e[i__] = cosr * e[i__] - sinr * d__[i__];
g = sinr * d__[i__ + 1];
d__[i__ + 1] = cosr * d__[i__ + 1];
dlartg_(&f, &g, &cosl, &sinl, &r__);
d__[i__] = r__;
f = cosl * e[i__] + sinl * d__[i__ + 1];
d__[i__ + 1] = cosl * d__[i__ + 1] - sinl * e[i__];
if (i__ < m - 1) {
g = sinl * e[i__ + 1];
e[i__ + 1] = cosl * e[i__ + 1];
}
work[i__ - ll + 1] = cosr;
work[i__ - ll + 1 + nm1] = sinr;
work[i__ - ll + 1 + nm12] = cosl;
work[i__ - ll + 1 + nm13] = sinl;
}
e[m - 1] = f;
if (*ncvt > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncvt, &work[1], &work[*n], &vt[ll + vt_dim1], ldvt,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*nru > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"R", (char *)"V", (char *)"F", nru, &i__1, &work[nm12 + 1], &work[nm13 + 1],
&u[ll * u_dim1 + 1], ldu, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*ncc > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"F", &i__1, ncc, &work[nm12 + 1], &work[nm13 + 1],
&c__[ll + c_dim1], ldc, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if ((d__1 = e[m - 1], abs(d__1)) <= thresh) {
e[m - 1] = 0.;
}
} else {
f = ((d__1 = d__[m], abs(d__1)) - shift) * (d_lmp_sign(&c_b49, &d__[m]) + shift / d__[m]);
g = e[m - 1];
i__1 = ll + 1;
for (i__ = m; i__ >= i__1; --i__) {
dlartg_(&f, &g, &cosr, &sinr, &r__);
if (i__ < m) {
e[i__] = r__;
}
f = cosr * d__[i__] + sinr * e[i__ - 1];
e[i__ - 1] = cosr * e[i__ - 1] - sinr * d__[i__];
g = sinr * d__[i__ - 1];
d__[i__ - 1] = cosr * d__[i__ - 1];
dlartg_(&f, &g, &cosl, &sinl, &r__);
d__[i__] = r__;
f = cosl * e[i__ - 1] + sinl * d__[i__ - 1];
d__[i__ - 1] = cosl * d__[i__ - 1] - sinl * e[i__ - 1];
if (i__ > ll + 1) {
g = sinl * e[i__ - 2];
e[i__ - 2] = cosl * e[i__ - 2];
}
work[i__ - ll] = cosr;
work[i__ - ll + nm1] = -sinr;
work[i__ - ll + nm12] = cosl;
work[i__ - ll + nm13] = -sinl;
}
e[ll] = f;
if ((d__1 = e[ll], abs(d__1)) <= thresh) {
e[ll] = 0.;
}
if (*ncvt > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncvt, &work[nm12 + 1], &work[nm13 + 1],
&vt[ll + vt_dim1], ldvt, (ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*nru > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"R", (char *)"V", (char *)"B", nru, &i__1, &work[1], &work[*n], &u[ll * u_dim1 + 1], ldu,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
if (*ncc > 0) {
i__1 = m - ll + 1;
dlasr_((char *)"L", (char *)"V", (char *)"B", &i__1, ncc, &work[1], &work[*n], &c__[ll + c_dim1], ldc,
(ftnlen)1, (ftnlen)1, (ftnlen)1);
}
}
}
goto L60;
L160:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (d__[i__] < 0.) {
d__[i__] = -d__[i__];
if (*ncvt > 0) {
dscal_(ncvt, &c_b72, &vt[i__ + vt_dim1], ldvt);
}
}
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
isub = 1;
smin = d__[1];
i__2 = *n + 1 - i__;
for (j = 2; j <= i__2; ++j) {
if (d__[j] <= smin) {
isub = j;
smin = d__[j];
}
}
if (isub != *n + 1 - i__) {
d__[isub] = d__[*n + 1 - i__];
d__[*n + 1 - i__] = smin;
if (*ncvt > 0) {
dswap_(ncvt, &vt[isub + vt_dim1], ldvt, &vt[*n + 1 - i__ + vt_dim1], ldvt);
}
if (*nru > 0) {
dswap_(nru, &u[isub * u_dim1 + 1], &c__1, &u[(*n + 1 - i__) * u_dim1 + 1], &c__1);
}
if (*ncc > 0) {
dswap_(ncc, &c__[isub + c_dim1], ldc, &c__[*n + 1 - i__ + c_dim1], ldc);
}
}
}
goto L220;
L200:
*info = 0;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
if (e[i__] != 0.) {
++(*info);
}
}
L220:
return 0;
}
#ifdef __cplusplus
}
#endif