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1e8b2ad5a07fd32e63b55d7d52e1264829b96bb4
lammps/lib/linalg/dlasq5.cpp
Axel Kohlmeyer 1e8b2ad5a0 whitespace fixes
2022-12-28 13:48:43 -05:00

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/* fortran/dlasq5.f -- translated by f2c (version 20200916).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"
/* > \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLASQ5 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq5.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq5.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, */
/* DNM1, DNM2, IEEE, EPS ) */
/* .. Scalar Arguments .. */
/* LOGICAL IEEE */
/* INTEGER I0, N0, PP */
/* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION Z( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLASQ5 computes one dqds transform in ping-pong form, one */
/* > version for IEEE machines another for non IEEE machines. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] I0 */
/* > \verbatim */
/* > I0 is INTEGER */
/* > First index. */
/* > \endverbatim */
/* > */
/* > \param[in] N0 */
/* > \verbatim */
/* > N0 is INTEGER */
/* > Last index. */
/* > \endverbatim */
/* > */
/* > \param[in] Z */
/* > \verbatim */
/* > Z is DOUBLE PRECISION array, dimension ( 4*N ) */
/* > Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */
/* > an extra argument. */
/* > \endverbatim */
/* > */
/* > \param[in] PP */
/* > \verbatim */
/* > PP is INTEGER */
/* > PP=0 for ping, PP=1 for pong. */
/* > \endverbatim */
/* > */
/* > \param[in] TAU */
/* > \verbatim */
/* > TAU is DOUBLE PRECISION */
/* > This is the shift. */
/* > \endverbatim */
/* > */
/* > \param[in] SIGMA */
/* > \verbatim */
/* > SIGMA is DOUBLE PRECISION */
/* > This is the accumulated shift up to this step. */
/* > \endverbatim */
/* > */
/* > \param[out] DMIN */
/* > \verbatim */
/* > DMIN is DOUBLE PRECISION */
/* > Minimum value of d. */
/* > \endverbatim */
/* > */
/* > \param[out] DMIN1 */
/* > \verbatim */
/* > DMIN1 is DOUBLE PRECISION */
/* > Minimum value of d, excluding D( N0 ). */
/* > \endverbatim */
/* > */
/* > \param[out] DMIN2 */
/* > \verbatim */
/* > DMIN2 is DOUBLE PRECISION */
/* > Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
/* > \endverbatim */
/* > */
/* > \param[out] DN */
/* > \verbatim */
/* > DN is DOUBLE PRECISION */
/* > d(N0), the last value of d. */
/* > \endverbatim */
/* > */
/* > \param[out] DNM1 */
/* > \verbatim */
/* > DNM1 is DOUBLE PRECISION */
/* > d(N0-1). */
/* > \endverbatim */
/* > */
/* > \param[out] DNM2 */
/* > \verbatim */
/* > DNM2 is DOUBLE PRECISION */
/* > d(N0-2). */
/* > \endverbatim */
/* > */
/* > \param[in] IEEE */
/* > \verbatim */
/* > IEEE is LOGICAL */
/* > Flag for IEEE or non IEEE arithmetic. */
/* > \endverbatim */
/* > */
/* > \param[in] EPS */
/* > \verbatim */
/* > EPS is DOUBLE PRECISION */
/* > This is the value of epsilon used. */
/* > \endverbatim */
/* > */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup auxOTHERcomputational */
/* ===================================================================== */
/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *tau, doublereal *sigma, doublereal *dmin__,
doublereal *dmin1, doublereal *dmin2, doublereal *dn, doublereal *
dnm1, doublereal *dnm2, logical *ieee, doublereal *eps)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Local variables */
doublereal d__;
integer j4, j4p2;
doublereal emin, temp, dthresh;
/* -- LAPACK computational routine -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameter .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--z__;
/* Function Body */
if (*n0 - *i0 - 1 <= 0) {
return 0;
}
dthresh = *eps * (*sigma + *tau);
if (*tau < dthresh * .5) {
*tau = 0.;
}
if (*tau != 0.) {
j4 = (*i0 << 2) + *pp - 3;
emin = z__[j4 + 4];
d__ = z__[j4] - *tau;
*dmin__ = d__;
*dmin1 = -z__[j4];
if (*ieee) {
/* Code for IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
temp = z__[j4 + 1] / z__[j4 - 2];
d__ = d__ * temp - *tau;
*dmin__ = min(*dmin__,d__);
z__[j4] = z__[j4 - 1] * temp;
/* Computing MIN */
d__1 = z__[j4];
emin = min(d__1,emin);
/* L10: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
temp = z__[j4 + 2] / z__[j4 - 3];
d__ = d__ * temp - *tau;
*dmin__ = min(*dmin__,d__);
z__[j4 - 1] = z__[j4] * temp;
/* Computing MIN */
d__1 = z__[j4 - 1];
emin = min(d__1,emin);
/* L20: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dn);
} else {
/* Code for non IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
if (d__ < 0.) {
return 0;
} else {
z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]);
d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4];
emin = min(d__1,d__2);
/* L30: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
if (d__ < 0.) {
return 0;
} else {
z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]);
d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4 - 1];
emin = min(d__1,d__2);
/* L40: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
if (*dnm2 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
if (*dnm1 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dn);
}
} else {
/* This is the version that sets d's to zero if they are small enough */
j4 = (*i0 << 2) + *pp - 3;
emin = z__[j4 + 4];
d__ = z__[j4] - *tau;
*dmin__ = d__;
*dmin1 = -z__[j4];
if (*ieee) {
/* Code for IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
temp = z__[j4 + 1] / z__[j4 - 2];
d__ = d__ * temp - *tau;
if (d__ < dthresh) {
d__ = 0.;
}
*dmin__ = min(*dmin__,d__);
z__[j4] = z__[j4 - 1] * temp;
/* Computing MIN */
d__1 = z__[j4];
emin = min(d__1,emin);
/* L50: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
temp = z__[j4 + 2] / z__[j4 - 3];
d__ = d__ * temp - *tau;
if (d__ < dthresh) {
d__ = 0.;
}
*dmin__ = min(*dmin__,d__);
z__[j4 - 1] = z__[j4] * temp;
/* Computing MIN */
d__1 = z__[j4 - 1];
emin = min(d__1,emin);
/* L60: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dn);
} else {
/* Code for non IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
if (d__ < 0.) {
return 0;
} else {
z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]);
d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau;
}
if (d__ < dthresh) {
d__ = 0.;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4];
emin = min(d__1,d__2);
/* L70: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
if (d__ < 0.) {
return 0;
} else {
z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]);
d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau;
}
if (d__ < dthresh) {
d__ = 0.;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4 - 1];
emin = min(d__1,d__2);
/* L80: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
if (*dnm2 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
if (*dnm1 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dn);
}
}
z__[j4 + 2] = *dn;
z__[(*n0 << 2) - *pp] = emin;
return 0;
/* End of DLASQ5 */
} /* dlasq5_ */
#ifdef __cplusplus
}
#endif
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