Files
lammps/lib/linalg/dlaed8.cpp
Axel Kohlmeyer 1e8b2ad5a0 whitespace fixes
2022-12-28 13:48:43 -05:00

611 lines
19 KiB
C++

/* fortran/dlaed8.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"
/* Table of constant values */
static doublereal c_b3 = -1.;
static integer c__1 = 1;
/* > \brief \b DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original
matrix is dense. */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DLAED8 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed8.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed8.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed8.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, */
/* CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, */
/* GIVCOL, GIVNUM, INDXP, INDX, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, */
/* $ QSIZ */
/* DOUBLE PRECISION RHO */
/* .. */
/* .. Array Arguments .. */
/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */
/* $ INDXQ( * ), PERM( * ) */
/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), */
/* $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DLAED8 merges the two sets of eigenvalues together into a single */
/* > sorted set. Then it tries to deflate the size of the problem. */
/* > There are two ways in which deflation can occur: when two or more */
/* > eigenvalues are close together or if there is a tiny element in the */
/* > Z vector. For each such occurrence the order of the related secular */
/* > equation problem is reduced by one. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] ICOMPQ */
/* > \verbatim */
/* > ICOMPQ is INTEGER */
/* > = 0: Compute eigenvalues only. */
/* > = 1: Compute eigenvectors of original dense symmetric matrix */
/* > also. On entry, Q contains the orthogonal matrix used */
/* > to reduce the original matrix to tridiagonal form. */
/* > \endverbatim */
/* > */
/* > \param[out] K */
/* > \verbatim */
/* > K is INTEGER */
/* > The number of non-deflated eigenvalues, and the order of the */
/* > related secular equation. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] QSIZ */
/* > \verbatim */
/* > QSIZ is INTEGER */
/* > The dimension of the orthogonal matrix used to reduce */
/* > the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > On entry, the eigenvalues of the two submatrices to be */
/* > combined. On exit, the trailing (N-K) updated eigenvalues */
/* > (those which were deflated) sorted into increasing order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* > Q is DOUBLE PRECISION array, dimension (LDQ,N) */
/* > If ICOMPQ = 0, Q is not referenced. Otherwise, */
/* > on entry, Q contains the eigenvectors of the partially solved */
/* > system which has been previously updated in matrix */
/* > multiplies with other partially solved eigensystems. */
/* > On exit, Q contains the trailing (N-K) updated eigenvectors */
/* > (those which were deflated) in its last N-K columns. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ */
/* > \verbatim */
/* > LDQ is INTEGER */
/* > The leading dimension of the array Q. LDQ >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] INDXQ */
/* > \verbatim */
/* > INDXQ is INTEGER array, dimension (N) */
/* > The permutation which separately sorts the two sub-problems */
/* > in D into ascending order. Note that elements in the second */
/* > half of this permutation must first have CUTPNT added to */
/* > their values in order to be accurate. */
/* > \endverbatim */
/* > */
/* > \param[in,out] RHO */
/* > \verbatim */
/* > RHO is DOUBLE PRECISION */
/* > On entry, the off-diagonal element associated with the rank-1 */
/* > cut which originally split the two submatrices which are now */
/* > being recombined. */
/* > On exit, RHO has been modified to the value required by */
/* > DLAED3. */
/* > \endverbatim */
/* > */
/* > \param[in] CUTPNT */
/* > \verbatim */
/* > CUTPNT is INTEGER */
/* > The location of the last eigenvalue in the leading */
/* > sub-matrix. min(1,N) <= CUTPNT <= N. */
/* > \endverbatim */
/* > */
/* > \param[in] Z */
/* > \verbatim */
/* > Z is DOUBLE PRECISION array, dimension (N) */
/* > On entry, Z contains the updating vector (the last row of */
/* > the first sub-eigenvector matrix and the first row of the */
/* > second sub-eigenvector matrix). */
/* > On exit, the contents of Z are destroyed by the updating */
/* > process. */
/* > \endverbatim */
/* > */
/* > \param[out] DLAMDA */
/* > \verbatim */
/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */
/* > A copy of the first K eigenvalues which will be used by */
/* > DLAED3 to form the secular equation. */
/* > \endverbatim */
/* > */
/* > \param[out] Q2 */
/* > \verbatim */
/* > Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) */
/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
/* > a copy of the first K eigenvectors which will be used by */
/* > DLAED7 in a matrix multiply (DGEMM) to update the new */
/* > eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] LDQ2 */
/* > \verbatim */
/* > LDQ2 is INTEGER */
/* > The leading dimension of the array Q2. LDQ2 >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] W */
/* > \verbatim */
/* > W is DOUBLE PRECISION array, dimension (N) */
/* > The first k values of the final deflation-altered z-vector and */
/* > will be passed to DLAED3. */
/* > \endverbatim */
/* > */
/* > \param[out] PERM */
/* > \verbatim */
/* > PERM is INTEGER array, dimension (N) */
/* > The permutations (from deflation and sorting) to be applied */
/* > to each eigenblock. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVPTR */
/* > \verbatim */
/* > GIVPTR is INTEGER */
/* > The number of Givens rotations which took place in this */
/* > subproblem. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVCOL */
/* > \verbatim */
/* > GIVCOL is INTEGER array, dimension (2, N) */
/* > Each pair of numbers indicates a pair of columns to take place */
/* > in a Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVNUM */
/* > \verbatim */
/* > GIVNUM is DOUBLE PRECISION array, dimension (2, N) */
/* > Each number indicates the S value to be used in the */
/* > corresponding Givens rotation. */
/* > \endverbatim */
/* > */
/* > \param[out] INDXP */
/* > \verbatim */
/* > INDXP is INTEGER array, dimension (N) */
/* > The permutation used to place deflated values of D at the end */
/* > of the array. INDXP(1:K) points to the nondeflated D-values */
/* > and INDXP(K+1:N) points to the deflated eigenvalues. */
/* > \endverbatim */
/* > */
/* > \param[out] INDX */
/* > \verbatim */
/* > INDX is INTEGER array, dimension (N) */
/* > The permutation used to sort the contents of D into ascending */
/* > order. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup auxOTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA */
/* ===================================================================== */
/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer
*qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq,
doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer
*givptr, integer *givcol, doublereal *givnum, integer *indxp, integer
*indx, integer *info)
{
/* System generated locals */
integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
doublereal c__;
integer i__, j;
doublereal s, t;
integer k2, n1, n2, jp, n1p1;
doublereal eps, tau, tol;
integer jlam, imax, jmax;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *), dscal_(
integer *, doublereal *, doublereal *, integer *), dcopy_(integer
*, doublereal *, integer *, doublereal *, integer *);
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *,
ftnlen);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *,
integer *, integer *, integer *), dlacpy_(char *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
ftnlen), xerbla_(char *, integer *, ftnlen);
/* -- 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 .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
--d__;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--indxq;
--z__;
--dlamda;
q2_dim1 = *ldq2;
q2_offset = 1 + q2_dim1;
q2 -= q2_offset;
--w;
--perm;
givcol -= 3;
givnum -= 3;
--indxp;
--indx;
/* Function Body */
*info = 0;
if (*icompq < 0 || *icompq > 1) {
*info = -1;
} else if (*n < 0) {
*info = -3;
} else if (*icompq == 1 && *qsiz < *n) {
*info = -4;
} else if (*ldq < max(1,*n)) {
*info = -7;
} else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
*info = -10;
} else if (*ldq2 < max(1,*n)) {
*info = -14;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DLAED8", &i__1, (ftnlen)6);
return 0;
}
/* Need to initialize GIVPTR to O here in case of quick exit */
/* to prevent an unspecified code behavior (usually sigfault) */
/* when IWORK array on entry to *stedc is not zeroed */
/* (or at least some IWORK entries which used in *laed7 for GIVPTR). */
*givptr = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
n1 = *cutpnt;
n2 = *n - n1;
n1p1 = n1 + 1;
if (*rho < 0.) {
dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
}
/* Normalize z so that norm(z) = 1 */
t = 1. / sqrt(2.);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
indx[j] = j;
/* L10: */
}
dscal_(n, &t, &z__[1], &c__1);
*rho = (d__1 = *rho * 2., abs(d__1));
/* Sort the eigenvalues into increasing order */
i__1 = *n;
for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
indxq[i__] += *cutpnt;
/* L20: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
dlamda[i__] = d__[indxq[i__]];
w[i__] = z__[indxq[i__]];
/* L30: */
}
i__ = 1;
j = *cutpnt + 1;
dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__[i__] = dlamda[indx[i__]];
z__[i__] = w[indx[i__]];
/* L40: */
}
/* Calculate the allowable deflation tolerance */
imax = idamax_(n, &z__[1], &c__1);
jmax = idamax_(n, &d__[1], &c__1);
eps = dlamch_((char *)"Epsilon", (ftnlen)7);
tol = eps * 8. * (d__1 = d__[jmax], abs(d__1));
/* If the rank-1 modifier is small enough, no more needs to be done */
/* except to reorganize Q so that its columns correspond with the */
/* elements in D. */
if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) {
*k = 0;
if (*icompq == 0) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
/* L50: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1
+ 1], &c__1);
/* L60: */
}
dlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq,
(ftnlen)1);
}
return 0;
}
/* If there are multiple eigenvalues then the problem deflates. Here */
/* the number of equal eigenvalues are found. As each equal */
/* eigenvalue is found, an elementary reflector is computed to rotate */
/* the corresponding eigensubspace so that the corresponding */
/* components of Z are zero in this new basis. */
*k = 0;
k2 = *n + 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
if (j == *n) {
goto L110;
}
} else {
jlam = j;
goto L80;
}
/* L70: */
}
L80:
++j;
if (j > *n) {
goto L100;
}
if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {
/* Deflate due to small z component. */
--k2;
indxp[k2] = j;
} else {
/* Check if eigenvalues are close enough to allow deflation. */
s = z__[jlam];
c__ = z__[j];
/* Find sqrt(a**2+b**2) without overflow or */
/* destructive underflow. */
tau = dlapy2_(&c__, &s);
t = d__[j] - d__[jlam];
c__ /= tau;
s = -s / tau;
if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {
/* Deflation is possible. */
z__[j] = tau;
z__[jlam] = 0.;
/* Record the appropriate Givens rotation */
++(*givptr);
givcol[(*givptr << 1) + 1] = indxq[indx[jlam]];
givcol[(*givptr << 1) + 2] = indxq[indx[j]];
givnum[(*givptr << 1) + 1] = c__;
givnum[(*givptr << 1) + 2] = s;
if (*icompq == 1) {
drot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[
indxq[indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
}
t = d__[jlam] * c__ * c__ + d__[j] * s * s;
d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
d__[jlam] = t;
--k2;
i__ = 1;
L90:
if (k2 + i__ <= *n) {
if (d__[jlam] < d__[indxp[k2 + i__]]) {
indxp[k2 + i__ - 1] = indxp[k2 + i__];
indxp[k2 + i__] = jlam;
++i__;
goto L90;
} else {
indxp[k2 + i__ - 1] = jlam;
}
} else {
indxp[k2 + i__ - 1] = jlam;
}
jlam = j;
} else {
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
jlam = j;
}
}
goto L80;
L100:
/* Record the last eigenvalue. */
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
L110:
/* Sort the eigenvalues and corresponding eigenvectors into DLAMDA */
/* and Q2 respectively. The eigenvalues/vectors which were not */
/* deflated go into the first K slots of DLAMDA and Q2 respectively, */
/* while those which were deflated go into the last N - K slots. */
if (*icompq == 0) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
/* L120: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
dcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
, &c__1);
/* L130: */
}
}
/* The deflated eigenvalues and their corresponding vectors go back */
/* into the last N - K slots of D and Q respectively. */
if (*k < *n) {
if (*icompq == 0) {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
} else {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
i__1 = *n - *k;
dlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*
k + 1) * q_dim1 + 1], ldq, (ftnlen)1);
}
}
return 0;
/* End of DLAED8 */
} /* dlaed8_ */
#ifdef __cplusplus
}
#endif