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remove redundant comments from generated C++ files. clean up with clang-format.

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Axel Kohlmeyer
2022-12-28 16:31:50 -05:00
parent f157ba2389
commit 57713cf9a3
211 changed files with 6255 additions and 54891 deletions
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lib/linalg/zlaed8.cpp
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@ -1,315 +1,35 @@
/* fortran/zlaed8.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 ZLAED8 used by ZSTEDC. 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 ZLAED8 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaed8.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaed8.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaed8.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, */
/* Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, */
/* GIVCOL, GIVNUM, INFO ) */
/* .. Scalar Arguments .. */
/* INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ */
/* DOUBLE PRECISION RHO */
/* .. */
/* .. Array Arguments .. */
/* INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), */
/* $ INDXQ( * ), PERM( * ) */
/* DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), */
/* $ Z( * ) */
/* COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZLAED8 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[out] K */
/* > \verbatim */
/* > K is INTEGER */
/* > Contains the number of non-deflated eigenvalues. */
/* > This is 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 unitary matrix used to reduce */
/* > the dense or band matrix to tridiagonal form. */
/* > QSIZ >= N if ICOMPQ = 1. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Q */
/* > \verbatim */
/* > Q is COMPLEX*16 array, dimension (LDQ,N) */
/* > 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,out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > On entry, D contains the eigenvalues of the two submatrices to */
/* > be combined. On exit, D contains the trailing (N-K) updated */
/* > eigenvalues (those which were deflated) sorted into increasing */
/* > order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] RHO */
/* > \verbatim */
/* > RHO is DOUBLE PRECISION */
/* > Contains the off diagonal element associated with the rank-1 */
/* > cut which originally split the two submatrices which are now */
/* > being recombined. RHO is modified during the computation to */
/* > the value required by DLAED3. */
/* > \endverbatim */
/* > */
/* > \param[in] CUTPNT */
/* > \verbatim */
/* > CUTPNT is INTEGER */
/* > Contains 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 input this vector contains the updating vector (the last */
/* > row of the first sub-eigenvector matrix and the first row of */
/* > the second sub-eigenvector matrix). The contents of Z are */
/* > destroyed during the updating process. */
/* > \endverbatim */
/* > */
/* > \param[out] DLAMDA */
/* > \verbatim */
/* > DLAMDA is DOUBLE PRECISION array, dimension (N) */
/* > Contains 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 COMPLEX*16 array, dimension (LDQ2,N) */
/* > If ICOMPQ = 0, Q2 is not referenced. Otherwise, */
/* > Contains 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) */
/* > This will hold the first k values of the final */
/* > deflation-altered z-vector and will be passed to DLAED3. */
/* > \endverbatim */
/* > */
/* > \param[out] INDXP */
/* > \verbatim */
/* > INDXP is INTEGER array, dimension (N) */
/* > This will contain the permutation used to place deflated */
/* > values of D at the end of the array. On output 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) */
/* > This will contain the permutation used to sort the contents of */
/* > D into ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in] INDXQ */
/* > \verbatim */
/* > INDXQ is INTEGER array, dimension (N) */
/* > This contains 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[out] PERM */
/* > \verbatim */
/* > PERM is INTEGER array, dimension (N) */
/* > Contains the permutations (from deflation and sorting) to be */
/* > applied to each eigenblock. */
/* > \endverbatim */
/* > */
/* > \param[out] GIVPTR */
/* > \verbatim */
/* > GIVPTR is INTEGER */
/* > Contains 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] 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 complex16OTHERcomputational */
/* ===================================================================== */
/* Subroutine */ int zlaed8_(integer *k, integer *n, integer *qsiz,
doublecomplex *q, integer *ldq, doublereal *d__, doublereal *rho,
integer *cutpnt, doublereal *z__, doublereal *dlamda, doublecomplex *
q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx,
integer *indxq, integer *perm, integer *givptr, integer *givcol,
doublereal *givnum, integer *info)
int zlaed8_(integer *k, integer *n, integer *qsiz, doublecomplex *q, integer *ldq, doublereal *d__,
doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
doublecomplex *q2, integer *ldq2, doublereal *w, integer *indxp, integer *indx,
integer *indxq, integer *perm, integer *givptr, integer *givcol, doublereal *givnum,
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 dscal_(integer *, doublereal *, doublereal *,
integer *), dcopy_(integer *, doublereal *, integer *, doublereal
*, integer *), zdrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *), zcopy_(
integer *, doublecomplex *, integer *, doublecomplex *, integer *)
;
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *,
ftnlen);
extern int dscal_(integer *, doublereal *, doublereal *, integer *),
dcopy_(integer *, doublereal *, integer *, doublereal *, integer *),
zdrot_(integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublereal *,
doublereal *),
zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, 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 *), xerbla_(char *, integer *,
ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, 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 */
extern int dlamrg_(integer *, integer *, doublereal *, integer *, integer *, integer *),
xerbla_(char *, integer *, ftnlen),
zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, ftnlen);
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
@ -326,19 +46,16 @@ f"> */
--perm;
givcol -= 3;
givnum -= 3;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -2;
} else if (*qsiz < *n) {
*info = -3;
} else if (*ldq < max(1,*n)) {
} else if (*ldq < max(1, *n)) {
*info = -5;
} else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
} else if (*cutpnt < min(1, *n) || *cutpnt > *n) {
*info = -8;
} else if (*ldq2 < max(1,*n)) {
} else if (*ldq2 < max(1, *n)) {
*info = -12;
}
if (*info != 0) {
@ -346,51 +63,31 @@ f"> */
xerbla_((char *)"ZLAED8", &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;
@ -399,48 +96,26 @@ f"> */
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;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
perm[j] = indxq[indx[j]];
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1]
, &c__1);
/* L50: */
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1);
}
zlacpy_((char *)"A", qsiz, n, &q2[q2_dim1 + 1], ldq2, &q[q_dim1 + 1], ldq, (
ftnlen)1);
zlacpy_((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) {
@ -450,7 +125,6 @@ f"> */
jlam = j;
goto L70;
}
/* L60: */
}
L70:
++j;
@ -458,47 +132,31 @@ L70:
goto L90;
}
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;
zdrot_(qsiz, &q[indxq[indx[jlam]] * q_dim1 + 1], &c__1, &q[indxq[
indx[j]] * q_dim1 + 1], &c__1, &c__, &s);
zdrot_(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;
L80:
L80:
if (k2 + i__ <= *n) {
if (d__[jlam] < d__[indxp[k2 + i__]]) {
indxp[k2 + i__ - 1] = indxp[k2 + i__];
@ -522,48 +180,27 @@ L80:
}
goto L70;
L90:
/* Record the last eigenvalue. */
++(*k);
w[*k] = z__[jlam];
dlamda[*k] = d__[jlam];
indxp[*k] = jlam;
L100:
/* 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. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jp = indxp[j];
dlamda[j] = d__[jp];
perm[j] = indxq[indx[jp]];
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &
c__1);
/* L110: */
zcopy_(qsiz, &q[perm[j] * q_dim1 + 1], &c__1, &q2[j * q2_dim1 + 1], &c__1);
}
/* The deflated eigenvalues and their corresponding vectors go back */
/* into the last N - K slots of D and Q respectively. */
if (*k < *n) {
i__1 = *n - *k;
dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
i__1 = *n - *k;
zlacpy_((char *)"A", qsiz, &i__1, &q2[(*k + 1) * q2_dim1 + 1], ldq2, &q[(*k +
1) * q_dim1 + 1], ldq, (ftnlen)1);
zlacpy_((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 ZLAED8 */
} /* zlaed8_ */
}
#ifdef __cplusplus
}
}
#endif