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convert linalg library from Fortran to C++

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This commit is contained in:
Axel Kohlmeyer
2022-12-28 13:18:38 -05:00
parent 7cceabe5bd
commit c5a87f75d6
410 changed files with 80736 additions and 30 deletions
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lib/linalg/zstedc.cpp Normal file
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/* fortran/zstedc.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 integer c__9 = 9;
static integer c__0 = 0;
static integer c__2 = 2;
static doublereal c_b17 = 0.;
static doublereal c_b18 = 1.;
static integer c__1 = 1;
/* > \brief \b ZSTEDC */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download ZSTEDC + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zstedc.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zstedc.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zstedc.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, */
/* LRWORK, IWORK, LIWORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER COMPZ */
/* INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N */
/* .. */
/* .. Array Arguments .. */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) */
/* COMPLEX*16 WORK( * ), Z( LDZ, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
/* > symmetric tridiagonal matrix using the divide and conquer method. */
/* > The eigenvectors of a full or band complex Hermitian matrix can also */
/* > be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this */
/* > matrix to tridiagonal form. */
/* > */
/* > This code makes very mild assumptions about floating point */
/* > arithmetic. It will work on machines with a guard digit in */
/* > add/subtract, or on those binary machines without guard digits */
/* > which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
/* > It could conceivably fail on hexadecimal or decimal machines */
/* > without guard digits, but we know of none. See DLAED3 for details. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] COMPZ */
/* > \verbatim */
/* > COMPZ is CHARACTER*1 */
/* > = 'N': Compute eigenvalues only. */
/* > = 'I': Compute eigenvectors of tridiagonal matrix also. */
/* > = 'V': Compute eigenvectors of original Hermitian matrix */
/* > also. On entry, Z contains the unitary matrix used */
/* > to reduce the original matrix to tridiagonal form. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] D */
/* > \verbatim */
/* > D is DOUBLE PRECISION array, dimension (N) */
/* > On entry, the diagonal elements of the tridiagonal matrix. */
/* > On exit, if INFO = 0, the eigenvalues in ascending order. */
/* > \endverbatim */
/* > */
/* > \param[in,out] E */
/* > \verbatim */
/* > E is DOUBLE PRECISION array, dimension (N-1) */
/* > On entry, the subdiagonal elements of the tridiagonal matrix. */
/* > On exit, E has been destroyed. */
/* > \endverbatim */
/* > */
/* > \param[in,out] Z */
/* > \verbatim */
/* > Z is COMPLEX*16 array, dimension (LDZ,N) */
/* > On entry, if COMPZ = 'V', then Z contains the unitary */
/* > matrix used in the reduction to tridiagonal form. */
/* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
/* > orthonormal eigenvectors of the original Hermitian matrix, */
/* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
/* > of the symmetric tridiagonal matrix. */
/* > If COMPZ = 'N', then Z is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[in] LDZ */
/* > \verbatim */
/* > LDZ is INTEGER */
/* > The leading dimension of the array Z. LDZ >= 1. */
/* > If eigenvectors are desired, then LDZ >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is INTEGER */
/* > The dimension of the array WORK. */
/* > If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. */
/* > If COMPZ = 'V' and N > 1, LWORK must be at least N*N. */
/* > Note that for COMPZ = 'V', then if N is less than or */
/* > equal to the minimum divide size, usually 25, then LWORK need */
/* > only be 1. */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal sizes of the WORK, RWORK and */
/* > IWORK arrays, returns these values as the first entries of */
/* > the WORK, RWORK and IWORK arrays, and no error message */
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* > RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) */
/* > On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LRWORK */
/* > \verbatim */
/* > LRWORK is INTEGER */
/* > The dimension of the array RWORK. */
/* > If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. */
/* > If COMPZ = 'V' and N > 1, LRWORK must be at least */
/* > 1 + 3*N + 2*N*lg N + 4*N**2 , */
/* > where lg( N ) = smallest integer k such */
/* > that 2**k >= N. */
/* > If COMPZ = 'I' and N > 1, LRWORK must be at least */
/* > 1 + 4*N + 2*N**2 . */
/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* > equal to the minimum divide size, usually 25, then LRWORK */
/* > need only be max(1,2*(N-1)). */
/* > */
/* > If LRWORK = -1, then a workspace query is assumed; the */
/* > routine only calculates the optimal sizes of the WORK, RWORK */
/* > and IWORK arrays, returns these values as the first entries */
/* > of the WORK, RWORK and IWORK arrays, and no error message */
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
/* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LIWORK */
/* > \verbatim */
/* > LIWORK is INTEGER */
/* > The dimension of the array IWORK. */
/* > If COMPZ = 'N' or N <= 1, LIWORK must be at least 1. */
/* > If COMPZ = 'V' or N > 1, LIWORK must be at least */
/* > 6 + 6*N + 5*N*lg N. */
/* > If COMPZ = 'I' or N > 1, LIWORK must be at least */
/* > 3 + 5*N . */
/* > Note that for COMPZ = 'I' or 'V', then if N is less than or */
/* > equal to the minimum divide size, usually 25, then LIWORK */
/* > need only be 1. */
/* > */
/* > If LIWORK = -1, then a workspace query is assumed; the */
/* > routine only calculates the optimal sizes of the WORK, RWORK */
/* > and IWORK arrays, returns these values as the first entries */
/* > of the WORK, RWORK and IWORK arrays, and no error message */
/* > related to LWORK or LRWORK or LIWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > = 0: successful exit. */
/* > < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > > 0: The algorithm failed to compute an eigenvalue while */
/* > working on the submatrix lying in rows and columns */
/* > INFO/(N+1) through mod(INFO,N+1). */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \ingroup complex16OTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA */
/* ===================================================================== */
/* Subroutine */ int zstedc_(char *compz, integer *n, doublereal *d__,
doublereal *e, doublecomplex *z__, integer *ldz, doublecomplex *work,
integer *lwork, doublereal *rwork, integer *lrwork, integer *iwork,
integer *liwork, integer *info, ftnlen compz_len)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2;
/* Builtin functions */
double log(doublereal);
integer pow_ii(integer *, integer *);
double sqrt(doublereal);
/* Local variables */
integer i__, j, k, m;
doublereal p;
integer ii, ll, lgn;
doublereal eps, tiny;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
integer lwmin, start;
extern /* Subroutine */ int zswap_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaed0_(integer *, integer *,
doublereal *, doublereal *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, integer *, integer *);
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, ftnlen), dstedc_(char *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, integer *, ftnlen), dlaset_(
char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, ftnlen), xerbla_(char *, integer *,
ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
integer finish;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
ftnlen);
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), zlacrm_(integer *, integer *, doublecomplex *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
doublereal *);
integer liwmin, icompz;
extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
ftnlen), zlacpy_(char *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, ftnlen);
doublereal orgnrm;
integer lrwmin;
logical lquery;
integer smlsiz;
extern /* Subroutine */ int zsteqr_(char *, integer *, doublereal *,
doublereal *, doublecomplex *, integer *, doublereal *, 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__;
--e;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--work;
--rwork;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1 || *lrwork == -1 || *liwork == -1;
if (lsame_(compz, (char *)"N", (ftnlen)1, (ftnlen)1)) {
icompz = 0;
} else if (lsame_(compz, (char *)"V", (ftnlen)1, (ftnlen)1)) {
icompz = 1;
} else if (lsame_(compz, (char *)"I", (ftnlen)1, (ftnlen)1)) {
icompz = 2;
} else {
icompz = -1;
}
if (icompz < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n)) {
*info = -6;
}
if (*info == 0) {
/* Compute the workspace requirements */
smlsiz = ilaenv_(&c__9, (char *)"ZSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
if (*n <= 1 || icompz == 0) {
lwmin = 1;
liwmin = 1;
lrwmin = 1;
} else if (*n <= smlsiz) {
lwmin = 1;
liwmin = 1;
lrwmin = *n - 1 << 1;
} else if (icompz == 1) {
lgn = (integer) (log((doublereal) (*n)) / log(2.));
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
lwmin = *n * *n;
/* Computing 2nd power */
i__1 = *n;
lrwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2);
liwmin = *n * 6 + 6 + *n * 5 * lgn;
} else if (icompz == 2) {
lwmin = 1;
/* Computing 2nd power */
i__1 = *n;
lrwmin = (*n << 2) + 1 + (i__1 * i__1 << 1);
liwmin = *n * 5 + 3;
}
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*lrwork < lrwmin && ! lquery) {
*info = -10;
} else if (*liwork < liwmin && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"ZSTEDC", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*n == 1) {
if (icompz != 0) {
i__1 = z_dim1 + 1;
z__[i__1].r = 1., z__[i__1].i = 0.;
}
return 0;
}
/* If the following conditional clause is removed, then the routine */
/* will use the Divide and Conquer routine to compute only the */
/* eigenvalues, which requires (3N + 3N**2) real workspace and */
/* (2 + 5N + 2N lg(N)) integer workspace. */
/* Since on many architectures DSTERF is much faster than any other */
/* algorithm for finding eigenvalues only, it is used here */
/* as the default. If the conditional clause is removed, then */
/* information on the size of workspace needs to be changed. */
/* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */
if (icompz == 0) {
dsterf_(n, &d__[1], &e[1], info);
goto L70;
}
/* If N is smaller than the minimum divide size (SMLSIZ+1), then */
/* solve the problem with another solver. */
if (*n <= smlsiz) {
zsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &rwork[1],
info, (ftnlen)1);
} else {
/* If COMPZ = 'I', we simply call DSTEDC instead. */
if (icompz == 2) {
dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &rwork[1], n, (ftnlen)4);
ll = *n * *n + 1;
i__1 = *lrwork - ll + 1;
dstedc_((char *)"I", n, &d__[1], &e[1], &rwork[1], n, &rwork[ll], &i__1, &
iwork[1], liwork, info, (ftnlen)1);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * z_dim1;
i__4 = (j - 1) * *n + i__;
z__[i__3].r = rwork[i__4], z__[i__3].i = 0.;
/* L10: */
}
/* L20: */
}
goto L70;
}
/* From now on, only option left to be handled is COMPZ = 'V', */
/* i.e. ICOMPZ = 1. */
/* Scale. */
orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1);
if (orgnrm == 0.) {
goto L70;
}
eps = dlamch_((char *)"Epsilon", (ftnlen)7);
start = 1;
/* while ( START <= N ) */
L30:
if (start <= *n) {
/* Let FINISH be the position of the next subdiagonal entry */
/* such that E( FINISH ) <= TINY or FINISH = N if no such */
/* subdiagonal exists. The matrix identified by the elements */
/* between START and FINISH constitutes an independent */
/* sub-problem. */
finish = start;
L40:
if (finish < *n) {
tiny = eps * sqrt((d__1 = d__[finish], abs(d__1))) * sqrt((
d__2 = d__[finish + 1], abs(d__2)));
if ((d__1 = e[finish], abs(d__1)) > tiny) {
++finish;
goto L40;
}
}
/* (Sub) Problem determined. Compute its size and solve it. */
m = finish - start + 1;
if (m > smlsiz) {
/* Scale. */
orgnrm = dlanst_((char *)"M", &m, &d__[start], &e[start], (ftnlen)1);
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[
start], &m, info, (ftnlen)1);
i__1 = m - 1;
i__2 = m - 1;
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[
start], &i__2, info, (ftnlen)1);
zlaed0_(n, &m, &d__[start], &e[start], &z__[start * z_dim1 +
1], ldz, &work[1], n, &rwork[1], &iwork[1], info);
if (*info > 0) {
*info = (*info / (m + 1) + start - 1) * (*n + 1) + *info %
(m + 1) + start - 1;
goto L70;
}
/* Scale back. */
dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[
start], &m, info, (ftnlen)1);
} else {
dsteqr_((char *)"I", &m, &d__[start], &e[start], &rwork[1], &m, &
rwork[m * m + 1], info, (ftnlen)1);
zlacrm_(n, &m, &z__[start * z_dim1 + 1], ldz, &rwork[1], &m, &
work[1], n, &rwork[m * m + 1]);
zlacpy_((char *)"A", n, &m, &work[1], n, &z__[start * z_dim1 + 1],
ldz, (ftnlen)1);
if (*info > 0) {
*info = start * (*n + 1) + finish;
goto L70;
}
}
start = finish + 1;
goto L30;
}
/* endwhile */
/* Use Selection Sort to minimize swaps of eigenvectors */
i__1 = *n;
for (ii = 2; ii <= i__1; ++ii) {
i__ = ii - 1;
k = i__;
p = d__[i__];
i__2 = *n;
for (j = ii; j <= i__2; ++j) {
if (d__[j] < p) {
k = j;
p = d__[j];
}
/* L50: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
zswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1],
&c__1);
}
/* L60: */
}
}
L70:
work[1].r = (doublereal) lwmin, work[1].i = 0.;
rwork[1] = (doublereal) lrwmin;
iwork[1] = liwmin;
return 0;
/* End of ZSTEDC */
} /* zstedc_ */
#ifdef __cplusplus
}
#endif