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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/dstedc.cpp Normal file
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/* fortran/dstedc.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 DSTEDC */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSTEDC + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstedc.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstedc.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstedc.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, */
/* LIWORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER COMPZ */
/* INTEGER INFO, LDZ, LIWORK, LWORK, N */
/* .. */
/* .. Array Arguments .. */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
/* > symmetric tridiagonal matrix using the divide and conquer method. */
/* > The eigenvectors of a full or band real symmetric matrix can also be */
/* > found if DSYTRD or DSPTRD or DSBTRD 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 dense symmetric */
/* > matrix also. On entry, Z contains the orthogonal */
/* > 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 DOUBLE PRECISION array, dimension (LDZ,N) */
/* > On entry, if COMPZ = 'V', then Z contains the orthogonal */
/* > 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 symmetric 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 DOUBLE PRECISION 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 N <= 1 then LWORK must be at least 1. */
/* > If COMPZ = 'V' and N > 1 then LWORK 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 then LWORK must be at least */
/* > ( 1 + 4*N + 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 LWORK need */
/* > only be max(1,2*(N-1)). */
/* > */
/* > If LWORK = -1, then a workspace query is assumed; the routine */
/* > only calculates the optimal size of the WORK array, returns */
/* > this value as the first entry of the WORK array, and no error */
/* > message related to LWORK 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 then LIWORK must be at least 1. */
/* > If COMPZ = 'V' and N > 1 then LIWORK must be at least */
/* > ( 6 + 6*N + 5*N*lg N ). */
/* > If COMPZ = 'I' and N > 1 then 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 size of the IWORK array, */
/* > returns this value as the first entry of the IWORK array, and */
/* > no error message related to 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 auxOTHERcomputational */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Jeff Rutter, Computer Science Division, University of California */
/* > at Berkeley, USA \n */
/* > Modified by Francoise Tisseur, University of Tennessee */
/* > */
/* ===================================================================== */
/* Subroutine */ int dstedc_(char *compz, integer *n, doublereal *d__,
doublereal *e, doublereal *z__, integer *ldz, doublereal *work,
integer *lwork, integer *iwork, integer *liwork, integer *info,
ftnlen compz_len)
{
/* System generated locals */
integer z_dim1, z_offset, i__1, i__2;
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, lgn;
doublereal eps, tiny;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen);
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer lwmin;
extern /* Subroutine */ int dlaed0_(integer *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *);
integer start;
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, ftnlen), dlacpy_(char *, integer *, integer
*, doublereal *, integer *, doublereal *, integer *, ftnlen),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
integer finish;
extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
ftnlen);
extern /* Subroutine */ int dsterf_(integer *, doublereal *, doublereal *,
integer *), dlasrt_(char *, integer *, doublereal *, integer *,
ftnlen);
integer liwmin, icompz;
extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *,
doublereal *, doublereal *, integer *, doublereal *, integer *,
ftnlen);
doublereal orgnrm;
logical lquery;
integer smlsiz, storez, strtrw;
/* -- 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;
--iwork;
/* Function Body */
*info = 0;
lquery = *lwork == -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 *)"DSTEDC", (char *)" ", &c__0, &c__0, &c__0, &c__0, (
ftnlen)6, (ftnlen)1);
if (*n <= 1 || icompz == 0) {
liwmin = 1;
lwmin = 1;
} else if (*n <= smlsiz) {
liwmin = 1;
lwmin = *n - 1 << 1;
} else {
lgn = (integer) (log((doublereal) (*n)) / log(2.));
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (pow_ii(&c__2, &lgn) < *n) {
++lgn;
}
if (icompz == 1) {
/* Computing 2nd power */
i__1 = *n;
lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2);
liwmin = *n * 6 + 6 + *n * 5 * lgn;
} else if (icompz == 2) {
/* Computing 2nd power */
i__1 = *n;
lwmin = (*n << 2) + 1 + i__1 * i__1;
liwmin = *n * 5 + 3;
}
}
work[1] = (doublereal) lwmin;
iwork[1] = liwmin;
if (*lwork < lwmin && ! lquery) {
*info = -8;
} else if (*liwork < liwmin && ! lquery) {
*info = -10;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DSTEDC", &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) {
z__[z_dim1 + 1] = 1.;
}
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 L50;
}
/* If N is smaller than the minimum divide size (SMLSIZ+1), then */
/* solve the problem with another solver. */
if (*n <= smlsiz) {
dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info,
(ftnlen)1);
} else {
/* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */
/* use. */
if (icompz == 1) {
storez = *n * *n + 1;
} else {
storez = 1;
}
if (icompz == 2) {
dlaset_((char *)"Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz, (
ftnlen)4);
}
/* Scale. */
orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1);
if (orgnrm == 0.) {
goto L50;
}
eps = dlamch_((char *)"Epsilon", (ftnlen)7);
start = 1;
/* while ( START <= N ) */
L10:
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;
L20:
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 L20;
}
}
/* (Sub) Problem determined. Compute its size and solve it. */
m = finish - start + 1;
if (m == 1) {
start = finish + 1;
goto L10;
}
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);
if (icompz == 1) {
strtrw = 1;
} else {
strtrw = start;
}
dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw +
start * z_dim1], ldz, &work[1], n, &work[storez], &
iwork[1], info);
if (*info != 0) {
*info = (*info / (m + 1) + start - 1) * (*n + 1) + *info %
(m + 1) + start - 1;
goto L50;
}
/* Scale back. */
dlascl_((char *)"G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[
start], &m, info, (ftnlen)1);
} else {
if (icompz == 1) {
/* Since QR won't update a Z matrix which is larger than */
/* the length of D, we must solve the sub-problem in a */
/* workspace and then multiply back into Z. */
dsteqr_((char *)"I", &m, &d__[start], &e[start], &work[1], &m, &
work[m * m + 1], info, (ftnlen)1);
dlacpy_((char *)"A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[
storez], n, (ftnlen)1);
dgemm_((char *)"N", (char *)"N", n, &m, &m, &c_b18, &work[storez], n, &
work[1], &m, &c_b17, &z__[start * z_dim1 + 1],
ldz, (ftnlen)1, (ftnlen)1);
} else if (icompz == 2) {
dsteqr_((char *)"I", &m, &d__[start], &e[start], &z__[start +
start * z_dim1], ldz, &work[1], info, (ftnlen)1);
} else {
dsterf_(&m, &d__[start], &e[start], info);
}
if (*info != 0) {
*info = start * (*n + 1) + finish;
goto L50;
}
}
start = finish + 1;
goto L10;
}
/* endwhile */
if (icompz == 0) {
/* Use Quick Sort */
dlasrt_((char *)"I", n, &d__[1], info, (ftnlen)1);
} else {
/* 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];
}
/* L30: */
}
if (k != i__) {
d__[k] = d__[i__];
d__[i__] = p;
dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1
+ 1], &c__1);
}
/* L40: */
}
}
}
L50:
work[1] = (doublereal) lwmin;
iwork[1] = liwmin;
return 0;
/* End of DSTEDC */
} /* dstedc_ */
#ifdef __cplusplus
}
#endif