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

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/* fortran/dsygst.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__1 = 1;
static integer c_n1 = -1;
static doublereal c_b14 = 1.;
static doublereal c_b16 = -.5;
static doublereal c_b19 = -1.;
static doublereal c_b52 = .5;
/* > \brief \b DSYGST */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DSYGST + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygst.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygst.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER UPLO */
/* INTEGER INFO, ITYPE, LDA, LDB, N */
/* .. */
/* .. Array Arguments .. */
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > DSYGST reduces a real symmetric-definite generalized eigenproblem */
/* > to standard form. */
/* > */
/* > If ITYPE = 1, the problem is A*x = lambda*B*x, */
/* > and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) */
/* > */
/* > If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or */
/* > B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. */
/* > */
/* > B must have been previously factorized as U**T*U or L*L**T by DPOTRF. */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] ITYPE */
/* > \verbatim */
/* > ITYPE is INTEGER */
/* > = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); */
/* > = 2 or 3: compute U*A*U**T or L**T*A*L. */
/* > \endverbatim */
/* > */
/* > \param[in] UPLO */
/* > \verbatim */
/* > UPLO is CHARACTER*1 */
/* > = 'U': Upper triangle of A is stored and B is factored as */
/* > U**T*U; */
/* > = 'L': Lower triangle of A is stored and B is factored as */
/* > L*L**T. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the matrices A and B. N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
/* > On entry, the symmetric matrix A. If UPLO = 'U', the leading */
/* > N-by-N upper triangular part of A contains the upper */
/* > triangular part of the matrix A, and the strictly lower */
/* > triangular part of A is not referenced. If UPLO = 'L', the */
/* > leading N-by-N lower triangular part of A contains the lower */
/* > triangular part of the matrix A, and the strictly upper */
/* > triangular part of A is not referenced. */
/* > */
/* > On exit, if INFO = 0, the transformed matrix, stored in the */
/* > same format as A. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is DOUBLE PRECISION array, dimension (LDB,N) */
/* > The triangular factor from the Cholesky factorization of B, */
/* > as returned by DPOTRF. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= max(1,N). */
/* > \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 doubleSYcomputational */
/* ===================================================================== */
/* Subroutine */ int dsygst_(integer *itype, char *uplo, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
info, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer k, kb, nb;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsymm_(
char *, char *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, ftnlen, ftnlen);
logical upper;
extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen), dsygs2_(
integer *, char *, integer *, doublereal *, integer *, doublereal
*, integer *, integer *, ftnlen), dsyr2k_(char *, char *, integer
*, integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen)
, xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, 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 Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_((char *)"DSYGST", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = ilaenv_(&c__1, (char *)"DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
dsygs2_(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info, (
ftnlen)1);
} else {
/* Use blocked code */
if (*itype == 1) {
if (upper) {
/* Compute inv(U**T)*A*inv(U) */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(k:n,k:n) */
dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info, (ftnlen)1);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
dtrsm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &
i__3, &c_b14, &b[k + k * b_dim1], ldb, &a[k +
(k + kb) * a_dim1], lda, (ftnlen)4, (ftnlen)1,
(ftnlen)9, (ftnlen)8);
i__3 = *n - k - kb + 1;
dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b14, &a[k + (k + kb) * a_dim1], lda, (
ftnlen)4, (ftnlen)1);
i__3 = *n - k - kb + 1;
dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b19, &a[k +
(k + kb) * a_dim1], lda, &b[k + (k + kb) *
b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) *
a_dim1], lda, (ftnlen)1, (ftnlen)9);
i__3 = *n - k - kb + 1;
dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b16, &a[k + k *
a_dim1], lda, &b[k + (k + kb) * b_dim1], ldb,
&c_b14, &a[k + (k + kb) * a_dim1], lda, (
ftnlen)4, (ftnlen)1);
i__3 = *n - k - kb + 1;
dtrsm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb,
&i__3, &c_b14, &b[k + kb + (k + kb) * b_dim1]
, ldb, &a[k + (k + kb) * a_dim1], lda, (
ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L**T) */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(k:n,k:n) */
dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info, (ftnlen)1);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
dtrsm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3,
&kb, &c_b14, &b[k + k * b_dim1], ldb, &a[k +
kb + k * a_dim1], lda, (ftnlen)5, (ftnlen)1, (
ftnlen)9, (ftnlen)8);
i__3 = *n - k - kb + 1;
dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen)
5, (ftnlen)1);
i__3 = *n - k - kb + 1;
dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b19, &a[
k + kb + k * a_dim1], lda, &b[k + kb + k *
b_dim1], ldb, &c_b14, &a[k + kb + (k + kb) *
a_dim1], lda, (ftnlen)1, (ftnlen)12);
i__3 = *n - k - kb + 1;
dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b16, &a[k + k *
a_dim1], lda, &b[k + kb + k * b_dim1], ldb, &
c_b14, &a[k + kb + k * a_dim1], lda, (ftnlen)
5, (ftnlen)1);
i__3 = *n - k - kb + 1;
dtrsm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &
i__3, &kb, &c_b14, &b[k + kb + (k + kb) *
b_dim1], ldb, &a[k + kb + k * a_dim1], lda, (
ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U**T */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
dtrmm_((char *)"Left", uplo, (char *)"No transpose", (char *)"Non-unit", &i__3, &
kb, &c_b14, &b[b_offset], ldb, &a[k * a_dim1 + 1],
lda, (ftnlen)4, (ftnlen)1, (ftnlen)12, (ftnlen)8)
;
i__3 = k - 1;
dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1);
i__3 = k - 1;
dsyr2k_(uplo, (char *)"No transpose", &i__3, &kb, &c_b14, &a[k *
a_dim1 + 1], lda, &b[k * b_dim1 + 1], ldb, &c_b14,
&a[a_offset], lda, (ftnlen)1, (ftnlen)12);
i__3 = k - 1;
dsymm_((char *)"Right", uplo, &i__3, &kb, &c_b52, &a[k + k *
a_dim1], lda, &b[k * b_dim1 + 1], ldb, &c_b14, &a[
k * a_dim1 + 1], lda, (ftnlen)5, (ftnlen)1);
i__3 = k - 1;
dtrmm_((char *)"Right", uplo, (char *)"Transpose", (char *)"Non-unit", &i__3, &kb,
&c_b14, &b[k + k * b_dim1], ldb, &a[k * a_dim1 +
1], lda, (ftnlen)5, (ftnlen)1, (ftnlen)9, (ftnlen)
8);
dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info, (ftnlen)1);
/* L30: */
}
} else {
/* Compute L**T*A*L */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = min(i__3,nb);
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
dtrmm_((char *)"Right", uplo, (char *)"No transpose", (char *)"Non-unit", &kb, &
i__3, &c_b14, &b[b_offset], ldb, &a[k + a_dim1],
lda, (ftnlen)5, (ftnlen)1, (ftnlen)12, (ftnlen)8);
i__3 = k - 1;
dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k *
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k +
a_dim1], lda, (ftnlen)4, (ftnlen)1);
i__3 = k - 1;
dsyr2k_(uplo, (char *)"Transpose", &i__3, &kb, &c_b14, &a[k +
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[
a_offset], lda, (ftnlen)1, (ftnlen)9);
i__3 = k - 1;
dsymm_((char *)"Left", uplo, &kb, &i__3, &c_b52, &a[k + k *
a_dim1], lda, &b[k + b_dim1], ldb, &c_b14, &a[k +
a_dim1], lda, (ftnlen)4, (ftnlen)1);
i__3 = k - 1;
dtrmm_((char *)"Left", uplo, (char *)"Transpose", (char *)"Non-unit", &kb, &i__3,
&c_b14, &b[k + k * b_dim1], ldb, &a[k + a_dim1],
lda, (ftnlen)4, (ftnlen)1, (ftnlen)9, (ftnlen)8);
dsygs2_(itype, uplo, &kb, &a[k + k * a_dim1], lda, &b[k +
k * b_dim1], ldb, info, (ftnlen)1);
/* L40: */
}
}
}
}
return 0;
/* End of DSYGST */
} /* dsygst_ */
#ifdef __cplusplus
}
#endif
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