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hypre/lapack/dsygs2.c

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/*BHEADER**********************************************************************
* Copyright (c) 2006 The Regents of the University of California.
* Produced at the Lawrence Livermore National Laboratory.
* Written by the HYPRE team. UCRL-CODE-222953.
* All rights reserved.
*
* This file is part of HYPRE (see http://www.llnl.gov/CASC/hypre/).
* Please see the COPYRIGHT_and_LICENSE file for the copyright notice,
* disclaimer, contact information and the GNU Lesser General Public License.
*
* HYPRE is free software; you can redistribute it and/or modify it under the
* terms of the GNU General Public License (as published by the Free Software
* Foundation) version 2.1 dated February 1999.
*
* HYPRE is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the IMPLIED WARRANTY OF MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the terms and conditions of the GNU General
* Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* $Revision$
***********************************************************************EHEADER*/
#include "../blas/hypre_blas.h"
#include "hypre_lapack.h"
#include "f2c.h"
/* Subroutine */ int dsygs2_(integer *itype, char *uplo, integer *n,
doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
DSYGS2 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')*A*inv(U) or inv(L)*A*inv(L')
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` or L'*A*L.
B must have been previously factorized as U'*U or L*L' by DPOTRF.
Arguments
=========
ITYPE (input) INTEGER
= 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
= 2 or 3: compute U*A*U' or L'*A*L.
UPLO (input) CHARACTER
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored, and how B has been factorized.
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) 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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by DPOTRF.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
static doublereal c_b6 = -1.;
static integer c__1 = 1;
static doublereal c_b27 = 1.;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
extern /* Subroutine */ int dsyr2_(char *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *);
static integer k;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *);
static logical upper;
extern /* Subroutine */ int dtrmv_(char *, char *, char *, integer *,
doublereal *, integer *, doublereal *, integer *), dtrsv_(char *, char *, char *, integer *, doublereal *,
integer *, doublereal *, integer *);
static doublereal ct;
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal akk, bkk;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*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_("DSYGS2", &i__1);
return 0;
}
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(k:n,k:n) */
akk = a_ref(k, k);
bkk = b_ref(k, k);
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
a_ref(k, k) = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
dscal_(&i__2, &d__1, &a_ref(k, k + 1), lda);
ct = akk * -.5;
i__2 = *n - k;
daxpy_(&i__2, &ct, &b_ref(k, k + 1), ldb, &a_ref(k, k + 1)
, lda);
i__2 = *n - k;
dsyr2_(uplo, &i__2, &c_b6, &a_ref(k, k + 1), lda, &b_ref(
k, k + 1), ldb, &a_ref(k + 1, k + 1), lda);
i__2 = *n - k;
daxpy_(&i__2, &ct, &b_ref(k, k + 1), ldb, &a_ref(k, k + 1)
, lda);
i__2 = *n - k;
dtrsv_(uplo, "Transpose", "Non-unit", &i__2, &b_ref(k + 1,
k + 1), ldb, &a_ref(k, k + 1), lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(k:n,k:n) */
akk = a_ref(k, k);
bkk = b_ref(k, k);
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
a_ref(k, k) = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
dscal_(&i__2, &d__1, &a_ref(k + 1, k), &c__1);
ct = akk * -.5;
i__2 = *n - k;
daxpy_(&i__2, &ct, &b_ref(k + 1, k), &c__1, &a_ref(k + 1,
k), &c__1);
i__2 = *n - k;
dsyr2_(uplo, &i__2, &c_b6, &a_ref(k + 1, k), &c__1, &
b_ref(k + 1, k), &c__1, &a_ref(k + 1, k + 1), lda);
i__2 = *n - k;
daxpy_(&i__2, &ct, &b_ref(k + 1, k), &c__1, &a_ref(k + 1,
k), &c__1);
i__2 = *n - k;
dtrsv_(uplo, "No transpose", "Non-unit", &i__2, &b_ref(k
+ 1, k + 1), ldb, &a_ref(k + 1, k), &c__1);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the upper triangle of A(1:k,1:k) */
akk = a_ref(k, k);
bkk = b_ref(k, k);
i__2 = k - 1;
dtrmv_(uplo, "No transpose", "Non-unit", &i__2, &b[b_offset],
ldb, &a_ref(1, k), &c__1);
ct = akk * .5;
i__2 = k - 1;
daxpy_(&i__2, &ct, &b_ref(1, k), &c__1, &a_ref(1, k), &c__1);
i__2 = k - 1;
dsyr2_(uplo, &i__2, &c_b27, &a_ref(1, k), &c__1, &b_ref(1, k),
&c__1, &a[a_offset], lda);
i__2 = k - 1;
daxpy_(&i__2, &ct, &b_ref(1, k), &c__1, &a_ref(1, k), &c__1);
i__2 = k - 1;
dscal_(&i__2, &bkk, &a_ref(1, k), &c__1);
/* Computing 2nd power */
d__1 = bkk;
a_ref(k, k) = akk * (d__1 * d__1);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
/* Update the lower triangle of A(1:k,1:k) */
akk = a_ref(k, k);
bkk = b_ref(k, k);
i__2 = k - 1;
dtrmv_(uplo, "Transpose", "Non-unit", &i__2, &b[b_offset],
ldb, &a_ref(k, 1), lda);
ct = akk * .5;
i__2 = k - 1;
daxpy_(&i__2, &ct, &b_ref(k, 1), ldb, &a_ref(k, 1), lda);
i__2 = k - 1;
dsyr2_(uplo, &i__2, &c_b27, &a_ref(k, 1), lda, &b_ref(k, 1),
ldb, &a[a_offset], lda);
i__2 = k - 1;
daxpy_(&i__2, &ct, &b_ref(k, 1), ldb, &a_ref(k, 1), lda);
i__2 = k - 1;
dscal_(&i__2, &bkk, &a_ref(k, 1), lda);
/* Computing 2nd power */
d__1 = bkk;
a_ref(k, k) = akk * (d__1 * d__1);
/* L40: */
}
}
}
return 0;
/* End of DSYGS2 */
} /* dsygs2_ */
#undef b_ref
#undef a_ref
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