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/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program 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, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_LAPACK_POCON_HEADER
#define TEMPLATE_LAPACK_POCON_HEADER
template<class Treal>
int template_lapack_pocon(const char *uplo, const integer *n, const Treal *a, const integer *
lda, const Treal *anorm, Treal *rcond, Treal *work, integer *
iwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DPOCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite matrix using the
Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by DPOTRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
ANORM (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the symmetric matrix A.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (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 */
integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1;
Treal d__1;
/* Local variables */
integer kase;
Treal scale;
logical upper;
integer ix;
Treal scalel;
Treal scaleu;
Treal ainvnm;
char normin[1];
Treal smlnum;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--work;
--iwork;
/* Function Body */
*info = 0;
upper = template_blas_lsame(uplo, "U");
if (! upper && ! template_blas_lsame(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < maxMACRO(1,*n)) {
*info = -4;
} else if (*anorm < 0.) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("POCON ", &i__1);
return 0;
}
/* Quick return if possible */
*rcond = 0.;
if (*n == 0) {
*rcond = 1.;
return 0;
} else if (*anorm == 0.) {
return 0;
}
smlnum = template_lapack_lamch("Safe minimum", (Treal)0);
/* Estimate the 1-norm of inv(A). */
kase = 0;
*(unsigned char *)normin = 'N';
L10:
template_lapack_lacon(n, &work[*n + 1], &work[1], &iwork[1], &ainvnm, &kase);
if (kase != 0) {
if (upper) {
/* Multiply by inv(U'). */
template_lapack_latrs("Upper", "Transpose", "Non-unit", normin, n, &a[a_offset],
lda, &work[1], &scalel, &work[(*n << 1) + 1], info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(U). */
template_lapack_latrs("Upper", "No transpose", "Non-unit", normin, n, &a[
a_offset], lda, &work[1], &scaleu, &work[(*n << 1) + 1],
info);
} else {
/* Multiply by inv(L). */
template_lapack_latrs("Lower", "No transpose", "Non-unit", normin, n, &a[
a_offset], lda, &work[1], &scalel, &work[(*n << 1) + 1],
info);
*(unsigned char *)normin = 'Y';
/* Multiply by inv(L'). */
template_lapack_latrs("Lower", "Transpose", "Non-unit", normin, n, &a[a_offset],
lda, &work[1], &scaleu, &work[(*n << 1) + 1], info);
}
/* Multiply by 1/SCALE if doing so will not cause overflow. */
scale = scalel * scaleu;
if (scale != 1.) {
ix = template_blas_idamax(n, &work[1], &c__1);
if (scale < (d__1 = work[ix], absMACRO(d__1)) * smlnum || scale == 0.)
{
goto L20;
}
template_lapack_rscl(n, &scale, &work[1], &c__1);
}
goto L10;
}
/* Compute the estimate of the reciprocal condition number. */
if (ainvnm != 0.) {
*rcond = 1. / ainvnm / *anorm;
}
L20:
return 0;
/* End of DPOCON */
} /* dpocon_ */
#endif
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