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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 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_LANST_HEADER
#define TEMPLATE_LAPACK_LANST_HEADER
template<class Treal>
Treal template_lapack_lanst(const char *norm, const integer *n, const Treal *d__, const Treal *e)
{
/* -- LAPACK auxiliary 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
=======
DLANST returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric tridiagonal matrix A.
Description
===========
DLANST returns the value
DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in DLANST as described
above.
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANST is
set to zero.
D (input) DOUBLE PRECISION array, dimension (N)
The diagonal elements of A.
E (input) DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal or super-diagonal elements of A.
=====================================================================
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
/* System generated locals */
integer i__1;
Treal ret_val, d__1, d__2, d__3, d__4, d__5;
/* Local variables */
integer i__;
Treal scale;
Treal anorm;
Treal sum;
--e;
--d__;
/* Initialization added by Elias to get rid of compiler warnings. */
anorm = 0;
/* Function Body */
if (*n <= 0) {
anorm = 0.;
} else if (template_blas_lsame(norm, "M")) {
/* Find max(abs(A(i,j))). */
anorm = (d__1 = d__[*n], absMACRO(d__1));
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__2 = anorm, d__3 = (d__1 = d__[i__], absMACRO(d__1));
anorm = maxMACRO(d__2,d__3);
/* Computing MAX */
d__2 = anorm, d__3 = (d__1 = e[i__], absMACRO(d__1));
anorm = maxMACRO(d__2,d__3);
/* L10: */
}
} else if (template_blas_lsame(norm, "O") || *(unsigned char *)
norm == '1' || template_blas_lsame(norm, "I")) {
/* Find norm1(A). */
if (*n == 1) {
anorm = absMACRO(d__[1]);
} else {
/* Computing MAX */
d__3 = absMACRO(d__[1]) + absMACRO(e[1]), d__4 = (d__1 = e[*n - 1], absMACRO(
d__1)) + (d__2 = d__[*n], absMACRO(d__2));
anorm = maxMACRO(d__3,d__4);
i__1 = *n - 1;
for (i__ = 2; i__ <= i__1; ++i__) {
/* Computing MAX */
d__4 = anorm, d__5 = (d__1 = d__[i__], absMACRO(d__1)) + (d__2 = e[
i__], absMACRO(d__2)) + (d__3 = e[i__ - 1], absMACRO(d__3));
anorm = maxMACRO(d__4,d__5);
/* L20: */
}
}
} else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (*n > 1) {
i__1 = *n - 1;
template_lapack_lassq(&i__1, &e[1], &c__1, &scale, &sum);
sum *= 2;
}
template_lapack_lassq(n, &d__[1], &c__1, &scale, &sum);
anorm = scale * template_blas_sqrt(sum);
}
ret_val = anorm;
return ret_val;
/* End of DLANST */
} /* dlanst_ */
#endif
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