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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>.
*/
/** @file matrix_norm.cc
@brief Code for computing Euclidean norm of a dense matrix.
@author: Elias Rudberg <em>responsible</em>
*/
#include <stdlib.h>
#include <cmath>
#include "matrix_norm.h"
#include "memorymanag.h"
#include "output.h"
#include "../matrix/mat_gblas.h"
static ergo_real
get_largest_eigenvalue(int n, const ergo_real* M)
{
int lwork = 3*n*n;
ergo_real* work = (ergo_real*)ergo_malloc(lwork*sizeof(ergo_real));
ergo_real* eigvalList = (ergo_real*)ergo_malloc(n*sizeof(ergo_real));
ergo_real* A = (ergo_real*)ergo_malloc(n*n*sizeof(ergo_real));
memcpy(A, M, n*n*sizeof(ergo_real));
int info = -1;
mat::syev("N", "U", &n, A,
&n, eigvalList, work, &lwork,
&info);
if(info != 0)
{
do_output(LOG_CAT_ERROR, LOG_AREA_INTEGRALS, "error in get_largest_eigenvalue, in syev, info = %i", info);
exit(EXIT_FAILURE);
}
ergo_real largestEigenvalue = eigvalList[n-1];
ergo_free(work);
ergo_free(eigvalList);
ergo_free(A);
return largestEigenvalue;
}
ergo_real
get_euclidean_norm(int m, int n, const ergo_real* A)
{
if(n > m)
{
// Create transpose
ergo_real* AT = (ergo_real*)ergo_malloc(n*m*sizeof(ergo_real));
int i, j;
for(i = 0; i < n; i++)
for(j = 0; j < m; j++)
AT[j*n+i] = A[i*m+j];
// Compute norm of AT, which is the same as norm of A
ergo_real normOfTranspose = get_euclidean_norm(n, m, AT);
ergo_free(AT);
return normOfTranspose;
}
// Create matrix AT*A ( n * n matrix )
ergo_real* ATA = (ergo_real*)ergo_malloc(n*n*sizeof(ergo_real));
int i, j, k;
for(i = 0; i < n; i++)
for(j = 0; j < n; j++)
{
ergo_real sum = 0;
for(k = 0; k < m; k++)
sum += A[i*m+k]*A[j*m+k];
ATA[i*n+j] = sum;
}
// Get largest abs eigenvalue of ATA
ergo_real largestEigenvalue = get_largest_eigenvalue(n, ATA);
// The Euclidean norm is given by
// the square root of the largest abs eigenvalue of ATA
ergo_real euclideanNorm = template_blas_sqrt(largestEigenvalue);
ergo_free(ATA);
return euclideanNorm;
}
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