2021-02-09 13:40:52 +01:00
|
|
|
// SM-MaponiA3_f.cpp
|
2021-02-03 12:13:09 +01:00
|
|
|
// Algorithm 3 from P. Maponi,
|
|
|
|
// p. 283, doi:10.1016/j.laa.2006.07.007
|
2021-02-04 11:39:00 +01:00
|
|
|
#include "SM_MaponiA3.hpp"
|
2021-02-03 12:13:09 +01:00
|
|
|
#include "Helpers.hpp"
|
2021-01-27 17:19:41 +01:00
|
|
|
|
2021-02-09 13:40:52 +01:00
|
|
|
void MaponiA3(double *Slater0, double *Slater_inv, unsigned int M, unsigned int N_updates, double *Updates, unsigned int *Updates_index) {
|
|
|
|
|
|
|
|
unsigned int k, l, lbar, i, j, tmp = M;
|
2021-02-03 11:02:15 +01:00
|
|
|
unsigned int *p = new unsigned int[M+1];
|
2021-02-02 15:05:47 +01:00
|
|
|
double alpha, beta;
|
2021-02-09 13:40:52 +01:00
|
|
|
double *breakdown = new double[M+1];
|
|
|
|
double *Al = new double[M*M];
|
2021-02-03 14:49:13 +01:00
|
|
|
p[0] = 0;
|
2021-02-02 15:05:47 +01:00
|
|
|
for (i = 0; i < M; i++) {
|
2021-02-03 14:49:13 +01:00
|
|
|
p[i+1] = i + 1;
|
2021-02-02 15:05:47 +01:00
|
|
|
}
|
|
|
|
|
|
|
|
// Declare auxiliary solution matrix ylk
|
|
|
|
double ***ylk = new double**[M];
|
|
|
|
for (l = 0; l < M; l++) {
|
|
|
|
ylk[l] = new double*[M+1];
|
|
|
|
for (k = 0; k < M+1; k++) {
|
|
|
|
ylk[l][k] = new double[M+1];
|
|
|
|
}
|
|
|
|
}
|
2021-02-03 14:49:13 +01:00
|
|
|
|
2021-02-02 15:05:47 +01:00
|
|
|
// Initialize ylk with zeros
|
|
|
|
for (l = 0; l < M; l++) {
|
|
|
|
for (k = 0; k < M+1; k++) {
|
|
|
|
for (i = 0; i < M+1; i++) {
|
|
|
|
ylk[l][k][i] = 0;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Calculate all the y0k in M^2 multiplications instead of M^3
|
|
|
|
for (k = 1; k < M+1; k++) {
|
|
|
|
for (i = 1; i < M+1; i++) {
|
2021-02-09 13:40:52 +01:00
|
|
|
ylk[0][k][i] = Slater_inv[(i-1)*M+(i-1)] * Updates[(i-1)*M+(k-1)];
|
2021-02-02 15:05:47 +01:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
// Calculate all the ylk from the y0k
|
|
|
|
for (l = 1; l < M; l++) {
|
|
|
|
for (j = l; j < M+1; j++) {
|
|
|
|
breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
|
|
|
|
}
|
|
|
|
lbar = getMaxIndex(breakdown, M+1);
|
|
|
|
for (i = 0; i < M; i++) {
|
|
|
|
breakdown[i] = 0;
|
|
|
|
}
|
|
|
|
tmp = p[l];
|
|
|
|
p[l] = p[lbar];
|
|
|
|
p[lbar] = tmp;
|
|
|
|
for (k = l+1; k < M+1; k++) {
|
|
|
|
beta = 1 + ylk[l-1][p[l]][p[l]];
|
|
|
|
if (beta == 0) {
|
|
|
|
cout << "Break-down condition occured. Exiting..." << endl;
|
|
|
|
exit;
|
|
|
|
}
|
|
|
|
for (i = 1; i < M+1; i++) {
|
|
|
|
alpha = ylk[l-1][p[k]][p[l]] / beta;
|
|
|
|
ylk[l][p[k]][i] = ylk[l-1][p[k]][i] - alpha * ylk[l-1][p[l]][i];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2021-02-03 14:49:13 +01:00
|
|
|
// Keep the memory location of the passed array 'Slater_inv' before 'Slater_inv'
|
|
|
|
// gets reassigned by 'matMul(...)' in the next line, by creating a new
|
|
|
|
// pointer 'copy' that points to whereever 'Slater_inv' points to now.
|
2021-02-09 13:40:52 +01:00
|
|
|
double *copy = Slater_inv;
|
2021-02-03 14:49:13 +01:00
|
|
|
|
2021-02-09 14:44:54 +01:00
|
|
|
double *U = new double[M*M];
|
2021-02-09 13:40:52 +01:00
|
|
|
// Construct A-inverse from A0-inverse and the ylk
|
2021-02-02 15:05:47 +01:00
|
|
|
for (l = 0; l < M; l++) {
|
|
|
|
k = l+1;
|
2021-02-09 14:44:54 +01:00
|
|
|
for (unsigned int i = 0; i < M; i++) {
|
|
|
|
for (unsigned int j = 0; j < M; j++) {
|
|
|
|
U[i*M+j] = ylk[l][p[k]][i+1] * ((p[k]-1) == j);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
2021-02-02 15:05:47 +01:00
|
|
|
beta = 1 + ylk[l][p[k]][p[k]];
|
|
|
|
for (i = 0; i < M; i++) {
|
|
|
|
for (j = 0; j < M; j++) {
|
2021-02-09 14:44:54 +01:00
|
|
|
Al[i*M+j] = (i == j) - U[i*M+j] / beta;
|
2021-02-02 15:05:47 +01:00
|
|
|
}
|
|
|
|
}
|
|
|
|
Slater_inv = matMul(Al, Slater_inv, M);
|
|
|
|
}
|
2021-02-02 17:06:32 +01:00
|
|
|
|
2021-02-03 14:49:13 +01:00
|
|
|
// Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
|
2021-02-02 15:05:47 +01:00
|
|
|
for (i = 0; i < M; i++) {
|
2021-02-09 13:40:52 +01:00
|
|
|
for (j = 0; j < M; j++) {
|
|
|
|
copy[i*M+j] = Slater_inv[i*M+j];
|
|
|
|
}
|
2021-02-02 15:05:47 +01:00
|
|
|
}
|
|
|
|
|
|
|
|
for (l = 0; l < M; l++) {
|
|
|
|
for (k = 0; k < M+1; k++) {
|
|
|
|
delete [] ylk[l][k];
|
|
|
|
}
|
2021-02-09 13:40:52 +01:00
|
|
|
delete [] ylk[l];
|
2021-02-02 15:05:47 +01:00
|
|
|
}
|
2021-02-09 14:44:54 +01:00
|
|
|
delete [] Al, U;
|
2021-02-03 14:49:13 +01:00
|
|
|
delete [] p, breakdown;
|
2021-02-09 13:40:52 +01:00
|
|
|
}
|
|
|
|
|
|
|
|
extern "C" {
|
|
|
|
void MaponiA3_f(double **linSlater0, double **linSlater_inv, unsigned int *Dim, unsigned int *N_updates, double **linUpdates, unsigned int **Updates_index)
|
|
|
|
{
|
|
|
|
MaponiA3(*linSlater0, *linSlater_inv, *Dim, *N_updates, *linUpdates, *Updates_index);
|
|
|
|
}
|
|
|
|
}
|