Sherman-Morrison/SM_MaponiA3.cpp
François Coppens 84fffdb7fa Prepared the example matrix of Example 8 of the paper and its
decomposition in the Fortran code and made a basic call to the
subroutine MYSUBROUTINE, which is bound to the C++ void function
'Sherman-Morrison();. For now compilation fails with lots of undefined
references.'
2021-02-04 13:12:47 +01:00

111 lines
3.3 KiB
C++

// SM-MaponiA3.cpp
// Algorithm 3 from P. Maponi,
// p. 283, doi:10.1016/j.laa.2006.07.007
#include "SM_MaponiA3.hpp"
#include "Helpers.hpp"
void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) {
unsigned int k, l, lbar, i, j, tmp, M = *Dim;
unsigned int *p = new unsigned int[M+1];
unsigned int **Id = new unsigned int*[M];
double alpha, beta;
double **U, *breakdown = new double[M+1];
double **Al = new double*[M];
p[0] = 0;
for (i = 0; i < M; i++) {
p[i+1] = i + 1;
Id[i] = new unsigned int[M];
Al[i] = new double[M];
}
// 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];
}
}
// Initialize identity matrix
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
if (i != j) Id[i][j] = 0;
else Id[i][j] = 1;
}
}
// 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++) {
ylk[0][k][i] = Slater_inv[i-1][i-1] * Updates[i-1][k-1];
}
}
// 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];
}
}
}
// Construct A-inverse from A0-inverse and the ylk
// 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.
double **copy = Slater_inv;
for (l = 0; l < M; l++) {
k = l+1;
U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
beta = 1 + ylk[l][p[k]][p[k]];
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
Al[i][j] = Id[i][j] - U[i][j] / beta;
}
}
Slater_inv = matMul(Al, Slater_inv, M);
}
// Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
copy[i][j] = Slater_inv[i][j];
}
}
for (l = 0; l < M; l++) {
for (k = 0; k < M+1; k++) {
delete [] ylk[l][k];
}
delete [] ylk[l], Id[l], U[l], Al[l], Slater_inv[l];
}
delete [] p, breakdown;
}