mirror of
https://github.com/TREX-CoE/Sherman-Morrison.git
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48c27eb47e
that is smaller than the size of the Slater-matrix * Removed the Slater-matrix as an argument, since it is not used in the algo. * Added a manual 4x4 example to debug MaponiA3 to work with a number of updates that is smaller than the size of the Slater-matrix * Added a new Octave script to quickly check if the computes inverse is correct.
125 lines
3.7 KiB
C++
125 lines
3.7 KiB
C++
// SM-MaponiA3_f.cpp
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// Algorithm 3 from P. Maponi,
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// p. 283, doi:10.1016/j.laa.2006.07.007
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#include "SM_MaponiA3.hpp"
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#include "Helpers.hpp"
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void MaponiA3(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index) {
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unsigned int k, l, lbar, i, j, tmp, component;
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unsigned int *p = new unsigned int[N_updates + 1];
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double alpha, beta;
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double *breakdown = new double[N_updates + 1];
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double *Al = new double[Dim * Dim];
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p[0] = 0;
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for (i = 0; i < N_updates; i++) {
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p[i + 1] = i + 1;
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}
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// Declare auxiliary solution matrix ylk
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double ***ylk = new double **[N_updates];
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for (l = 0; l < N_updates; l++) {
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ylk[l] = new double *[N_updates + 1];
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for (k = 0; k < N_updates + 1; k++) {
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ylk[l][k] = new double[Dim + 1] {0};
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}
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}
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cout << endl;
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// Calculate all the y0k in Dim^2 multiplications instead of Dim^3
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for (k = 1; k < N_updates + 1; k++) {
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for (i = 1; i < Dim + 1; i++) {
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cout << k << "," << i << endl;
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ylk[0][k][i] =
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Slater_inv[(i - 1) * Dim + (i - 1)] * Updates[(i - 1) * Dim + (k - 1)];
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}
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}
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cout << "y0k = " << endl;
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for (k = 1; k < N_updates + 1; k++) {
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cout << "[ ";
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for (i = 1; i < Dim + 1; i++) {
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cout << ylk[0][k][i] << " ";
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}
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cout << " ]" << endl;
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}
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cout << endl;
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showVector(p, N_updates + 1, "p");
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showVector(Updates_index, N_updates, "Updates_index");
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// Calculate all the ylk from the y0k
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for (l = 1; l < N_updates; l++) {
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for (j = l; j < N_updates + 1; j++) {
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component = Updates_index[p[j] - 1];
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cout << component << endl;
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breakdown[j] = abs(1 + ylk[l - 1][p[j]][component]);
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}
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lbar = getMaxIndex(breakdown, N_updates + 1);
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// Reset breakdown back to 0 for next round to avoid case where its first element is always the largest
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for (i = 0; i < N_updates + 1; i++) {
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breakdown[i] = 0;
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}
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tmp = p[l];
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p[l] = p[lbar];
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p[lbar] = tmp;
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component = Updates_index[p[l] - 1];
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beta = 1 + ylk[l - 1][p[l]][component];
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if (beta == 0) {
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cout << "Break-down occured. Exiting..." << endl;
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exit;
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}
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for (k = l + 1; k < N_updates + 1; k++) {
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alpha = ylk[l - 1][p[k]][component] / beta;
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for (i = 1; i < Dim + 1; i++) {
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ylk[l][p[k]][i] = ylk[l - 1][p[k]][i] - alpha * ylk[l - 1][p[l]][i];
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}
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}
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}
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// Keep the memory location of the passed array 'Slater_inv' before
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// 'Slater_inv' gets reassigned by 'matMul(...)' in the next line, by creating
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// a new pointer 'copy' that points to whereever 'Slater_inv' points to now.
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double *copy = Slater_inv;
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// Construct A-inverse from A0-inverse and the ylk
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for (l = 0; l < N_updates; l++) {
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k = l + 1;
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component = Updates_index[p[k] - 1];
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beta = 1 + ylk[l][p[k]][component];
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for (i = 0; i < Dim; i++) {
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for (j = 0; j < Dim; j++) {
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Al[i * Dim + j] = (i == j) - (j == p[k]-1) * ylk[l][p[k]][i + 1] / beta;
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}
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}
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Slater_inv = matMul(Al, Slater_inv, Dim);
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}
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// Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
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for (i = 0; i < Dim; i++) {
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for (j = 0; j < Dim; j++) {
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copy[i * Dim + j] = Slater_inv[i * Dim + j];
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}
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}
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for (l = 0; l < N_updates; l++) {
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for (k = 0; k < N_updates + 1; k++) {
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delete[] ylk[l][k];
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}
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delete[] ylk[l];
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}
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delete[] Al;
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delete[] p, breakdown;
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}
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extern "C" {
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void MaponiA3_f(double **linSlater_inv, unsigned int *Dim,
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unsigned int *N_updates, double **linUpdates,
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unsigned int **Updates_index) {
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MaponiA3(*linSlater_inv, *Dim,
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*N_updates, *linUpdates,
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*Updates_index);
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}
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}
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