Sherman-Morrison/SM_MaponiA3.cpp
François Coppens 8d63dd1701 The algorithm now works for the following 4x4 example with 2 updates:
S = [1,0,1,-1; 0,1,1,0; -1,0,-1,0; 1,1,1,1]
S_inv = [1,-1,1,1; 1,0,2,1; -1,1,-2,-1; -1,0,-1,0]
u1 = [0,-2,0,0]
u2 = [0,-1,0,0]
upd_idx = [2,4]

To go from Maponi's examples where the number of updates is always equal
to the the dimension of the matrix, and the decomposition is always
diagonal, to cases with a non-diagonal decomposition and a number of
updates unequal to its size, the following changed needed to be made:

* in the calculation of the {y0k} an extra inner for-loop needs to be
  added to make it a full matrix-vector multiplication due to the fact
  that A0 is not a diagonal matrix

* in some places the use of the update-order vector p needs
  the be replaced with that of upd_idx to make sure the correct
  component of the ylk is selected and the proper rank-1 matrices are
  constructed

* when a matrix is passed from Fortran to C++ with 2D adressing, it is
  passed in colum-major order. The passed matrix needs to be transposed
  before passing to C++. Doing this inside the algorithm will break
  compatibility with called from C/C++.
2021-02-22 15:41:30 +01:00

116 lines
3.4 KiB
C++

// SM-MaponiA3_f.cpp
// Algorithm 3 from P. Maponi,
// p. 283, doi:10.1016/j.laa.2006.07.007
#include "SM_MaponiA3.hpp"
#include "Helpers.hpp"
void MaponiA3(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
double *Updates, unsigned int *Updates_index) {
unsigned int k, l, lbar, i, j, tmp, component;
unsigned int *p = new unsigned int[N_updates + 1];
double alpha, beta;
double *breakdown = new double[N_updates + 1];
double *Al = new double[Dim * Dim];
p[0] = 0;
for (i = 0; i < N_updates; i++) {
p[i + 1] = i + 1;
}
// Declare auxiliary solution matrix ylk
double ***ylk = new double **[N_updates];
for (l = 0; l < N_updates; l++) {
ylk[l] = new double *[N_updates + 1];
for (k = 0; k < N_updates + 1; k++) {
ylk[l][k] = new double[Dim + 1] {0};
}
}
// Calculate the y0k
for (k = 1; k < N_updates + 1; k++) {
for (i = 1; i < Dim + 1; i++) {
for (j = 1; j < Dim + 1; j++) {
ylk[0][k][i] += Slater_inv[(i-1) + (j-1)*Dim]
* Updates[(k-1)*Dim + (j-1)];
}
}
}
// Calculate all the ylk from the y0k
for (l = 1; l < N_updates; l++) {
for (j = l; j < N_updates + 1; j++) {
component = Updates_index[p[j] - 1];
breakdown[j] = abs(1 + ylk[l - 1][p[j]][component]);
}
lbar = getMaxIndex(breakdown, N_updates + 1);
// Reset breakdown back to 0 for next round to avoid case where its
// first element is always the largest
for (i = 0; i < N_updates + 1; i++) {
breakdown[i] = 0;
}
tmp = p[l];
p[l] = p[lbar];
p[lbar] = tmp;
component = Updates_index[p[l] - 1];
beta = 1 + ylk[l - 1][p[l]][component];
if (beta == 0) {
cout << "Break-down occured. Exiting..." << endl;
exit;
}
for (k = l + 1; k < N_updates + 1; k++) {
alpha = ylk[l - 1][p[k]][component] / beta;
for (i = 1; i < Dim + 1; i++) {
ylk[l][p[k]][i] = ylk[l - 1][p[k]][i] - alpha * ylk[l - 1][p[l]][i];
}
}
}
// 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;
Slater_inv = transpose(Slater_inv, Dim);
// Construct A-inverse from A0-inverse and the ylk
for (l = 0; l < N_updates; l++) { // l = 0, 1
k = l + 1; // k = 1, 2
component = Updates_index[p[k] - 1]; // comp = 2, 4
beta = 1 + ylk[l][p[k]][component];
for (i = 0; i < Dim; i++) {
for (j = 0; j < Dim; j++) {
Al[i * Dim + j] = (i == j) - (j == component - 1) * ylk[l][p[k]][i + 1] / beta;
}
}
Slater_inv = matMul(Al, Slater_inv, Dim);
}
Slater_inv = transpose(Slater_inv, Dim);
// Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
for (i = 0; i < Dim; i++) {
for (j = 0; j < Dim; j++) {
copy[i * Dim + j] = Slater_inv[i * Dim + j];
}
}
for (l = 0; l < N_updates; l++) {
for (k = 0; k < N_updates + 1; k++) {
delete[] ylk[l][k];
}
delete[] ylk[l];
}
delete[] Al;
delete[] p, breakdown;
}
extern "C" {
void MaponiA3_f(double **linSlater_inv, unsigned int *Dim,
unsigned int *N_updates, double **linUpdates,
unsigned int **Updates_index) {
MaponiA3(*linSlater_inv, *Dim,
*N_updates, *linUpdates,
*Updates_index);
}
}