2021-02-09 13:40:52 +01:00
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// SM-MaponiA3_f.cpp
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2021-02-03 12:13:09 +01:00
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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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2021-02-04 11:39:00 +01:00
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#include "SM_MaponiA3.hpp"
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2021-02-03 12:13:09 +01:00
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#include "Helpers.hpp"
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2021-01-27 17:19:41 +01:00
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2021-02-25 12:17:45 +01:00
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void MaponiA3(double *Slater_inv, unsigned int Dim,
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unsigned int N_updates, double *Updates,
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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] {0};
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double alpha, beta;
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double *breakdown = new double[N_updates + 1] {0};
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double *Al = new double[Dim * Dim];
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// Populate update-order vector
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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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2021-02-19 19:11:44 +01:00
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// Calculate the y0k
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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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for (j = 1; j < Dim + 1; j++) {
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2021-02-23 08:28:09 +01:00
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ylk[0][k][i] += Slater_inv[(i-1)*Dim + (j-1)]
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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++.
2021-02-21 18:28:08 +01:00
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* Updates[(k-1)*Dim + (j-1)];
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}
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}
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}
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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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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
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// 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 (fabs(beta) < 1e-6) {
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cout << "Break-down occured. Exiting..." << endl;
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exit(1);
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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]
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- 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,
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// by creating a new pointer 'copy' that points to whereever
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// '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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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++.
2021-02-21 18:28:08 +01:00
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for (l = 0; l < N_updates; l++) { // l = 0, 1
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k = l + 1; // k = 1, 2
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component = Updates_index[p[k] - 1]; // comp = 2, 4
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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 == component-1)
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* 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
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// 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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2021-02-09 15:05:11 +01:00
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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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