Merge pull request #2 from fmgjcoppens/fix/upd-inverse

Fix/upd inverse
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François Coppens 2021-02-03 15:05:01 +01:00 committed by GitHub
commit 5531d9eb12
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7 changed files with 169 additions and 163 deletions

126
Helpers.hpp Normal file
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@ -0,0 +1,126 @@
// Helpers.hpp
// Some usefull helper functions to support the Maponi algorithm.
#include <iostream>
#include <cmath>
#include <string>
using namespace std;
template<typename T>
unsigned int getMaxIndex(T *vector, unsigned int size) {
unsigned int i;
unsigned int max = vector[0];
unsigned int maxi = 0;
for (i = 1; i < size; i++) {
if (vector[i] > max) {
max = vector[i];
maxi = i;
}
}
return maxi;
}
template<typename T>
void showScalar(T scalar, string name) {
cout << name << " = " << scalar << endl << endl;
}
template<typename T>
void showVector(T *vector, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ " << vector[i] << " ]" << endl;
}
cout << endl;
}
template<typename T>
void showMatrix(T **matrix, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ ";
for (unsigned int j = 0; j < size; j++) {
cout << matrix[i][j] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
template<typename T>
void showMatrixT(T **matrix, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ ";
for (unsigned int j = 0; j < size; j++) {
cout << matrix[j][i] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
template<typename T>
T **matMul(T **A, T **B, unsigned int size) {
T **C = new T*[size];
for (unsigned int i = 0; i < size; i++) {
C[i] = new T[size];
}
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
for (unsigned int k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
template<typename T1, typename T2>
T1 **outProd(T1 *vec1, T2 *vec2, unsigned int size) {
T1 **C = new T1*[size];
for (unsigned int i = 0; i < size; i++) {
C[i] = new T1[size];
}
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
C[i][j] = vec1[i+1] * vec2[j];
}
}
return C;
}
template<typename T>
T matDet(T **A, unsigned int M) {
int det = 0, p, h, k, i, j;
T **temp = new T*[M];
for (int i = 0; i < M; i++) temp[i] = new T[M];
if(M == 1) {
return A[0][0];
}
else if(M == 2) {
det = (A[0][0] * A[1][1] - A[0][1] * A[1][0]);
return det;
}
else {
for(p = 0; p < M; p++) {
h = 0;
k = 0;
for(i = 1; i < M; i++) {
for( j = 0; j < M; j++) {
if(j == p) {
continue;
}
temp[h][k] = A[i][j];
k++;
if(k == M-1) {
h++;
k = 0;
}
}
}
det = det + A[0][p] * pow(-1, p) * matDet(temp, M-1);
}
return det;
}
delete [] temp;
}

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@ -1,23 +1,21 @@
// 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];
double *breakdown = new double[M+1];
unsigned int **Id = new unsigned int*[M];
double alpha, beta;
for (i = 0; i < M+1; i++) {
p[i] = i;
}
int **Id = new int*[M];
for (i = 0; i < M; i++) Id[i] = new int[M];
double **U, *breakdown = new double[M+1];
double **Al = new double*[M];
p[0] = 0;
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
if (i != j) Id[i][j] = 0;
else Id[i][j] = 1;
}
p[i+1] = i + 1;
Id[i] = new unsigned int[M];
Al[i] = new double[M];
}
// Declare auxiliary solution matrix ylk
@ -28,6 +26,15 @@ void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, uns
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++) {
@ -70,9 +77,10 @@ void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, uns
}
// Construct A-inverse from A0-inverse and the ylk
double **U;
double **Al = new double*[M];
for (i = 0; i < M; i++) Al[i] = new double[M];
// 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;
@ -86,18 +94,18 @@ void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, uns
Slater_inv = matMul(Al, Slater_inv, M);
}
delete [] p, breakdown;
// Assign the new values of 'Slater_inv' to the old values in 'copy[][]'
for (i = 0; i < M; i++) {
delete [] Id[i];
delete [] U[i];
delete [] Al[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];
delete [] ylk[l], Id[l], U[l], Al[l], Slater_inv[l];
}
delete [] p, breakdown;
}

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@ -1,127 +1,3 @@
// SM-MaponiA3.hpp
#include <iostream>
#include <cmath>
#include <string>
using namespace std;
void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index);
template<typename T>
unsigned int getMaxIndex(T *vector, unsigned int size) {
unsigned int i;
unsigned int max = vector[0];
unsigned int maxi = 0;
for (i = 1; i < size; i++) {
if (vector[i] > max) {
max = vector[i];
maxi = i;
}
}
return maxi;
}
template<typename T>
void showScalar(T scalar, string name) {
cout << name << " = " << scalar << endl << endl;
}
template<typename T>
void showVector(T* vector, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ " << vector[i] << " ]" << endl;
}
cout << endl;
}
template<typename T>
void showMatrix(T** matrix, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ ";
for (unsigned int j = 0; j < size; j++) {
cout << matrix[i][j] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
template<typename T>
void showMatrixT(T** matrix, unsigned int size, string name) {
cout << name << " = " << endl;
for (unsigned int i = 0; i < size; i++) {
cout << "[ ";
for (unsigned int j = 0; j < size; j++) {
cout << matrix[j][i] << " ";
}
cout << " ]" << endl;
}
cout << endl;
}
template<typename T>
T** matMul(T** A, T** B, unsigned int size) {
T** C = new T*[size];
for (unsigned int i = 0; i < size; i++) {
C[i] = new T[size];
}
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
for (unsigned int k = 0; k < size; k++) {
C[i][j] += A[i][k] * B[k][j];
}
}
}
return C;
}
template<typename T1, typename T2>
T1** outProd(T1* vec1, T2* vec2, unsigned int size) {
T1** C = new T1*[size];
for (unsigned int i = 0; i < size; i++) {
C[i] = new T1[size];
}
for (unsigned int i = 0; i < size; i++) {
for (unsigned int j = 0; j < size; j++) {
C[i][j] = vec1[i+1] * vec2[j];
}
}
return C;
}
template<typename T>
T matDet(T** A, unsigned int M) {
int det = 0, p, h, k, i, j;
T** temp = new T*[M];
for (int i = 0; i < M; i++) temp[i] = new T[M];
if(M == 1) {
return A[0][0];
}
else if(M == 2) {
det = (A[0][0] * A[1][1] - A[0][1] * A[1][0]);
return det;
}
else {
for(p = 0; p < M; p++) {
h = 0;
k = 0;
for(i = 1; i < M; i++) {
for( j = 0; j < M; j++) {
if(j == p) {
continue;
}
temp[h][k] = A[i][j];
k++;
if(k == M-1) {
h++;
k = 0;
}
}
}
det = det + A[0][p] * pow(-1, p) * matDet(temp, M-1);
}
return det;
}
delete [] temp;
}

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@ -1,7 +1,6 @@
// Algorithm 3 from P. Maponi,
// p. 283, doi:10.1016/j.laa.2006.07.007
// main.cpp
#include "SM-MaponiA3.hpp"
#include "Helpers.hpp"
#include <cstdlib>
#include <ctime>
@ -12,7 +11,7 @@ int main() {
unsigned int M = 3; // Dimension of the Slater-matrix
unsigned int i, j; // Indices for iterators
// Declare and allocate all vectors and matrices
// Declare, allocate all vectors and matrices and fill them with zeros
unsigned int *Ar_index = new unsigned int[M];
int **A = new int*[M]; // The matrix to be inverted
int **A0 = new int*[M]; // A diagonal matrix with the digonal elements of A
@ -24,8 +23,7 @@ int main() {
Ar[i] = new int[M];
A0_inv[i] = new double[M];
}
// Initialize all matrices with zeros
// Fill with zeros
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++) {
A0[i][j] = 0;
@ -34,11 +32,10 @@ int main() {
}
}
// Initialize A with M=3 and Eq. (17) from paper
// Initialize A with M=3 and fill acc. to Eq. (17) from paper
A[0][0] = 1; A[0][1] = 1; A[0][2] = -1;
A[1][0] = 1; A[1][1] = 1; A[1][2] = 0;
A[2][0] = -1; A[2][1] = 0; A[2][2] = -1;
// // Fill A with random numbers from [-randRange,randRange]
// // and check if A and A0 are invertable
// do {
@ -51,11 +48,13 @@ int main() {
// A0[i][i] = A[i][i];
// }
// } while (matDet(A, M) == 0 || matDet(A0, M) == 0);
showMatrix(A, M, "A");
// Init the update matrix Ar, A0_inv and Ar_index
// Initialize the diagonal matrix A0,
// the inverse of A0_inv of diagonal matrix A0_inv
// and the update matrix Ar
for (i = 0; i < M; i++) {
A0[i][i] = A[i][i];
A0_inv[i][i] = 1.0/A[i][i];
Ar_index[i] = i;
for (j = 0; j < M; j++) {
@ -63,18 +62,15 @@ int main() {
}
}
// Define pointers dim and n_updates to use in Sherman-Morrison(...) function call
unsigned int *dim = new unsigned int(M);
unsigned int *n_updates = new unsigned int(M);
Sherman_Morrison(A0, A0_inv, dim, n_updates, Ar, Ar_index);
showMatrix(A0_inv, M, "A0_inv");
// Deallocate all vectors and matrices
for (i = 0; i < M; i++) {
delete [] A[i];
delete [] A0[i];
delete [] A0_inv[i];
delete [] Ar[i];
delete [] A[i], A0[i], A0_inv[i], Ar[i];
}
delete [] A, A0, A0_inv, Ar, Ar_index;
delete dim, n_updates;