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https://github.com/TREX-CoE/Sherman-Morrison.git
synced 2024-07-23 03:07:46 +02:00
Extracted the SM algorithm and wrote it as a void function that updates the passed old inverse. Does not work yet. For some reason the changes in the inverse do not persist when the function is finished. Also the inverse is not correct.
This commit is contained in:
François Coppens
parent
7d3ffe1d2a
commit
9d47bf9bb3
287
SM-MaponiA3.cpp
287
SM-MaponiA3.cpp
@ -8,160 +8,87 @@
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#include <ctime>
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using namespace std;
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uint getMaxIndex(double* arr, uint size);
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uint getMaxIndex(double *arr, uint size);
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template<typename T>void showScalar(T scalar, string name);
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template<typename T>void showVector(T* vector, uint size, string name);
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template<typename T>void showMatrix(T** matrix, uint size, string name);
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template<typename T>void showMatrixT(T** matrix, uint size, string name);
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template<typename T>T** matMul(T** A, T** B, uint size);
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template<typename T1, typename T2>T1** outProd(T1* vec1, T2* vec2, uint size);
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template<typename T>T matDet(T** A, int M);
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template<typename T>void showVector(T *vector, uint size, string name);
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template<typename T>void showMatrix(T **matrix, uint size, string name);
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template<typename T>void showMatrixT(T **matrix, uint size, string name);
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template<typename T>T **matMul(T **A, T **B, uint size);
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template<typename T1, typename T2>T1 **outProd(T1 *vec1, T2 *vec2, uint size);
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template<typename T>T matDet(T **A, int M);
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void Sherman_Morrison(int **Slater0, double **Slater_inv, uint *Dim, uint *N_updates, int **Updates, uint *Updates_index);
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int main() {
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srand((unsigned) time(0));
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uint randRange = 1; // to get random integers in range [-randRange, randRange]
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uint M = 3;
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uint i, j, k, l, lbar, tmp;
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double alpha, beta;
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uint M = 3; // Dimension of the Slater-matrix
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uint i, j; // Indices for iterators
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// Declare and allocate all vectors and matrices
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uint* p = new uint[M+1];
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double* breakdown = new double[M+1];
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int** A = new int*[M];
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int** A0 = new int*[M];
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int** Ar = new int*[M];
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int** Id = new int*[M];
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double** A0inv = new double*[M];
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double** Ainv; //= new double*[M];
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uint *indices_of_updates = new uint[M];
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int **A = new int*[M]; // The matrix to be inverted
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int **A0 = new int*[M]; // A diagonal matrix with the digonal elements of A
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int **Ar = new int*[M]; // The update matrix
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double **A0inv = new double*[M]; // Inverse of A0
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for (i = 0; i < M; i++) {
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A[i] = new int[M];
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//Ainv[i] = new double[M];
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A0[i] = new int[M];
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A0inv[i] = new double[M];
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Ar[i] = new int[M];
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Id[i] = new int[M];
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}
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double*** ylk = new double**[M];
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for (l = 0; l < M; l++) {
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ylk[l] = new double*[M+1];
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for (k = 0; k < M+1; k++) {
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ylk[l][k] = new double[M+1];
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}
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A0inv[i] = new double[M];
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}
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// Initialize all matrices with zeros
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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A0[i][j] = 0;
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A0inv[i][j] = 0;
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Ar[i][j] = 0;
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Id[i][j] = 0;
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A0inv[i][j] = 0;
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}
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}
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// Initialize ylk with zeros
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for (l = 0; l < M; l++) {
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for (k = 0; k < M+1; k++) {
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for (i = 0; i < M+1; i++) {
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ylk[l][k][i] = 0;
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}
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}
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}
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// Initialize A with M=3 and Eq. (17) from paper
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A[0][0] = 1; A[0][1] = 1; A[0][2] = -1;
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A[1][0] = 1; A[1][1] = 1; A[1][2] = 0;
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A[2][0] = -1; A[2][1] = 0; A[2][2] = -1;
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// // Initialize A with M=3 and Eq. (17) from paper
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// A[0][0] = 1; A[0][1] = 1; A[0][2] = -1;
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// A[1][0] = 1; A[1][1] = 1; A[1][2] = 0;
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// A[2][0] = -1; A[2][1] = 0; A[2][2] = -1;
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// // Fill A with random numbers from [-randRange,randRange]
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// // and check if A and A0 are invertable
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// do {
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// for (i = 0; i < M; i++) {
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// for (j = 0; j < M; j++) {
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// A[i][j] = rand()%(2*randRange+1)-randRange;
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// }
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// }
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// for (i = 0; i < M; i++) {
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// A0[i][i] = A[i][i];
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// }
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// } while (matDet(A, M) == 0 || matDet(A0, M) == 0);
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showMatrix(A, M, "A");
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// Fill A with random numbers from [-1,1]
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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A[i][j] = rand()%(2*randRange+1)-randRange;
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}
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}
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// Define identity matrix, A0, A0inv and p
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p[0] = 0;
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for (i = 0; i < M; i++) {
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Id[i][i] = 1;
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A0[i][i] = A[i][i];
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A0inv[i][i] = 1.0/A[i][i];
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p[i+1] = i+1;
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}
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// Init Ar
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// Init Ar: the update matrix
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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Ar[i][j] = A[i][j] - A0[i][j];
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}
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}
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showMatrix(A, M, "A");
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// showMatrix(A0, M, M, "A0");
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// showMatrix(Ar, M, M, "Ar");
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// showMatrix(A0inv, M, M, "A0inv");
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// Calculate all the y0k in M^2 multiplications instead of M^3
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for (k = 1; k < M+1; k++) {
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for (i = 1; i < M+1; i++) {
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ylk[0][k][i] = A0inv[i-1][i-1] * Ar[i-1][k-1];
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}
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// showVector(ylk[0][k], M+1, "y0k");
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// Define A0inv
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for (i = 0; i < M; i++) {
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A0inv[i][i] = 1.0/A[i][i];
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}
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// showMatrixT(ylk[0], M+1, "y0k");
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showMatrix(A0inv, M, "A0inv");
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// Calculate all the ylk from the y0k
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// showVector(p, M+1, "p");
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for (l = 1; l < M; l++) {
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for (j = l; j < M+1; j++) {
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breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
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}
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// showVector(breakdown, M+1, "break-down vector");
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lbar = getMaxIndex(breakdown, M+1);
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// showScalar(lbar, "lbar");
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for (i = 0; i < M; 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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// showVector(p, M+1, "p");
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for (k = l+1; k < M+1; k++) {
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beta = 1 + ylk[l-1][p[l]][p[l]];
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if (beta == 0) {
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cout << "Break-down condition occured. Exiting..." << endl;
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exit;
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}
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for (i = 1; i < M+1; i++) {
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alpha = ylk[l-1][p[k]][p[l]] / beta;
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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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// showVector(ylk[l][p[k]], M+1, "ylk");
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}
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// Populate indices_of_updates
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for (i = 0; i < M; i++) {
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indices_of_updates[i] = i;
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}
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// showMatrixT(ylk[1], M+1, "y1k");
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// showMatrixT(ylk[2], M+1, "y2k");
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// Construct A-inverse from A0-inverse and the ylk
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double** U;
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double** Ap = new double*[M];
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for (i = 0; i < M; i++) Ap[i] = new double[M];
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Ainv = A0inv;
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for (l = 0; l < M; l++) {
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k = l+1;
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U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
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beta = 1 + ylk[l][p[k]][p[k]];
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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Ap[i][j] = Id[i][j] - U[i][j] / beta;
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}
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}
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Ainv = matMul(Ap, Ainv, M);
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}
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showMatrixT(Ainv, M, "Ainv");
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uint *dim = new uint(M);
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Sherman_Morrison(A0, A0inv, dim, dim, Ar, indices_of_updates);
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showMatrixT(A0inv, M, "A0inv");
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// Deallocate all vectors and matrices
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for (i = 0; i < M; i++) {
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@ -169,24 +96,14 @@ int main() {
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delete [] A0[i];
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delete [] A0inv[i];
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delete [] Ar[i];
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delete [] Id[i];
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delete [] U[i];
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delete [] Ap[i];
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}
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for (l = 0; l < M; l++) {
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for (k = 0; k < M+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 [] p, breakdown, A, Ainv, A0, A0inv, Ar, Id, ylk;
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delete [] A, A0, A0inv, Ar;
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return 0;
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}
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uint getMaxIndex(double* arr, uint size) {
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uint getMaxIndex(double *arr, uint size) {
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uint i;
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uint max = arr[0];
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uint maxi = 0;
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@ -274,7 +191,7 @@ T matDet(T** A, int M) {
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int det = 0, p, h, k, i, j;
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T** temp = new T*[M];
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for (int i = 0; i < M; i++) temp[i] = new T[M];
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if(M==1) {
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if(M == 1) {
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return A[0][0];
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}
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else if(M == 2) {
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@ -303,4 +220,108 @@ T matDet(T** A, int M) {
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return det;
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}
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delete [] temp;
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}
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void Sherman_Morrison(int **Slater0, double **Slater_inv, uint *Dim, uint *N_updates, int **Updates, uint *Updates_index) {
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cout << "We just entered Sherman-Morrison" << endl;
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showMatrix(Slater_inv, *Dim, "Slater_inv");
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uint k, l, lbar, i, j, tmp, M = *Dim;
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uint *p = new uint[M+1];
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double *breakdown = new double[M+1];
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double alpha, beta;
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for (i = 0; i < M+1; i++) {
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p[i] = i;
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}
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int **Id = new int*[M];
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for (i = 0; i < M; i++) Id[i] = new int[M];
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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if (i != j) Id[i][j] = 0;
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else Id[i][j] = 1;
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}
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}
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// Declare auxiliary solution matrix ylk
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double ***ylk = new double**[M];
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for (l = 0; l < M; l++) {
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ylk[l] = new double*[M+1];
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for (k = 0; k < M+1; k++) {
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ylk[l][k] = new double[M+1];
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}
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}
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// Initialize ylk with zeros
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for (l = 0; l < M; l++) {
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for (k = 0; k < M+1; k++) {
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for (i = 0; i < M+1; i++) {
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ylk[l][k][i] = 0;
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}
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}
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}
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// Calculate all the y0k in M^2 multiplications instead of M^3
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for (k = 1; k < M+1; k++) {
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for (i = 1; i < M+1; i++) {
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ylk[0][k][i] = Slater_inv[i-1][i-1] * Updates[i-1][k-1];
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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 < M; l++) {
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for (j = l; j < M+1; j++) {
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breakdown[j] = abs( 1 + ylk[l-1][p[j]][p[j]] );
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}
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lbar = getMaxIndex(breakdown, M+1);
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for (i = 0; i < M; 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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for (k = l+1; k < M+1; k++) {
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beta = 1 + ylk[l-1][p[l]][p[l]];
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if (beta == 0) {
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cout << "Break-down condition occured. Exiting..." << endl;
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exit;
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}
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for (i = 1; i < M+1; i++) {
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alpha = ylk[l-1][p[k]][p[l]] / beta;
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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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cout << "Just before the final construction of the inverse..." << endl;
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showMatrix(Slater_inv, M, "Slater_inv");
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// Construct A-inverse from A0-inverse and the ylk
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double** U;
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double** Al = new double*[M];
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for (i = 0; i < M; i++) Al[i] = new double[M];
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for (l = 0; l < M; l++) {
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k = l+1;
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U = outProd(ylk[l][p[k]], Id[p[k]-1], M);
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beta = 1 + ylk[l][p[k]][p[k]];
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for (i = 0; i < M; i++) {
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for (j = 0; j < M; j++) {
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Al[i][j] = Id[i][j] - U[i][j] / beta;
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}
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}
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Slater_inv = matMul(Al, Slater_inv, M);
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}
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cout << "Just after the final construction of the inverse..." << endl;
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showMatrix(Slater_inv, M, "Slater_inv");
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for (i = 0; i < M; i++) {
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delete [] U[i];
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delete [] Al[i];
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}
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for (l = 0; l < M; l++) {
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for (k = 0; k < M+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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}
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