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https://github.com/TREX-CoE/Sherman-Morrison.git
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First implementation of Woodbury 2x2 and 3x3 kernels.
This commit is contained in:
Francois Coppens
parent
288bc83e19
commit
efe96cbeea
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@ -56,6 +56,45 @@ void showMatrix(T *matrix, unsigned int M, std::string name) {
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std::cout << std::endl;
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}
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template <typename T>
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void showMatrix2(T *matrix, unsigned int M, unsigned int N, std::string name) {
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std::cout.precision(17);
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std::cout << name << " = [" << std::endl;
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for (unsigned int i = 0; i < M; i++) {
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std::cout << "[";
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for (unsigned int j = 0; j < N; j++) {
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if (matrix[i * N + j] >= 0) {
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std::cout << " " << matrix[i * N + j] << ",";
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} else {
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std::cout << " " << matrix[i * N + j] << ",";
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}
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}
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std::cout << " ]," << std::endl;
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}
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std::cout << "]" << std::endl;
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std::cout << std::endl;
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}
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template <typename T>
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void showMatrixNS(T *matrix, unsigned int M, unsigned int N, std::string name) {
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std::cout.precision(17);
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std::cout << name << " = [" << std::endl;
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for (unsigned int i = 0; i < M; i++) {
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std::cout << "[";
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for (unsigned int j = 0; j < N; j++) {
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if (matrix[i * N + j] >= 0) {
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std::cout << " " << matrix[i * N + j] << ",";
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} else {
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std::cout << " " << matrix[i * N + j] << ",";
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}
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}
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std::cout << " ]," << std::endl;
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}
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std::cout << "]" << std::endl;
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std::cout << std::endl;
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}
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template <typename T> T *transpose(T *A, unsigned int M) {
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T *B = new T[M * M];
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for (unsigned int i = 0; i < M; i++) {
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@ -77,6 +116,18 @@ template <typename T> void matMul(T *A, T *B, T *C, unsigned int M) {
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}
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}
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template <typename T1, typename T2, typename T3>
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static inline void matMul2(T1 *A, T2 *B, T3 *C, unsigned int M, unsigned int N, unsigned int P) {
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for(unsigned int i = 0; i < M; i++) {
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for(unsigned int j = 0; j < P; j++) {
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C[i * P + j] = 0;
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for(unsigned int k = 0; k < N; k++) {
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C[i * P + j] += A[i * N + k] * B[k * P + j];
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}
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}
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}
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}
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template <typename T1, typename T2>
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T1 *outProd(T1 *vec1, T2 *vec2, unsigned int M) {
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T1 *C = new T1[M * M];
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@ -1,7 +1,7 @@
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// Woodbury 2x2 kernel
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void WB2(double *Slater_inv, unsigned int Dim,
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bool WB2(double *Slater_inv, unsigned int Dim,
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double *Updates, unsigned int *Updates_index);
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// Woodbury 3x3 kernel
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void WB3(double *Slater_inv, unsigned int Dim,
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bool WB3(double *Slater_inv, unsigned int Dim,
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double *Updates, unsigned int *Updates_index);
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@ -3,6 +3,10 @@ unset THRESHOLD
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unset MKL
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ENV=$1
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echo
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echo "Sherman-Morrison-Woodbury parameters"
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echo "------------------------------------"
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## Set Sherman-Morrison root dir
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PWD=$(pwd)
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SRCDIR=$(dirname $BASH_SOURCE)
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13
src/SMWB.cpp
13
src/SMWB.cpp
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@ -5,12 +5,15 @@
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// Sherman-Morrison-Woodbury kernel 1
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// WB2, WB3, SM2 mixing scheme 1
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void SMWB1(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index) {
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void SMWB1(double *Slater_inv, unsigned int Dim, unsigned int N_updates, double *Updates, unsigned int *Updates_index) {
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std::cerr << "Called Sherman-Morrison-Woodbury kernel 1 with " << N_updates << " updates" << std::endl;
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WB3(Slater_inv, Dim, Updates, Updates_index);
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WB2(Slater_inv, Dim, Updates, Updates_index);
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SM2(Slater_inv, Dim, N_updates, Updates, Updates_index);
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bool ok;
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ok = WB2(Slater_inv, Dim, Updates, Updates_index);
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if (!ok) {
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std::cerr << "Woodbury kernel failed!" << std::endl;
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SM2(Slater_inv, Dim, N_updates, Updates, Updates_index);
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}
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}
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extern "C" {
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135
src/Woodbury.cpp
135
src/Woodbury.cpp
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@ -5,65 +5,126 @@
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// (S + U * V)^{-1} = S^{-1} - S^{-1} * U * B^{-1} * V * S^{-1}
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// B := 1 + V * C, 2 x 2
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// C := S^{-1} * U, dim x 2
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// D := V * S^{-1}, 2 x dim
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//
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// All matrices are stored in row-major order
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#include "Woodbury.hpp"
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#include "Helpers.hpp"
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// Woodbury 2x2 kernel:
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void WB2(double *Slater_inv, unsigned int Dim,
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double *Updates, unsigned int *Updates_index) {
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bool WB2(double *Slater_inv, unsigned int Dim, double *Updates,
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unsigned int *Updates_index) {
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std::cerr << "Called Woodbury 2x2 kernel" << std::endl;
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// Construct V from Updates_index
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unsigned int *V = new unsigned int[2 * Dim]{0};
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for (unsigned int i = 0; i < Dim; i++) {
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if (i == Updates_index[0] - 1) V[i] = 1;
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if (Dim + i == Updates_index[1] - 1) V[Dim + i] = 1;
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}
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unsigned int V[2 * Dim]{0}; // 2 x Dim matrix stored in row-major order
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V[Updates_index[0] - 1] = 1;
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V[Dim + Updates_index[1] - 1] = 1;
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// Compute B from U, V and Slater_inv
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// Compute C
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double C[2 * Dim]{0};
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matMul2(Slater_inv, Updates, C, Dim, Dim, 2);
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// Compute B
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double B[4]{0};
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double Binv[4]{0};
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double C[4]{0};
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double D[2*Dim]{0};
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// Compute C
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < 2; j++) {
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for (unsigned int k = 0; k < Dim; k++) {
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C[i * Dim + j] += Slater_inv[i * Dim + k] * Updates[k * Dim + j];
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}
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}
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}
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// Compute B
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for (unsigned int i = 0; i < 2; i++) {
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for (unsigned int j = 0; j < 2; j++) {
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for (unsigned int k = 0; k < Dim; k++) {
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B[i * Dim + j] += (i == j) + V[i * Dim + k] * C[k * Dim + j];
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}
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}
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}
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matMul2(V, C, B, 2, Dim, 2);
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// Compute 1 + B
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B[0] += 1;
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B[3] += 1;
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// Invert B with explicit formula for 2x2 inversion
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// Invert 1 + B with explicit formula for 2x2 inversion
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double idet = 1.0 / (B[0] * B[3] - B[1] * B[2]);
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double Binv[4]{0};
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Binv[0] = idet * B[3];
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Binv[1] = -1.0 * idet * B[1];
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Binv[2] = -1.0 * idet * B[2];
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Binv[3] = idet * B[0];
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// Compute (S + U * V)^{-1} with Woobury identity
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// Check if determinant of inverted matrix is not zero
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double det = B[0] * B[3] - B[1] * B[2];
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if (std::fabs(det) < threshold()) {
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std::cerr << "Determinant approached 0!" << std::endl;
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return false;
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}
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// Compute (S + U * V)^{-1} with Woobury identity
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double D[2 * Dim]{0};
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matMul2(V, Slater_inv, D, 2, Dim, Dim);
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double tmp[2 * Dim]{0};
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matMul2(Binv, D, tmp, 2, 2, Dim);
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double tmp2[Dim * Dim]{0};
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matMul2(C, tmp, tmp2, Dim, 2, Dim);
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for (unsigned int i = 0; i < Dim * Dim; i++) {
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Slater_inv[i] -= tmp2[i];
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}
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return true;
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}
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// Woodbury 3x3 kernel
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void WB3(double *Slater_inv, unsigned int Dim,
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double *Updates, unsigned int *Updates_index) {
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std::cerr << "Called Woodbury 3x3 kernel" << std::endl;
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bool WB3(double *Slater_inv, unsigned int Dim, double *Updates,
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unsigned int *Updates_index) {
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std::cerr << "Called Woodbury 3x3 kernel" << std::endl;
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// Construct V from Updates_index
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// Construct V from Updates_index
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unsigned int V[3 * Dim]{0}; // 2 x Dim matrix stored in row-major order
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V[Updates_index[0] - 1] = 1;
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V[Dim + Updates_index[1] - 1] = 1;
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V[2 * Dim + Updates_index[2] - 1] = 1;
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// Compute B from U, V and Slater_inv
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// Compute C
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double C[3 * Dim]{0};
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matMul2(Slater_inv, Updates, C, Dim, Dim, 3);
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// Compute B
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double B[9]{0};
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matMul2(V, C, B, 3, Dim, 3);
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// Compute 1 + B
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B[0] += 1;
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B[4] += 1;
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B[8] += 1;
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// Invert B with explicit formula for 3x3 inversion
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double Binv[9];
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Binv[0] = B[4] * B[8] - B[5] * B[7];
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Binv[3] = B[5] * B[6] - B[3] * B[8];
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Binv[6] = B[3] * B[7] - B[4] * B[6];
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// Compute (S + U * V)^{-1} with Woobury identity
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Binv[1] = B[2] * B[7] - B[1] * B[8];
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Binv[4] = B[0] * B[8] - B[2] * B[6];
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Binv[7] = B[1] * B[6] - B[0] * B[7];
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}
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Binv[2] = B[1] * B[5] - B[2] * B[4];
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Binv[5] = B[2] * B[3] - B[0] * B[5];
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Binv[8] = B[0] * B[4] - B[1] * B[3];
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// Check if determinant of inverted matrix is not zero
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// If so, exigt and return false.
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double det;
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det = B[0] * (B[4] * B[8] - B[5] * B[7]) -
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B[1] * (B[3] * B[8] - B[5] * B[6]) + B[2] * (B[3] * B[7] - B[4] * B[6]);
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if (std::fabs(det) < threshold()) {
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std::cerr << "Determinant approached 0!" << std::endl;
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return false;
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}
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// Compute (S + U * V)^{-1} with Woobury identity
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double D[3 * Dim]{0};
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matMul2(V, Slater_inv, D, 3, Dim, Dim);
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double tmp[3 * Dim]{0};
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matMul2(Binv, D, tmp, 3, 3, Dim);
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double tmp2[Dim * Dim]{0};
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matMul2(C, tmp, tmp2, Dim, 3, Dim);
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for (unsigned int i = 0; i < Dim * Dim; i++) {
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Slater_inv[i] -= tmp2[i];
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}
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return true;
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}
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extern "C" {
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bool WB2_f(double **linSlater_inv, unsigned int *Dim, double **linUpdates,
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unsigned int **Updates_index) {
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WB2(*linSlater_inv, *Dim, *linUpdates, *Updates_index);
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}
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bool WB3_f(double **linSlater_inv, unsigned int *Dim, double **linUpdates,
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unsigned int **Updates_index) {
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WB3(*linSlater_inv, *Dim, *linUpdates, *Updates_index);
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}
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}
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10
todo.txt
10
todo.txt
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@ -1,10 +0,0 @@
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-=={TODO}==-
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* Looking at the eigenvalues of the intermediate matrix after a problematic update is
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* plotting the ratio of the moduli of the maximum and the minimum eigenvalues of
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* Use valgrind to find the problem with MaponiA3S
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* Contact Claudia if she would be interested in sharing datasets from Champ to test with SM
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* Make a representative selection of update cycles for presentatoin puroses
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