First implementation of Woodbury 2x2 and 3x3 kernels.

This commit is contained in:
Francois Coppens 2021-06-10 08:46:40 +02:00
parent 288bc83e19
commit efe96cbeea
6 changed files with 165 additions and 56 deletions

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@ -56,6 +56,45 @@ void showMatrix(T *matrix, unsigned int M, std::string name) {
std::cout << std::endl; std::cout << std::endl;
} }
template <typename T>
void showMatrix2(T *matrix, unsigned int M, unsigned int N, std::string name) {
std::cout.precision(17);
std::cout << name << " = [" << std::endl;
for (unsigned int i = 0; i < M; i++) {
std::cout << "[";
for (unsigned int j = 0; j < N; j++) {
if (matrix[i * N + j] >= 0) {
std::cout << " " << matrix[i * N + j] << ",";
} else {
std::cout << " " << matrix[i * N + j] << ",";
}
}
std::cout << " ]," << std::endl;
}
std::cout << "]" << std::endl;
std::cout << std::endl;
}
template <typename T>
void showMatrixNS(T *matrix, unsigned int M, unsigned int N, std::string name) {
std::cout.precision(17);
std::cout << name << " = [" << std::endl;
for (unsigned int i = 0; i < M; i++) {
std::cout << "[";
for (unsigned int j = 0; j < N; j++) {
if (matrix[i * N + j] >= 0) {
std::cout << " " << matrix[i * N + j] << ",";
} else {
std::cout << " " << matrix[i * N + j] << ",";
}
}
std::cout << " ]," << std::endl;
}
std::cout << "]" << std::endl;
std::cout << std::endl;
}
template <typename T> T *transpose(T *A, unsigned int M) { template <typename T> T *transpose(T *A, unsigned int M) {
T *B = new T[M * M]; T *B = new T[M * M];
for (unsigned int i = 0; i < M; i++) { for (unsigned int i = 0; i < M; i++) {
@ -77,6 +116,18 @@ template <typename T> void matMul(T *A, T *B, T *C, unsigned int M) {
} }
} }
template <typename T1, typename T2, typename T3>
static inline void matMul2(T1 *A, T2 *B, T3 *C, unsigned int M, unsigned int N, unsigned int P) {
for(unsigned int i = 0; i < M; i++) {
for(unsigned int j = 0; j < P; j++) {
C[i * P + j] = 0;
for(unsigned int k = 0; k < N; k++) {
C[i * P + j] += A[i * N + k] * B[k * P + j];
}
}
}
}
template <typename T1, typename T2> template <typename T1, typename T2>
T1 *outProd(T1 *vec1, T2 *vec2, unsigned int M) { T1 *outProd(T1 *vec1, T2 *vec2, unsigned int M) {
T1 *C = new T1[M * M]; T1 *C = new T1[M * M];

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@ -1,7 +1,7 @@
// Woodbury 2x2 kernel // Woodbury 2x2 kernel
void WB2(double *Slater_inv, unsigned int Dim, bool WB2(double *Slater_inv, unsigned int Dim,
double *Updates, unsigned int *Updates_index); double *Updates, unsigned int *Updates_index);
// Woodbury 3x3 kernel // Woodbury 3x3 kernel
void WB3(double *Slater_inv, unsigned int Dim, bool WB3(double *Slater_inv, unsigned int Dim,
double *Updates, unsigned int *Updates_index); double *Updates, unsigned int *Updates_index);

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@ -3,6 +3,10 @@ unset THRESHOLD
unset MKL unset MKL
ENV=$1 ENV=$1
echo
echo "Sherman-Morrison-Woodbury parameters"
echo "------------------------------------"
## Set Sherman-Morrison root dir ## Set Sherman-Morrison root dir
PWD=$(pwd) PWD=$(pwd)
SRCDIR=$(dirname $BASH_SOURCE) SRCDIR=$(dirname $BASH_SOURCE)

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@ -5,13 +5,16 @@
// Sherman-Morrison-Woodbury kernel 1 // Sherman-Morrison-Woodbury kernel 1
// WB2, WB3, SM2 mixing scheme 1 // WB2, WB3, SM2 mixing scheme 1
void SMWB1(double *Slater_inv, unsigned int Dim, unsigned int N_updates, void SMWB1(double *Slater_inv, unsigned int Dim, unsigned int N_updates, double *Updates, unsigned int *Updates_index) {
double *Updates, unsigned int *Updates_index) {
std::cerr << "Called Sherman-Morrison-Woodbury kernel 1 with " << N_updates << " updates" << std::endl; std::cerr << "Called Sherman-Morrison-Woodbury kernel 1 with " << N_updates << " updates" << std::endl;
WB3(Slater_inv, Dim, Updates, Updates_index);
WB2(Slater_inv, Dim, Updates, Updates_index); bool ok;
ok = WB2(Slater_inv, Dim, Updates, Updates_index);
if (!ok) {
std::cerr << "Woodbury kernel failed!" << std::endl;
SM2(Slater_inv, Dim, N_updates, Updates, Updates_index); SM2(Slater_inv, Dim, N_updates, Updates, Updates_index);
} }
}
extern "C" { extern "C" {
void SMWB1_f(double **linSlater_inv, unsigned int *Dim, unsigned int *N_updates, void SMWB1_f(double **linSlater_inv, unsigned int *Dim, unsigned int *N_updates,

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@ -5,65 +5,126 @@
// (S + U * V)^{-1} = S^{-1} - S^{-1} * U * B^{-1} * V * S^{-1} // (S + U * V)^{-1} = S^{-1} - S^{-1} * U * B^{-1} * V * S^{-1}
// B := 1 + V * C, 2 x 2 // B := 1 + V * C, 2 x 2
// C := S^{-1} * U, dim x 2 // C := S^{-1} * U, dim x 2
// D := V * S^{-1}, 2 x dim
//
// All matrices are stored in row-major order
#include "Woodbury.hpp" #include "Woodbury.hpp"
#include "Helpers.hpp" #include "Helpers.hpp"
// Woodbury 2x2 kernel: // Woodbury 2x2 kernel:
void WB2(double *Slater_inv, unsigned int Dim, bool WB2(double *Slater_inv, unsigned int Dim, double *Updates,
double *Updates, unsigned int *Updates_index) { unsigned int *Updates_index) {
std::cerr << "Called Woodbury 2x2 kernel" << std::endl; std::cerr << "Called Woodbury 2x2 kernel" << std::endl;
// Construct V from Updates_index // Construct V from Updates_index
unsigned int *V = new unsigned int[2 * Dim]{0}; unsigned int V[2 * Dim]{0}; // 2 x Dim matrix stored in row-major order
for (unsigned int i = 0; i < Dim; i++) { V[Updates_index[0] - 1] = 1;
if (i == Updates_index[0] - 1) V[i] = 1; V[Dim + Updates_index[1] - 1] = 1;
if (Dim + i == Updates_index[1] - 1) V[Dim + i] = 1;
}
// Compute B from U, V and Slater_inv
double B[4]{0};
double Binv[4]{0};
double C[4]{0};
double D[2*Dim]{0};
// Compute C // Compute C
for (unsigned int i = 0; i < Dim; i++) { double C[2 * Dim]{0};
for (unsigned int j = 0; j < 2; j++) { matMul2(Slater_inv, Updates, C, Dim, Dim, 2);
for (unsigned int k = 0; k < Dim; k++) {
C[i * Dim + j] += Slater_inv[i * Dim + k] * Updates[k * Dim + j];
}
}
}
// Compute B // Compute B
for (unsigned int i = 0; i < 2; i++) { double B[4]{0};
for (unsigned int j = 0; j < 2; j++) { matMul2(V, C, B, 2, Dim, 2);
for (unsigned int k = 0; k < Dim; k++) { // Compute 1 + B
B[i * Dim + j] += (i == j) + V[i * Dim + k] * C[k * Dim + j]; B[0] += 1;
} B[3] += 1;
}
}
// Invert B with explicit formula for 2x2 inversion // Invert 1 + B with explicit formula for 2x2 inversion
double idet = 1.0 / (B[0] * B[3] - B[1] * B[2]); double idet = 1.0 / (B[0] * B[3] - B[1] * B[2]);
double Binv[4]{0};
Binv[0] = idet * B[3]; Binv[0] = idet * B[3];
Binv[1] = -1.0 * idet * B[1]; Binv[1] = -1.0 * idet * B[1];
Binv[2] = -1.0 * idet * B[2]; Binv[2] = -1.0 * idet * B[2];
Binv[3] = idet * B[0]; Binv[3] = idet * B[0];
// Compute (S + U * V)^{-1} with Woobury identity // Check if determinant of inverted matrix is not zero
double det = B[0] * B[3] - B[1] * B[2];
if (std::fabs(det) < threshold()) {
std::cerr << "Determinant approached 0!" << std::endl;
return false;
}
// Compute (S + U * V)^{-1} with Woobury identity
double D[2 * Dim]{0};
matMul2(V, Slater_inv, D, 2, Dim, Dim);
double tmp[2 * Dim]{0};
matMul2(Binv, D, tmp, 2, 2, Dim);
double tmp2[Dim * Dim]{0};
matMul2(C, tmp, tmp2, Dim, 2, Dim);
for (unsigned int i = 0; i < Dim * Dim; i++) {
Slater_inv[i] -= tmp2[i];
}
return true;
} }
// Woodbury 3x3 kernel // Woodbury 3x3 kernel
void WB3(double *Slater_inv, unsigned int Dim, bool WB3(double *Slater_inv, unsigned int Dim, double *Updates,
double *Updates, unsigned int *Updates_index) { unsigned int *Updates_index) {
std::cerr << "Called Woodbury 3x3 kernel" << std::endl; std::cerr << "Called Woodbury 3x3 kernel" << std::endl;
// Construct V from Updates_index // Construct V from Updates_index
unsigned int V[3 * Dim]{0}; // 2 x Dim matrix stored in row-major order
V[Updates_index[0] - 1] = 1;
V[Dim + Updates_index[1] - 1] = 1;
V[2 * Dim + Updates_index[2] - 1] = 1;
// Compute B from U, V and Slater_inv // Compute C
double C[3 * Dim]{0};
matMul2(Slater_inv, Updates, C, Dim, Dim, 3);
// Compute B
double B[9]{0};
matMul2(V, C, B, 3, Dim, 3);
// Compute 1 + B
B[0] += 1;
B[4] += 1;
B[8] += 1;
// Invert B with explicit formula for 3x3 inversion double Binv[9];
Binv[0] = B[4] * B[8] - B[5] * B[7];
Binv[3] = B[5] * B[6] - B[3] * B[8];
Binv[6] = B[3] * B[7] - B[4] * B[6];
Binv[1] = B[2] * B[7] - B[1] * B[8];
Binv[4] = B[0] * B[8] - B[2] * B[6];
Binv[7] = B[1] * B[6] - B[0] * B[7];
Binv[2] = B[1] * B[5] - B[2] * B[4];
Binv[5] = B[2] * B[3] - B[0] * B[5];
Binv[8] = B[0] * B[4] - B[1] * B[3];
// Check if determinant of inverted matrix is not zero
// If so, exigt and return false.
double det;
det = B[0] * (B[4] * B[8] - B[5] * B[7]) -
B[1] * (B[3] * B[8] - B[5] * B[6]) + B[2] * (B[3] * B[7] - B[4] * B[6]);
if (std::fabs(det) < threshold()) {
std::cerr << "Determinant approached 0!" << std::endl;
return false;
}
// Compute (S + U * V)^{-1} with Woobury identity // Compute (S + U * V)^{-1} with Woobury identity
double D[3 * Dim]{0};
matMul2(V, Slater_inv, D, 3, Dim, Dim);
double tmp[3 * Dim]{0};
matMul2(Binv, D, tmp, 3, 3, Dim);
double tmp2[Dim * Dim]{0};
matMul2(C, tmp, tmp2, Dim, 3, Dim);
for (unsigned int i = 0; i < Dim * Dim; i++) {
Slater_inv[i] -= tmp2[i];
}
return true;
}
extern "C" {
bool WB2_f(double **linSlater_inv, unsigned int *Dim, double **linUpdates,
unsigned int **Updates_index) {
WB2(*linSlater_inv, *Dim, *linUpdates, *Updates_index);
}
bool WB3_f(double **linSlater_inv, unsigned int *Dim, double **linUpdates,
unsigned int **Updates_index) {
WB3(*linSlater_inv, *Dim, *linUpdates, *Updates_index);
}
} }

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@ -1,10 +0,0 @@
-=={TODO}==-
* Looking at the eigenvalues of the intermediate matrix after a problematic update is
* plotting the ratio of the moduli of the maximum and the minimum eigenvalues of
* Use valgrind to find the problem with MaponiA3S
* Contact Claudia if she would be interested in sharing datasets from Champ to test with SM
* Make a representative selection of update cycles for presentatoin puroses