mirror of
https://github.com/TREX-CoE/qmckl.git
synced 2024-06-30 00:44:52 +02:00
Added and tested Woodbury 3x3 kernel to QMCkl.
Residual = wb3 14 9.92936e-07 1.90518e-11 ok -- cycle 14 Residual = qmckl_wb3 14 9.92936e-07 1.90518e-11 ok -- cycle 14. #25
This commit is contained in:
Francois Coppens
parent
fdb8f5d50a
commit
c6d00d5c5b
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@ -7,39 +7,39 @@
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static double threshold();
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// Naïve Sherman Morrison
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bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index);
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bool qmckl_sherman_morrison(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index);
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// Woodbury 2x2 kernel
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bool qmckl_woodbury_2(double *Slater_inv, const unsigned int Dim, double *Updates,
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const unsigned int *Updates_index);
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bool qmckl_woodbury_2(double *Slater_inv, const uint64_t Dim, double *Updates,
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const uint64_t *Updates_index);
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// Woodbury 3x3 kernel
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bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Updates,
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const unsigned int *Updates_index);
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bool qmckl_woodbury_3(double *Slater_inv, const uint64_t Dim, double *Updates,
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const uint64_t *Updates_index);
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// Sherman Morrison, with J. Slagel splitting (caller function)
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void qmckl_sherman_morrison_splitting(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 qmckl_sherman_morrison_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index);
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// Sherman Morrison, with J. Slagel splitting
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// http://hdl.handle.net/10919/52966
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static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index,
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double *later_updates, unsigned int *later_index,
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unsigned int *later);
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static void slagel_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index,
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double *later_updates, uint64_t *later_index,
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uint64_t *later);
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// Mixed Sherman-Morrison-Woodbury kernel using
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// Woodbury 2x2 and Sherman-Morrison with update-splitting
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void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const unsigned int Dim,
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const unsigned int N_updates, double *Updates,
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unsigned int *Updates_index);
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void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const uint64_t Dim,
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const uint64_t N_updates, double *Updates,
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uint64_t *Updates_index);
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// Mixed Sherman-Morrison-Woodbury kernel using
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// Woodbury 3x3, Woodbury 2x2 and Sherman-Morrison with update-splitting
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void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const unsigned int Dim,
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const unsigned int N_updates, double *Updates,
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unsigned int *Updates_index);
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void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const uint64_t Dim,
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const uint64_t N_updates, double *Updates,
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uint64_t *Updates_index);
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@ -53,8 +53,8 @@ static double threshold() {
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}
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// Naïve Sherman Morrison
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bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index) {
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bool qmckl_sherman_morrison(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index) {
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// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
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// std::cerr << "Called qmckl_sherman_morrison with " << N_updates << " updates" << std::endl;
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// #endif
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@ -62,13 +62,13 @@ bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N
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double C[Dim];
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double D[Dim];
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unsigned int l = 0;
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uint64_t l = 0;
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// For each update
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while (l < N_updates) {
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// C = A^{-1} x U_l
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for (unsigned int i = 0; i < Dim; i++) {
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for (uint64_t i = 0; i < Dim; i++) {
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C[i] = 0;
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t j = 0; j < Dim; j++) {
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C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
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}
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}
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@ -81,13 +81,13 @@ bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N
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double iden = 1 / den;
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// D = v^T x A^{-1}
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t j = 0; j < Dim; j++) {
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D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
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}
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// A^{-1} = A^{-1} - C x D / den
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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double update = C[i] * D[j] * iden;
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Slater_inv[i * Dim + j] -= update;
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}
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@ -99,8 +99,8 @@ bool qmckl_sherman_morrison(double *Slater_inv, unsigned int Dim, unsigned int N
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}
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// Woodbury 2x2 kernel
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bool qmckl_woodbury_2(double *Slater_inv, const unsigned int Dim, double *Updates,
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const unsigned int *Updates_index) {
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bool qmckl_woodbury_2(double *Slater_inv, const uint64_t Dim, double *Updates,
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const uint64_t *Updates_index) {
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/*
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C := S^{-1} * U, dim x 2
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B := 1 + V * C, 2 x 2
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@ -110,16 +110,16 @@ bool qmckl_woodbury_2(double *Slater_inv, const unsigned int Dim, double *Update
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// std::cerr << "Called Woodbury 2x2 kernel" << std::endl;
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// #endif
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const unsigned int row1 = (Updates_index[0] - 1);
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const unsigned int row2 = (Updates_index[1] - 1);
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const uint64_t row1 = (Updates_index[0] - 1);
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const uint64_t row2 = (Updates_index[1] - 1);
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// Compute C = S_inv * U !! NON-STANDARD MATRIX MULTIPLICATION BECAUSE
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// OF LAYOUT OF 'Updates' !!
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double C[2 * Dim];
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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 (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < 2; j++) {
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C[i * 2 + j] = 0;
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for (unsigned int k = 0; k < Dim; k++) {
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for (uint64_t k = 0; k < Dim; k++) {
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C[i * 2 + j] += Slater_inv[i * Dim + k] * Updates[Dim * j + k];
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}
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}
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@ -146,16 +146,16 @@ bool qmckl_woodbury_2(double *Slater_inv, const unsigned int Dim, double *Update
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// Compute tmp = B^{-1} x (V.S^{-1})
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double tmp[2 * Dim];
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for (unsigned int i = 0; i < 2; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < 2; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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tmp[i * Dim + j] = Binv[i * 2] * Slater_inv[row1 * Dim + j];
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tmp[i * Dim + j] += Binv[i * 2 + 1] * Slater_inv[row2 * Dim + j];
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}
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}
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// Compute (S + U V)^{-1} = S^{-1} - C x tmp
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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Slater_inv[i * Dim + j] -= C[i * 2] * tmp[j];
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Slater_inv[i * Dim + j] -= C[i * 2 + 1] * tmp[Dim + j];
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}
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@ -165,8 +165,8 @@ bool qmckl_woodbury_2(double *Slater_inv, const unsigned int Dim, double *Update
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}
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// Woodbury 3x3 kernel
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bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Updates,
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const unsigned int *Updates_index) {
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bool qmckl_woodbury_3(double *Slater_inv, const uint64_t Dim, double *Updates,
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const uint64_t *Updates_index) {
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/*
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C := S^{-1} * U, dim x 3
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B := 1 + V * C, 3 x 3
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@ -176,17 +176,17 @@ bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Update
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// std::cerr << "Called Woodbury 3x3 kernel" << std::endl;
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// #endif
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const unsigned int row1 = (Updates_index[0] - 1);
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const unsigned int row2 = (Updates_index[1] - 1);
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const unsigned int row3 = (Updates_index[2] - 1);
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const uint64_t row1 = (Updates_index[0] - 1);
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const uint64_t row2 = (Updates_index[1] - 1);
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const uint64_t row3 = (Updates_index[2] - 1);
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// Compute C = S_inv * U !! NON-STANDARD MATRIX MULTIPLICATION BECAUSE
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// OF LAYOUT OF 'Updates' !!
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double C[3 * Dim];
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < 3; j++) {
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for (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < 3; j++) {
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C[i * 3 + j] = 0;
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for (unsigned int k = 0; k < Dim; k++) {
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for (uint64_t k = 0; k < Dim; k++) {
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C[i * 3 + j] += Slater_inv[i * Dim + k] * Updates[Dim * j + k];
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}
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}
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@ -226,8 +226,8 @@ bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Update
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// Compute tmp = B^{-1} x (V.S^{-1})
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double tmp[3 * Dim];
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for (unsigned int i = 0; i < 3; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < 3; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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tmp[i * Dim + j] = Binv[i * 3] * Slater_inv[row1 * Dim + j];
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tmp[i * Dim + j] += Binv[i * 3 + 1] * Slater_inv[row2 * Dim + j];
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tmp[i * Dim + j] += Binv[i * 3 + 2] * Slater_inv[row3 * Dim + j];
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@ -235,8 +235,8 @@ bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Update
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}
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// Compute (S + U V)^{-1} = S^{-1} - C x tmp
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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Slater_inv[i * Dim + j] -= C[i * 3] * tmp[j];
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Slater_inv[i * Dim + j] -= C[i * 3 + 1] * tmp[Dim + j];
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Slater_inv[i * Dim + j] -= C[i * 3 + 2] * tmp[2 * Dim + j];
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@ -248,15 +248,15 @@ bool qmckl_woodbury_3(double *Slater_inv, const unsigned int Dim, double *Update
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// Sherman Morrison, with J. Slagel splitting (caller function)
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// http://hdl.handle.net/10919/52966
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void qmckl_sherman_morrison_splitting(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 qmckl_sherman_morrison_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index) {
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// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
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// std::cerr << "Called qmckl_sherman_morrison_splitting with " << N_updates << " updates" << std::endl;
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// #endif
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double later_updates[Dim * N_updates];
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unsigned int later_index[N_updates];
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unsigned int later = 0;
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uint64_t later_index[N_updates];
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uint64_t later = 0;
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slagel_splitting(Slater_inv, Dim, N_updates, Updates, Updates_index, later_updates,
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later_index, &later);
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@ -268,10 +268,10 @@ void qmckl_sherman_morrison_splitting(double *Slater_inv, unsigned int Dim, unsi
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// Sherman Morrison, with J. Slagel splitting
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// http://hdl.handle.net/10919/52966
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static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int N_updates,
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double *Updates, unsigned int *Updates_index,
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double *later_updates, unsigned int *later_index,
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unsigned int *later) {
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static void slagel_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
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double *Updates, uint64_t *Updates_index,
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double *later_updates, uint64_t *later_index,
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uint64_t *later) {
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// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
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// std::cerr << "Called slagel_splitting with " << N_updates << " updates" << std::endl;
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// #endif
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@ -279,13 +279,13 @@ static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int
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double C[Dim];
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double D[Dim];
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unsigned int l = 0;
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uint64_t l = 0;
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// For each update
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while (l < N_updates) {
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// C = S^{-1} x U_l
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for (unsigned int i = 0; i < Dim; i++) {
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for (uint64_t i = 0; i < Dim; i++) {
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C[i] = 0;
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t j = 0; j < Dim; j++) {
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C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
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}
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}
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@ -295,7 +295,7 @@ static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int
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if (fabs(den) < threshold()) {
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// U_l = U_l / 2 (do the split)
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for (unsigned int i = 0; i < Dim; i++) {
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for (uint64_t i = 0; i < Dim; i++) {
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later_updates[*later * Dim + i] = Updates[l * Dim + i] / 2.0;
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C[i] /= 2.0;
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}
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@ -307,13 +307,13 @@ static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int
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double iden = 1 / den;
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// D = v^T x S^{-1}
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t j = 0; j < Dim; j++) {
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D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
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}
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// S^{-1} = S^{-1} - C x D / den
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for (unsigned int i = 0; i < Dim; i++) {
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for (unsigned int j = 0; j < Dim; j++) {
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for (uint64_t i = 0; i < Dim; i++) {
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for (uint64_t j = 0; j < Dim; j++) {
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double update = C[i] * D[j] * iden;
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Slater_inv[i * Dim + j] -= update;
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}
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@ -324,32 +324,32 @@ static void slagel_splitting(double *Slater_inv, unsigned int Dim, unsigned int
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// Sherman-Morrison-Woodbury 2x2 kernel
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// qmckl_woodbury_2, slagel_splitting mixing scheme
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void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const unsigned int Dim,
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const unsigned int N_updates, double *Updates,
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unsigned int *Updates_index) {
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void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const uint64_t Dim,
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const uint64_t N_updates, double *Updates,
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uint64_t *Updates_index) {
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// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
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// std::cerr << "Called qmckl_sherman_morrison_woodbury_2 with " << N_updates
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// << " updates" << std::endl;
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// #endif
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unsigned int n_of_2blocks = N_updates / 2;
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unsigned int remainder = N_updates % 2;
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unsigned int length_2block = 2 * Dim;
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unsigned int length_1block = 1 * Dim;
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uint64_t n_of_2blocks = N_updates / 2;
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uint64_t remainder = N_updates % 2;
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uint64_t length_2block = 2 * Dim;
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uint64_t length_1block = 1 * Dim;
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// Apply first 2*n_of_2blocks updates in n_of_2blocks blocks of 2 updates with
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// Woodbury 2x2 kernel
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double later_updates[Dim * N_updates];
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unsigned int later_index[N_updates];
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unsigned int later = 0;
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uint64_t later_index[N_updates];
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uint64_t later = 0;
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if (n_of_2blocks > 0) {
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for (unsigned int i = 0; i < n_of_2blocks; i++) {
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for (uint64_t i = 0; i < n_of_2blocks; i++) {
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double *Updates_2block = &Updates[i * length_2block];
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unsigned int *Updates_index_2block = &Updates_index[i * 2];
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uint64_t *Updates_index_2block = &Updates_index[i * 2];
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bool ok;
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ok = qmckl_woodbury_2(Slater_inv, Dim, Updates_2block, Updates_index_2block);
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if (!ok) { // Send the entire block to slagel_splitting
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unsigned int l = 0;
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uint64_t l = 0;
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slagel_splitting(Slater_inv, Dim, 2, Updates_2block, Updates_index_2block,
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later_updates + (Dim * later), later_index + later, &l);
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later = later + l;
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@ -359,8 +359,8 @@ void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const unsigned int Di
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if (remainder == 1) { // Apply last remaining update with slagel_splitting
|
||||
double *Updates_1block = &Updates[n_of_2blocks * length_2block];
|
||||
unsigned int *Updates_index_1block = &Updates_index[2 * n_of_2blocks];
|
||||
unsigned int l = 0;
|
||||
uint64_t *Updates_index_1block = &Updates_index[2 * n_of_2blocks];
|
||||
uint64_t l = 0;
|
||||
slagel_splitting(Slater_inv, Dim, 1, Updates_1block, Updates_index_1block,
|
||||
later_updates + (Dim * later), later_index + later, &l);
|
||||
later = later + l;
|
||||
|
|
@ -373,33 +373,33 @@ void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const unsigned int Di
|
|||
|
||||
// Sherman-Morrison-Woodbury 3x3 kernel
|
||||
// qmckl_woodbury_2, qmckl_woodbury_3, slagel_splitting mixing scheme
|
||||
void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const unsigned int Dim,
|
||||
const unsigned int N_updates, double *Updates,
|
||||
unsigned int *Updates_index) {
|
||||
void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const uint64_t Dim,
|
||||
const uint64_t N_updates, double *Updates,
|
||||
uint64_t *Updates_index) {
|
||||
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
|
||||
// std::cerr << "Called qmckl_sherman_morrison_woodbury_3 with " << N_updates
|
||||
// << " updates" << std::endl;
|
||||
// #endif
|
||||
|
||||
unsigned int n_of_3blocks = N_updates / 3;
|
||||
unsigned int remainder = N_updates % 3;
|
||||
unsigned int length_3block = 3 * Dim;
|
||||
unsigned int length_2block = 2 * Dim;
|
||||
unsigned int length_1block = 1 * Dim;
|
||||
uint64_t n_of_3blocks = N_updates / 3;
|
||||
uint64_t remainder = N_updates % 3;
|
||||
uint64_t length_3block = 3 * Dim;
|
||||
uint64_t length_2block = 2 * Dim;
|
||||
uint64_t length_1block = 1 * Dim;
|
||||
|
||||
// Apply first 3*n_of_3blocks updates in n_of_3blocks blocks of 3 updates with
|
||||
// Woodbury 3x3 kernel
|
||||
double later_updates[Dim * N_updates];
|
||||
unsigned int later_index[N_updates];
|
||||
unsigned int later = 0;
|
||||
uint64_t later_index[N_updates];
|
||||
uint64_t later = 0;
|
||||
if (n_of_3blocks > 0) {
|
||||
for (unsigned int i = 0; i < n_of_3blocks; i++) {
|
||||
for (uint64_t i = 0; i < n_of_3blocks; i++) {
|
||||
double *Updates_3block = &Updates[i * length_3block];
|
||||
unsigned int *Updates_index_3block = &Updates_index[i * 3];
|
||||
uint64_t *Updates_index_3block = &Updates_index[i * 3];
|
||||
bool ok;
|
||||
ok = qmckl_woodbury_3(Slater_inv, Dim, Updates_3block, Updates_index_3block);
|
||||
if (!ok) { // Send the entire block to slagel_splitting
|
||||
unsigned int l = 0;
|
||||
uint64_t l = 0;
|
||||
slagel_splitting(Slater_inv, Dim, 3, Updates_3block, Updates_index_3block,
|
||||
later_updates + (Dim * later), later_index + later, &l);
|
||||
later = later + l;
|
||||
|
|
@ -409,11 +409,11 @@ void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const unsigned int Di
|
|||
|
||||
if (remainder == 2) { // Apply last remaining block of 2 updates with Woodbury 2x2 kernel
|
||||
double *Updates_2block = &Updates[n_of_3blocks * length_3block];
|
||||
unsigned int *Updates_index_2block = &Updates_index[3 * n_of_3blocks];
|
||||
uint64_t *Updates_index_2block = &Updates_index[3 * n_of_3blocks];
|
||||
bool ok;
|
||||
ok = qmckl_woodbury_2(Slater_inv, Dim, Updates_2block, Updates_index_2block);
|
||||
if (!ok) { // Send the entire block to slagel_splitting
|
||||
unsigned int l = 0;
|
||||
uint64_t l = 0;
|
||||
slagel_splitting(Slater_inv, Dim, 2, Updates_2block, Updates_index_2block,
|
||||
later_updates + (Dim * later), later_index + later, &l);
|
||||
later = later + l;
|
||||
|
|
@ -421,8 +421,8 @@ void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const unsigned int Di
|
|||
}
|
||||
else if (remainder == 1) { // Apply last remaining update with slagel_splitting
|
||||
double *Updates_1block = &Updates[n_of_3blocks * length_3block];
|
||||
unsigned int *Updates_index_1block = &Updates_index[3 * n_of_3blocks];
|
||||
unsigned int l = 0;
|
||||
uint64_t *Updates_index_1block = &Updates_index[3 * n_of_3blocks];
|
||||
uint64_t l = 0;
|
||||
slagel_splitting(Slater_inv, Dim, 1, Updates_1block, Updates_index_1block,
|
||||
later_updates + (Dim * later), later_index + later, &l);
|
||||
later = later + l;
|
||||
|
|
|
|||
|
|
@ -29,6 +29,7 @@ int main() {
|
|||
qmckl_exit_code rc;
|
||||
#+end_src
|
||||
|
||||
|
||||
* Sherman-Morrison Helper Functions
|
||||
|
||||
Helper functions that are used by the Sherman-Morrison-Woodbury
|
||||
|
|
@ -66,7 +67,6 @@ This function is used to set the threshold value that is used in the kernels to
|
|||
double* const thresh );
|
||||
#+end_src
|
||||
|
||||
|
||||
*** Source Fortran
|
||||
|
||||
#+begin_src f90 :tangle (eval f)
|
||||
|
|
@ -96,7 +96,6 @@ return QMCKL_SUCCESS;
|
|||
}
|
||||
#+end_src
|
||||
|
||||
|
||||
*** Performance
|
||||
|
||||
** C interface :noexport:
|
||||
|
|
@ -338,7 +337,7 @@ assert(rc == QMCKL_SUCCESS);
|
|||
|
||||
* Woodbury 2x2
|
||||
|
||||
[TODO: FMJC] Add main body intro.
|
||||
This is the Woodbury 3x3 kernel.
|
||||
|
||||
** ~qmckl_woodbury_2~
|
||||
:PROPERTIES:
|
||||
|
|
@ -543,6 +542,225 @@ assert(rc == QMCKL_SUCCESS);
|
|||
#+end_src
|
||||
|
||||
|
||||
* Woodbury 3x3
|
||||
|
||||
This is the Woodbury 3x3 kernel.
|
||||
|
||||
** ~qmckl_woodbury_3~
|
||||
:PROPERTIES:
|
||||
:Name: qmckl_woodbury_3
|
||||
:CRetType: qmckl_exit_code
|
||||
:FRetType: qmckl_exit_code
|
||||
:END:
|
||||
|
||||
This is the simplest of the available Sherman-Morrison-Woodbury
|
||||
kernels in QMCkl. It applies rank-1 updates one by one in the order
|
||||
that is given. It only checks if the denominator in the
|
||||
Sherman-Morrison formula is not too close to zero (and exit with an
|
||||
error if it does) during the application of an update.
|
||||
|
||||
#+NAME: qmckl_woodbury_3_args
|
||||
| qmckl_context | context | in | Global state |
|
||||
| uint64_t | Dim | in | Leading dimension of Slater_inv |
|
||||
| double | Updates[3*Dim] | in | Array containing the updates |
|
||||
| uint64_t | Updates_index[3] | in | Array containing the rank-1 updates |
|
||||
| double | Slater_inv[Dim*Dim] | inout | Array containing the inverse of a Slater-matrix |
|
||||
|
||||
*** Requirements
|
||||
|
||||
Add description of the input variables. (see for e.g. qmckl_distance.org)
|
||||
|
||||
*** C header
|
||||
|
||||
#+CALL: generate_c_header(table=qmckl_woodbury_3_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_src c :tangle (eval h_func) :comments org
|
||||
qmckl_exit_code qmckl_woodbury_3_c (
|
||||
const qmckl_context context,
|
||||
const uint64_t Dim,
|
||||
const double* Updates,
|
||||
const uint64_t* Updates_index,
|
||||
double* Slater_inv );
|
||||
#+end_src
|
||||
|
||||
*** Source Fortran
|
||||
|
||||
#+begin_src f90 :tangle (eval f)
|
||||
integer function qmckl_woodbury_3_f(context, Slater_inv, Dim, &
|
||||
Updates, Updates_index) result(info)
|
||||
use qmckl
|
||||
implicit none
|
||||
integer(qmckl_context) , intent(in) :: context
|
||||
integer*8 , intent(in), value :: Dim
|
||||
integer*8 , intent(in) :: Updates_index(3)
|
||||
real*8 , intent(in) :: Updates(3*Dim)
|
||||
real*8 , intent(inout) :: Slater_inv(Dim*Dim)
|
||||
!logical, external :: qmckl_woodbury_3_f
|
||||
info = qmckl_woodbury_2(context, Dim, Updates, Updates_index, Slater_inv)
|
||||
end function qmckl_woodbury_3_f
|
||||
#+end_src
|
||||
|
||||
*** Source C
|
||||
|
||||
#+begin_src c :tangle (eval c) :comments org
|
||||
#include <stdbool.h>
|
||||
#include "qmckl.h"
|
||||
|
||||
qmckl_exit_code qmckl_woodbury_3_c(const qmckl_context context,
|
||||
const uint64_t Dim,
|
||||
const double* Updates,
|
||||
const uint64_t* Updates_index,
|
||||
double * Slater_inv) {
|
||||
/*
|
||||
C := S^{-1} * U, dim x 3
|
||||
B := 1 + V * C, 3 x 3
|
||||
D := V * S^{-1}, 3 x dim
|
||||
,*/
|
||||
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
|
||||
// std::cerr << "Called Woodbury 3x3 kernel" << std::endl;
|
||||
// #endif
|
||||
|
||||
const uint64_t row1 = (Updates_index[0] - 1);
|
||||
const uint64_t row2 = (Updates_index[1] - 1);
|
||||
const uint64_t row3 = (Updates_index[2] - 1);
|
||||
|
||||
// Compute C = S_inv * U !! NON-STANDARD MATRIX MULTIPLICATION BECAUSE
|
||||
// OF LAYOUT OF 'Updates' !!
|
||||
double C[3 * Dim];
|
||||
for (uint64_t i = 0; i < Dim; i++) {
|
||||
for (uint64_t j = 0; j < 3; j++) {
|
||||
C[i * 3 + j] = 0;
|
||||
for (uint64_t k = 0; k < Dim; k++) {
|
||||
C[i * 3 + j] += Slater_inv[i * Dim + k] * Updates[Dim * j + k];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Compute B = 1 + V.C
|
||||
const double B0 = C[row1 * 3] + 1;
|
||||
const double B1 = C[row1 * 3 + 1];
|
||||
const double B2 = C[row1 * 3 + 2];
|
||||
const double B3 = C[row2 * 3];
|
||||
const double B4 = C[row2 * 3 + 1] + 1;
|
||||
const double B5 = C[row2 * 3 + 2];
|
||||
const double B6 = C[row3 * 3];
|
||||
const double B7 = C[row3 * 3 + 1];
|
||||
const double B8 = C[row3 * 3 + 2] + 1;
|
||||
|
||||
// Check if determinant of B is not too close to zero
|
||||
double det;
|
||||
det = B0 * (B4 * B8 - B5 * B7) - B1 * (B3 * B8 - B5 * B6) +
|
||||
B2 * (B3 * B7 - B4 * B6);
|
||||
double thresh = 0.0;
|
||||
qmckl_exit_code rc = qmckl_sherman_morrison_threshold_c(&thresh);
|
||||
if (fabs(det) < thresh) {
|
||||
return QMCKL_FAILURE;
|
||||
}
|
||||
|
||||
// Compute B^{-1} with explicit formula for 3x3 inversion
|
||||
double Binv[9], idet = 1.0 / det;
|
||||
Binv[0] = (B4 * B8 - B7 * B5) * idet;
|
||||
Binv[1] = -(B1 * B8 - B7 * B2) * idet;
|
||||
Binv[2] = (B1 * B5 - B4 * B2) * idet;
|
||||
Binv[3] = -(B3 * B8 - B6 * B5) * idet;
|
||||
Binv[4] = (B0 * B8 - B6 * B2) * idet;
|
||||
Binv[5] = -(B0 * B5 - B3 * B2) * idet;
|
||||
Binv[6] = (B3 * B7 - B6 * B4) * idet;
|
||||
Binv[7] = -(B0 * B7 - B6 * B1) * idet;
|
||||
Binv[8] = (B0 * B4 - B3 * B1) * idet;
|
||||
|
||||
// Compute tmp = B^{-1} x (V.S^{-1})
|
||||
double tmp[3 * Dim];
|
||||
for (uint64_t i = 0; i < 3; i++) {
|
||||
for (uint64_t j = 0; j < Dim; j++) {
|
||||
tmp[i * Dim + j] = Binv[i * 3] * Slater_inv[row1 * Dim + j];
|
||||
tmp[i * Dim + j] += Binv[i * 3 + 1] * Slater_inv[row2 * Dim + j];
|
||||
tmp[i * Dim + j] += Binv[i * 3 + 2] * Slater_inv[row3 * Dim + j];
|
||||
}
|
||||
}
|
||||
|
||||
// Compute (S + U V)^{-1} = S^{-1} - C x tmp
|
||||
for (uint64_t i = 0; i < Dim; i++) {
|
||||
for (uint64_t j = 0; j < Dim; j++) {
|
||||
Slater_inv[i * Dim + j] -= C[i * 3] * tmp[j];
|
||||
Slater_inv[i * Dim + j] -= C[i * 3 + 1] * tmp[Dim + j];
|
||||
Slater_inv[i * Dim + j] -= C[i * 3 + 2] * tmp[2 * Dim + j];
|
||||
}
|
||||
}
|
||||
|
||||
return QMCKL_SUCCESS;
|
||||
}
|
||||
|
||||
#+end_src
|
||||
|
||||
*** Performance...
|
||||
|
||||
** C interface :noexport:
|
||||
|
||||
#+CALL: generate_c_interface(table=qmckl_woodbury_3_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_src f90 :tangle (eval f) :comments org :exports none
|
||||
integer(c_int32_t) function qmckl_woodbury_3 &
|
||||
(context, Dim, Updates, Updates_index, Slater_inv) &
|
||||
bind(C) result(info)
|
||||
|
||||
use, intrinsic :: iso_c_binding
|
||||
implicit none
|
||||
|
||||
integer (c_int64_t) , intent(in) , value :: context
|
||||
integer (c_int64_t) , intent(in) , value :: Dim
|
||||
real (c_double ) , intent(in) :: Updates(3*Dim)
|
||||
integer (c_int64_t) , intent(in) :: Updates_index(3)
|
||||
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
|
||||
|
||||
integer(c_int32_t), external :: qmckl_woodbury_3_c
|
||||
info = qmckl_woodbury_3_c &
|
||||
(context, Dim, Updates, Updates_index, Slater_inv)
|
||||
|
||||
end function qmckl_woodbury_3
|
||||
#+end_src
|
||||
|
||||
#+CALL: generate_f_interface(table=qmckl_woodbury_3_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
|
||||
interface
|
||||
integer(c_int32_t) function qmckl_woodbury_3 &
|
||||
(context, Dim, Updates, Updates_index, Slater_inv) &
|
||||
bind(C)
|
||||
use, intrinsic :: iso_c_binding
|
||||
import
|
||||
implicit none
|
||||
|
||||
integer (c_int64_t) , intent(in) , value :: context
|
||||
integer (c_int64_t) , intent(in) , value :: Dim
|
||||
real (c_double ) , intent(in) :: Updates(3*Dim)
|
||||
integer (c_int64_t) , intent(in) :: Updates_index(3)
|
||||
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
|
||||
|
||||
end function qmckl_woodbury_3
|
||||
end interface
|
||||
#+end_src
|
||||
|
||||
*** Test :noexport:
|
||||
|
||||
[TODO: FMJC] Write tests for the Sherman-Morrison part.
|
||||
|
||||
|
||||
#+begin_src c :tangle (eval c_test)
|
||||
const uint64_t woodbury3_Dim = 3;
|
||||
const uint64_t woodbury3_Updates_index[3] = {1, 1, 1};
|
||||
const double woodbury3_Updates[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
|
||||
double woodbury3_Slater_inv[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
|
||||
|
||||
// [TODO : FMJC ] add realistic tests
|
||||
|
||||
rc = qmckl_woodbury_3_c(context, woodbury3_Dim, woodbury3_Updates, woodbury3_Updates_index, woodbury3_Slater_inv);
|
||||
assert(rc == QMCKL_SUCCESS);
|
||||
#+end_src
|
||||
|
||||
|
||||
* End of files
|
||||
|
||||
|
|
@ -556,3 +774,4 @@ assert(rc == QMCKL_SUCCESS);
|
|||
|
||||
# -*- mode: org -*-
|
||||
# vim: syntax=c
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user