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Fixed tests. Everything compiles successfully and passes all tests. #25

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Francois Coppens 2021-07-27 06:59:44 +02:00
parent 41be86fe59
commit 0e4ea1f81b
2 changed files with 5 additions and 437 deletions
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434
org/qmckl_sherman_morrison_woodbury.cpp
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@ -1,434 +0,0 @@
#include <math.h>
// Sherman-Morrison-Woodbury break-down threshold
#ifndef THRESHOLD
#define THRESHOLD 1e-3
#endif
static double threshold();
// Naïve Sherman Morrison
bool qmckl_sherman_morrison(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
double *Updates, uint64_t *Updates_index);
// Woodbury 2x2 kernel
bool qmckl_woodbury_2(double *Slater_inv, const uint64_t Dim, double *Updates,
const uint64_t *Updates_index);
// Woodbury 3x3 kernel
bool qmckl_woodbury_3(double *Slater_inv, const uint64_t Dim, double *Updates,
const uint64_t *Updates_index);
// Sherman Morrison, with J. Slagel splitting (caller function)
void qmckl_sherman_morrison_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
double *Updates, uint64_t *Updates_index);
// Sherman Morrison, with J. Slagel splitting
// http://hdl.handle.net/10919/52966
static void slagel_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
double *Updates, uint64_t *Updates_index,
double *later_updates, uint64_t *later_index,
uint64_t *later);
// Mixed Sherman-Morrison-Woodbury kernel using
// Woodbury 2x2 and Sherman-Morrison with update-splitting
void qmckl_sherman_morrison_woodbury_2(double *Slater_inv, const uint64_t Dim,
const uint64_t N_updates, double *Updates,
uint64_t *Updates_index);
// Mixed Sherman-Morrison-Woodbury kernel using
// Woodbury 3x3, Woodbury 2x2 and Sherman-Morrison with update-splitting
void qmckl_sherman_morrison_woodbury_3(double *Slater_inv, const uint64_t Dim,
const uint64_t N_updates, double *Updates,
uint64_t *Updates_index);
// Sherman-Morrison-Woodbury break-down threshold
static double threshold() {
const double threshold = THRESHOLD;
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
// std::cerr << "Break-down threshold set to: " << threshold << std::endl;
// #endif
return threshold;
}
// Naïve Sherman Morrison
bool qmckl_sherman_morrison(double *Slater_inv, uint64_t Dim, 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 with " << N_updates << " updates" << std::endl;
// #endif
double C[Dim];
double D[Dim];
uint64_t l = 0;
// For each update
while (l < N_updates) {
// C = A^{-1} x U_l
for (uint64_t i = 0; i < Dim; i++) {
C[i] = 0;
for (uint64_t j = 0; j < Dim; j++) {
C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
}
}
// Denominator
double den = 1 + C[Updates_index[l] - 1];
if (fabs(den) < threshold()) {
return QMCKL_FAILURE;
}
double iden = 1 / den;
// D = v^T x A^{-1}
for (uint64_t j = 0; j < Dim; j++) {
D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
}
// A^{-1} = A^{-1} - C x D / den
for (uint64_t i = 0; i < Dim; i++) {
for (uint64_t j = 0; j < Dim; j++) {
double update = C[i] * D[j] * iden;
Slater_inv[i * Dim + j] -= update;
}
}
l += 1;
}
return QMCKL_SUCCESS;
}
// Woodbury 2x2 kernel
bool qmckl_woodbury_2(double *Slater_inv, const uint64_t Dim, double *Updates,
const uint64_t *Updates_index) {
/*
C := S^{-1} * U, dim x 2
B := 1 + V * C, 2 x 2
D := V * S^{-1}, 2 x dim
*/
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
// std::cerr << "Called Woodbury 2x2 kernel" << std::endl;
// #endif
const uint64_t row1 = (Updates_index[0] - 1);
const uint64_t row2 = (Updates_index[1] - 1);
// Compute C = S_inv * U !! NON-STANDARD MATRIX MULTIPLICATION BECAUSE
// OF LAYOUT OF 'Updates' !!
double C[2 * Dim];
for (uint64_t i = 0; i < Dim; i++) {
for (uint64_t j = 0; j < 2; j++) {
C[i * 2 + j] = 0;
for (uint64_t k = 0; k < Dim; k++) {
C[i * 2 + j] += Slater_inv[i * Dim + k] * Updates[Dim * j + k];
}
}
}
// Compute B = 1 + V * C
const double B0 = C[row1 * 2] + 1;
const double B1 = C[row1 * 2 + 1];
const double B2 = C[row2 * 2];
const double B3 = C[row2 * 2 + 1] + 1;
// Check if determinant of inverted matrix is not zero
double det = B0 * B3 - B1 * B2;
if (fabs(det) < threshold()) {
return QMCKL_FAILURE;
}
// Compute B^{-1} with explicit formula for 2x2 inversion
double Binv[4], idet = 1.0 / det;
Binv[0] = idet * B3;
Binv[1] = -1.0 * idet * B1;
Binv[2] = -1.0 * idet * B2;
Binv[3] = idet * B0;
// Compute tmp = B^{-1} x (V.S^{-1})
double tmp[2 * Dim];
for (uint64_t i = 0; i < 2; i++) {
for (uint64_t j = 0; j < Dim; j++) {
tmp[i * Dim + j] = Binv[i * 2] * Slater_inv[row1 * Dim + j];
tmp[i * Dim + j] += Binv[i * 2 + 1] * Slater_inv[row2 * 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 * 2] * tmp[j];
Slater_inv[i * Dim + j] -= C[i * 2 + 1] * tmp[Dim + j];
}
}
return QMCKL_SUCCESS;
}
// Woodbury 3x3 kernel
bool qmckl_woodbury_3(double *Slater_inv, const uint64_t Dim, double *Updates,
const uint64_t *Updates_index) {
/*
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);
if (fabs(det) < threshold()) {
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;
}
// Sherman Morrison, with J. Slagel splitting (caller function)
// http://hdl.handle.net/10919/52966
void qmckl_sherman_morrison_splitting(double *Slater_inv, uint64_t Dim, 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_splitting with " << N_updates << " updates" << std::endl;
// #endif
double later_updates[Dim * N_updates];
uint64_t later_index[N_updates];
uint64_t later = 0;
slagel_splitting(Slater_inv, Dim, N_updates, Updates, Updates_index, later_updates,
later_index, &later);
if (later > 0) {
qmckl_sherman_morrison_splitting(Slater_inv, Dim, later, later_updates, later_index);
}
}
// Sherman Morrison, with J. Slagel splitting
// http://hdl.handle.net/10919/52966
static void slagel_splitting(double *Slater_inv, uint64_t Dim, uint64_t N_updates,
double *Updates, uint64_t *Updates_index,
double *later_updates, uint64_t *later_index,
uint64_t *later) {
// #ifdef DEBUG // Leave commented out since debugging information is not yet implemented in QMCkl.
// std::cerr << "Called slagel_splitting with " << N_updates << " updates" << std::endl;
// #endif
double C[Dim];
double D[Dim];
uint64_t l = 0;
// For each update
while (l < N_updates) {
// C = S^{-1} x U_l
for (uint64_t i = 0; i < Dim; i++) {
C[i] = 0;
for (uint64_t j = 0; j < Dim; j++) {
C[i] += Slater_inv[i * Dim + j] * Updates[l * Dim + j];
}
}
// Denominator
double den = 1 + C[Updates_index[l] - 1];
if (fabs(den) < threshold()) {
// U_l = U_l / 2 (do the split)
for (uint64_t i = 0; i < Dim; i++) {
later_updates[*later * Dim + i] = Updates[l * Dim + i] / 2.0;
C[i] /= 2.0;
}
later_index[*later] = Updates_index[l];
(*later)++;
den = 1 + C[Updates_index[l] - 1];
}
double iden = 1 / den;
// D = v^T x S^{-1}
for (uint64_t j = 0; j < Dim; j++) {
D[j] = Slater_inv[(Updates_index[l] - 1) * Dim + j];
}
// S^{-1} = S^{-1} - C x D / den
for (uint64_t i = 0; i < Dim; i++) {
for (uint64_t j = 0; j < Dim; j++) {
double update = C[i] * D[j] * iden;
Slater_inv[i * Dim + j] -= update;
}
}
l += 1;
}
}
// Sherman-Morrison-Woodbury 2x2 kernel
// qmckl_woodbury_2, slagel_splitting mixing scheme
void qmckl_sherman_morrison_woodbury_2(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_2 with " << N_updates
// << " updates" << std::endl;
// #endif
uint64_t n_of_2blocks = N_updates / 2;
uint64_t remainder = N_updates % 2;
uint64_t length_2block = 2 * Dim;
uint64_t length_1block = 1 * Dim;
// Apply first 2*n_of_2blocks updates in n_of_2blocks blocks of 2 updates with
// Woodbury 2x2 kernel
double later_updates[Dim * N_updates];
uint64_t later_index[N_updates];
uint64_t later = 0;
if (n_of_2blocks > 0) {
for (uint64_t i = 0; i < n_of_2blocks; i++) {
double *Updates_2block = &Updates[i * length_2block];
uint64_t *Updates_index_2block = &Updates_index[i * 2];
bool ok;
ok = qmckl_woodbury_2(Slater_inv, Dim, Updates_2block, Updates_index_2block);
if (!ok) { // Send the entire block to slagel_splitting
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;
}
}
}
if (remainder == 1) { // Apply last remaining update with slagel_splitting
double *Updates_1block = &Updates[n_of_2blocks * length_2block];
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;
}
if (later > 0) {
qmckl_sherman_morrison_splitting(Slater_inv, Dim, later, later_updates, later_index);
}
}
// 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 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
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];
uint64_t later_index[N_updates];
uint64_t later = 0;
if (n_of_3blocks > 0) {
for (uint64_t i = 0; i < n_of_3blocks; i++) {
double *Updates_3block = &Updates[i * length_3block];
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
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;
}
}
}
if (remainder == 2) { // Apply last remaining block of 2 updates with Woodbury 2x2 kernel
double *Updates_2block = &Updates[n_of_3blocks * length_3block];
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
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;
}
}
else if (remainder == 1) { // Apply last remaining update with slagel_splitting
double *Updates_1block = &Updates[n_of_3blocks * length_3block];
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;
}
if (later > 0) {
qmckl_sherman_morrison_splitting(Slater_inv, Dim, later, later_updates, later_index);
}
}

8
org/qmckl_sherman_morrison_woodbury.org
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@ -1346,6 +1346,7 @@ qmckl_exit_code qmckl_sherman_morrison_smw3s_c(const qmckl_context context,
if (later > 0) { if (later > 0) {
rc = qmckl_sherman_morrison_splitting_c(local_context, Dim, later, later_updates, later_index, breakdown, Slater_inv); rc = qmckl_sherman_morrison_splitting_c(local_context, Dim, later, later_updates, later_index, breakdown, Slater_inv);
} }
return QMCKL_SUCCESS;
} }
#+end_src #+end_src
@ -1408,9 +1409,9 @@ qmckl_exit_code qmckl_sherman_morrison_smw3s_c(const qmckl_context context,
#+begin_src c :tangle (eval c_test) #+begin_src c :tangle (eval c_test)
const uint64_t smw3s__Dim = 3; const uint64_t smw3s_Dim = 3;
const uint64_t smw3s__N_updates = 3; const uint64_t smw3s_N_updates = 3;
const uint64_t smw3s__Updates_index[3] = {1, 1, 1}; const uint64_t smw3s_Updates_index[3] = {1, 1, 1};
const double smw3s_Updates[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; const double smw3s_Updates[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
const double smw3s_breakdown = 1e-3; const double smw3s_breakdown = 1e-3;
double smw3s_Slater_inv[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; double smw3s_Slater_inv[9] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
@ -1565,6 +1566,7 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s_c(const qmckl_context context,
if (later > 0) { if (later > 0) {
rc = qmckl_sherman_morrison_splitting_c(local_context, Dim, later, later_updates, later_index, breakdown, Slater_inv); rc = qmckl_sherman_morrison_splitting_c(local_context, Dim, later, later_updates, later_index, breakdown, Slater_inv);
} }
return QMCKL_SUCCESS;
} }
#+end_src #+end_src