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Started adding the pedagogical kernels for the HAVE_DOC builds.

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Francois Coppens 2023-02-02 17:04:34 +01:00
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org/qmckl_sherman_morrison_woodbury.org
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@ -9,281 +9,307 @@
* Headers
#+begin_src elisp :noexport :results none :exports none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
#+begin_src c :comments link :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "assert.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <math.h>
#include "qmckl.h"
#include "assert.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <math.h>
int main() {
qmckl_context context;
context = qmckl_context_create();
qmckl_exit_code rc;
int main() {
qmckl_context context;
context = qmckl_context_create();
qmckl_exit_code rc;
#+end_src
#+NAME:kernel_generator_range
#+begin_src python :noweb yes :exports none
range(2, 22)
range(2, 22)
#+end_src
* Naïve Sherman-Morrison
** ~qmckl_sherman_morrison_naive~
:PROPERTIES:
:Name: qmckl_sherman_morrison_naive
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
:PROPERTIES:
:Name: qmckl_sherman_morrison_naive
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
This is the simplest of the available Sherman-Morrison-Woodbury kernels. 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 when an update is evaluated. It will exit with an error code of the denominator is too close to zero.
This is the simplest of the available Sherman-Morrison-Woodbury kernels. 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 when an update is evaluated. It will exit with an error code of the denominator is too close to zero.
The formula for any update $u_j$ (index $j$ is suppresed for clarity) that is applied is
\[
The formula for any update $u_j$ (index $j$ is suppresed for clarity) that is applied is
\[
(S + uv^T)^{-1} = S^{-1} - \frac{S^{-1} uv^T S^{-1}}{1 + v^T S^{-1} u}
\]
\]
where
$S$ is the Slater-matrix,
$u$ and $v^T$ are the column and row vectors containing the updates,
$S^{-1}$ is the inverse of the Slater-matrix.
where
$S$ is the Slater-matrix,
$u$ and $v^T$ are the column and row vectors containing the updates,
$S^{-1}$ is the inverse of the Slater-matrix.
Even though the Slater-matrix $S$ with all updates applied at once is invertable, during the course of applying
updates to the inverse Slater-matrix $S^{-1}$ one-by-one it can happen that one of the intermediate inverse
matrices $S^{-1}$ becomes singular. Therefore a global threshold value $\epsilon$ is defined that is used to
evaluate each individual update $u_j$ when it is applied.
Even though the Slater-matrix $S$ with all updates applied at once is invertable, during the course of applying
updates to the inverse Slater-matrix $S^{-1}$ one-by-one it can happen that one of the intermediate inverse
matrices $S^{-1}$ becomes singular. Therefore a global threshold value $\epsilon$ is defined that is used to
evaluate each individual update $u_j$ when it is applied.
This value sets the lower bound for which the
denominator $1+v_j^TS^{-1}u_j$ is considered to be too small and will most probably result in a singular matrix
$S$, or at least in an inverse of $S$ of very poor numerical quality. Therefore, when $1+v_j^TS^{-1}u_j \geq \epsilon$,
the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
This value sets the lower bound for which the
denominator $1+v_j^TS^{-1}u_j$ is considered to be too small and will most probably result in a singular matrix
$S$, or at least in an inverse of $S$ of very poor numerical quality. Therefore, when $1+v_j^TS^{-1}u_j \geq \epsilon$,
the update is applied as usual and the kernel exits with return code \texttt{QMCKL_SUCCESS}.
If $1+v_j^TS^{-1}u_j \leq \epsilon$ the update is rejected and the kernel exits with return code \texttt{QMCKL_FAILURE}.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
#+NAME: qmckl_sherman_morrison_naive_args
| qmckl_context | context | in | Global state |
| uint64_t | LDS | in | Leading dimension of Slater_inv |
| uint64_t | Dim | in | Dimension of Slater_inv |
| uint64_t | N_updates | in | Number of rank-1 updates to be applied to Slater_inv |
| double | Updates[N_updates*Dim] | in | Array containing the updates |
| uint64_t | Updates_index[N_updates] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[LDS*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of the Slater-matrix |
#+NAME: qmckl_sherman_morrison_naive_args
| qmckl_context | context | in | Global state |
| uint64_t | LDS | in | Leading dimension of Slater_inv |
| uint64_t | Dim | in | Dimension of Slater_inv |
| uint64_t | N_updates | in | Number of rank-1 updates to be applied to Slater_inv |
| double | Updates[N_updates*Dim] | in | Array containing the updates |
| uint64_t | Updates_index[N_updates] | in | Array containing the rank-1 updates |
| double | breakdown | in | Break-down parameter on which to fail or not |
| double | Slater_inv[LDS*Dim] | inout | Array containing the inverse of a Slater-matrix |
| double* | determinant | inout | Determinant of the Slater-matrix |
*** Requirements
* ~context~ is not ~QMCKL_NULL_CONTEXT~
* ~LDS >= 2~
* ~Dim >= 2~
* ~N_updates >= 1~
* ~Updates~ is allocated with $N_updates \times Dim$ elements
* ~Updates_index~ is allocated with $N_updates$ elements
* ~breakdown~ is a small number such that $0 < breakdown << 1$
* ~Slater_inv~ is allocated with $Dim \times Dim$ elements
* ~context~ is not ~QMCKL_NULL_CONTEXT~
* ~LDS >= 2~
* ~Dim >= 2~
* ~N_updates >= 1~
* ~Updates~ is allocated with $N_updates \times Dim$ elements
* ~Updates_index~ is allocated with $N_updates$ elements
* ~breakdown~ is a small number such that $0 < breakdown << 1$
* ~Slater_inv~ is allocated with $Dim \times Dim$ elements
*** Fortran source
#+begin_src f90 :tangle (eval f)
integer function qmckl_sherman_morrison_naive_doc_f &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: Dim
integer (c_int64_t) , intent(in) , value :: N_updates
real (c_double ) , intent(in) :: Updates(N_updates*Dim)
integer (c_int64_t) , intent(in) :: Updates_index(N_updates)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
write(*,*) "Function 'qmckl_sherman_morrison_naive_doc_f' does nothing for now..."
end function qmckl_sherman_morrison_naive_doc_f
#+end_src
*** C header
#+CALL: generate_c_header(table=qmckl_sherman_morrison_naive_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+CALL: generate_c_header(table=qmckl_sherman_morrison_naive_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_sherman_morrison_naive(
const qmckl_context context,
const uint64_t LDS,
const uint64_t Dim,
const uint64_t N_updates,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv,
double* determinant);
#+end_src
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_sherman_morrison_naive(
const qmckl_context context,
const uint64_t LDS,
const uint64_t Dim,
const uint64_t N_updates,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv,
double* determinant);
#+end_src
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_sherman_morrison_naive_doc(
const qmckl_context context,
const uint64_t Dim,
const uint64_t N_updates,
const double* Updates,
const uint64_t* Updates_index,
const double breakdown,
double* Slater_inv,
double* determinant);
#+end_src
*** C source
#+begin_src c :tangle (eval c) :comments org
#include <stdbool.h>
#include <math.h>
#include "qmckl.h"
#include "config.h"
// Order important because
// __GNUC__ also set in ICC, ICX and CLANG
// __clang__ also set in ICX
#if defined(__INTEL_COMPILER)
#define IVDEP _Pragma("ivdep")
#define ALIGNED _Pragma("vector aligned")
#elif defined(__INTEL_LLVM_COMPILER)
#define IVDEP _Pragma("ivdep")
#define ALIGNED _Pragma("vector aligned")
#elif defined(__clang__)
#define IVDEP _Pragma("clang loop vectorize(enable)")
#define ALIGNED
#elif defined(__GNUC__)
#define IVDEP _Pragma("GCC ivdep")
#define ALIGNED
#endif
#+begin_src c :tangle (eval c) :comments org
#include <stdbool.h>
#include <math.h>
#include "qmckl.h"
#include "config.h"
qmckl_exit_code qmckl_sherman_morrison_naive_hpc(
const qmckl_context context,
const uint64_t LDS,
const uint64_t Dim,
const uint64_t N_updates,
const double* __restrict Updates,
const uint64_t* __restrict Updates_index,
const double breakdown,
double* __restrict Slater_inv,
double* __restrict determinant) {
// Order important because
// __GNUC__ also set in ICC, ICX and CLANG
// __clang__ also set in ICX
#if defined(__INTEL_COMPILER)
#define IVDEP _Pragma("ivdep")
#define ALIGNED _Pragma("vector aligned")
#elif defined(__INTEL_LLVM_COMPILER)
#define IVDEP _Pragma("ivdep")
#define ALIGNED _Pragma("vector aligned")
#elif defined(__clang__)
#define IVDEP _Pragma("clang loop vectorize(enable)")
#define ALIGNED
#elif defined(__GNUC__)
#define IVDEP _Pragma("GCC ivdep")
#define ALIGNED
#endif
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_NULL_CONTEXT,
"qmckl_sherman_morrison_naive_hpc",
NULL);
}
qmckl_exit_code qmckl_sherman_morrison_naive_hpc(
const qmckl_context context,
const uint64_t LDS,
const uint64_t Dim,
const uint64_t N_updates,
const double* __restrict Updates,
const uint64_t* __restrict Updates_index,
const double breakdown,
double* __restrict Slater_inv,
double* __restrict determinant) {
double __attribute__((aligned(8))) C[Dim];
double __attribute__((aligned(8))) D[LDS];
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_NULL_CONTEXT,
"qmckl_sherman_morrison_naive_hpc",
NULL);
}
double __attribute__((aligned(8))) C[Dim];
double __attribute__((aligned(8))) D[LDS];
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++) {
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] = 0.0f;
IVDEP
ALIGNED
for (uint64_t j = 0; j < LDS; j++) {
C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j];
C[i] += Slater_inv[i * LDS + j] * Updates[l * LDS + j];
}
}
}
// Denominator: v_l^T * C
const int cui = Updates_index[l] - 1;
double den = 1.0f + C[cui];
// Denominator: v_l^T * C
const int cui = Updates_index[l] - 1;
double den = 1.0f + C[cui];
if (fabs(den) < breakdown) {
if (fabs(den) < breakdown)
return QMCKL_FAILURE;
}
double iden = 1.0f / den;
// Update det(A)
if (determinant)
double iden = 1.0f / den;
// Update det(A)
if (determinant)
*determinant *= den;
// selecting column: v_l^T * S_inv
IVDEP
ALIGNED
for (uint64_t j = 0; j < LDS; j++) {
// selecting column: v_l^T * S_inv
IVDEP
ALIGNED
for (uint64_t j = 0; j < LDS; j++) {
D[j] = Slater_inv[cui * LDS + j];
}
}
// A^{-1} = A^{-1} - C x D / den
for (uint64_t i = 0; i < Dim; i++) {
// A^{-1} = A^{-1} - C x D / den
for (uint64_t i = 0; i < Dim; i++) {
IVDEP
ALIGNED
for (uint64_t j = 0; j < LDS; j++) {
const double update = C[i] * D[j] * iden;
Slater_inv[i * LDS + j] -= update;
const double update = C[i] * D[j] * iden;
Slater_inv[i * LDS + j] -= update;
}
}
l += 1;
}
l += 1;
}
return QMCKL_SUCCESS;
}
#+end_src
#+NAME:naive_template_code
#+begin_src c
static inline qmckl_exit_code qmckl_sherman_morrison_naive_{Dim}(
const qmckl_context context,
const uint64_t N_updates,
const double* __restrict Updates,
const uint64_t* __restrict Updates_index,
const double breakdown,
double* __restrict Slater_inv,
double* __restrict determinant) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_NULL_CONTEXT,
"qmckl_sherman_morrison_naive_{Dim}",
NULL);
}
#define D{Dim}_P ((1+({Dim}-1)/SIMD_LENGTH)*SIMD_LENGTH)
double __attribute__((aligned(8))) C[{Dim}];
double __attribute__((aligned(8))) D[D{Dim}_P];
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;
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];
return QMCKL_SUCCESS;
}
}
#+end_src
// Denominator
const int cui = Updates_index[l] - 1;
double den = 1.0f + C[cui];
#+NAME:naive_template_code
#+begin_src c
static inline qmckl_exit_code qmckl_sherman_morrison_naive_{Dim}(
const qmckl_context context,
const uint64_t N_updates,
const double* __restrict Updates,
const uint64_t* __restrict Updates_index,
const double breakdown,
double* __restrict Slater_inv,
double* __restrict determinant) {
if (fabs(den) < breakdown) {
return QMCKL_FAILURE;
}
double iden = 1.0f / den;
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith(context,
QMCKL_NULL_CONTEXT,
"qmckl_sherman_morrison_naive_{Dim}",
NULL);
}
// Update det(A)
if (determinant)
*determinant *= den;
#define D{Dim}_P ((1+({Dim}-1)/SIMD_LENGTH)*SIMD_LENGTH)
// selecting column: D = v_l^T * S_inv
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
D[j] = Slater_inv[cui * D{Dim}_P + j];
}
double __attribute__((aligned(8))) C[{Dim}];
double __attribute__((aligned(8))) D[D{Dim}_P];
// A^{-1} = A^{-1} - C x D / den
for (uint64_t i = 0; i < {Dim}; i++) {
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
double update = C[i] * D[j] * iden;
Slater_inv[i * D{Dim}_P + j] -= update;
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;
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
C[i] += Slater_inv[i * D{Dim}_P + j] * Updates[l * D{Dim}_P + j];
}
}
// Denominator
const int cui = Updates_index[l] - 1;
double den = 1.0f + C[cui];
if (fabs(den) < breakdown) {
return QMCKL_FAILURE;
}
double iden = 1.0f / den;
// Update det(A)
if (determinant)
*determinant *= den;
// selecting column: D = v_l^T * S_inv
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
D[j] = Slater_inv[cui * D{Dim}_P + j];
}
// A^{-1} = A^{-1} - C x D / den
for (uint64_t i = 0; i < {Dim}; i++) {
IVDEP
ALIGNED
for (uint64_t j = 0; j < D{Dim}_P; j++) {
double update = C[i] * D[j] * iden;
Slater_inv[i * D{Dim}_P + j] -= update;
}
}
l += 1;
}
return QMCKL_SUCCESS;
}
}
l += 1;
}
return QMCKL_SUCCESS;
}
#+end_src
#+end_src
#+NAME:naive_kernel_generator
#+begin_src python :noweb yes :exports none
@ -298,10 +324,6 @@ for Dim in <<kernel_generator_range>>:
return '\n'.join(result)
#+end_src
#+NAME:naive_switch-case_generator
#+begin_src python :noweb yes :exports none
text="""
@ -322,10 +344,6 @@ for Dim in <<kernel_generator_range>>:
return '\n'.join(result)
#+end_src
#+begin_src c :tangle (eval c) :comments org :noweb yes
<<naive_kernel_generator()>>
@ -346,6 +364,7 @@ qmckl_exit_code qmckl_sherman_morrison_naive(const qmckl_context context,
NULL);
}
#ifdef HAVE_HPC
if (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // Most cases
switch (Dim) {
<<naive_switch-case_generator()>>
@ -363,20 +382,115 @@ qmckl_exit_code qmckl_sherman_morrison_naive(const qmckl_context context,
determinant);
}
#else
return qmckl_sherman_morrison_naive_doc(context,
Dim,
N_updates,
Updates,
Updates_index,
breakdown,
Slater_inv,
determinant);
#endif
return QMCKL_FAILURE;
}
#+end_src
*** Test :noexport:
The tests for the kernels are executed on datasets that are extracted from a run of
QMC=Chem on Benzene (21 spin-up/21 spin down electrons) using 329 unique alpha determinants.
The tests are run such that the kernels reject the computed inverse whenever the computed
intermediate determinants or denominators are smaller than 1e-3. This is the default value in
QMC=Chem. The tests will return QMCKL_SUCCESS whenever all the elements of the final matrix
$R=S.S^-1 - 1$ are smaller than the given tolerance value of 1e-3, and will return
QMCKL_FAILURE if the values are larger than this tolerance value.
#+begin_src c :tangle (eval c_test)
const uint64_t Dim = 21;
const uint64_t LDS = (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH;
const double breakdown = 1e-3;
const double tolerance = 1e-3;
double res[441];
#include "sm_test.h"
*** Performance
assert(Updates1 != NULL);
assert(Updates_index1 != NULL);
assert(Slater_inv1 != NULL);
This function performs best when there is only 1 rank-1 update in the update cycle. It is not useful to
use Sherman-Morrison with update splitting for these cycles since splitting can never resolve a situation
where applying the update causes singular behaviour.
// original determinant of Slater1 (before applying updates)
double det = 3.407025646103221e-10;
rc = qmckl_sherman_morrison_naive(context,
LDS,
Dim,
N_updates1,
Updates1,
Updates_index1,
breakdown,
Slater_inv1,
&det);
// Check that the determinant is updated properly
assert(fabs(det + 4.120398385068217e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
for (unsigned int k = 0; k < Dim; k++) {
res[i * Dim + j] += Slater1[i * Dim + k] * Slater_inv1[k * LDS + j];
}
}
}
rc = QMCKL_SUCCESS;
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
if (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
rc = QMCKL_FAILURE;
}
if (i != j && fabs(res[i * Dim + j]) > tolerance) {
rc = QMCKL_FAILURE;
}
}
}
assert(rc == QMCKL_SUCCESS);
#+end_src
** Performance
This function performs best when there is only 1 rank-1 update in the update cycle. It is
not useful to use Sherman-Morrison with update splitting for these cycles since splitting
can never resolve a situation where applying the update causes singular behaviour.
** C interface
#+begin_src f90 :tangle (eval f) :comments org :exports none
interface
integer(c_int32_t) function qmckl_sherman_morrison_naive_doc &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv, determinant) &
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
integer (c_int64_t) , intent(in) , value :: N_updates
real (c_double ) , intent(in) :: Updates(N_updates*Dim)
integer (c_int64_t) , intent(in) :: Updates_index(N_updates)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
integer(c_int32_t), external :: qmckl_sherman_morrison_naive_doc_f
info = qmckl_sherman_morrison_naive_doc_f &
(context, Dim, N_updates, Updates, &
Updates_index, breakdown, Slater_inv, determinant)
end function qmckl_sherman_morrison_naive_doc
end interface
#+end_src
** Fortran interface :noexport:
:PROPERTIES:
@ -412,63 +526,31 @@ qmckl_exit_code qmckl_sherman_morrison_naive(const qmckl_context context,
end interface
#+end_src
*** Test :noexport:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_sherman_morrison_naive_doc &
(context, Dim, N_updates, Updates, Updates_index, breakdown, Slater_inv, determinant) &
bind(C)
The tests for the kernels are executed on datasets that are extracted from a run of QMC=Chem on Benzene (21 spin-up/21 spin down electrons) using 329 unique alpha determinants. The tests are run such that the kernels reject the computed inverse whenever the computed intermediate determinants or denominators are smaller than 1e-3. This is the default value in QMC=Chem. The tests will return QMCKL_SUCCESS whenever all the elements of the final matrix $R=S.S^-1 - 1$ are smaller than the given tolerance value of 1e-3, and will return QMCKL_FAILURE if the values are larger than this tolerance value.
use, intrinsic :: iso_c_binding
import
implicit none
#+begin_src c :tangle (eval c_test)
const uint64_t Dim = 21;
const uint64_t LDS = (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH;
const double breakdown = 1e-3;
const double tolerance = 1e-3;
double res[441];
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: Dim
integer (c_int64_t) , intent(in) , value :: N_updates
real (c_double ) , intent(in) :: Updates(N_updates*Dim)
integer (c_int64_t) , intent(in) :: Updates_index(N_updates)
real (c_double ) , intent(in) , value :: breakdown
real (c_double ) , intent(inout) :: Slater_inv(Dim*Dim)
real (c_double ) , intent(inout) :: determinant
#include "sm_test.h"
assert(Updates1 != NULL);
assert(Updates_index1 != NULL);
assert(Slater_inv1 != NULL);
// original determinant of Slater1 (before applying updates)
double det = 3.407025646103221e-10;
rc = qmckl_sherman_morrison_naive(context,
LDS,
Dim,
N_updates1,
Updates1,
Updates_index1,
breakdown,
Slater_inv1,
&det);
// Check that the determinant is updated properly
assert(fabs(det + 4.120398385068217e-10) < 1e-15);
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
res[i * Dim + j] = 0;
for (unsigned int k = 0; k < Dim; k++) {
res[i * Dim + j] += Slater1[i * Dim + k] * Slater_inv1[k * LDS + j];
}
}
}
rc = QMCKL_SUCCESS;
for (unsigned int i = 0; i < Dim; i++) {
for (unsigned int j = 0; j < Dim; j++) {
if (i == j && fabs(res[i * Dim + j] - 1) > tolerance) {
rc = QMCKL_FAILURE;
}
if (i != j && fabs(res[i * Dim + j]) > tolerance) {
rc = QMCKL_FAILURE;
}
}
}
assert(rc == QMCKL_SUCCESS);
#+end_src
end function qmckl_sherman_morrison_naive_doc
end interface
#+end_src
* Woodbury 2x2
** ~qmckl_woodbury_2x2~
** ~qmckl_woodbury_2x2~
:PROPERTIES:
:Name: qmckl_woodbury_2x2
:CRetType: qmckl_exit_code
@ -790,13 +872,12 @@ qmckl_exit_code qmckl_woodbury_2x2(const qmckl_context context,
*** Performance
This function is most efficient when used in cases where there are only 2 rank-1 updates and
it is sure they will not result in a singular matrix.
** Fortran interface :noexport:
** Fortran interface :noexport:
:PROPERTIES:
:Name: qmckl_woodbury_2x2
:CRetType: qmckl_exit_code
@ -860,7 +941,6 @@ assert(rc == QMCKL_SUCCESS);
#+end_src
* Woodbury 3x3
** ~qmckl_woodbury_3x3~
:PROPERTIES:
:Name: qmckl_woodbury_3x3
@ -1209,13 +1289,12 @@ qmckl_exit_code qmckl_woodbury_3x3(const qmckl_context context,
#+end_src
*** Performance...
This function is most efficient when used in cases where there are only 3 rank-1 updates and
it is sure they will not result in a singular matrix.
** Fortran interface :noexport:
** Fortran interface :noexport:
:PROPERTIES:
:Name: qmckl_woodbury_3x3
:CRetType: qmckl_exit_code
@ -1279,7 +1358,6 @@ assert(rc == QMCKL_SUCCESS);
#+end_src
* Sherman-Morrison with update splitting
** ~qmckl_sherman_morrison_splitting~
:PROPERTIES:
:Name: qmckl_sherman_morrison_splitting
@ -1314,7 +1392,6 @@ assert(rc == QMCKL_SUCCESS);
If the determinant of the Slater-matrix is passed, it will be updated to the determinant resulting
from applying the updates to the original matrix.
*** Requirements
* ~context~ is not ~QMCKL_NULL_CONTEXT~
@ -1454,8 +1531,7 @@ assert(rc == QMCKL_SUCCESS);
#+end_src
* Woodbury 3x3 and 2x2 with Sherman-Morrison and update splitting
** ~qmckl_sherman_morrison_smw32s~
** ~qmckl_sherman_morrison_smw32s~
:PROPERTIES:
:Name: qmckl_sherman_morrison_smw32s
:CRetType: qmckl_exit_code
@ -1639,7 +1715,7 @@ qmckl_exit_code qmckl_sherman_morrison_smw32s(const qmckl_context context,
This kernel performs best for update cycles with 2 or more rank-1 updates and the fail-rate is low.
** Fortran interface :noexport:
** Fortran interface :noexport:
:PROPERTIES:
:Name: qmckl_sherman_morrison_smw32s
:CRetType: qmckl_exit_code