mirror of
https://github.com/TREX-CoE/qmckl.git
synced 2025-01-03 10:06:09 +01:00
Added WB2 kernel back.
This commit is contained in:
Francois Coppens
parent
db13db8afa
commit
883416d84c
@ -89,15 +89,15 @@ from applying the updates to the original matrix.
|
||||
| ~determinant~ | ~double~ | 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
|
||||
* ~determinant > 0~
|
||||
- ~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
|
||||
- ~determinant > 0~
|
||||
|
||||
*** Pedagogical kernel source (in Fortran)
|
||||
The following source code written in Fortran is inteded to illustrate how the kernel works. Even though the kernel is
|
||||
@ -251,7 +251,7 @@ integer function qmckl_sm_naive_doc_f(context, &
|
||||
end function qmckl_sm_naive_doc_f
|
||||
#+end_src
|
||||
|
||||
**** C interface to the pedagogical kernel (not directly exposed)
|
||||
**** C interface (not directly exposed)
|
||||
The following Fortran function ~qmckl_sm_naive_doc~ makes sure
|
||||
that the pedagogical kernel ~qmckl_sm_naive_doc_f~, written in
|
||||
Fortran, can be called from C using the ~ISO_C_BINDING~. The Fortran function ~qmckl_sm_naive_doc~ will be exposed in the header file 'qmckl.h'
|
||||
@ -1418,6 +1418,382 @@ This function cannot be used by itself and is used in Sherman-Morrison with upda
|
||||
with Sherman-Morrison and update splitting. Please look at the performance reccomendations for those two kernels.
|
||||
|
||||
|
||||
* Woodbury 2x2
|
||||
** ~qmckl_woodbury_2x2~
|
||||
:PROPERTIES:
|
||||
:Name: qmckl_woodbury_2x2
|
||||
:CRetType: qmckl_exit_code
|
||||
:FRetType: qmckl_exit_code
|
||||
:END:
|
||||
|
||||
*** Introduction
|
||||
The Woodbury 2x2 kernel. It is used to apply two rank-1 updates at once. The formula used in
|
||||
this algorithm is called the Woodbury Matrix Identity
|
||||
\[
|
||||
(S + U V)^{-1} = S^{-1} - C B^{-1} D
|
||||
\]
|
||||
where
|
||||
$S$ is the Slater-matrix
|
||||
$U$ and $V$ are the matrices containing the updates and the canonical basis matrix
|
||||
$S^{-1}$ is the inverse of the Slater-matrix
|
||||
$C:= S^{-1}U$, a Dim $\times 2$ matrix
|
||||
$B := 1 + VC$, the $2 \times 2$ matrix that is going to be inverted
|
||||
$D := VS^{-1}$, a $2 \times Dim$ 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.
|
||||
|
||||
*** API
|
||||
#+NAME: qmckl_woodbury_2x2_args
|
||||
| Variable | Type | In/Out | Description |
|
||||
|-----------------+-------------------+-------+-------------------------------------------------|
|
||||
| ~context~ | ~qmckl_context~ | in | Global state |
|
||||
| ~LDS~ | ~uint64_t~ | in | Leading dimension of Slater_inv |
|
||||
| ~Dim~ | ~uint64_t~ | in | Dimension of Slater_inv |
|
||||
| ~Updates~ | ~double[2*Dim]~ | in | Array containing the updates |
|
||||
| ~Updates_index~ | ~uint64_t[2]~ | in | Array containing the rank-1 updates |
|
||||
| ~breakdown~ | ~double~ | in | Break-down parameter on which to fail or not |
|
||||
| ~Slater_inv~ | ~double[LDS*Dim]~ | inout | Array containing the inverse of a Slater-matrix |
|
||||
| ~determinant~ | ~double~ | inout | Determinant of Slater-matrix |
|
||||
|
||||
*** Requirements
|
||||
- ~context~ is not ~qmckl_null_context~
|
||||
- ~LDS >= 2~
|
||||
- ~Dim >= 2~
|
||||
- ~Updates~ is allocated with $2 \times Dim$ elements
|
||||
- ~Updates_index~ is allocated with $2$ elements
|
||||
- ~breakdown~ is a small number such that $0 < breakdown << 1$
|
||||
- ~Slater_inv~ is allocated with $Dim \times Dim$ elements
|
||||
|
||||
*** Pedagogical kernel source (in Fortran)
|
||||
**** C interface (not directly exposed)
|
||||
*** C headers (exposed in qmckl.h)
|
||||
#+CALL: generate_c_header(table=qmckl_woodbury_2x2_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_src c :tangle (eval h_func) :comments org
|
||||
qmckl_exit_code qmckl_woodbury_2x2 (
|
||||
const qmckl_context context,
|
||||
const uint64_t LDS,
|
||||
const uint64_t Dim,
|
||||
const double* Updates,
|
||||
const uint64_t* Updates_index,
|
||||
const double breakdown,
|
||||
double* Slater_inv,
|
||||
double* determinant );
|
||||
#+end_src
|
||||
|
||||
*** C sources
|
||||
#+begin_src c :tangle (eval c) :comments org
|
||||
qmckl_exit_code qmckl_woodbury_2x2_hpc(const qmckl_context context,
|
||||
const uint64_t LDS,
|
||||
const uint64_t Dim,
|
||||
const double* __restrict Updates,
|
||||
const uint64_t* __restrict Updates_index,
|
||||
const double breakdown,
|
||||
double* __restrict Slater_inv,
|
||||
double* __restrict determinant) {
|
||||
/*
|
||||
C := S^{-1} * U, dim x 2
|
||||
B := 1 + V * C, 2 x 2
|
||||
D := V * S^{-1}, 2 x dim
|
||||
*/
|
||||
|
||||
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
||||
return qmckl_failwith(context,
|
||||
QMCKL_NULL_CONTEXT,
|
||||
"qmckl_woodbury_2x2_hpc",
|
||||
NULL);
|
||||
}
|
||||
|
||||
const uint64_t row1 = (Updates_index[0] - 1);
|
||||
const uint64_t row2 = (Updates_index[1] - 1);
|
||||
|
||||
// Compute C = (S^T)^{-1}U : Dim x 2
|
||||
double __attribute__((aligned(8))) C[2 * Dim];
|
||||
for (uint64_t i = 0; i < Dim; i++) {
|
||||
C[i * 2] = 0;
|
||||
C[i * 2 + 1] = 0;
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t k = 0; k < LDS; k++) {
|
||||
C[i * 2] += Slater_inv[i * LDS + k] * Updates[k];
|
||||
C[i * 2 + 1] += Slater_inv[i * LDS + k] * Updates[LDS + k];
|
||||
}
|
||||
}
|
||||
|
||||
// Compute B = 1 + VC : 2 x 2
|
||||
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) < breakdown) {
|
||||
return QMCKL_FAILURE;
|
||||
}
|
||||
|
||||
// Update det(S) when passed
|
||||
if (determinant)
|
||||
*determinant *= det;
|
||||
|
||||
// Compute B^{-1} with explicit formula for 2 x 2 inversion
|
||||
double __attribute__((aligned(8))) 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;
|
||||
|
||||
// tmp = B^{-1}D : 2 x LDS
|
||||
double __attribute__((aligned(8))) tmp[2 * LDS];
|
||||
double* r1dim = &(Slater_inv[row1 * LDS]);
|
||||
double* r2dim = &(Slater_inv[row2 * LDS]);
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t j = 0; j < LDS; j++) {
|
||||
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
||||
tmp[LDS + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
||||
}
|
||||
|
||||
// Compute (S^T)^{-1} - C * tmp : Dim x LDS
|
||||
for (uint64_t i = 0; i < Dim; i++) {
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t j = 0; j < LDS; j++) {
|
||||
Slater_inv[i * LDS + j] -= C[i * 2] * tmp[j];
|
||||
Slater_inv[i * LDS + j] -= C[i * 2 + 1] * tmp[LDS + j];
|
||||
}
|
||||
}
|
||||
|
||||
return QMCKL_SUCCESS;
|
||||
}
|
||||
#+end_src
|
||||
|
||||
#+NAME:woodbury_2x2_kernel_template
|
||||
#+begin_src c
|
||||
static inline qmckl_exit_code qmckl_woodbury_2x2_{Dim}(
|
||||
const qmckl_context context,
|
||||
const double* __restrict Updates,
|
||||
const uint64_t* __restrict Updates_index,
|
||||
const double breakdown,
|
||||
double* __restrict Slater_inv,
|
||||
double* __restrict determinant) {
|
||||
/*
|
||||
C := S^{-1} * U, dim x 2
|
||||
B := 1 + V * C, 2 x 2
|
||||
D := V * S^{-1}, 2 x dim
|
||||
*/
|
||||
|
||||
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
||||
return qmckl_failwith(context,
|
||||
QMCKL_NULL_CONTEXT,
|
||||
"qmckl_woodbury_2x2_{Dim}",
|
||||
NULL);
|
||||
}
|
||||
|
||||
const uint64_t row1 = (Updates_index[0] - 1);
|
||||
const uint64_t row2 = (Updates_index[1] - 1);
|
||||
|
||||
// Compute C = (S^T)^{-1}U : {Dim} x 2
|
||||
double __attribute__((aligned(8))) C[2 * {Dim}];
|
||||
for (uint64_t i = 0; i < {Dim}; i++) {
|
||||
C[i * 2] = 0;
|
||||
C[i * 2 + 1] = 0;
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t k = 0; k < D{Dim}_P; k++) {
|
||||
C[i * 2] += Slater_inv[i * D{Dim}_P + k] * Updates[k];
|
||||
C[i * 2 + 1] += Slater_inv[i * D{Dim}_P + k] * Updates[D{Dim}_P + k];
|
||||
}
|
||||
}
|
||||
|
||||
// Compute B = 1 + VC : 2 x 2
|
||||
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) < breakdown) {
|
||||
return QMCKL_FAILURE;
|
||||
}
|
||||
|
||||
// Update det(S) when passed
|
||||
if (determinant)
|
||||
*determinant *= det;
|
||||
|
||||
// Compute B^{-1} with explicit formula for 2 x 2 inversion
|
||||
double __attribute__((aligned(8))) 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;
|
||||
|
||||
// tmp = B^{-1}D : 2 x D{Dim}_P
|
||||
double __attribute__((aligned(8))) tmp[2 * D{Dim}_P];
|
||||
double* r1dim = &(Slater_inv[row1 * D{Dim}_P]);
|
||||
double* r2dim = &(Slater_inv[row2 * D{Dim}_P]);
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t j = 0; j < D{Dim}_P; j++) {
|
||||
tmp[j] = Binv[0] * r1dim[j] + Binv[1] * r2dim[j];
|
||||
tmp[D{Dim}_P + j] = Binv[2] * r1dim[j] + Binv[3] * r2dim[j];
|
||||
}
|
||||
|
||||
// Compute (S^T)^{-1} - C * tmp : {Dim} x D{Dim}_P
|
||||
for (uint64_t i = 0; i < {Dim}; i++) {
|
||||
IVDEP
|
||||
ALIGNED
|
||||
for (uint64_t j = 0; j < D{Dim}_P; j++) {
|
||||
Slater_inv[i * D{Dim}_P + j] -= C[i * 2] * tmp[j];
|
||||
Slater_inv[i * D{Dim}_P + j] -= C[i * 2 + 1] * tmp[D{Dim}_P + j];
|
||||
}
|
||||
}
|
||||
|
||||
return QMCKL_SUCCESS;
|
||||
}
|
||||
#+end_src
|
||||
|
||||
#+NAME:woodbury_2x2_kernel_generator
|
||||
#+begin_src python :noweb yes :exports none
|
||||
text="""
|
||||
<<woodbury_2x2_kernel_template>>
|
||||
"""
|
||||
result = []
|
||||
for Dim in <<kernel_generator_range>>:
|
||||
Dim=str(Dim)
|
||||
result.append(text.replace("{Dim}",Dim) )
|
||||
|
||||
return ''.join(result)
|
||||
#+end_src
|
||||
|
||||
#+NAME:woodbury_2x2_switch-case_generator
|
||||
#+begin_src python :noweb yes :exports none
|
||||
text="""
|
||||
case {Dim}:
|
||||
return qmckl_woodbury_2x2_{Dim}(context,
|
||||
Updates,
|
||||
Updates_index,
|
||||
breakdown,
|
||||
Slater_inv,
|
||||
determinant);"""
|
||||
result = []
|
||||
for Dim in <<kernel_generator_range>>:
|
||||
Dim=str(Dim)
|
||||
result.append(text.replace("{Dim}",Dim) )
|
||||
|
||||
return ''.join(result)
|
||||
#+end_src
|
||||
|
||||
#+begin_src c :tangle (eval c) :comments org :noweb yes
|
||||
<<woodbury_2x2_kernel_generator()>>
|
||||
|
||||
qmckl_exit_code qmckl_woodbury_2x2(const qmckl_context context,
|
||||
const uint64_t LDS,
|
||||
const uint64_t Dim,
|
||||
const double* Updates,
|
||||
const uint64_t* Updates_index,
|
||||
const double breakdown,
|
||||
double* Slater_inv,
|
||||
double* determinant) {
|
||||
|
||||
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
||||
return qmckl_failwith(context,
|
||||
QMCKL_NULL_CONTEXT,
|
||||
"qmckl_woodbury_2x2",
|
||||
NULL);
|
||||
}
|
||||
|
||||
if (LDS == (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH) { // Most cases
|
||||
switch (Dim) {
|
||||
<<woodbury_2x2_switch-case_generator()>>
|
||||
}
|
||||
}
|
||||
else { // When SIMD_LENGTH > 1, called with LDS == Dim AND Dim != (1+(Dim-1)/SIMD_LENGTH)*SIMD_LENGTH)
|
||||
return qmckl_woodbury_2x2_hpc(context,
|
||||
LDS,
|
||||
Dim,
|
||||
Updates,
|
||||
Updates_index,
|
||||
breakdown,
|
||||
Slater_inv,
|
||||
determinant);
|
||||
|
||||
}
|
||||
|
||||
return QMCKL_FAILURE;
|
||||
}
|
||||
#+end_src
|
||||
|
||||
*** Fortran interfaces (exposed in qmckl_f.F90)
|
||||
:PROPERTIES:
|
||||
:Name: qmckl_woodbury_2x2
|
||||
:CRetType: qmckl_exit_code
|
||||
:FRetType: qmckl_exit_code
|
||||
:END:
|
||||
|
||||
#+CALL: generate_f_interface(table=qmckl_woodbury_2x2_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_2x2 &
|
||||
(context, LDS, Dim, 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 :: LDS
|
||||
integer (c_int64_t) , intent(in) , value :: Dim
|
||||
real (c_double ) , intent(in) :: Updates(2*Dim)
|
||||
integer (c_int64_t) , intent(in) :: Updates_index(2)
|
||||
real (c_double ) , intent(in) , value :: breakdown
|
||||
real (c_double ) , intent(inout) :: Slater_inv(LDS*Dim)
|
||||
real (c_double ) , intent(inout) :: determinant
|
||||
|
||||
end function qmckl_woodbury_2x2
|
||||
end interface
|
||||
#+end_src
|
||||
|
||||
*** 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.
|
||||
|
||||
*** Tests
|
||||
#+begin_src c :tangle (eval c_test)
|
||||
assert(Updates2 != NULL);
|
||||
assert(Updates_index2 != NULL);
|
||||
assert(Slater_inv2 != NULL);
|
||||
det = -1.4432116661319376e-11;
|
||||
rc = qmckl_woodbury_2x2(context, LDS, Dim, Updates2, Updates_index2, breakdown, Slater_inv2, &det);
|
||||
assert(fabs(det-2.367058141251457e-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] += Slater2[i * Dim + k] * Slater_inv2[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
|
||||
|
||||
|
||||
* Sherman-Morrison with Slagel Splitting
|
||||
** ~qmckl_sm_splitting~
|
||||
:PROPERTIES:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user