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#+TITLE: Molecular Orbitals
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
The molecular orbitals (MOs) are defined in the basis of AOs along with a AO to MO
coefficient matrix \[C\]. Using these coefficients (e.g. from Hartree Fock SCF method)
the MOs are defined as follows:
\[
\phi_i(\mathbf{r}) = C_i * \chi_i (\mathbf{r})
\]
In this section we demonstrate how to use the QMCkl specific DGEMM
function to calculate the MOs.
* Headers :noexport:
#+begin_src elisp :noexport :results none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
#+begin_src c :tangle (eval h_private_func)
#ifndef QMCKL_MO_HPF
#define QMCKL_MO_HPF
#+end_src
#+begin_src c :tangle (eval h_private_type)
#ifndef QMCKL_MO_HPT
#define QMCKL_MO_HPT
#include <stdbool.h>
#+end_src
#+begin_src c :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "assert.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <stdio.h>
#include <math.h>
#include "chbrclf.h"
#include "qmckl_ao_private_func.h"
#include "qmckl_mo_private_func.h"
int main() {
qmckl_context context;
context = qmckl_context_create();
qmckl_exit_code rc;
#+end_src
#+begin_src c :tangle (eval c)
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#ifdef HAVE_STDINT_H
#include <stdint.h>
#elif HAVE_INTTYPES_H
#include <inttypes.h>
#endif
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>
#include "qmckl.h"
#include "qmckl_context_private_type.h"
#include "qmckl_memory_private_type.h"
#include "qmckl_memory_private_func.h"
#include "qmckl_ao_private_type.h"
#include "qmckl_ao_private_func.h"
#include "qmckl_mo_private_type.h"
#include "qmckl_mo_private_func.h"
#+end_src
* Context
The following arrays are stored in the context:
|-----------------+--------------------+----------------------------------------|
| ~mo_num~ | | Number of MOs |
| ~coefficient~ | ~[mo_num][ao_num]~ | Orbital coefficients |
| ~coefficient_t~ | ~[ao_num][mo_num]~ | Transposed of the Orbital coefficients |
|-----------------+--------------------+----------------------------------------|
Computed data:
|---------------+--------------------------+-------------------------------------------------------------------------------------|
| ~mo_vgl~ | ~[point_num][5][mo_num]~ | Value, gradients, Laplacian of the MOs at point positions |
| ~mo_vgl_date~ | ~uint64_t~ | Late modification date of Value, gradients, Laplacian of the MOs at point positions |
|---------------+--------------------------+-------------------------------------------------------------------------------------|
** Data structure
#+begin_src c :comments org :tangle (eval h_private_type)
typedef struct qmckl_mo_basis_struct {
int64_t mo_num;
double * restrict coefficient;
double * restrict coefficient_t;
double * restrict mo_vgl;
uint64_t mo_vgl_date;
int32_t uninitialized;
bool provided;
} qmckl_mo_basis_struct;
#+end_src
The ~uninitialized~ integer contains one bit set to one for each
initialization function which has not been called. It becomes equal
to zero after all initialization functions have been called. The
struct is then initialized and ~provided == true~.
Some values are initialized by default, and are not concerned by
this mechanism.
#+begin_src c :comments org :tangle (eval h_private_func)
qmckl_exit_code qmckl_init_mo_basis(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c)
qmckl_exit_code qmckl_init_mo_basis(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
ctx->mo_basis.uninitialized = (1 << 2) - 1;
return QMCKL_SUCCESS;
}
#+end_src
** Access functions
#+begin_src c :comments org :tangle (eval h_func) :exports none
qmckl_exit_code
qmckl_get_mo_basis_mo_num (const qmckl_context context,
int64_t* mo_num);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code
qmckl_get_mo_basis_mo_num (const qmckl_context context,
int64_t* mo_num)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_INVALID_CONTEXT,
"qmckl_get_mo_basis_mo_num",
NULL);
return (int64_t) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1;
if ( (ctx->mo_basis.uninitialized & mask) != 0) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_get_mo_basis_mo_num",
NULL);
}
assert (ctx->mo_basis.mo_num > (int64_t) 0);
,*mo_num = ctx->mo_basis.mo_num;
return QMCKL_SUCCESS;
}
#+end_src
#+begin_src c :comments org :tangle (eval h_func) :exports none
qmckl_exit_code
qmckl_get_mo_basis_coefficient (const qmckl_context context,
double* const coefficient,
const int64_t size_max);
#+end_src
#+begin_src c :comments org :tangle (eval c) :exports none
qmckl_exit_code
qmckl_get_mo_basis_coefficient (const qmckl_context context,
double* const coefficient,
const int64_t size_max)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_INVALID_CONTEXT,
"qmckl_get_mo_basis_coefficient",
NULL);
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 1;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_get_mo_basis_coefficient",
NULL);
}
if (coefficient == NULL) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_get_mo_basis_coefficient",
"NULL pointer");
}
if (size_max < ctx->ao_basis.ao_num * ctx->mo_basis.mo_num) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_3,
"qmckl_get_mo_basis_coefficient",
"Array too small. Expected mo_num * ao_num");
}
assert (ctx->mo_basis.coefficient != NULL);
memcpy(coefficient, ctx->mo_basis.coefficient,
ctx->ao_basis.ao_num * ctx->mo_basis.mo_num * sizeof(double));
return QMCKL_SUCCESS;
}
#+end_src
When all the data for the AOs have been provided, the following
function returns ~true~.
#+begin_src c :comments org :tangle (eval h_func)
bool qmckl_mo_basis_provided (const qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :exports none
bool qmckl_mo_basis_provided(const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
return ctx->mo_basis.provided;
}
#+end_src
*** Fortran interfaces
#+begin_src f90 :tangle (eval fh_func) :comments org
interface
integer(c_int32_t) function qmckl_get_mo_basis_mo_num (context, &
mo_num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: mo_num
end function qmckl_get_mo_basis_mo_num
end interface
interface
integer(c_int32_t) function qmckl_get_mo_basis_coefficient(context, &
coefficient, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
double precision, intent(out) :: coefficient(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_mo_basis_coefficient
end interface
#+end_src
** Initialization functions
To set the basis set, all the following functions need to be
called.
#+begin_src c :comments org :tangle (eval h_func)
qmckl_exit_code qmckl_set_mo_basis_mo_num (qmckl_context context, const int64_t mo_num);
qmckl_exit_code qmckl_set_mo_basis_coefficient (qmckl_context context, const double * coefficient);
#+end_src
#+NAME:pre
#+begin_src c :exports none
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
#+end_src
#+NAME:post
#+begin_src c :exports none
ctx->mo_basis.uninitialized &= ~mask;
ctx->mo_basis.provided = (ctx->mo_basis.uninitialized == 0);
if (ctx->mo_basis.provided) {
qmckl_exit_code rc_ = qmckl_finalize_mo_basis(context);
if (rc_ != QMCKL_SUCCESS) return rc_;
}
return QMCKL_SUCCESS;
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_set_mo_basis_mo_num(qmckl_context context, const int64_t mo_num) {
<<pre>>
if (mo_num <= 0) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_mo_basis_mo_num",
"mo_num <= 0");
}
int32_t mask = 1 ;
ctx->mo_basis.mo_num = mo_num;
<<post>>
}
qmckl_exit_code qmckl_set_mo_basis_coefficient(qmckl_context context, const double* coefficient) {
<<pre>>
int32_t mask = 1 << 1;
if (ctx->mo_basis.coefficient != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->mo_basis.coefficient);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_mo_basis_coefficient",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ctx->ao_basis.ao_num * ctx->mo_basis.mo_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_mo_basis_coefficient",
NULL);
}
memcpy(new_array, coefficient, mem_info.size);
ctx->mo_basis.coefficient = new_array;
<<post>>
}
#+end_src
When the basis set is completely entered, other data structures are
computed to accelerate the calculations.
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_mo_basis(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_mo_basis(qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_INVALID_CONTEXT,
"qmckl_finalize_mo_basis",
NULL);
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = ctx->ao_basis.ao_num * ctx->mo_basis.mo_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_finalize_mo_basis",
NULL);
}
assert (ctx->mo_basis.coefficient != NULL);
if (ctx->mo_basis.coefficient_t != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->mo_basis.coefficient);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_finalize_mo_basis",
NULL);
}
}
for (int64_t i=0 ; i<ctx->ao_basis.ao_num ; ++i) {
for (int64_t j=0 ; j<ctx->mo_basis.mo_num ; ++j) {
new_array[i*ctx->mo_basis.mo_num + j] = ctx->mo_basis.coefficient[j*ctx->ao_basis.ao_num + i];
}
}
ctx->mo_basis.coefficient_t = new_array;
qmckl_exit_code rc = QMCKL_SUCCESS;
return rc;
}
#+end_src
* Computation
** Computation of MOs
*** Get
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl(qmckl_context context,
double* const mo_vgl,
const int64_t size_max);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl(qmckl_context context,
double* const mo_vgl,
const int64_t size_max)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_exit_code rc;
rc = qmckl_provide_ao_vgl(context);
if (rc != QMCKL_SUCCESS) return rc;
rc = qmckl_provide_mo_vgl(context);
if (rc != QMCKL_SUCCESS) return rc;
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
const int64_t sze = ctx->point.num * 5 * ctx->mo_basis.mo_num;
if (size_max < sze) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_3,
"qmckl_get_mo_basis_mo_vgl",
"input array too small");
}
memcpy(mo_vgl, ctx->mo_basis.mo_vgl, sze * sizeof(double));
return QMCKL_SUCCESS;
}
#+end_src
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_get_mo_basis_mo_vgl (context, &
mo_vgl, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
double precision, intent(out) :: mo_vgl(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_mo_basis_mo_vgl
end interface
#+end_src
Uses the given array to compute the VGL.
#+begin_src c :comments org :tangle (eval h_func) :noweb yes
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl_inplace (qmckl_context context,
double* const mo_vgl,
const int64_t size_max);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code
qmckl_get_mo_basis_mo_vgl_inplace (qmckl_context context,
double* const mo_vgl,
const int64_t size_max)
{
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return qmckl_failwith( context,
QMCKL_INVALID_CONTEXT,
"qmckl_get_mo_basis_mo_vgl",
NULL);
}
qmckl_exit_code rc;
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
const int64_t sze = ctx->mo_basis.mo_num * 5 * ctx->point.num;
if (size_max < sze) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_3,
"qmckl_get_mo_basis_mo_vgl",
"input array too small");
}
rc = qmckl_context_touch(context);
if (rc != QMCKL_SUCCESS) return rc;
double* old_array = ctx->mo_basis.mo_vgl;
ctx->mo_basis.mo_vgl = mo_vgl;
rc = qmckl_provide_mo_vgl(context);
if (rc != QMCKL_SUCCESS) return rc;
ctx->mo_basis.mo_vgl = old_array;
return QMCKL_SUCCESS;
}
#+end_src
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_get_mo_basis_mo_vgl_inplace (context, &
mo_vgl, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
double precision, intent(out) :: mo_vgl(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_mo_basis_mo_vgl_inplace
end interface
#+end_src
*** Provide
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context);
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_provide_mo_vgl(qmckl_context context)
{
qmckl_exit_code rc;
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
if (!ctx->ao_basis.provided) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_ao_basis",
NULL);
}
rc = qmckl_provide_ao_vgl(context);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_ao_basis",
NULL);
}
if (!ctx->mo_basis.provided) {
return qmckl_failwith( context,
QMCKL_NOT_PROVIDED,
"qmckl_mo_basis",
NULL);
}
/* Compute if necessary */
if (ctx->point.date > ctx->mo_basis.mo_vgl_date) {
/* Allocate array */
if (ctx->mo_basis.mo_vgl == NULL) {
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = 5 * ctx->point.num * ctx->mo_basis.mo_num * sizeof(double);
double* mo_vgl = (double*) qmckl_malloc(context, mem_info);
if (mo_vgl == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_mo_basis_mo_vgl",
NULL);
}
ctx->mo_basis.mo_vgl = mo_vgl;
}
rc = qmckl_compute_mo_basis_mo_vgl(context,
ctx->ao_basis.ao_num,
ctx->mo_basis.mo_num,
ctx->point.num,
ctx->mo_basis.coefficient_t,
ctx->ao_basis.ao_vgl,
ctx->mo_basis.mo_vgl);
if (rc != QMCKL_SUCCESS) {
return rc;
}
ctx->mo_basis.mo_vgl_date = ctx->date;
}
return QMCKL_SUCCESS;
}
#+end_src
*** Compute
:PROPERTIES:
:Name: qmckl_compute_mo_basis_mo_vgl
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
#+NAME: qmckl_mo_basis_mo_vgl_args
| Variable | Type | In/Out | Description |
|---------------------+--------------------------------+--------+-------------------------------------------------|
| ~context~ | ~qmckl_context~ | in | Global state |
| ~ao_num~ | ~int64_t~ | in | Number of AOs |
| ~mo_num~ | ~int64_t~ | in | Number of MOs |
| ~point_num~ | ~int64_t~ | in | Number of points |
| ~coef_normalized_t~ | ~double[mo_num][ao_num]~ | in | Transpose of the AO to MO transformation matrix |
| ~ao_vgl~ | ~double[point_num][5][ao_num]~ | in | Value, gradients and Laplacian of the AOs |
| ~mo_vgl~ | ~double[point_num][5][mo_num]~ | out | Value, gradients and Laplacian of the MOs |
The matrix of AO values is very sparse, so we use a sparse-dense
matrix multiplication instead of a dgemm, as exposed in
https://dx.doi.org/10.1007/978-3-642-38718-0_14.
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_mo_basis_mo_vgl_doc_f(context, &
ao_num, mo_num, point_num, &
coef_normalized_t, ao_vgl, mo_vgl) &
result(info)
use qmckl
implicit none
integer(qmckl_context), intent(in) :: context
integer*8 , intent(in) :: ao_num, mo_num
integer*8 , intent(in) :: point_num
double precision , intent(in) :: ao_vgl(ao_num,5,point_num)
double precision , intent(in) :: coef_normalized_t(mo_num,ao_num)
double precision , intent(out) :: mo_vgl(mo_num,5,point_num)
integer*8 :: i,j,k
double precision :: c1, c2, c3, c4, c5
do j=1,point_num
mo_vgl(:,:,j) = 0.d0
do k=1,ao_num
if (ao_vgl(k,1,j) /= 0.d0) then
c1 = ao_vgl(k,1,j)
c2 = ao_vgl(k,2,j)
c3 = ao_vgl(k,3,j)
c4 = ao_vgl(k,4,j)
c5 = ao_vgl(k,5,j)
do i=1,mo_num
mo_vgl(i,1,j) = mo_vgl(i,1,j) + coef_normalized_t(i,k) * c1
mo_vgl(i,2,j) = mo_vgl(i,2,j) + coef_normalized_t(i,k) * c2
mo_vgl(i,3,j) = mo_vgl(i,3,j) + coef_normalized_t(i,k) * c3
mo_vgl(i,4,j) = mo_vgl(i,4,j) + coef_normalized_t(i,k) * c4
mo_vgl(i,5,j) = mo_vgl(i,5,j) + coef_normalized_t(i,k) * c5
end do
end if
end do
end do
end function qmckl_compute_mo_basis_mo_vgl_doc_f
#+end_src
#+CALL: generate_c_header(table=qmckl_mo_basis_mo_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_mo_vgl"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_compute_mo_basis_mo_vgl (
const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );
#+end_src
#+CALL: generate_c_header(table=qmckl_mo_basis_mo_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_mo_vgl_doc"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_compute_mo_basis_mo_vgl_doc (
const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );
#+end_src
#+CALL: generate_c_interface(table=qmckl_mo_basis_mo_vgl_args,rettyp=get_value("CRetType"),fname="qmckl_compute_mo_basis_mo_vgl_doc"))
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_compute_mo_basis_mo_vgl_doc &
(context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl) &
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 :: ao_num
integer (c_int64_t) , intent(in) , value :: mo_num
integer (c_int64_t) , intent(in) , value :: point_num
real (c_double ) , intent(in) :: coef_normalized_t(ao_num,mo_num)
real (c_double ) , intent(in) :: ao_vgl(ao_num,5,point_num)
real (c_double ) , intent(out) :: mo_vgl(mo_num,5,point_num)
integer(c_int32_t), external :: qmckl_compute_mo_basis_mo_vgl_doc_f
info = qmckl_compute_mo_basis_mo_vgl_doc_f &
(context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl)
end function qmckl_compute_mo_basis_mo_vgl_doc
#+end_src
#+begin_src c :tangle (eval c) :comments org
qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl )
{
#ifdef HAVE_HPC
return qmckl_compute_mo_basis_mo_vgl_hpc (context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl);
#else
return qmckl_compute_mo_basis_mo_vgl_doc (context, ao_num, mo_num, point_num, coef_normalized_t, ao_vgl, mo_vgl);
#endif
}
#+end_src
*** HPC version
#+begin_src c :tangle (eval h_func) :comments org
#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl_hpc (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* coef_normalized_t,
const double* ao_vgl,
double* const mo_vgl );
#endif
#+end_src
#+begin_src c :tangle (eval c) :comments org
#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_vgl_hpc (const qmckl_context context,
const int64_t ao_num,
const int64_t mo_num,
const int64_t point_num,
const double* restrict coef_normalized_t,
const double* restrict ao_vgl,
double* restrict const mo_vgl )
{
#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for (int64_t ipoint=0 ; ipoint < point_num ; ++ipoint) {
double* restrict const vgl1 = &(mo_vgl[ipoint*5*mo_num]);
const double* restrict avgl1 = &(ao_vgl[ipoint*5*ao_num]);
double* restrict const vgl2 = vgl1 + mo_num;
double* restrict const vgl3 = vgl1 + (mo_num << 1);
double* restrict const vgl4 = vgl1 + (mo_num << 1) + mo_num;
double* restrict const vgl5 = vgl1 + (mo_num << 2);
const double* restrict avgl2 = avgl1 + ao_num;
const double* restrict avgl3 = avgl1 + (ao_num << 1);
const double* restrict avgl4 = avgl1 + (ao_num << 1) + ao_num;
const double* restrict avgl5 = avgl1 + (ao_num << 2);
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] = 0.;
vgl2[i] = 0.;
vgl3[i] = 0.;
vgl4[i] = 0.;
vgl5[i] = 0.;
}
int64_t nidx=0;
int64_t idx[ao_num];
double av1[ao_num];
double av2[ao_num];
double av3[ao_num];
double av4[ao_num];
double av5[ao_num];
for (int64_t k=0 ; k<ao_num ; ++k) {
const double* restrict ck1 = coef_normalized_t + k*mo_num;
if (avgl1[k] != 0.) {
idx[nidx] = k;
av1[nidx] = avgl1[k];
av2[nidx] = avgl2[k];
av3[nidx] = avgl3[k];
av4[nidx] = avgl4[k];
av5[nidx] = avgl5[k];
++nidx;
}
}
int64_t n;
for (n=0 ; n < nidx-4 ; n+=4) {
int64_t k = idx[n];
const double* restrict ck1 = coef_normalized_t + idx[n ]*mo_num;
const double* restrict ck2 = coef_normalized_t + idx[n+1]*mo_num;
const double* restrict ck3 = coef_normalized_t + idx[n+2]*mo_num;
const double* restrict ck4 = coef_normalized_t + idx[n+3]*mo_num;
const double a11 = av1[n ];
const double a21 = av1[n+1];
const double a31 = av1[n+2];
const double a41 = av1[n+3];
const double a12 = av2[n ];
const double a22 = av2[n+1];
const double a32 = av2[n+2];
const double a42 = av2[n+3];
const double a13 = av3[n ];
const double a23 = av3[n+1];
const double a33 = av3[n+2];
const double a43 = av3[n+3];
const double a14 = av4[n ];
const double a24 = av4[n+1];
const double a34 = av4[n+2];
const double a44 = av4[n+3];
const double a15 = av5[n ];
const double a25 = av5[n+1];
const double a35 = av5[n+2];
const double a45 = av5[n+3];
#ifdef HAVE_OPENMP
#pragma omp simd
#endif
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] = vgl1[i] + ck1[i] * a11 + ck2[i] * a21 + ck3[i] * a31 + ck4[i] * a41;
vgl2[i] = vgl2[i] + ck1[i] * a12 + ck2[i] * a22 + ck3[i] * a32 + ck4[i] * a42;
vgl3[i] = vgl3[i] + ck1[i] * a13 + ck2[i] * a23 + ck3[i] * a33 + ck4[i] * a43;
vgl4[i] = vgl4[i] + ck1[i] * a14 + ck2[i] * a24 + ck3[i] * a34 + ck4[i] * a44;
vgl5[i] = vgl5[i] + ck1[i] * a15 + ck2[i] * a25 + ck3[i] * a35 + ck4[i] * a45;
}
}
int64_t n0 = nidx-4;
n0 = n0 < 0 ? 0 : n0;
for (int64_t n=n0 ; n < nidx ; n+=1) {
const double* restrict ck = coef_normalized_t + idx[n]*mo_num;
const double a1 = av1[n];
const double a2 = av2[n];
const double a3 = av3[n];
const double a4 = av4[n];
const double a5 = av5[n];
#ifdef HAVE_OPENMP
#pragma omp simd
#endif
for (int64_t i=0 ; i<mo_num ; ++i) {
vgl1[i] += ck[i] * a1;
vgl2[i] += ck[i] * a2;
vgl3[i] += ck[i] * a3;
vgl4[i] += ck[i] * a4;
vgl5[i] += ck[i] * a5;
}
}
}
return QMCKL_SUCCESS;
}
#endif
#+end_src
*** Test
#+begin_src python :results output :exports none
import numpy as np
def f(a,x,y):
return np.sum( [c * np.exp( -b*(np.linalg.norm(x-y))**2) for b,c in a] )
def df(a,x,y,n):
h0 = 1.e-6
if n == 1: h = np.array([h0,0.,0.])
elif n == 2: h = np.array([0.,h0,0.])
elif n == 3: h = np.array([0.,0.,h0])
return ( f(a,x+h,y) - f(a,x-h,y) ) / (2.*h0)
def d2f(a,x,y,n):
h0 = 1.e-6
if n == 1: h = np.array([h0,0.,0.])
elif n == 2: h = np.array([0.,h0,0.])
elif n == 3: h = np.array([0.,0.,h0])
return ( f(a,x+h,y) - 2.*f(a,x,y) + f(a,x-h,y) ) / h0**2
def lf(a,x,y):
return d2f(a,x,y,1) + d2f(a,x,y,2) + d2f(a,x,y,3)
elec_26_w1 = np.array( [ 1.49050402641, 2.90106987953, -1.05920815468 ] )
elec_15_w2 = np.array( [ -2.20180344582,-1.9113150239, 2.2193744778600002 ] )
nucl_1 = np.array( [ 1.096243353458458e+00, 8.907054016973815e-01, 7.777092280258892e-01 ] )
nucl_2 = np.array( [ 1.168459237342663e+00, 1.125660720053393e+00, 2.833370314829343e+00 ] )
#double prim_vgl[prim_num][5][walk_num][elec_num];
x = elec_26_w1 ; y = nucl_1
a = [( 8.236000E+03, -1.130000E-04 * 6.1616545431994848e+02 ),
( 1.235000E+03, -8.780000E-04 * 1.4847738511079908e+02 ),
( 2.808000E+02, -4.540000E-03 * 4.8888635917437597e+01 ),
( 7.927000E+01, -1.813300E-02 * 1.8933972232608955e+01 ),
( 2.559000E+01, -5.576000E-02 * 8.1089160941724145e+00 ),
( 8.997000E+00, -1.268950E-01 * 3.7024003863155635e+00 ),
( 3.319000E+00, -1.703520E-01 * 1.7525302846177560e+00 ),
( 9.059000E-01, 1.403820E-01 * 6.6179013183966806e-01 ),
( 3.643000E-01, 5.986840E-01 * 3.3419848027174592e-01 ),
( 1.285000E-01, 3.953890E-01 * 1.5296336817449557e-01 )]
print ( "[1][0][0][26] : %25.15e"% f(a,x,y))
print ( "[1][1][0][26] : %25.15e"% df(a,x,y,1))
print ( "[1][2][0][26] : %25.15e"% df(a,x,y,2))
print ( "[1][3][0][26] : %25.15e"% df(a,x,y,3))
print ( "[1][4][0][26] : %25.15e"% lf(a,x,y))
x = elec_15_w2 ; y = nucl_2
a = [(3.387000E+01, 6.068000E-03 *1.0006253235944540e+01),
(5.095000E+00, 4.530800E-02 *2.4169531573445120e+00),
(1.159000E+00, 2.028220E-01 *7.9610924849766440e-01),
(3.258000E-01, 5.039030E-01 *3.0734305383061117e-01),
(1.027000E-01, 3.834210E-01 *1.2929684417481876e-01)]
print ( "[0][1][15][14] : %25.15e"% f(a,x,y))
print ( "[1][1][15][14] : %25.15e"% df(a,x,y,1))
print ( "[2][1][15][14] : %25.15e"% df(a,x,y,2))
print ( "[3][1][15][14] : %25.15e"% df(a,x,y,3))
print ( "[4][1][15][14] : %25.15e"% lf(a,x,y))
#+end_src
#+begin_src c :tangle (eval c_test) :exports none
{
#define walk_num chbrclf_walk_num
#define elec_num chbrclf_elec_num
#define shell_num chbrclf_shell_num
#define ao_num chbrclf_ao_num
int64_t elec_up_num = chbrclf_elec_up_num;
int64_t elec_dn_num = chbrclf_elec_dn_num;
double* elec_coord = &(chbrclf_elec_coord[0][0][0]);
const int64_t nucl_num = chbrclf_nucl_num;
const double* nucl_charge = chbrclf_charge;
const double* nucl_coord = &(chbrclf_nucl_coord[0][0]);
rc = qmckl_set_electron_num (context, elec_up_num, elec_dn_num);
assert (rc == QMCKL_SUCCESS);
rc = qmckl_set_electron_walk_num (context, walk_num);
assert (rc == QMCKL_SUCCESS);
assert(qmckl_electron_provided(context));
rc = qmckl_set_electron_coord (context, 'N', elec_coord, walk_num*elec_num*3);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_nucleus_num (context, nucl_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_nucleus_coord (context, 'T', &(nucl_coord[0]), nucl_num*3);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_nucleus_charge(context, nucl_charge, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(qmckl_nucleus_provided(context));
const int64_t * nucleus_index = &(chbrclf_basis_nucleus_index[0]);
const int64_t * nucleus_shell_num = &(chbrclf_basis_nucleus_shell_num[0]);
const int32_t * shell_ang_mom = &(chbrclf_basis_shell_ang_mom[0]);
const int64_t * shell_prim_num = &(chbrclf_basis_shell_prim_num[0]);
const int64_t * shell_prim_index = &(chbrclf_basis_shell_prim_index[0]);
const double * shell_factor = &(chbrclf_basis_shell_factor[0]);
const double * exponent = &(chbrclf_basis_exponent[0]);
const double * coefficient = &(chbrclf_basis_coefficient[0]);
const double * prim_factor = &(chbrclf_basis_prim_factor[0]);
const double * ao_factor = &(chbrclf_basis_ao_factor[0]);
const char typ = 'G';
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_type (context, typ);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_num (context, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_prim_num (context, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_nucleus_index (context, nucleus_index, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_nucleus_shell_num (context, nucleus_shell_num, nucl_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_ang_mom (context, shell_ang_mom, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_factor (context, shell_factor, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_prim_num (context, shell_prim_num, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_prim_index (context, shell_prim_index, chbrclf_shell_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_exponent (context, exponent, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_coefficient (context, coefficient, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_prim_factor (context, prim_factor, chbrclf_prim_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_ao_basis_ao_num(context, chbrclf_ao_num);
assert(rc == QMCKL_SUCCESS);
rc = qmckl_set_ao_basis_ao_factor (context, ao_factor, chbrclf_ao_num);
assert(rc == QMCKL_SUCCESS);
assert(qmckl_ao_basis_provided(context));
double ao_vgl[walk_num*elec_num][5][chbrclf_ao_num];
rc = qmckl_get_ao_basis_ao_vgl(context, &(ao_vgl[0][0][0]),
(int64_t) 5*walk_num*elec_num*chbrclf_ao_num);
assert (rc == QMCKL_SUCCESS);
/* Set up MO data */
const int64_t mo_num = chbrclf_mo_num;
rc = qmckl_set_mo_basis_mo_num(context, mo_num);
assert (rc == QMCKL_SUCCESS);
const double * mo_coefficient = &(chbrclf_mo_coef[0]);
rc = qmckl_set_mo_basis_coefficient(context, mo_coefficient);
assert (rc == QMCKL_SUCCESS);
assert(qmckl_mo_basis_provided(context));
double mo_vgl[walk_num*elec_num][5][chbrclf_mo_num];
rc = qmckl_get_mo_basis_mo_vgl(context, &(mo_vgl[0][0][0]), walk_num*elec_num*5*chbrclf_mo_num);
assert (rc == QMCKL_SUCCESS);
// Test overlap of MO
//double point_x[10];
//double point_y[10];
//double point_z[10];
//int32_t npoints=10;
//// obtain points
//double dr = 20./(npoints-1);
//double dr3 = dr*dr*dr;
//
//for (int i=0;i<npoints;++i) {
// point_x[i] = -10. + dr*i;
// point_y[i] = -10. + dr*i;
// point_z[i] = -10. + dr*i;
//}
//
//double ovlmo1 = 0.0;
//// Calculate overlap
//for (int i=0;i<npoints;++i) {
// fflush(stdout);
// for (int j=0;j<npoints;++j) {
// printf(" .. ");
// for (int k=0;k<npoints;++k) {
// printf(" . ");
// // Set point
// elec_coord[0] = point_x[i];
// elec_coord[1] = point_y[j];
// elec_coord[2] = point_z[k];
// rc = qmckl_set_electron_coord (context, 'N', elec_coord);
// assert(rc == QMCKL_SUCCESS);
//
// // Calculate value of MO (1st electron)
// double mo_vgl[5][walk_num][elec_num][chbrclf_mo_num];
// rc = qmckl_get_mo_basis_mo_vgl(context, &(mo_vgl[0][0][0][0]));
// assert (rc == QMCKL_SUCCESS);
// ovlmo1 += mo_vgl[0][0][0][0]*mo_vgl[0][0][0][0]*dr3;
// }
// }
//}
//printf("OVL MO1 = %10.15f\n",ovlmo1);
printf("\n");
printf(" mo_vgl mo_vgl[0][26][219] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][219] %25.15e\n", mo_vgl[2][1][3]);
printf(" mo_vgl mo_vgl[0][26][220] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][220] %25.15e\n", mo_vgl[2][1][3]);
printf(" mo_vgl mo_vgl[0][26][221] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][221] %25.15e\n", mo_vgl[2][1][3]);
printf(" mo_vgl mo_vgl[0][26][222] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][222] %25.15e\n", mo_vgl[2][1][3]);
printf(" mo_vgl mo_vgl[0][26][223] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][223] %25.15e\n", mo_vgl[2][1][3]);
printf(" mo_vgl mo_vgl[0][26][224] %25.15e\n", mo_vgl[2][0][3]);
printf(" mo_vgl mo_vgl[1][26][224] %25.15e\n", mo_vgl[2][1][3]);
printf("\n");
}
#+end_src
* End of files :noexport:
#+begin_src c :tangle (eval h_private_type)
#endif
#+end_src
#+begin_src c :tangle (eval h_private_func)
#endif
#+end_src
*** Test
#+begin_src c :tangle (eval c_test)
rc = qmckl_context_destroy(context);
assert (rc == QMCKL_SUCCESS);
return 0;
}
#+end_src
*** Compute file names
#+begin_src emacs-lisp
; The following is required to compute the file names
(setq pwd (file-name-directory buffer-file-name))
(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
(setq f (concat pwd name "_f.f90"))
(setq fh (concat pwd name "_fh.f90"))
(setq c (concat pwd name ".c"))
(setq h (concat name ".h"))
(setq h_private (concat name "_private.h"))
(setq c_test (concat pwd "test_" name ".c"))
(setq f_test (concat pwd "test_" name "_f.f90"))
; Minted
(require 'ox-latex)
(setq org-latex-listings 'minted)
(add-to-list 'org-latex-packages-alist '("" "listings"))
(add-to-list 'org-latex-packages-alist '("" "color"))
#+end_src
# -*- mode: org -*-
# vim: syntax=c
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