qmckl/src/qmckl_ao.org

# -*- mode: org -*-
# vim: syntax=c
#+TITLE: Atomic Orbitals

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This files contains all the routines for the computation of the
values, gradients and Laplacian of the atomic basis functions.

3 files are produced:
- a header file : =qmckl_ao.h=
- a source file : =qmckl_ao.f90=
- a test   file : =test_qmckl_ao.c=

*** Header
    #+BEGIN_SRC C :comments link  :tangle qmckl_ao.h
#ifndef QMCKL_AO_H
#define QMCKL_AO_H
#include "qmckl_context.h"
#include "qmckl_distance.h"
    #+END_SRC

*** Source
    #+BEGIN_SRC f90 :comments link :tangle qmckl_ao.f90

    #+END_SRC

*** Test
    #+BEGIN_SRC C :comments link :tangle test_qmckl_ao.c
#include <math.h>
#include "qmckl.h"
#include "munit.h"
MunitResult test_qmckl_ao() {
  qmckl_context context;
  context = qmckl_context_create();
    #+END_SRC


* Polynomials

   \[ P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c \]

** =qmckl_ao_powers=

   Computes all the powers of the =n= input data up to the given
   maximum value given in input for each of the $n$ points:
   
   \[ P_{ij} = X_j^i \]

*** Arguments

    | =context=  | input  | Global state                                      |
    | =n=        | input  | Number of values                                  |
    | =X(n)=     | input  | Array containing the input values                 |
    | =LMAX(n)=  | input  | Array containing the maximum power for each value |
    | =P(LDP,n)= | output | Array containing all the powers of $X$            |
    | =LDP=      | input  | Leading dimension of array =P=                    |
    
*** Requirements

    - =context= is not 0
    - =n= > 0
    - =X= is allocated with at least $n \times 8$ bytes
    - =LMAX= is allocated with at least $n \times 4$ bytes
    - =P= is allocated with at least $n \times \max_i \text{LMAX}_i \times 8$ bytes
    - =LDP= >= $\max_i$ =LMAX[i]=

*** Header
    #+BEGIN_SRC C :comments link :tangle qmckl_ao.h
qmckl_exit_code qmckl_ao_powers(qmckl_context context,
				int64_t n, 
				double *X, int32_t *LMAX,
				double *P, int64_t LDP);
    #+END_SRC
    
*** Source
    #+BEGIN_SRC f90 :comments link :tangle qmckl_ao.f90
integer function qmckl_ao_powers_f(context, n, X, LMAX, P, ldp) result(info)
  implicit none
  integer*8 , intent(in)  :: context
  integer*8 , intent(in)  :: n
  real*8    , intent(in)  :: X(n)
  integer   , intent(in)  :: LMAX(n)
  real*8    , intent(out) :: P(ldp,n)
  integer*8 , intent(in)  :: ldp

  integer*8  :: i,j

  info = 0

  if (context == 0_8) then
     info = -1
     return
  endif
  
  if (LDP < MAXVAL(LMAX)) then
     info = -2
     return
  endif
  
  do j=1,n
    P(1,j) = X(j)
    do i=2,LMAX(j)
       P(i,j) = P(i-1,j) * X(j) 
    end do
  end do

end function qmckl_ao_powers_f


integer(c_int32_t) function qmckl_ao_powers(context, n, X, LMAX, P, ldp) &
     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 :: n
  real    (c_double)  , intent(in)         :: X(n)
  integer (c_int32_t) , intent(in)         :: LMAX(n)
  real    (c_double)  , intent(out)        :: P(ldp,n)
  integer (c_int64_t) , intent(in) , value :: ldp
  
  integer, external :: qmckl_ao_powers_f
  info = qmckl_ao_powers_f(context, n, X, LMAX, P, ldp)
end function qmckl_ao_powers
    #+END_SRC

*** Test
  #+BEGIN_SRC C :comments link :tangle test_qmckl_ao.c
{
  int64_t n, LDP ;
  int32_t *LMAX ;
  double *X, *P ;
  int i, j;

  n = 100;
  LDP = 10;

  X = (double*) qmckl_malloc (context, n*sizeof(double));
  LMAX = (int32_t*) qmckl_malloc (context, n*sizeof(int32_t));
  P = (double*) qmckl_malloc (context, LDP*n*sizeof(double));

  for (j=0 ; j<n ; j++) {
      X[j] = -5. + 0.1 * (double) (j);
      LMAX[j] = 1 + (j % 9);
  }

  munit_assert_int64(QMCKL_SUCCESS, ==,
		     qmckl_ao_powers(context, n, X, LMAX, P, LDP) );

  for (j=0 ; j<n ; j++) {
    for (i=0 ; i<LMAX[j] ; i++) {
      munit_assert_double_equal( P[i+j*LDP], pow(X[j],i+1), 10 );
    }
  }
  qmckl_free(X);
  qmckl_free(P);
  qmckl_free(LMAX);
}

  #+END_SRC
  
** =qmckl_ao_polynomial_vgl=
   
   Computes the value, gradient and Laplacian of the Polynomials for each
   point given in input and for each center

*** Arguments

    | =context=    | input  | Global state                                         |
    | =X(3)=       | input  | Array containing the coordinates of the points       |
    | =R(3)=       | input  | Array containing the x,y,z coordinates of the center |
    | =lmax=       | input  | Maximum angular momentum                             |
    | =n=          | output | Number of computed polynomials                       |
    | =L(LDL,n)=   | output | Contains a,b,c for all =n= results                   |
    | =LDL=        | input  | Leading dimension of =L=                             |
    | =VGL(LDV,n)= | output | Value, gradients and Laplacian of the polynomials    |
    | =LDV=        | input  | Leading dimension of array =VGL=                     |
    
*** Requirements

    - =context= is not 0
    - =n= > 0
    - =X= is allocated with at least $3 \times 8$ bytes
    - =R= is allocated with at least $3 \times 8$ bytes
    - =lmax= >= 0
    - On output, =n= should be equal to (=lmax=+1)(=lmax=+2)(=lmax=+3)/6
    - =L= is allocated with at least $3 \times n \times 4$ bytes
    - =ldl= >= 3
    - =VGL= is allocated with at least $5 \times n \times 8$ bytes
    - =ldv= >= 5

*** Header
    #+BEGIN_SRC C :comments link :tangle qmckl_ao.h
qmckl_exit_code qmckl_ao_polynomial_vgl(qmckl_context context,
				double *X, double *R,
				int32_t lmax, int64_t *n,
				int32_t *L,   int64_t ldl,
				double *VGL,  int64_t ldv);
    #+END_SRC
    
*** Source
    #+BEGIN_SRC f90 :comments link :tangle qmckl_ao.f90
integer function qmckl_ao_polynomial_vgl_f(context, X, R, lmax, n, L, ldl, VGL, ldv) result(info)
  implicit none
  integer*8 , intent(in)  :: context
  real*8    , intent(in)  :: X(3), R(3)
  integer   , intent(in)  :: lmax
  integer*8 , intent(out) :: n
  integer   , intent(out) :: L(ldl,(lmax+1)*(lmax+2)*(lmax+3)/6)
  integer*8 , intent(in)  :: ldl
  real*8    , intent(out) :: VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)
  integer*8 , intent(in)  :: ldv

  integer*8         :: i,j
  integer           :: a,b,c,d
  real*8            :: Y(3)
  integer           :: lmax_array(3)
  real*8            :: pows(-2:lmax,3)
  integer, external :: qmckl_ao_powers_f

  info = 0

  if (context == 0_8) then
     info = -1
     return
  endif

  n = (lmax+1)*(lmax+2)*(lmax+3)/6

  if (ldl < 3) then
     info = -2
     return
  endif

  if (ldv < 5) then
     info = -3
     return
  endif


  do i=1,3
     Y(i) = X(i) - R(i)
  end do
  pows(-2:-1,1:3) = 0.d0
  pows(0,1:3) = 1.d0
  lmax_array(1:3) = lmax
  info = qmckl_ao_powers_f(context, 1_8, Y(1), (/lmax/), pows(1,1), size(pows,1,kind=8)) 
  if (info /= 0) return
  info = qmckl_ao_powers_f(context, 1_8, Y(2), (/lmax/), pows(1,2), size(pows,1,kind=8)) 
  if (info /= 0) return
  info = qmckl_ao_powers_f(context, 1_8, Y(3), (/lmax/), pows(1,3), size(pows,1,kind=8)) 
  if (info /= 0) return


  n=1
  vgl(1:5,1:n) = 0.d0
  l(1:3,n) = 0
  vgl(1,n) = 1.d0
  do d=1,lmax
     do a=0,d
	do b=0,d
	   do c=0,d
	      if (a+b+c == d) then
		 n = n+1
		 l(1,n) = a
		 l(2,n) = b
		 l(3,n) = c

		 vgl(1,n) = pows(a,1) * pows(b,2) * pows(c,3)

		 vgl(2,n) = dble(a) * pows(a-1,1) * pows(b  ,2) * pows(c  ,3)
		 vgl(3,n) = dble(b) * pows(a  ,1) * pows(b-1,2) * pows(c  ,3)
		 vgl(4,n) = dble(c) * pows(a  ,1) * pows(b  ,2) * pows(c-1,3)

		 vgl(5,n) = dble(a) * dble(a-1) * pows(a-2,1) * pows(b  ,2) * pows(c  ,3) &
		      + dble(b) * dble(b-1) * pows(a  ,1) * pows(b-2,2) * pows(c  ,3) &
		      + dble(c) * dble(c-1) * pows(a  ,1) * pows(b  ,2) * pows(c-2,3)
		 exit
	      end if
	   end do
	end do
     end do
  end do

end function qmckl_ao_polynomial_vgl_f

integer(c_int32_t) function qmckl_ao_polynomial_vgl(context, X, R, lmax, n, L, ldl, VGL, ldv) &
     bind(C) result(info)
  use, intrinsic :: iso_c_binding
  implicit none
  integer (c_int64_t) , intent(in) , value :: context
  real    (c_double)  , intent(in)         :: X(3), R(3)
  integer (c_int32_t) , intent(in) , value :: lmax
  integer (c_int64_t) , intent(out)        :: n
  integer (c_int32_t) , intent(out)        :: L(ldl,(lmax+1)*(lmax+2)*(lmax+3)/6)
  integer (c_int64_t) , intent(in) , value :: ldl
  real    (c_double)  , intent(out)        :: VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)
  integer (c_int64_t) , intent(in) , value :: ldv

  integer, external :: qmckl_ao_polynomial_vgl_f
  info = qmckl_ao_polynomial_vgl_f(context, X, R, lmax, n, L, ldl, VGL, ldv) 
end function qmckl_ao_polynomial_vgl
    #+END_SRC

*** Test
    #+BEGIN_SRC C :comments link :tangle test_qmckl_ao.c
{
#include <stdio.h>
  double X[3] = { 1.1 , 2.2 ,  3.3 };
  double R[3] = { 0.1 , 1.2 , -2.3 };
  double Y[3];
  int32_t lmax = 4;
  int64_t n = 0;
  int64_t ldl = 3;
  int64_t ldv = 100;
  int32_t* L_mem;
  int32_t* L[100];
  double*  VGL_mem;
  double* VGL[100];
  int j;

  int d = (lmax+1)*(lmax+2)*(lmax+3)/6;

  L_mem = (int32_t*) malloc(ldl*100*sizeof(int32_t));
  VGL_mem = (double*) malloc(ldv*100*sizeof(double));

  munit_assert_int64(QMCKL_SUCCESS, ==,
		     qmckl_ao_polynomial_vgl(context, X, R, lmax, &n, L_mem, ldl, VGL_mem, ldv) );

  munit_assert_int64( n, ==, d );
  for (j=0 ; j<n ; j++) {
    L[j] = &L_mem[j*ldl];
    VGL[j] = &VGL_mem[j*ldv];
  }

  Y[0] = X[0] - R[0];
  Y[1] = X[1] - R[1];
  Y[2] = X[2] - R[2];
  for (j=0 ; j<n ; j++) {
    munit_assert_int64( L[j][0], >=, 0 );
    munit_assert_int64( L[j][1], >=, 0 );
    munit_assert_int64( L[j][2], >=, 0 );
    munit_assert_double_equal( VGL[j][0], 
			       pow(Y[0],L[j][0]) * pow(Y[1],L[j][1]) * pow(Y[2],L[j][2]), 10 );
    if (L[j][0] < 1) {
      munit_assert_double_equal( VGL[j][1], 0., 10);
    } else {
      munit_assert_double_equal( VGL[j][1], 
				 L[j][0] * pow(Y[0],L[j][0]-1) * pow(Y[1],L[j][1]) * pow(Y[2],L[j][2]), 10 );
    }
    if (L[j][1] < 1) {
      munit_assert_double_equal( VGL[j][2], 0., 10);
    } else {
      munit_assert_double_equal( VGL[j][2], 
				 L[j][1] * pow(Y[0],L[j][0]) * pow(Y[1],L[j][1]-1) * pow(Y[2],L[j][2]), 10 );
    }
    if (L[j][2] < 1) {
      munit_assert_double_equal( VGL[j][3], 0., 10);
    } else {
      munit_assert_double_equal( VGL[j][3], 
				 L[j][2] * pow(Y[0],L[j][0]) * pow(Y[1],L[j][1]) * pow(Y[2],L[j][2]-1), 10 );
    }

    double w = 0.;
    if (L[j][0] > 1) w += L[j][0] * (L[j][0]-1) * pow(Y[0],L[j][0]-2) * pow(Y[1],L[j][1]) * pow(Y[2],L[j][2]);
    if (L[j][1] > 1) w += L[j][1] * (L[j][1]-1) * pow(Y[0],L[j][0]) * pow(Y[1],L[j][1]-2) * pow(Y[2],L[j][2]);
    if (L[j][2] > 1) w += L[j][2] * (L[j][2]-1) * pow(Y[0],L[j][0]) * pow(Y[1],L[j][1]) * pow(Y[2],L[j][2]-2);
    munit_assert_double_equal( VGL[j][4], w, 10 );
  }
  free(L_mem);
  free(VGL_mem);
}
    #+END_SRC

   

* TODO Gaussian basis functions

* TODO Slater basis functions
  
* End of files

*** Header
  #+BEGIN_SRC C :comments link :tangle qmckl_ao.h
#endif
  #+END_SRC

*** Test
  #+BEGIN_SRC C :comments link :tangle test_qmckl_ao.c
  if (qmckl_context_destroy(context) != QMCKL_SUCCESS)
    return QMCKL_FAILURE;
  return MUNIT_OK;
}

  #+END_SRC