TREX/qmckl

mirror of https://github.com/TREX-CoE/qmckl.git synced 2024-11-05 13:44:07 +01:00

Anthony Scemama 28fe475425 Fix examples in doc

2022-06-15 19:17:05 +02:00

55 KiB

Raw Blame History

Molecular Orbitals

Context
Computation

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.

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_value`	`[point_num][mo_num]`	Value of the MOs at point positions
`mo_value_date`	`uint64_t`	Late modification date of the value of the MOs at point positions
`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

typedef struct qmckl_mo_basis_struct {
int64_t   mo_num;
double * restrict coefficient;
double * restrict coefficient_t;

double * restrict mo_vgl;
double * restrict mo_value;
uint64_t  mo_vgl_date;
uint64_t  mo_value_date;

int32_t   uninitialized;
bool      provided;
} qmckl_mo_basis_struct;

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.

qmckl_exit_code qmckl_init_mo_basis(qmckl_context context);

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*) context;
assert (ctx != NULL);

ctx->mo_basis.uninitialized = (1 << 2) - 1;

return QMCKL_SUCCESS;
}

Access functions

When all the data for the AOs have been provided, the following function returns true.

bool qmckl_mo_basis_provided (const qmckl_context context);

Fortran interfaces

Initialization functions

To set the basis set, all the following functions need to be called.

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);

#+NAME:pre

#+NAME:post

When the basis set is completely entered, other data structures are computed to accelerate the calculations.

Computation

Computation of MOs: values only

Get

qmckl_exit_code
qmckl_get_mo_basis_mo_value(qmckl_context context,
                        double* const mo_value,
                        const int64_t size_max);

Uses the given array to compute the values.

qmckl_exit_code
qmckl_get_mo_basis_mo_value_inplace (qmckl_context context,
                                 double* const mo_value,
                                 const int64_t size_max);

Provide

Compute

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
`coefficient_t`	`double[mo_num][ao_num]`	in	Transpose of the AO to MO transformation matrix
`ao_value`	`double[point_num][ao_num]`	in	Value of the AOs
`mo_value`	`double[point_num][mo_num]`	out	Value 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.

integer function qmckl_compute_mo_basis_mo_value_doc_f(context, &
 ao_num, mo_num, point_num, &
 coefficient_t, ao_value, mo_value) &
 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_value(ao_num,point_num)
double precision      , intent(in)  :: coefficient_t(mo_num,ao_num)
double precision      , intent(out) :: mo_value(mo_num,point_num)
integer*8 :: i,j,k
double precision :: c1, c2, c3, c4, c5

integer*8 :: LDA, LDB, LDC

info = QMCKL_SUCCESS
if (.True.)  then    ! fast algorithm
 do j=1,point_num
    mo_value(:,j) = 0.d0
    do k=1,ao_num
       if (ao_value(k,j) /= 0.d0) then
          c1 = ao_value(k,j)
          do i=1,mo_num
             mo_value(i,j) = mo_value(i,j) + coefficient_t(i,k) * c1
          end do
       end if
    end do
 end do
 
else ! dgemm

LDA = size(coefficient_t,1)
LDB = size(ao_value,1) 
LDC = size(mo_value,1)

info = qmckl_dgemm(context,'N', 'N', mo_num, point_num, ao_num, 1.d0,     &
                                coefficient_t, LDA, ao_value, LDB, &
                                0.d0, mo_value, LDC)

end if

end function qmckl_compute_mo_basis_mo_value_doc_f

qmckl_exit_code qmckl_compute_mo_basis_mo_value (
      const qmckl_context context,
      const int64_t ao_num,
      const int64_t mo_num,
      const int64_t point_num,
      const double* coefficient_t,
      const double* ao_value,
      double* const mo_value );

qmckl_exit_code qmckl_compute_mo_basis_mo_value_doc (
      const qmckl_context context,
      const int64_t ao_num,
      const int64_t mo_num,
      const int64_t point_num,
      const double* coefficient_t,
      const double* ao_value,
      double* const mo_value );

qmckl_exit_code
qmckl_compute_mo_basis_mo_value (const qmckl_context context,
                             const int64_t ao_num,
                             const int64_t mo_num,
                             const int64_t point_num,
                             const double* coefficient_t,
                             const double* ao_value,
                             double* const mo_value )
{
#ifdef HAVE_HPC
return qmckl_compute_mo_basis_mo_value_hpc (context, ao_num, mo_num, point_num, coefficient_t, ao_value, mo_value);
#else
return qmckl_compute_mo_basis_mo_value_doc (context, ao_num, mo_num, point_num, coefficient_t, ao_value, mo_value);
#endif
}

HPC version

#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_value_hpc (const qmckl_context context,
                                 const int64_t ao_num,
                                 const int64_t mo_num,
                                 const int64_t point_num,
                                 const double* coefficient_t,
                                 const double* ao_value,
                                 double* const mo_value );
#endif

#ifdef HAVE_HPC
qmckl_exit_code
qmckl_compute_mo_basis_mo_value_hpc (const qmckl_context context,
                                 const int64_t ao_num,
                                 const int64_t mo_num,
                                 const int64_t point_num,
                                 const double* restrict coefficient_t,
                                 const double* restrict ao_value,
                                 double* restrict const mo_value )
{
assert (context != QMCKL_NULL_CONTEXT);

#ifdef HAVE_OPENMP
#pragma omp parallel for
#endif
for (int64_t ipoint=0 ; ipoint < point_num ; ++ipoint) {
double* restrict const vgl1  = &(mo_value[ipoint*mo_num]);
const double* restrict avgl1 = &(ao_value[ipoint*ao_num]);

for (int64_t i=0 ; i<mo_num ; ++i) {
  vgl1[i] = 0.;
}

int64_t nidx=0;
int64_t idx[ao_num];
double  av1[ao_num];
for (int64_t k=0 ; k<ao_num ; ++k) {
  if (avgl1[k] != 0.) {
    idx[nidx] = k;
    av1[nidx] = avgl1[k];
    ++nidx;
  }
}

int64_t n;

for (n=0 ; n < nidx-4 ; n+=4) {
  const double* restrict ck1 = coefficient_t + idx[n  ]*mo_num;
  const double* restrict ck2 = coefficient_t + idx[n+1]*mo_num;
  const double* restrict ck3 = coefficient_t + idx[n+2]*mo_num;
  const double* restrict ck4 = coefficient_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];

#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;
  }
}

const int64_t n0 = n < 0 ? 0 : n;
for (int64_t m=n0 ; m < nidx ; m+=1) {
  const double* restrict ck = coefficient_t + idx[m]*mo_num;
  const double a1 = av1[m];

#ifdef HAVE_OPENMP
#pragma omp simd
#endif
  for (int64_t i=0 ; i<mo_num ; ++i) {
    vgl1[i] += ck[i] * a1;
  }
}
}
return QMCKL_SUCCESS;
}
#endif

Computation of MOs: values, gradient, Laplacian

Get

qmckl_exit_code
qmckl_get_mo_basis_mo_vgl(qmckl_context context,
                      double* const mo_vgl,
                      const int64_t size_max);

Uses the given array to compute the VGL.

qmckl_exit_code
qmckl_get_mo_basis_mo_vgl_inplace (qmckl_context context,
                               double* const mo_vgl,
                               const int64_t size_max);

Provide

Compute

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
`coefficient_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.

integer function qmckl_compute_mo_basis_mo_vgl_doc_f(context, &
 ao_num, mo_num, point_num, &
 coefficient_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)  :: coefficient_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) + coefficient_t(i,k) * c1
          mo_vgl(i,2,j) = mo_vgl(i,2,j) + coefficient_t(i,k) * c2
          mo_vgl(i,3,j) = mo_vgl(i,3,j) + coefficient_t(i,k) * c3
          mo_vgl(i,4,j) = mo_vgl(i,4,j) + coefficient_t(i,k) * c4
          mo_vgl(i,5,j) = mo_vgl(i,5,j) + coefficient_t(i,k) * c5
       end do
    end if
 end do
end do
info = QMCKL_SUCCESS

! info = qmckl_dgemm(context,'N', 'N', mo_num, point_num, ao_num, 1.d0, &
!      coefficient_t, int(size(coefficient_t,1),8),      &
!      ao_vgl, int(size(ao_vgl,1),8), 0.d0,                  &
!      mo_vgl, int(size(mo_vgl,1),8))

end function qmckl_compute_mo_basis_mo_vgl_doc_f

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* coefficient_t,
      const double* ao_vgl,
      double* const mo_vgl );

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* coefficient_t,
      const double* ao_vgl,
      double* const mo_vgl );

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* coefficient_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, coefficient_t, ao_vgl, mo_vgl);
#else
return qmckl_compute_mo_basis_mo_vgl_doc (context, ao_num, mo_num, point_num, coefficient_t, ao_vgl, mo_vgl);
#endif
}

HPC version

#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* coefficient_t,
                               const double* ao_vgl,
                               double* const mo_vgl );
#endif

#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 coefficient_t,
                               const double* restrict ao_vgl,
                               double* restrict const mo_vgl )
{
assert (context != QMCKL_NULL_CONTEXT);

#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]);
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 avgl1 = &(ao_vgl[ipoint*5*ao_num]);
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) {
  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) {
  const double* restrict ck1 = coefficient_t + idx[n  ]*mo_num;
  const double* restrict ck2 = coefficient_t + idx[n+1]*mo_num;
  const double* restrict ck3 = coefficient_t + idx[n+2]*mo_num;
  const double* restrict ck4 = coefficient_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;
  }
}

const int64_t n0 = n < 0 ? 0 : n;
for (int64_t m=n0 ; m < nidx ; m+=1) {
  const double* restrict ck = coefficient_t + idx[m]*mo_num;
  const double a1 = av1[m];
  const double a2 = av2[m];
  const double a3 = av3[m];
  const double a4 = av4[m];
  const double a5 = av5[m];

#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

55 KiB Raw Blame History

Molecular Orbitals

Context

Data structure

Access functions

Fortran interfaces

Initialization functions

Computation

Computation of MOs: values only

Get

Provide

Compute

HPC version

Computation of MOs: values, gradient, Laplacian

Get

Provide

Compute

HPC version

Test

55 KiB

Raw Blame History