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se_core_matrix.F
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se_core_matrix.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Calculation of the Hamiltonian integral matrix <a|H|b> for
!> semi-empirical methods
!> \author JGH
! **************************************************************************************************
MODULE se_core_matrix
USE atomic_kind_types, ONLY: atomic_kind_type,&
get_atomic_kind,&
get_atomic_kind_set
USE cp_control_types, ONLY: dft_control_type
USE cp_dbcsr_api, ONLY: &
dbcsr_add, dbcsr_copy, dbcsr_deallocate_matrix, dbcsr_distribute, dbcsr_get_block_diag, &
dbcsr_get_block_p, dbcsr_p_type, dbcsr_replicate_all, dbcsr_set, dbcsr_sum_replicated, &
dbcsr_type
USE cp_dbcsr_operations, ONLY: dbcsr_allocate_matrix_set
USE cp_dbcsr_output, ONLY: cp_dbcsr_write_sparse_matrix
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_type
USE cp_output_handling, ONLY: cp_p_file,&
cp_print_key_finished_output,&
cp_print_key_should_output,&
cp_print_key_unit_nr
USE input_constants, ONLY: &
do_method_am1, do_method_mndo, do_method_mndod, do_method_pdg, do_method_pm3, &
do_method_pm6, do_method_pm6fm, do_method_pnnl, do_method_rm1
USE input_section_types, ONLY: section_vals_val_get
USE kinds, ONLY: dp
USE message_passing, ONLY: mp_para_env_type
USE particle_types, ONLY: particle_type
USE physcon, ONLY: evolt
USE qs_energy_types, ONLY: qs_energy_type
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_force_types, ONLY: qs_force_type
USE qs_kind_types, ONLY: get_qs_kind,&
qs_kind_type
USE qs_ks_types, ONLY: qs_ks_env_type,&
set_ks_env
USE qs_neighbor_list_types, ONLY: get_iterator_info,&
neighbor_list_iterate,&
neighbor_list_iterator_create,&
neighbor_list_iterator_p_type,&
neighbor_list_iterator_release,&
neighbor_list_set_p_type
USE qs_overlap, ONLY: build_overlap_matrix
USE qs_rho_types, ONLY: qs_rho_get,&
qs_rho_type
USE semi_empirical_int_arrays, ONLY: rij_threshold
USE semi_empirical_types, ONLY: get_se_param,&
semi_empirical_type
USE semi_empirical_utils, ONLY: get_se_type
USE virial_methods, ONLY: virial_pair_force
USE virial_types, ONLY: virial_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'se_core_matrix'
PUBLIC :: build_se_core_matrix
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param para_env ...
!> \param calculate_forces ...
! **************************************************************************************************
SUBROUTINE build_se_core_matrix(qs_env, para_env, calculate_forces)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mp_para_env_type), POINTER :: para_env
LOGICAL, INTENT(IN) :: calculate_forces
CHARACTER(LEN=*), PARAMETER :: routineN = 'build_se_core_matrix'
INTEGER :: after, atom_a, atom_b, handle, i, iatom, icol, icor, ikind, inode, irow, itype, &
iw, j, jatom, jkind, natom, natorb_a, nkind, nr_a, nra, nrb
INTEGER, ALLOCATABLE, DIMENSION(:) :: atom_of_kind, nrt
LOGICAL :: defined, found, omit_headers, use_virial
LOGICAL, ALLOCATABLE, DIMENSION(:) :: se_defined
REAL(KIND=dp) :: delta, dr, econst, eheat, eisol, kh, &
udd, uff, upp, uss, ZPa, ZPb, ZSa, ZSb
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: ZPt, ZSt
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: hmt, umt
REAL(KIND=dp), DIMENSION(16) :: ha, hb, ua
REAL(KIND=dp), DIMENSION(3) :: force_ab, rij
REAL(KIND=dp), DIMENSION(:), POINTER :: beta_a, sto_exponents_a
REAL(KIND=dp), DIMENSION(:, :), POINTER :: dsmat, h_block, h_blocka, pabmat, pamat, &
s_block
TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: matrix_h, matrix_p, matrix_s
TYPE(dbcsr_type), POINTER :: diagmat_h, diagmat_p
TYPE(dft_control_type), POINTER :: dft_control
TYPE(neighbor_list_iterator_p_type), &
DIMENSION(:), POINTER :: nl_iterator
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
POINTER :: sab_orb
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
TYPE(qs_energy_type), POINTER :: energy
TYPE(qs_force_type), DIMENSION(:), POINTER :: force
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(qs_ks_env_type), POINTER :: ks_env
TYPE(qs_rho_type), POINTER :: rho
TYPE(semi_empirical_type), POINTER :: se_kind_a
TYPE(virial_type), POINTER :: virial
! REAL(KIND=dp), DIMENSION(3) :: R
CALL timeset(routineN, handle)
NULLIFY (logger, energy)
logger => cp_get_default_logger()
NULLIFY (rho, force, atomic_kind_set, qs_kind_set, sab_orb, &
diagmat_h, diagmat_p, particle_set, matrix_p, ks_env)
CALL get_qs_env(qs_env, &
matrix_s=matrix_s, &
matrix_h=matrix_h, &
ks_env=ks_env, &
particle_set=particle_set, &
atomic_kind_set=atomic_kind_set, &
qs_kind_set=qs_kind_set, &
dft_control=dft_control, &
energy=energy, &
force=force, &
virial=virial, &
rho=rho, &
sab_orb=sab_orb)
! calculate overlap matrix
IF (calculate_forces) THEN
CALL build_overlap_matrix(ks_env, nderivative=1, matrix_s=matrix_s, &
matrix_name="OVERLAP", &
basis_type_a="ORB", &
basis_type_b="ORB", &
sab_nl=sab_orb)
CALL set_ks_env(ks_env, matrix_s=matrix_s)
use_virial = virial%pv_availability .AND. (.NOT. virial%pv_numer)
ELSE
CALL build_overlap_matrix(ks_env, matrix_s=matrix_s, &
matrix_name="OVERLAP", &
basis_type_a="ORB", &
basis_type_b="ORB", &
sab_nl=sab_orb)
CALL set_ks_env(ks_env, matrix_s=matrix_s)
use_virial = .FALSE.
END IF
IF (calculate_forces) THEN
CALL qs_rho_get(rho, rho_ao=matrix_p)
IF (SIZE(matrix_p) == 2) THEN
CALL dbcsr_add(matrix_p(1)%matrix, matrix_p(2)%matrix, alpha_scalar=1.0_dp, beta_scalar=1.0_dp)
END IF
delta = dft_control%qs_control%se_control%delta
CALL get_atomic_kind_set(atomic_kind_set=atomic_kind_set, &
atom_of_kind=atom_of_kind)
ALLOCATE (diagmat_p)
CALL dbcsr_get_block_diag(matrix_p(1)%matrix, diagmat_p)
CALL dbcsr_replicate_all(diagmat_p)
END IF
! Allocate the core Hamiltonian matrix
CALL dbcsr_allocate_matrix_set(matrix_h, 1)
ALLOCATE (matrix_h(1)%matrix)
CALL dbcsr_copy(matrix_h(1)%matrix, matrix_s(1)%matrix, "CORE HAMILTONIAN MATRIX")
CALL dbcsr_set(matrix_h(1)%matrix, 0.0_dp)
! Allocate a diagonal block matrix
ALLOCATE (diagmat_h)
CALL dbcsr_get_block_diag(matrix_s(1)%matrix, diagmat_h)
CALL dbcsr_set(diagmat_h, 0.0_dp)
CALL dbcsr_replicate_all(diagmat_h)
! kh might be set in qs_control
itype = get_se_type(dft_control%qs_control%method_id)
kh = 0.5_dp
nkind = SIZE(atomic_kind_set)
ALLOCATE (se_defined(nkind))
ALLOCATE (hmt(16, nkind))
ALLOCATE (umt(16, nkind))
ALLOCATE (ZSt(nkind))
ALLOCATE (ZPt(nkind))
ALLOCATE (nrt(nkind))
econst = 0.0_dp
DO ikind = 1, nkind
CALL get_atomic_kind(atomic_kind_set(ikind), natom=natom)
CALL get_qs_kind(qs_kind_set(ikind), se_parameter=se_kind_a)
CALL get_se_param(se_kind_a, defined=defined, natorb=natorb_a, &
beta=beta_a, uss=uss, upp=upp, udd=udd, uff=uff, eisol=eisol, eheat=eheat, &
nr=nr_a, sto_exponents=sto_exponents_a)
econst = econst - (eisol - eheat)*REAL(natom, dp)
se_defined(ikind) = (defined .AND. natorb_a >= 1)
hmt(1, ikind) = beta_a(0)
hmt(2:4, ikind) = beta_a(1)
hmt(5:9, ikind) = beta_a(2)
hmt(10:16, ikind) = beta_a(3)
umt(1, ikind) = uss
umt(2:4, ikind) = upp
umt(5:9, ikind) = udd
umt(10:16, ikind) = uff
ZSt(ikind) = sto_exponents_a(0)
ZPt(ikind) = sto_exponents_a(1)
nrt(ikind) = nr_a
END DO
energy%core_self = econst
CALL neighbor_list_iterator_create(nl_iterator, sab_orb)
DO WHILE (neighbor_list_iterate(nl_iterator) == 0)
CALL get_iterator_info(nl_iterator, ikind=ikind, jkind=jkind, iatom=iatom, jatom=jatom, inode=inode, r=rij)
IF (.NOT. se_defined(ikind)) CYCLE
IF (.NOT. se_defined(jkind)) CYCLE
ha(1:16) = hmt(1:16, ikind)
ua(1:16) = umt(1:16, ikind)
hb(1:16) = hmt(1:16, jkind)
nra = nrt(ikind)
nrb = nrt(jkind)
ZSa = ZSt(ikind)
ZSb = ZSt(jkind)
ZPa = ZPt(ikind)
ZPb = ZPt(jkind)
IF (inode == 1) THEN
SELECT CASE (dft_control%qs_control%method_id)
CASE (do_method_am1, do_method_rm1, do_method_mndo, do_method_pdg, &
do_method_pm3, do_method_pm6, do_method_pm6fm, do_method_mndod, do_method_pnnl)
NULLIFY (h_blocka)
CALL dbcsr_get_block_p(diagmat_h, iatom, iatom, h_blocka, found)
CPASSERT(ASSOCIATED(h_blocka))
IF (calculate_forces) THEN
CALL dbcsr_get_block_p(diagmat_p, iatom, iatom, pamat, found)
CPASSERT(ASSOCIATED(pamat))
END IF
END SELECT
END IF
dr = SUM(rij(:)**2)
IF (iatom == jatom .AND. dr < rij_threshold) THEN
SELECT CASE (dft_control%qs_control%method_id)
CASE DEFAULT
CPABORT("")
CASE (do_method_am1, do_method_rm1, do_method_mndo, do_method_pdg, &
do_method_pm3, do_method_pm6, do_method_pm6fm, do_method_mndod, do_method_pnnl)
DO i = 1, SIZE(h_blocka, 1)
h_blocka(i, i) = h_blocka(i, i) + ua(i)
END DO
END SELECT
ELSE
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
NULLIFY (h_block)
CALL dbcsr_get_block_p(matrix_h(1)%matrix, &
irow, icol, h_block, found)
CPASSERT(ASSOCIATED(h_block))
! two-centre one-electron term
NULLIFY (s_block)
! CALL dbcsr_get_block_p(matrix_s(1)%matrix,&
! irow,icol,s_block,found)
! CPPostcondition(ASSOCIATED(s_block),cp_failure_level,routineP,failure)
!
! if( irow == iatom )then
! R= -rij
! call makeS(R,nra,nrb,ZSa,ZSb,ZPa,ZPb,S)
! else
! R= rij
! call makeS(R,nrb,nra,ZSb,ZSa,ZPb,ZPa,S)
! endif
!
! do i=1,4
! do j=1,4
! s_block(i,j)=S(ix(i),ix(j))
! enddo
! enddo
CALL dbcsr_get_block_p(matrix_s(1)%matrix, &
irow, icol, s_block, found)
CPASSERT(ASSOCIATED(s_block))
IF (irow == iatom) THEN
DO i = 1, SIZE(h_block, 1)
DO j = 1, SIZE(h_block, 2)
h_block(i, j) = h_block(i, j) + kh*(ha(i) + hb(j))*s_block(i, j)
END DO
END DO
ELSE
DO i = 1, SIZE(h_block, 1)
DO j = 1, SIZE(h_block, 2)
h_block(i, j) = h_block(i, j) + kh*(ha(j) + hb(i))*s_block(i, j)
END DO
END DO
END IF
IF (calculate_forces) THEN
atom_a = atom_of_kind(iatom)
atom_b = atom_of_kind(jatom)
! if( irow == iatom )then
! R= -rij
! call makedS(R,nra,nrb,ZSa,ZSb,ZPa,ZPb,dS)
! else
! R= rij
! call makedS(R,nrb,nra,ZSb,ZSa,ZPb,ZPa,dS)
! endif
CALL dbcsr_get_block_p(matrix_p(1)%matrix, irow, icol, pabmat, found)
CPASSERT(ASSOCIATED(pabmat))
DO icor = 1, 3
force_ab(icor) = 0._dp
! CALL dbcsr_get_block_p(matrix_s(icor+1)%matrix,irow,icol,dsmat,found)
! CPPostcondition(ASSOCIATED(dsmat),cp_failure_level,routineP,failure)
!
! do i=1,4
! do j=1,4
! dsmat(i,j)=dS(ix(i),ix(j),icor)
! enddo
! enddo
CALL dbcsr_get_block_p(matrix_s(icor + 1)%matrix, irow, icol, dsmat, found)
CPASSERT(ASSOCIATED(dsmat))
dsmat = 2._dp*kh*dsmat*pabmat
IF (irow == iatom) THEN
DO i = 1, SIZE(h_block, 1)
DO j = 1, SIZE(h_block, 2)
force_ab(icor) = force_ab(icor) + (ha(i) + hb(j))*dsmat(i, j)
END DO
END DO
ELSE
DO i = 1, SIZE(h_block, 1)
DO j = 1, SIZE(h_block, 2)
force_ab(icor) = force_ab(icor) + (ha(j) + hb(i))*dsmat(i, j)
END DO
END DO
END IF
END DO
END IF
END IF
IF (calculate_forces .AND. (iatom /= jatom .OR. dr > rij_threshold)) THEN
IF (irow == iatom) force_ab = -force_ab
force(ikind)%all_potential(:, atom_a) = &
force(ikind)%all_potential(:, atom_a) - force_ab(:)
force(jkind)%all_potential(:, atom_b) = &
force(jkind)%all_potential(:, atom_b) + force_ab(:)
IF (use_virial) THEN
CALL virial_pair_force(virial%pv_virial, -1.0_dp, force_ab, rij)
END IF
END IF
END DO
CALL neighbor_list_iterator_release(nl_iterator)
DEALLOCATE (se_defined, hmt, umt, ZSt, ZPt, nrt)
CALL dbcsr_sum_replicated(diagmat_h)
CALL dbcsr_distribute(diagmat_h)
CALL dbcsr_add(matrix_h(1)%matrix, diagmat_h, 1.0_dp, 1.0_dp)
CALL set_ks_env(ks_env, matrix_h=matrix_h)
IF (BTEST(cp_print_key_should_output(logger%iter_info, &
qs_env%input, "DFT%PRINT%AO_MATRICES/CORE_HAMILTONIAN"), cp_p_file)) THEN
iw = cp_print_key_unit_nr(logger, qs_env%input, "DFT%PRINT%AO_MATRICES/CORE_HAMILTONIAN", &
extension=".Log")
CALL section_vals_val_get(qs_env%input, "DFT%PRINT%AO_MATRICES%NDIGITS", i_val=after)
CALL section_vals_val_get(qs_env%input, "DFT%PRINT%AO_MATRICES%OMIT_HEADERS", l_val=omit_headers)
after = MIN(MAX(after, 1), 16)
CALL cp_dbcsr_write_sparse_matrix(matrix_h(1)%matrix, 4, after, qs_env, para_env, &
scale=evolt, output_unit=iw, omit_headers=omit_headers)
CALL cp_print_key_finished_output(iw, logger, qs_env%input, &
"DFT%PRINT%AO_MATRICES/CORE_HAMILTONIAN")
END IF
IF (calculate_forces) THEN
IF (SIZE(matrix_p) == 2) THEN
CALL dbcsr_add(matrix_p(1)%matrix, matrix_p(2)%matrix, alpha_scalar=1.0_dp, beta_scalar=-1.0_dp)
END IF
DEALLOCATE (atom_of_kind)
CALL dbcsr_deallocate_matrix(diagmat_p)
END IF
CALL dbcsr_deallocate_matrix(diagmat_h)
CALL timestop(handle)
END SUBROUTINE build_se_core_matrix
! **************************************************************************************************
!> \brief ...
!> \param R ...
!> \param nra ...
!> \param nrb ...
!> \param ZSA ...
!> \param ZSB ...
!> \param ZPA ...
!> \param ZPB ...
!> \param S ...
! **************************************************************************************************
SUBROUTINE makeS(R, nra, nrb, ZSA, ZSB, ZPA, ZPB, S)
REAL(kind=dp), DIMENSION(3) :: R
INTEGER :: nra, nrb
REAL(kind=dp) :: ZSA, ZSB, ZPA, ZPB
REAL(kind=dp), DIMENSION(4, 4) :: S
INTEGER, DIMENSION(4, 4), PARAMETER :: &
nc1 = RESHAPE((/2, 4, 4, 6, 4, 3, 6, 7, 4, 6, 4, 8, 6, 7, 8, 5/), (/4, 4/)), &
nc2 = RESHAPE((/4, 4, 8, 8, 6, 8, 6, 12, 8, 8, 12, 8, 10, 12, 14, 16/), (/4, 4/)), &
nc3 = RESHAPE((/4, 6, 8, 10, 4, 8, 8, 12, 8, 6, 12, 14, 8, 12, 8, 16/), (/4, 4/)), &
nc4 = RESHAPE((/4, 8, 11, 14, 8, 6, 12, 14, 11, 12, 10, 20, 14, 14, 20, 12/), (/4, 4/)), &
nc5 = RESHAPE((/2, 4, 6, 8, 4, 4, 8, 8, 6, 8, 6, 12, 8, 8, 12, 8/), (/4, 4/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c1 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 &
, 1, 1, 1, 1, -1, 1, 2, 3, -1, -2, 1, 2, -2, -1, -3, 1, -3, -2, -1, -4, 0, -1, -2, 2, -1, &
1, -2, -1, 2, -2, 3, -3, 2, -1, -3, 6, 0, -1, -1, -2, 1, 0, -2, -4, -1, 2, -1, -3, 2, 4, 3&
, -4, 0, 0, 0, -3, 0, 0, 1, -1, 0, 1, 0, 3, -3, -1, 3, 1, 0, 0, 0, -1, 0, 0, 1, 2, 0, -1, &
0, 3, 1, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 &
, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c2 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 &
, 1, 1, 1, 1, -1, 1, 1, 2, -2, -1, 1, 1, -3, -2, -1, 1, -4, -3, -2, -1, 1, -1, 1, 1, 1, 1 &
, -2, 1, 1, 1, 1, -3, 1, 1, 1, 1, -1, -1, -1, 2, 1, -1, -2, -2, 3, -2, -2, -3, 6, 2, -1, &
-3, 0, 0, 1, -2, -2, -1, 1, 1, -3, 2, -1, 3, -4, -3, -2, -1, 0, 0, -1, -1, 1, 1, 1, -2, -1&
, -1, 2, 3, -4, 2, 4, 3, 0, 0, -1, -2, 0, -1, 0, -2, 3, 2, -2, -1, 6, 2, -1, -3, 0, 0, -1,&
-1, 0, 1, 0, 1, -1, -1, 1, -1, 1, -3, -1, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -4, 2, 4&
, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 1, -2, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0&
, 0, -3, -1, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c3 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, -1, -2, -3, -4, 1, -1, -2, -3, 1, 1, -1, -2, 2, 1, 1, -1, 1 &
, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, -1, -3, -6, -1, 1, 2, -2, 1, -2, 2, 1, &
-2, 2, -3, 3, 0, 2, 3, 4, 0, 1, 2, 3, -1, -1, 1, 2, -2, -1, -3, 1, 0, 1, -1, -4, 0, 1, 1, &
2, -1, 1, 2, 4, 1, -2, 3, 3, 0, 0, 3, 6, 0, -1, -2, 2, -1, 0, -2, -1, 2, -2, 1, -3, 0, 0, &
1, -1, 0, -1, -1, 3, 1, 0, -1, 1, -1, -1, -1, -3, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -2, -4, 0&
, 2, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, -2, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0 &
, 0, 1, -1, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c4 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -2, &
-3, 1, 1, -1, -2, 2, 1, 2, -1, 3, 2, 1, 3, -1, 1, 2, 3, -1, -1, 1, 2, -2, -1, -1, 1, -3, &
-2, -1, -2, 0, 1, -1, -3, 1, -1, 1, 1, -1, 1, -1, 2, -3, 1, 2, -1, 0, -1, 2, 4, -1, 1, -1 &
, -1, 2, -1, -1, -1, 4, -1, -1, -3, 0, 1, -1, -1, -1, 0, 1, 2, -1, -1, -1, -1, -1, -2, -1 &
, 3, 0, -1, 2, -1, 1, 0, -1, -2, -2, 1, 2, 2, 1, 2, -2, 1, 0, 0, -2, 4, 0, 0, -1, 1, 2, -1&
, 1, -1, -4, 1, 1, 2, 0, 0, 1, -3, 0, 0, 1, -1, 1, 1, -1, -1, 3, -1, 1, -3, 0, 0, -1, 3, 0&
, 0, -1, -2, -1, 1, 0, -1, 3, 2, -1, -1, 0, 0, 0, -3, 0, 0, 1, 2, 0, -1, 0, -1, -3, -2, -1&
, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, -1, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, &
-1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c5 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, 1, -1, -2, -3, 1, 1, -1, -2, 2, 1, 2, -1, 3, 2, 1, 3, 0, 1, &
-1, -3, 1, 1, 1, 1, -1, 1, 1, 2, -3, 1, 2, 1, 0, 1, 1, 1, -1, -1, 1, 2, 1, 1, -1, 1, 1, -2&
, 1, -3, 0, 0, 2, -1, 0, 0, 1, 2, -2, -1, -2, 2, 1, -2, -2, -3, 0, 0, 1, 3, 0, 0, 1, 1, 1,&
-1, 1, 1, -3, 1, -1, 1, 0, 0, 0, 3, 0, 0, -1, -2, 0, -1, 0, -1, 3, 2, -1, 3, 0, 0, 0, 1, 0&
, 0, -1, -1, 0, 1, 0, -2, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0,&
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,&
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 &
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, &
20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma1 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 1, 3, 1, 0, 3, 4, 1, 3&
, 2, 5, 3, 4, 5, 4, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 2, 3, 4, 2, 0, 0, 0, 1, 0, 0, 1, 2&
, 0, 1, 0, 3, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma2 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 1, 1, 3, 4, 2, 3, 3, 5, 3, 4&
, 5, 5, 4, 5, 6, 7, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 5, 6, 0, 0, 2, 2, 1, 2, 1, 4&
, 2, 2, 4, 3, 3, 4, 5, 6, 0, 0, 1, 1, 0, 1, 0, 3, 1, 1, 3, 2, 2, 3, 4, 5, 0, 0, 1, 1, 0, 1&
, 0, 3, 1, 1, 3, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 3, 4, 0, 0, 0, 0&
, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma3 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 1, 2, 3, 4, 1, 3, 4, 5, 3, 3&
, 5, 6, 4, 5, 5, 7, 0, 1, 2, 3, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 0, 1, 2, 3, 0, 2, 2, 4&
, 2, 1, 4, 5, 2, 4, 3, 6, 0, 0, 1, 2, 0, 1, 1, 3, 1, 0, 3, 4, 1, 3, 2, 5, 0, 0, 1, 2, 0, 1&
, 1, 3, 1, 0, 3, 4, 1, 3, 1, 5, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 0, 0, 0, 1&
, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma4 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4&
, 4, 6, 4, 5, 6, 6, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 2, 3, 1, 0, 3, 4&
, 2, 3, 4, 5, 3, 4, 5, 6, 0, 1, 2, 3, 1, 0, 3, 4, 2, 3, 2, 5, 3, 4, 5, 4, 0, 0, 2, 3, 0, 0&
, 2, 3, 2, 2, 2, 5, 3, 3, 5, 4, 0, 0, 1, 2, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 2, 0, 0, 1, 2&
, 0, 0, 1, 2, 1, 1, 0, 4, 2, 2, 4, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 4, 2, 2, 4, 2, 0, 0&
, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 1, 1, 3, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0&
, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2&
, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma5 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3&
, 4, 5, 3, 4, 5, 6, 0, 0, 2, 3, 0, 0, 3, 3, 2, 3, 2, 5, 3, 3, 5, 4, 0, 0, 1, 2, 0, 0, 2, 3&
, 1, 2, 2, 4, 2, 3, 4, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, 0, 1, 0, 0&
, 1, 1, 0, 1, 0, 3, 1, 1, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb1 = RESHAPE((/0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0, 2, 3, 2, 2, 4, 2, 2, 3, 2&
, 4, 2, 2, 2, 2, 4, 0, 3, 4, 3, 3, 0, 3, 3, 4, 3, 6, 3, 3, 3, 3, 6, 0, 0, 0, 4, 0, 0, 4, 4&
, 0, 4, 0, 4, 4, 4, 4, 8, 0, 0, 0, 5, 0, 0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0&
, 0, 6, 0, 0, 0, 6, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb2 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1&
, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0&
, 0, 3, 0, 0, 0, 0, 1, 2, 3, 1, 3, 3, 2, 3, 3, 1, 3, 2, 3, 3, 3, 3, 0, 0, 1, 4, 1, 1, 5, 1&
, 1, 4, 1, 5, 1, 1, 1, 1, 0, 0, 4, 5, 2, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 0, 0, 2, 3, 0, 2&
, 0, 2, 2, 3, 2, 7, 2, 2, 2, 2, 0, 0, 3, 4, 0, 3, 0, 5, 3, 4, 5, 6, 5, 5, 5, 5, 0, 0, 0, 0&
, 0, 0, 0, 3, 0, 0, 3, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 4, 6, 6, 6, 0, 0&
, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 5, 7, 7&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb3 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1&
, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3&
, 0, 0, 0, 0, 3, 0, 1, 3, 3, 3, 2, 3, 1, 3, 3, 2, 3, 3, 1, 3, 2, 3, 0, 1, 1, 1, 0, 1, 4, 1&
, 1, 5, 1, 1, 4, 1, 5, 1, 0, 2, 4, 4, 0, 4, 5, 4, 4, 4, 4, 4, 5, 4, 4, 4, 0, 0, 2, 2, 0, 2&
, 3, 2, 2, 0, 2, 2, 3, 2, 7, 2, 0, 0, 3, 5, 0, 3, 4, 5, 3, 0, 5, 5, 4, 5, 6, 5, 0, 0, 0, 3&
, 0, 0, 0, 3, 0, 0, 3, 3, 0, 3, 0, 3, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 6, 6, 0, 6, 0, 6, 0, 0&
, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 7, 0, 5, 0, 7&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0&
, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb4 = RESHAPE((/2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2&
, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3&
, 4, 3, 3, 3, 3, 4, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0, 2, 4, 4, 2, 4, 4, 2&
, 4, 4, 0, 4, 4, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 6, 2, 2, 0, 2, 6, 0, 3, 0, 0, 3, 0&
, 5, 5, 0, 5, 4, 0, 0, 5, 0, 2, 0, 1, 3, 5, 1, 0, 1, 1, 3, 1, 2, 5, 5, 1, 5, 8, 0, 0, 1, 3&
, 0, 0, 4, 6, 1, 4, 6, 3, 3, 6, 3, 6, 0, 0, 4, 1, 0, 0, 2, 4, 4, 2, 4, 1, 1, 4, 1, 4, 0, 0&
, 2, 4, 0, 0, 5, 5, 2, 5, 0, 6, 4, 5, 6, 8, 0, 0, 0, 2, 0, 0, 3, 3, 0, 3, 0, 4, 2, 3, 4, 6&
, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 2, 5, 6, 2, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 7, 3, 4&
, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3&
, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 5, 0, 0, 5, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb5 = RESHAPE((/2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2&
, 2, 2, 2, 2, 0, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 0, 0, 4, 4, 0, 0, 4, 0, 4, 4&
, 0, 4, 4, 0, 4, 0, 0, 1, 0, 0, 1, 2, 0, 5, 0, 0, 6, 0, 0, 5, 0, 6, 0, 0, 1, 5, 0, 0, 5, 1&
, 1, 5, 2, 5, 5, 1, 5, 2, 0, 0, 2, 1, 0, 0, 1, 6, 2, 1, 4, 1, 1, 6, 1, 8, 0, 0, 0, 2, 0, 0&
, 2, 3, 0, 2, 0, 6, 2, 3, 6, 4, 0, 0, 0, 3, 0, 0, 3, 4, 0, 3, 0, 2, 3, 4, 2, 6, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER :: k, k1, k2, mu
REAL(kind=dp) :: cp, ct, fac1, fac2, J, Jc, Jcc, Jss, rr, &
sp, st, xx, yy, za, zb
REAL(kind=dp), DIMENSION(3) :: v
REAL(kind=dp), DIMENSION(3, 3) :: Arot
S(:, :) = 0.0_dp
v(:) = R(:)
rr = SQRT(DOT_PRODUCT(v, v))
IF (rr < 1.0e-20_dp) THEN
DO mu = 1, 4
S(mu, mu) = 1.0_dp
END DO
ELSE
fac1 = 1.0_dp
IF (nra == 1) THEN
fac1 = fac1*2.0_dp
ELSE
IF (nra == 2) THEN
fac1 = fac1*SQRT(4.0_dp/3.0_dp)
ELSE
IF (nra == 3) THEN
fac1 = fac1*SQRT(8.0_dp/45.0_dp)
ELSE
IF (nra == 4) THEN
fac1 = fac1*SQRT(4.0_dp/315.0_dp)
ELSE
WRITE (*, *) 'nra= ', nra
RETURN
END IF
END IF
END IF
END IF
IF (nrb == 1) THEN
fac1 = fac1*2.0_dp
ELSE
IF (nrb == 2) THEN
fac1 = fac1*SQRT(4.0_dp/3.0_dp)
ELSE
IF (nrb == 3) THEN
fac1 = fac1*SQRT(8.0_dp/45.0_dp)
ELSE
IF (nrb == 4) THEN
fac1 = fac1*SQRT(4.0_dp/315.0_dp)
ELSE
WRITE (*, *) 'nrb= ', nrb
RETURN
END IF
END IF
END IF
END IF
ct = -v(3)/rr
IF (ABS(ct) < 1.0_dp) THEN
st = SQRT(1.0_dp - ct**2)
cp = -v(1)/(rr*st)
sp = -v(2)/(rr*st)
Arot(1, 1) = ct*cp
Arot(1, 2) = -sp
Arot(1, 3) = st*cp
Arot(2, 1) = ct*sp
Arot(2, 2) = cp
Arot(2, 3) = st*sp
Arot(3, 1) = -st
Arot(3, 2) = 0.0_dp
Arot(3, 3) = ct
ELSE
Arot(1, 1) = ct
Arot(1, 2) = 0.0_dp
Arot(1, 3) = 0.0_dp
Arot(2, 1) = 0.0_dp
Arot(2, 2) = 1.0_dp
Arot(2, 3) = 0.0_dp
Arot(3, 1) = 0.0_dp
Arot(3, 2) = 0.0_dp
Arot(3, 3) = ct
END IF
za = ZSA
zb = ZSB
fac2 = SQRT(za**(2*nra + 1)*zb**(2*nrb + 1))
xx = 0.5_dp*rr*(za + zb)
yy = 0.5_dp*rr*(za - zb)
J = 0.0_dp
DO k = 1, nc1(nra, nrb)
J = J + REAL(c1(nra, nrb, k), dp)*AA(ma1(nra, nrb, k), xx)*BB(mb1(nra, nrb, k), yy)
END DO
J = J*rr**(nra + nrb + 1)
J = J/2.0_dp**(nra + nrb + 2)
S(1, 1) = S(1, 1) + fac1*fac2*J
za = ZPA
zb = ZSB
fac2 = SQRT(za**(2*nra + 1)*zb**(2*nrb + 1))
xx = 0.5_dp*rr*(za + zb)
yy = 0.5_dp*rr*(za - zb)
Jc = 0.0_dp
DO k = 1, nc2(nra, nrb)
Jc = Jc + REAL(c2(nra, nrb, k), dp)*AA(ma2(nra, nrb, k), xx)*BB(mb2(nra, nrb, k), yy)
END DO
Jc = Jc*rr**(nra + nrb + 1)
Jc = Jc/2.0_dp**(nra + nrb + 2)
DO k1 = 1, 3
S(k1 + 1, 1) = S(k1 + 1, 1) &
& + SQRT(3.0_dp)*Arot(k1, 3)*fac1*fac2*Jc
END DO
za = ZSA
zb = ZPB
fac2 = SQRT(za**(2*nra + 1)*zb**(2*nrb + 1))
xx = 0.5_dp*rr*(za + zb)
yy = 0.5_dp*rr*(za - zb)
Jc = 0.0_dp
DO k = 1, nc3(nra, nrb)
Jc = Jc + REAL(c3(nra, nrb, k), dp)*AA(ma3(nra, nrb, k), xx)*BB(mb3(nra, nrb, k), yy)
END DO
Jc = Jc*rr**(nra + nrb + 1)
Jc = Jc/2.0_dp**(nra + nrb + 2)
DO k1 = 1, 3
S(1, k1 + 1) = S(1, k1 + 1) &
& - SQRT(3.0_dp)*Arot(k1, 3)*fac1*fac2*Jc
END DO
za = ZPA
zb = ZPB
fac2 = SQRT(za**(2*nra + 1)*zb**(2*nrb + 1))
xx = 0.5_dp*rr*(za + zb)
yy = 0.5_dp*rr*(za - zb)
Jss = 0.0_dp
DO k = 1, nc4(nra, nrb)
Jss = Jss + REAL(c4(nra, nrb, k), dp)*AA(ma4(nra, nrb, k), xx)*BB(mb4(nra, nrb, k), yy)
END DO
Jss = Jss*rr**(nra + nrb + 1)
Jss = Jss/2.0_dp**(nra + nrb + 2)
Jcc = 0.0_dp
DO k = 1, nc5(nra, nrb)
Jcc = Jcc + REAL(c5(nra, nrb, k), dp)*AA(ma5(nra, nrb, k), xx)*BB(mb5(nra, nrb, k), yy)
END DO
Jcc = Jcc*rr**(nra + nrb + 1)
Jcc = Jcc/2.0_dp**(nra + nrb + 2)
DO k1 = 1, 3
DO k2 = 1, 3
S(k1 + 1, k2 + 1) = S(k1 + 1, k2 + 1) &
& + 1.5_dp*Arot(k1, 1)*Arot(k2, 1)*fac1*fac2*Jss &
& + 1.5_dp*Arot(k1, 2)*Arot(k2, 2)*fac1*fac2*Jss &
& - 3.0_dp*Arot(k1, 3)*Arot(k2, 3)*fac1*fac2*Jcc
END DO
END DO
END IF
END SUBROUTINE makeS
! **************************************************************************************************
!> \brief ...
!> \param R ...
!> \param nra ...
!> \param nrb ...
!> \param ZSA ...
!> \param ZSB ...
!> \param ZPA ...
!> \param ZPB ...
!> \param dS ...
! **************************************************************************************************
SUBROUTINE makedS(R, nra, nrb, ZSA, ZSB, ZPA, ZPB, dS)
REAL(kind=dp), DIMENSION(3) :: R
INTEGER :: nra, nrb
REAL(kind=dp) :: ZSA, ZSB, ZPA, ZPB
REAL(kind=dp), DIMENSION(4, 4, 3) :: dS
INTEGER, DIMENSION(4, 4), PARAMETER :: &
nc1 = RESHAPE((/2, 4, 4, 6, 4, 3, 6, 7, 4, 6, 4, 8, 6, 7, 8, 5/), (/4, 4/)), &
nc2 = RESHAPE((/4, 4, 8, 8, 6, 8, 6, 12, 8, 8, 12, 8, 10, 12, 14, 16/), (/4, 4/)), &
nc3 = RESHAPE((/4, 6, 8, 10, 4, 8, 8, 12, 8, 6, 12, 14, 8, 12, 8, 16/), (/4, 4/)), &
nc4 = RESHAPE((/4, 8, 11, 14, 8, 6, 12, 14, 11, 12, 10, 20, 14, 14, 20, 12/), (/4, 4/)), &
nc5 = RESHAPE((/2, 4, 6, 8, 4, 4, 8, 8, 6, 8, 6, 12, 8, 8, 12, 8/), (/4, 4/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c1 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 &
, 1, 1, 1, 1, -1, 1, 2, 3, -1, -2, 1, 2, -2, -1, -3, 1, -3, -2, -1, -4, 0, -1, -2, 2, -1, &
1, -2, -1, 2, -2, 3, -3, 2, -1, -3, 6, 0, -1, -1, -2, 1, 0, -2, -4, -1, 2, -1, -3, 2, 4, 3&
, -4, 0, 0, 0, -3, 0, 0, 1, -1, 0, 1, 0, 3, -3, -1, 3, 1, 0, 0, 0, -1, 0, 0, 1, 2, 0, -1, &
0, 3, 1, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 &
, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c2 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 &
, 1, 1, 1, 1, -1, 1, 1, 2, -2, -1, 1, 1, -3, -2, -1, 1, -4, -3, -2, -1, 1, -1, 1, 1, 1, 1 &
, -2, 1, 1, 1, 1, -3, 1, 1, 1, 1, -1, -1, -1, 2, 1, -1, -2, -2, 3, -2, -2, -3, 6, 2, -1, &
-3, 0, 0, 1, -2, -2, -1, 1, 1, -3, 2, -1, 3, -4, -3, -2, -1, 0, 0, -1, -1, 1, 1, 1, -2, -1&
, -1, 2, 3, -4, 2, 4, 3, 0, 0, -1, -2, 0, -1, 0, -2, 3, 2, -2, -1, 6, 2, -1, -3, 0, 0, -1,&
-1, 0, 1, 0, 1, -1, -1, 1, -1, 1, -3, -1, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, -4, 2, 4&
, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 1, -2, -3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0&
, 0, -3, -1, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c3 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, -1, -2, -3, -4, 1, -1, -2, -3, 1, 1, -1, -2, 2, 1, 1, -1, 1 &
, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, -1, -3, -6, -1, 1, 2, -2, 1, -2, 2, 1, &
-2, 2, -3, 3, 0, 2, 3, 4, 0, 1, 2, 3, -1, -1, 1, 2, -2, -1, -3, 1, 0, 1, -1, -4, 0, 1, 1, &
2, -1, 1, 2, 4, 1, -2, 3, 3, 0, 0, 3, 6, 0, -1, -2, 2, -1, 0, -2, -1, 2, -2, 1, -3, 0, 0, &
1, -1, 0, -1, -1, 3, 1, 0, -1, 1, -1, -1, -1, -3, 0, 0, 0, 4, 0, 0, 0, -2, 0, 0, -2, -4, 0&
, 2, 0, -3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, -2, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0 &
, 0, 1, -1, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c4 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -2, &
-3, 1, 1, -1, -2, 2, 1, 2, -1, 3, 2, 1, 3, -1, 1, 2, 3, -1, -1, 1, 2, -2, -1, -1, 1, -3, &
-2, -1, -2, 0, 1, -1, -3, 1, -1, 1, 1, -1, 1, -1, 2, -3, 1, 2, -1, 0, -1, 2, 4, -1, 1, -1 &
, -1, 2, -1, -1, -1, 4, -1, -1, -3, 0, 1, -1, -1, -1, 0, 1, 2, -1, -1, -1, -1, -1, -2, -1 &
, 3, 0, -1, 2, -1, 1, 0, -1, -2, -2, 1, 2, 2, 1, 2, -2, 1, 0, 0, -2, 4, 0, 0, -1, 1, 2, -1&
, 1, -1, -4, 1, 1, 2, 0, 0, 1, -3, 0, 0, 1, -1, 1, 1, -1, -1, 3, -1, 1, -3, 0, 0, -1, 3, 0&
, 0, -1, -2, -1, 1, 0, -1, 3, 2, -1, -1, 0, 0, 0, -3, 0, 0, 1, 2, 0, -1, 0, -1, -3, -2, -1&
, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, -1, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, &
-1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: c5 = RESHAPE((/-1, -1, -1, -1, -1, -1, -1, -1, -1 &
, -1, -1, -1, -1, -1, -1, -1, 1, -1, -2, -3, 1, 1, -1, -2, 2, 1, 2, -1, 3, 2, 1, 3, 0, 1, &
-1, -3, 1, 1, 1, 1, -1, 1, 1, 2, -3, 1, 2, 1, 0, 1, 1, 1, -1, -1, 1, 2, 1, 1, -1, 1, 1, -2&
, 1, -3, 0, 0, 2, -1, 0, 0, 1, 2, -2, -1, -2, 2, 1, -2, -2, -3, 0, 0, 1, 3, 0, 0, 1, 1, 1,&
-1, 1, 1, -3, 1, -1, 1, 0, 0, 0, 3, 0, 0, -1, -2, 0, -1, 0, -1, 3, 2, -1, 3, 0, 0, 0, 1, 0&
, 0, -1, -1, 0, 1, 0, -2, -1, -1, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0,&
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,&
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 &
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, &
20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma1 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 1, 3, 1, 0, 3, 4, 1, 3&
, 2, 5, 3, 4, 5, 4, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 2, 3, 4, 2, 0, 0, 0, 1, 0, 0, 1, 2&
, 0, 1, 0, 3, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma2 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 1, 1, 3, 4, 2, 3, 3, 5, 3, 4&
, 5, 5, 4, 5, 6, 7, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 4, 3, 4, 5, 6, 0, 0, 2, 2, 1, 2, 1, 4&
, 2, 2, 4, 3, 3, 4, 5, 6, 0, 0, 1, 1, 0, 1, 0, 3, 1, 1, 3, 2, 2, 3, 4, 5, 0, 0, 1, 1, 0, 1&
, 0, 3, 1, 1, 3, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 3, 4, 0, 0, 0, 0&
, 0, 0, 0, 2, 0, 0, 2, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma3 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 1, 2, 3, 4, 1, 3, 4, 5, 3, 3&
, 5, 6, 4, 5, 5, 7, 0, 1, 2, 3, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 0, 1, 2, 3, 0, 2, 2, 4&
, 2, 1, 4, 5, 2, 4, 3, 6, 0, 0, 1, 2, 0, 1, 1, 3, 1, 0, 3, 4, 1, 3, 2, 5, 0, 0, 1, 2, 0, 1&
, 1, 3, 1, 0, 3, 4, 1, 3, 1, 5, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 0, 0, 0, 1&
, 0, 0, 0, 2, 0, 0, 2, 3, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 0, 0&
, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma4 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4&
, 4, 6, 4, 5, 6, 6, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 2, 3, 1, 0, 3, 4&
, 2, 3, 4, 5, 3, 4, 5, 6, 0, 1, 2, 3, 1, 0, 3, 4, 2, 3, 2, 5, 3, 4, 5, 4, 0, 0, 2, 3, 0, 0&
, 2, 3, 2, 2, 2, 5, 3, 3, 5, 4, 0, 0, 1, 2, 0, 0, 2, 3, 1, 2, 2, 4, 2, 3, 4, 2, 0, 0, 1, 2&
, 0, 0, 1, 2, 1, 1, 0, 4, 2, 2, 4, 2, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 4, 2, 2, 4, 2, 0, 0&
, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 1, 1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 1, 1, 3, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0&
, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2&
, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: ma5 = RESHAPE((/2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7&
, 5, 6, 7, 8, 0, 2, 3, 4, 2, 2, 4, 5, 3, 4, 4, 6, 4, 5, 6, 6, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3&
, 4, 5, 3, 4, 5, 6, 0, 0, 2, 3, 0, 0, 3, 3, 2, 3, 2, 5, 3, 3, 5, 4, 0, 0, 1, 2, 0, 0, 2, 3&
, 1, 2, 2, 4, 2, 3, 4, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, 0, 1, 0, 0&
, 1, 1, 0, 1, 0, 3, 1, 1, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb1 = RESHAPE((/0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0, 2, 3, 2, 2, 4, 2, 2, 3, 2&
, 4, 2, 2, 2, 2, 4, 0, 3, 4, 3, 3, 0, 3, 3, 4, 3, 6, 3, 3, 3, 3, 6, 0, 0, 0, 4, 0, 0, 4, 4&
, 0, 4, 0, 4, 4, 4, 4, 8, 0, 0, 0, 5, 0, 0, 5, 5, 0, 5, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0&
, 0, 6, 0, 0, 0, 6, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb2 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1&
, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0&
, 0, 3, 0, 0, 0, 0, 1, 2, 3, 1, 3, 3, 2, 3, 3, 1, 3, 2, 3, 3, 3, 3, 0, 0, 1, 4, 1, 1, 5, 1&
, 1, 4, 1, 5, 1, 1, 1, 1, 0, 0, 4, 5, 2, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 0, 0, 2, 3, 0, 2&
, 0, 2, 2, 3, 2, 7, 2, 2, 2, 2, 0, 0, 3, 4, 0, 3, 0, 5, 3, 4, 5, 6, 5, 5, 5, 5, 0, 0, 0, 0&
, 0, 0, 0, 3, 0, 0, 3, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 4, 6, 6, 6, 0, 0&
, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 5, 7, 7&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb3 = RESHAPE((/1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1&
, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3&
, 0, 0, 0, 0, 3, 0, 1, 3, 3, 3, 2, 3, 1, 3, 3, 2, 3, 3, 1, 3, 2, 3, 0, 1, 1, 1, 0, 1, 4, 1&
, 1, 5, 1, 1, 4, 1, 5, 1, 0, 2, 4, 4, 0, 4, 5, 4, 4, 4, 4, 4, 5, 4, 4, 4, 0, 0, 2, 2, 0, 2&
, 3, 2, 2, 0, 2, 2, 3, 2, 7, 2, 0, 0, 3, 5, 0, 3, 4, 5, 3, 0, 5, 5, 4, 5, 6, 5, 0, 0, 0, 3&
, 0, 0, 0, 3, 0, 0, 3, 3, 0, 3, 0, 3, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 6, 6, 0, 6, 0, 6, 0, 0&
, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 7, 0, 5, 0, 7&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0&
, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb4 = RESHAPE((/2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2&
, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3&
, 4, 3, 3, 3, 3, 4, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0, 2, 4, 4, 2, 4, 4, 2&
, 4, 4, 0, 4, 4, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 6, 2, 2, 0, 2, 6, 0, 3, 0, 0, 3, 0&
, 5, 5, 0, 5, 4, 0, 0, 5, 0, 2, 0, 1, 3, 5, 1, 0, 1, 1, 3, 1, 2, 5, 5, 1, 5, 8, 0, 0, 1, 3&
, 0, 0, 4, 6, 1, 4, 6, 3, 3, 6, 3, 6, 0, 0, 4, 1, 0, 0, 2, 4, 4, 2, 4, 1, 1, 4, 1, 4, 0, 0&
, 2, 4, 0, 0, 5, 5, 2, 5, 0, 6, 4, 5, 6, 8, 0, 0, 0, 2, 0, 0, 3, 3, 0, 3, 0, 4, 2, 3, 4, 6&
, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 2, 5, 6, 2, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 7, 3, 4&
, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3&
, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 5, 0, 0, 5, 0/), (/4, 4, 20/))
INTEGER, DIMENSION(4, 4, 20), PARAMETER :: mb5 = RESHAPE((/2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2&
, 2, 2, 2, 2, 0, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 4, 0, 0, 4, 4, 0, 0, 4, 0, 4, 4&
, 0, 4, 4, 0, 4, 0, 0, 1, 0, 0, 1, 2, 0, 5, 0, 0, 6, 0, 0, 5, 0, 6, 0, 0, 1, 5, 0, 0, 5, 1&
, 1, 5, 2, 5, 5, 1, 5, 2, 0, 0, 2, 1, 0, 0, 1, 6, 2, 1, 4, 1, 1, 6, 1, 8, 0, 0, 0, 2, 0, 0&
, 2, 3, 0, 2, 0, 6, 2, 3, 6, 4, 0, 0, 0, 3, 0, 0, 3, 4, 0, 3, 0, 2, 3, 4, 2, 6, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0&
, 0, 0, 0, 0, 0, 0, 0, 0/), (/4, 4, 20/))
INTEGER :: k, k1, k2, mu
REAL(kind=dp) :: cp, ct, dJ, dJc, dJcc, dJss, dxx, dyy, &
f, fac1, fac2, J, Jc, Jcc, Jss, rr, &