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few opt in cGTOs
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AbdAmmar
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23a242052d
@ -3,7 +3,7 @@ logical function ao_two_e_integral_zero(i,j,k,l)
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integer, intent(in) :: i,j,k,l
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ao_two_e_integral_zero = .False.
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if (.not.(read_ao_two_e_integrals.or.is_periodic)) then
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if (.not.(read_ao_two_e_integrals.or.is_periodic.or.use_cosgtos)) then
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if (ao_overlap_abs(j,l)*ao_overlap_abs(i,k) < ao_integrals_threshold) then
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ao_two_e_integral_zero = .True.
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return
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@ -11,27 +11,25 @@ double precision function ao_two_e_integral_cosgtos(i, j, k, l)
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implicit none
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include 'utils/constants.include.F'
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integer, intent(in) :: i, j, k, l
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integer, intent(in) :: i, j, k, l
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integer :: p, q, r, s
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integer :: num_i, num_j, num_k, num_l, dim1, I_power(3), J_power(3), K_power(3), L_power(3)
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integer :: iorder_p1(3), iorder_p2(3), iorder_q1(3), iorder_q2(3)
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double precision :: coef1, coef2, coef3, coef4
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complex*16 :: I_center(3), J_center(3), K_center(3), L_center(3)
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complex*16 :: expo1, expo2, expo3, expo4
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complex*16 :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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complex*16 :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv
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complex*16 :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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complex*16 :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv
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complex*16 :: integral1, integral2, integral3, integral4
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complex*16 :: integral5, integral6, integral7, integral8
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complex*16 :: integral_tot
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integer :: p, q, r, s
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integer :: num_i, num_j, num_k, num_l, dim1, I_power(3), J_power(3), K_power(3), L_power(3)
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integer :: iorder_p1(3), iorder_p2(3), iorder_p3(3), iorder_p4(3), iorder_q1(3), iorder_q2(3)
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double precision :: coef1, coef2, coef3, coef4
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complex*16 :: I_center(3), J_center(3), K_center(3), L_center(3)
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complex*16 :: expo1, expo2, expo3, expo4
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complex*16 :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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complex*16 :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv
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complex*16 :: P3_new(0:max_dim,3), P3_center(3), fact_p3, pp3, p3_inv
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complex*16 :: P4_new(0:max_dim,3), P4_center(3), fact_p4, pp4, p4_inv
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complex*16 :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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complex*16 :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv
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complex*16 :: integral1, integral2, integral3, integral4
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complex*16 :: integral5, integral6, integral7, integral8
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complex*16 :: integral_tot
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double precision :: ao_2e_cosgtos_schwartz_accel
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complex*16 :: ERI_cosgtos
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complex*16 :: general_primitive_integral_cosgtos
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double precision, external :: ao_2e_cosgtos_schwartz_accel
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complex*16, external :: ERI_cosgtos
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complex*16, external :: general_primitive_integral_cosgtos
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if(ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024) then
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@ -71,19 +69,11 @@ double precision function ao_two_e_integral_cosgtos(i, j, k, l)
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call give_explicit_cpoly_and_cgaussian(P1_new, P1_center, pp1, fact_p1, iorder_p1, &
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expo1, expo2, I_power, J_power, I_center, J_center, dim1)
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p1_inv = (1.d0,0.d0) / pp1
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p1_inv = (1.d0, 0.d0) / pp1
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call give_explicit_cpoly_and_cgaussian(P2_new, P2_center, pp2, fact_p2, iorder_p2, &
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conjg(expo1), expo2, I_power, J_power, I_center, J_center, dim1)
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p2_inv = (1.d0,0.d0) / pp2
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call give_explicit_cpoly_and_cgaussian(P3_new, P3_center, pp3, fact_p3, iorder_p3, &
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expo1, conjg(expo2), I_power, J_power, I_center, J_center, dim1)
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p3_inv = (1.d0,0.d0) / pp3
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call give_explicit_cpoly_and_cgaussian(P4_new, P4_center, pp4, fact_p4, iorder_p4, &
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conjg(expo1), conjg(expo2), I_power, J_power, I_center, J_center, dim1)
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p4_inv = (1.d0,0.d0) / pp4
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p2_inv = (1.d0, 0.d0) / pp2
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do r = 1, ao_prim_num(k)
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coef3 = coef2 * ao_coef_norm_ord_transp_cosgtos(r,k)
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@ -95,35 +85,43 @@ double precision function ao_two_e_integral_cosgtos(i, j, k, l)
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call give_explicit_cpoly_and_cgaussian(Q1_new, Q1_center, qq1, fact_q1, iorder_q1, &
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expo3, expo4, K_power, L_power, K_center, L_center, dim1)
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q1_inv = (1.d0,0.d0) / qq1
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q1_inv = (1.d0, 0.d0) / qq1
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call give_explicit_cpoly_and_cgaussian(Q2_new, Q2_center, qq2, fact_q2, iorder_q2, &
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conjg(expo3), expo4, K_power, L_power, K_center, L_center, dim1)
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q2_inv = (1.d0,0.d0) / qq2
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q2_inv = (1.d0, 0.d0) / qq2
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integral1 = general_primitive_integral_cosgtos(dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral1 = general_primitive_integral_cosgtos(dim1, &
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P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral2 = general_primitive_integral_cosgtos(dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral2 = general_primitive_integral_cosgtos(dim1, &
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P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral3 = general_primitive_integral_cosgtos(dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral3 = general_primitive_integral_cosgtos(dim1, &
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P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral4 = general_primitive_integral_cosgtos(dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral4 = general_primitive_integral_cosgtos(dim1, &
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P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral5 = general_primitive_integral_cosgtos(dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral5 = general_primitive_integral_cosgtos(dim1, &
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conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral6 = general_primitive_integral_cosgtos(dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral6 = general_primitive_integral_cosgtos(dim1, &
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conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral7 = general_primitive_integral_cosgtos(dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral7 = general_primitive_integral_cosgtos(dim1, &
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conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
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Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
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integral8 = general_primitive_integral_cosgtos(dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral8 = general_primitive_integral_cosgtos(dim1, &
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conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
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Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
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integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8
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@ -158,57 +156,57 @@ double precision function ao_two_e_integral_cosgtos(i, j, k, l)
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coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l)
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expo4 = ao_expo_ord_transp_cosgtos(s,l)
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integral1 = ERI_cosgtos( expo1, expo2, expo3, expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral1 = ERI_cosgtos(expo1, expo2, expo3, expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral2 = ERI_cosgtos( expo1, expo2, conjg(expo3), expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral2 = ERI_cosgtos(expo1, expo2, conjg(expo3), expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral3 = ERI_cosgtos( conjg(expo1), expo2, expo3, expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral3 = ERI_cosgtos(conjg(expo1), expo2, expo3, expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral4 = ERI_cosgtos( conjg(expo1), expo2, conjg(expo3), expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral4 = ERI_cosgtos(conjg(expo1), expo2, conjg(expo3), expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral5 = ERI_cosgtos( expo1, conjg(expo2), expo3, expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral5 = ERI_cosgtos(expo1, conjg(expo2), expo3, expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral6 = ERI_cosgtos( expo1, conjg(expo2), conjg(expo3), expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral6 = ERI_cosgtos(expo1, conjg(expo2), conjg(expo3), expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral7 = ERI_cosgtos( conjg(expo1), conjg(expo2), expo3, expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral7 = ERI_cosgtos(conjg(expo1), conjg(expo2), expo3, expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral8 = ERI_cosgtos( conjg(expo1), conjg(expo2), conjg(expo3), expo4 &
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, I_power(1), J_power(1), K_power(1), L_power(1) &
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, I_power(2), J_power(2), K_power(2), L_power(2) &
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, I_power(3), J_power(3), K_power(3), L_power(3) )
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integral8 = ERI_cosgtos(conjg(expo1), conjg(expo2), conjg(expo3), expo4, &
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I_power(1), J_power(1), K_power(1), L_power(1), &
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I_power(2), J_power(2), K_power(2), L_power(2), &
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I_power(3), J_power(3), K_power(3), L_power(3))
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integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8
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ao_two_e_integral_cosgtos = ao_two_e_integral_cosgtos + coef4 * 2.d0 * real(integral_tot)
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enddo ! s
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enddo ! r
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enddo ! q
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enddo ! p
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enddo ! r
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enddo ! q
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enddo ! p
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endif
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endif
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endif ! same centers
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endif ! do schwartz
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end
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@ -228,14 +226,12 @@ double precision function ao_2e_cosgtos_schwartz_accel(i, j, k, l)
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integer :: p, q, r, s
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integer :: num_i, num_j, num_k, num_l, dim1, I_power(3), J_power(3), K_power(3), L_power(3)
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integer :: iorder_p1(3), iorder_p2(3), iorder_p3(3), iorder_p4(3), iorder_q1(3), iorder_q2(3)
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integer :: iorder_p1(3), iorder_p2(3), iorder_q1(3), iorder_q2(3)
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double precision :: coef1, coef2, coef3, coef4
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complex*16 :: I_center(3), J_center(3), K_center(3), L_center(3)
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complex*16 :: expo1, expo2, expo3, expo4
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complex*16 :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
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complex*16 :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv
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complex*16 :: P3_new(0:max_dim,3), P3_center(3), fact_p3, pp3, p3_inv
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complex*16 :: P4_new(0:max_dim,3), P4_center(3), fact_p4, pp4, p4_inv
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complex*16 :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
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complex*16 :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv
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complex*16 :: integral1, integral2, integral3, integral4
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@ -288,47 +284,46 @@ double precision function ao_2e_cosgtos_schwartz_accel(i, j, k, l)
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call give_explicit_cpoly_and_cgaussian(P1_new, P1_center, pp1, fact_p1, iorder_p1, &
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expo1, expo2, K_power, L_power, K_center, L_center, dim1)
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p1_inv = (1.d0,0.d0) / pp1
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p1_inv = (1.d0, 0.d0) / pp1
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call give_explicit_cpoly_and_cgaussian(P2_new, P2_center, pp2, fact_p2, iorder_p2, &
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conjg(expo1), expo2, K_power, L_power, K_center, L_center, dim1)
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p2_inv = (1.d0,0.d0) / pp2
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p2_inv = (1.d0, 0.d0) / pp2
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|
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call give_explicit_cpoly_and_cgaussian(P3_new, P3_center, pp3, fact_p3, iorder_p3, &
|
||||
expo1, conjg(expo2), K_power, L_power, K_center, L_center, dim1)
|
||||
p3_inv = (1.d0,0.d0) / pp3
|
||||
integral1 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian(P4_new, P4_center, pp4, fact_p4, iorder_p4, &
|
||||
conjg(expo1), conjg(expo2), K_power, L_power, K_center, L_center, dim1)
|
||||
p4_inv = (1.d0,0.d0) / pp4
|
||||
integral2 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral1 = general_primitive_integral_cosgtos(dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
integral3 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral2 = general_primitive_integral_cosgtos(dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
integral4 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral3 = general_primitive_integral_cosgtos(dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
integral5 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral4 = general_primitive_integral_cosgtos(dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
integral6 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral5 = general_primitive_integral_cosgtos(dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
integral7 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral6 = general_primitive_integral_cosgtos(dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral7 = general_primitive_integral_cosgtos(dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral8 = general_primitive_integral_cosgtos(dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
integral8 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8
|
||||
|
||||
|
||||
schwartz_kl(s,r) = coef2 * 2.d0 * real(integral_tot)
|
||||
|
||||
schwartz_kl(0,r) = max(schwartz_kl(0,r), schwartz_kl(s,r))
|
||||
@ -346,45 +341,45 @@ double precision function ao_2e_cosgtos_schwartz_accel(i, j, k, l)
|
||||
coef2 = coef1 * ao_coef_norm_ord_transp_cosgtos(q,j)
|
||||
expo2 = ao_expo_ord_transp_cosgtos(q,j)
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( P1_new, P1_center, pp1, fact_p1, iorder_p1 &
|
||||
, expo1, expo2, I_power, J_power, I_center, J_center, dim1 )
|
||||
p1_inv = (1.d0,0.d0) / pp1
|
||||
call give_explicit_cpoly_and_cgaussian(P1_new, P1_center, pp1, fact_p1, iorder_p1, &
|
||||
expo1, expo2, I_power, J_power, I_center, J_center, dim1)
|
||||
p1_inv = (1.d0, 0.d0) / pp1
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( P2_new, P2_center, pp2, fact_p2, iorder_p2 &
|
||||
, conjg(expo1), expo2, I_power, J_power, I_center, J_center, dim1 )
|
||||
p2_inv = (1.d0,0.d0) / pp2
|
||||
call give_explicit_cpoly_and_cgaussian(P2_new, P2_center, pp2, fact_p2, iorder_p2, &
|
||||
conjg(expo1), expo2, I_power, J_power, I_center, J_center, dim1)
|
||||
p2_inv = (1.d0, 0.d0) / pp2
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( P3_new, P3_center, pp3, fact_p3, iorder_p3 &
|
||||
, expo1, conjg(expo2), I_power, J_power, I_center, J_center, dim1 )
|
||||
p3_inv = (1.d0,0.d0) / pp3
|
||||
integral1 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( P4_new, P4_center, pp4, fact_p4, iorder_p4 &
|
||||
, conjg(expo1), conjg(expo2), I_power, J_power, I_center, J_center, dim1 )
|
||||
p4_inv = (1.d0,0.d0) / pp4
|
||||
integral2 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 &
|
||||
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 )
|
||||
integral3 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 &
|
||||
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 )
|
||||
integral4 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 &
|
||||
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 )
|
||||
integral5 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 &
|
||||
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 )
|
||||
integral6 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 &
|
||||
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 )
|
||||
integral7 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1)
|
||||
|
||||
integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 &
|
||||
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 )
|
||||
|
||||
integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 &
|
||||
, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 )
|
||||
|
||||
integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 &
|
||||
, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 )
|
||||
integral8 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2)
|
||||
|
||||
integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8
|
||||
|
||||
@ -404,46 +399,53 @@ double precision function ao_2e_cosgtos_schwartz_accel(i, j, k, l)
|
||||
coef4 = coef3 * ao_coef_norm_ord_transp_cosgtos(s,l)
|
||||
expo4 = ao_expo_ord_transp_cosgtos(s,l)
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q1 &
|
||||
, expo3, expo4, K_power, L_power, K_center, L_center, dim1 )
|
||||
q1_inv = (1.d0,0.d0) / qq1
|
||||
call give_explicit_cpoly_and_cgaussian(Q1_new, Q1_center, qq1, fact_q1, iorder_q1, &
|
||||
expo3, expo4, K_power, L_power, K_center, L_center, dim1)
|
||||
q1_inv = (1.d0, 0.d0) / qq1
|
||||
|
||||
call give_explicit_cpoly_and_cgaussian( Q2_new, Q2_center, qq2, fact_q2, iorder_q2 &
|
||||
, conjg(expo3), expo4, K_power, L_power, K_center, L_center, dim1 )
|
||||
q2_inv = (1.d0,0.d0) / qq2
|
||||
call give_explicit_cpoly_and_cgaussian(Q2_new, Q2_center, qq2, fact_q2, iorder_q2, &
|
||||
conjg(expo3), expo4, K_power, L_power, K_center, L_center, dim1)
|
||||
q2_inv = (1.d0, 0.d0) / qq2
|
||||
|
||||
integral1 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 &
|
||||
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 )
|
||||
integral1 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
|
||||
|
||||
integral2 = general_primitive_integral_cosgtos( dim1, P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1 &
|
||||
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 )
|
||||
integral2 = general_primitive_integral_cosgtos(dim1, &
|
||||
P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p1, &
|
||||
Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
|
||||
|
||||
integral3 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 &
|
||||
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 )
|
||||
integral3 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
|
||||
|
||||
integral4 = general_primitive_integral_cosgtos( dim1, P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2 &
|
||||
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 )
|
||||
integral4 = general_primitive_integral_cosgtos(dim1, &
|
||||
P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p2, &
|
||||
Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
|
||||
|
||||
integral5 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
|
||||
|
||||
integral5 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 &
|
||||
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 )
|
||||
integral6 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P2_new), conjg(P2_center), conjg(fact_p2), conjg(pp2), conjg(p2_inv), iorder_p2, &
|
||||
Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
|
||||
|
||||
integral6 = general_primitive_integral_cosgtos( dim1, P3_new, P3_center, fact_p3, pp3, p3_inv, iorder_p3 &
|
||||
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 )
|
||||
integral7 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1)
|
||||
|
||||
integral7 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 &
|
||||
, Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q1 )
|
||||
|
||||
integral8 = general_primitive_integral_cosgtos( dim1, P4_new, P4_center, fact_p4, pp4, p4_inv, iorder_p4 &
|
||||
, Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2 )
|
||||
integral8 = general_primitive_integral_cosgtos(dim1, &
|
||||
conjg(P1_new), conjg(P1_center), conjg(fact_p1), conjg(pp1), conjg(p1_inv), iorder_p1, &
|
||||
Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q2)
|
||||
|
||||
integral_tot = integral1 + integral2 + integral3 + integral4 + integral5 + integral6 + integral7 + integral8
|
||||
|
||||
ao_2e_cosgtos_schwartz_accel = ao_2e_cosgtos_schwartz_accel + coef4 * 2.d0 * real(integral_tot)
|
||||
enddo ! s
|
||||
enddo ! r
|
||||
enddo ! q
|
||||
enddo ! p
|
||||
enddo ! r
|
||||
enddo ! q
|
||||
enddo ! p
|
||||
|
||||
else
|
||||
|
||||
@ -705,14 +707,6 @@ complex*16 function general_primitive_integral_cosgtos(dim, P_new, P_center, fac
|
||||
p10_2 = pq_inv_2 * p10_1 * q ! 0.5d0*q/(pq + p*p)
|
||||
p01_2 = pq_inv_2 * p01_1 * p ! 0.5d0*p/(q*q + pq)
|
||||
|
||||
! get \sqrt(p + q)
|
||||
!ppq = p + q
|
||||
!ppq_re = REAL (ppq)
|
||||
!ppq_im = AIMAG(ppq)
|
||||
!ppq_mod = dsqrt(ppq_re*ppq_re + ppq_im*ppq_im)
|
||||
!sq_ppq_re = sq_op5 * dsqrt(ppq_re + ppq_mod)
|
||||
!sq_ppq_im = 0.5d0 * ppq_im / sq_ppq_re
|
||||
!sq_ppq = sq_ppq_re + (0.d0, 1.d0) * sq_ppq_im
|
||||
sq_ppq = zsqrt(p + q)
|
||||
|
||||
! ---
|
||||
@ -727,13 +721,13 @@ complex*16 function general_primitive_integral_cosgtos(dim, P_new, P_center, fac
|
||||
do i = 0, iorder_p(1)
|
||||
|
||||
tmp_p = P_new(i,1)
|
||||
tmp_mod = dsqrt(REAL(tmp_p)*REAL(tmp_p) + AIMAG(tmp_p)*AIMAG(tmp_p))
|
||||
tmp_mod = dsqrt(real(tmp_p)*real(tmp_p) + aimag(tmp_p)*aimag(tmp_p))
|
||||
if(tmp_mod < thresh) cycle
|
||||
|
||||
do j = 0, iorder_q(1)
|
||||
|
||||
tmp_q = tmp_p * Q_new(j,1)
|
||||
tmp_mod = dsqrt(REAL(tmp_q)*REAL(tmp_q) + AIMAG(tmp_q)*AIMAG(tmp_q))
|
||||
tmp_mod = dsqrt(real(tmp_q)*real(tmp_q) + aimag(tmp_q)*aimag(tmp_q))
|
||||
if(tmp_mod < thresh) cycle
|
||||
|
||||
!DIR$ FORCEINLINE
|
||||
@ -1089,8 +1083,8 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine give_cpolynom_mult_center_x( P_center, Q_center, a_x, d_x, p, q, n_pt_in &
|
||||
, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, d, n_pt_out)
|
||||
subroutine give_cpolynom_mult_center_x(P_center, Q_center, a_x, d_x, p, q, n_pt_in, &
|
||||
pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, d, n_pt_out)
|
||||
|
||||
BEGIN_DOC
|
||||
! subroutine that returns the explicit polynom in term of the "t"
|
||||
@ -1142,12 +1136,6 @@ subroutine give_cpolynom_mult_center_x( P_center, Q_center, a_x, d_x, p, q, n_pt
|
||||
call I_x1_pol_mult_cosgtos(a_x, d_x, B10, B01, B00, C00, D00, d, n_pt1, n_pt_in)
|
||||
n_pt_out = n_pt1
|
||||
|
||||
! print *, ' '
|
||||
! print *, a_x, d_x
|
||||
! print *, real(B10), real(B01), real(B00), real(C00), real(D00)
|
||||
! print *, n_pt1, real(d(0:n_pt1))
|
||||
! print *, ' '
|
||||
|
||||
if(n_pt1 < 0) then
|
||||
n_pt_out = -1
|
||||
do i = 0, n_pt_in
|
||||
@ -1501,4 +1489,3 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
|
||||
|
||||
@ -44,7 +44,6 @@ double precision function ao_two_e_integral(i, j, k, l)
|
||||
logical, external :: do_schwartz_accel
|
||||
|
||||
if(use_cosgtos) then
|
||||
!print *, ' use_cosgtos for ao_two_e_integral ?', use_cosgtos
|
||||
|
||||
ao_two_e_integral = ao_two_e_integral_cosgtos(i, j, k, l)
|
||||
|
||||
@ -54,17 +53,17 @@ double precision function ao_two_e_integral(i, j, k, l)
|
||||
|
||||
else if (do_schwartz_accel(i,j,k,l)) then
|
||||
|
||||
ao_two_e_integral = ao_two_e_integral_schwartz_accel(i,j,k,l)
|
||||
ao_two_e_integral = ao_two_e_integral_schwartz_accel(i,j,k,l)
|
||||
|
||||
else
|
||||
|
||||
dim1 = n_pt_max_integrals
|
||||
dim1 = n_pt_max_integrals
|
||||
|
||||
num_i = ao_nucl(i)
|
||||
num_j = ao_nucl(j)
|
||||
num_k = ao_nucl(k)
|
||||
num_l = ao_nucl(l)
|
||||
ao_two_e_integral = 0.d0
|
||||
num_i = ao_nucl(i)
|
||||
num_j = ao_nucl(j)
|
||||
num_k = ao_nucl(k)
|
||||
num_l = ao_nucl(l)
|
||||
ao_two_e_integral = 0.d0
|
||||
|
||||
if (num_i /= num_j .or. num_k /= num_l .or. num_j /= num_k)then
|
||||
do p = 1, 3
|
||||
|
||||
@ -1,9 +1,12 @@
|
||||
|
||||
program deb_ao_2e_int
|
||||
|
||||
!call check_ao_two_e_integral_cosgtos()
|
||||
call check_crint1()
|
||||
implicit none
|
||||
|
||||
call check_ao_two_e_integral_cosgtos()
|
||||
!call check_crint1()
|
||||
!call check_crint2()
|
||||
!call check_crint3()
|
||||
|
||||
end
|
||||
|
||||
@ -14,8 +17,8 @@ subroutine check_ao_two_e_integral_cosgtos()
|
||||
implicit none
|
||||
|
||||
integer :: i, j, k, l
|
||||
double precision :: tmp1, tmp2
|
||||
double precision :: acc, nrm, dif
|
||||
double precision :: tmp1, tmp2
|
||||
|
||||
double precision, external :: ao_two_e_integral
|
||||
double precision, external :: ao_two_e_integral_cosgtos
|
||||
@ -23,31 +26,31 @@ subroutine check_ao_two_e_integral_cosgtos()
|
||||
acc = 0.d0
|
||||
nrm = 0.d0
|
||||
|
||||
i = 1
|
||||
j = 6
|
||||
k = 1
|
||||
l = 16
|
||||
! do i = 1, ao_num
|
||||
! do k = 1, ao_num
|
||||
! do j = 1, ao_num
|
||||
! do l = 1, ao_num
|
||||
i = 11
|
||||
j = 100
|
||||
k = 74
|
||||
l = 104
|
||||
! do i = 1, ao_num
|
||||
! do k = 1, ao_num
|
||||
! do j = 1, ao_num
|
||||
! do l = 1, ao_num
|
||||
|
||||
tmp1 = ao_two_e_integral (i, j, k, l)
|
||||
tmp2 = ao_two_e_integral_cosgtos(i, j, k, l)
|
||||
|
||||
dif = dabs(tmp1 - tmp2)
|
||||
if(dif .gt. 1d-12) then
|
||||
dif = abs(tmp1 - tmp2)
|
||||
!if(dif .gt. 1d-10) then
|
||||
print*, ' error on:', i, j, k, l
|
||||
print*, tmp1, tmp2, dif
|
||||
stop
|
||||
endif
|
||||
!stop
|
||||
!endif
|
||||
|
||||
! acc += dif
|
||||
! nrm += dabs(tmp1)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
acc += dif
|
||||
nrm += abs(tmp1)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
print *, ' acc (%) = ', dif * 100.d0 / nrm
|
||||
|
||||
@ -73,8 +76,9 @@ subroutine check_crint1()
|
||||
(+1d+4, +1d+4) /)
|
||||
complex*16 :: rho
|
||||
complex*16 :: int_an, int_nm
|
||||
|
||||
double precision, external :: rint
|
||||
complex*16, external :: crint_1, crint_2, crint_quad
|
||||
complex*16, external :: crint_1, crint_2
|
||||
|
||||
n = 10
|
||||
dif_thr = 1d-7
|
||||
@ -92,9 +96,9 @@ subroutine check_crint1()
|
||||
acc_im = 0.d0
|
||||
nrm_im = 0.d0
|
||||
do i = 0, n
|
||||
!int_an = crint_1 (i, rho)
|
||||
int_an = crint_2 (i, rho)
|
||||
int_nm = crint_quad(i, rho)
|
||||
!int_an = crint_1(i, rho)
|
||||
int_an = crint_2(i, rho)
|
||||
call crint_quad_1(i, rho, 100000000, int_nm)
|
||||
|
||||
dif_re = dabs(real(int_an) - real(int_nm))
|
||||
dif_im = dabs(aimag(int_an) - aimag(int_nm))
|
||||
@ -185,4 +189,144 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine check_crint3()
|
||||
|
||||
implicit none
|
||||
|
||||
integer :: i_test, n_test
|
||||
integer :: nx, ny, n, n_quad
|
||||
integer :: i, seed_size, clock_time
|
||||
double precision :: xr(1:4), x
|
||||
double precision :: yr(1:4), y
|
||||
double precision :: dif_re, dif_im, acc_re, nrm_re, acc_im, nrm_im
|
||||
double precision :: delta_ref
|
||||
double precision :: t1, t2, t_int1, t_int2
|
||||
complex*16 :: rho
|
||||
complex*16 :: int1_old, int1_ref, int2_old, int2_ref
|
||||
integer, allocatable :: seed(:)
|
||||
|
||||
complex*16, external :: crint_2
|
||||
|
||||
call random_seed(size=seed_size)
|
||||
allocate(seed(seed_size))
|
||||
call system_clock(count=clock_time)
|
||||
seed = clock_time + 37 * (/ (i, i=0, seed_size-1) /)
|
||||
!seed = 123456789
|
||||
call random_seed(put=seed)
|
||||
|
||||
|
||||
t_int1 = 0.d0
|
||||
t_int2 = 0.d0
|
||||
|
||||
n_test = 5
|
||||
|
||||
acc_re = 0.d0
|
||||
nrm_re = 0.d0
|
||||
acc_im = 0.d0
|
||||
nrm_im = 0.d0
|
||||
do i_test = 1, n_test
|
||||
|
||||
! Re(rho)
|
||||
call random_number(xr)
|
||||
x = xr(1)
|
||||
if(xr(2) .gt. 0.5d0) x = -x
|
||||
nx = int(15.d0 * xr(3))
|
||||
if(xr(4) .gt. 0.5d0) nx = -nx
|
||||
x = x * 10.d0**nx
|
||||
|
||||
! Im(rho)
|
||||
call random_number(yr)
|
||||
y = yr(1)
|
||||
if(yr(2) .gt. 0.5d0) y = -y
|
||||
ny = int(5.d0 * yr(3))
|
||||
if(yr(4) .gt. 0.5d0) ny = -ny
|
||||
y = y * 10.d0**ny
|
||||
|
||||
rho = x + (0.d0, 1.d0) * y
|
||||
|
||||
call random_number(x)
|
||||
x = 31.d0 * x
|
||||
n = int(x)
|
||||
!if(n.eq.0) cycle
|
||||
|
||||
print*, " n = ", n
|
||||
print*, " rho = ", real(rho), aimag(rho)
|
||||
|
||||
call wall_time(t1)
|
||||
int1_old = crint_2(n, rho)
|
||||
!n_quad = 10000000
|
||||
!call crint_quad_1(n, rho, n_quad, int1_old)
|
||||
!!delta_ref = 1.d0
|
||||
!!do while(delta_ref .gt. 1d-12)
|
||||
!! n_quad = n_quad * 10
|
||||
!! !print*, " delta = ", delta_ref
|
||||
!! !print*, " increasing n_quad to:", n_quad
|
||||
!! call crint_quad_1(n, rho, n_quad, int1_ref)
|
||||
!! delta_ref = abs(int1_ref - int1_old)
|
||||
!! int1_old = int1_ref
|
||||
!! if(n_quad .ge. 1000000000) then
|
||||
!! print*, ' convergence was not reached for crint_quad_1'
|
||||
!! print*, " delta = ", delta_ref
|
||||
!! exit
|
||||
!! endif
|
||||
!!enddo
|
||||
call wall_time(t2)
|
||||
t_int1 = t_int1 + t2 - t1
|
||||
!print*, " n_quad for crint_quad_1:", n_quad
|
||||
|
||||
call wall_time(t1)
|
||||
n_quad = 10000000
|
||||
call crint_quad_12(n, rho, n_quad, int2_old)
|
||||
!delta_ref = 1.d0
|
||||
!do while(delta_ref .gt. 1d-12)
|
||||
! n_quad = n_quad * 10
|
||||
! !print*, " delta = ", delta_ref
|
||||
! !print*, " increasing n_quad to:", n_quad
|
||||
! call crint_quad_12(n, rho, n_quad, int2_ref)
|
||||
! delta_ref = abs(int2_ref - int2_old)
|
||||
! int2_old = int2_ref
|
||||
! if(n_quad .ge. 1000000000) then
|
||||
! print*, ' convergence was not reached for crint_quad_2'
|
||||
! print*, " delta = ", delta_ref
|
||||
! exit
|
||||
! endif
|
||||
!enddo
|
||||
call wall_time(t2)
|
||||
t_int2 = t_int2 + t2 - t1
|
||||
!print*, " n_quad for crint_quad_2:", n_quad
|
||||
|
||||
dif_re = dabs(real(int1_old) - real(int2_old))
|
||||
dif_im = dabs(aimag(int1_old) - aimag(int2_old))
|
||||
if((dif_re .gt. 1d-10) .or. (dif_im .gt. 1d-10)) then
|
||||
print*, ' important error found: '
|
||||
print*, " n = ", n
|
||||
print*, " rho = ", real(rho), aimag(rho)
|
||||
print*, real(int1_old), real(int2_old), dif_re
|
||||
print*, aimag(int1_old), aimag(int2_old), dif_im
|
||||
!stop
|
||||
endif
|
||||
|
||||
if((real(int1_old) /= real(int1_old)) .or. (aimag(int1_old) /= aimag(int1_old)) .or. &
|
||||
(real(int2_old) /= real(int2_old)) .or. (aimag(int2_old) /= aimag(int2_old)) ) then
|
||||
cycle
|
||||
else
|
||||
acc_re += dif_re
|
||||
acc_im += dif_im
|
||||
nrm_re += dabs(real(int1_old))
|
||||
nrm_im += dabs(aimag(int1_old))
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*, "accuracy on real part (%):", 100.d0 * acc_re / (nrm_re + 1d-15)
|
||||
print*, "accuracy on imag part (%):", 100.d0 * acc_im / (nrm_im + 1d-15)
|
||||
|
||||
print*, "crint_quad_1 wall time (sec) = ", t_int1
|
||||
print*, "crint_quad_2 wall time (sec) = ", t_int2
|
||||
|
||||
|
||||
deallocate(seed)
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
|
||||
@ -145,68 +145,6 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
!subroutine give_explicit_poly_and_gaussian_double(P_new,P_center,p,fact_k,iorder,alpha,beta,gama,a,b,A_center,B_center,Nucl_center,dim)
|
||||
! BEGIN_DOC
|
||||
! ! Transforms the product of
|
||||
! ! (x-x_A)^a(1) (x-x_B)^b(1) (x-x_A)^a(2) (y-y_B)^b(2) (z-z_A)^a(3) (z-z_B)^b(3)
|
||||
! ! exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta) exp(-(r-Nucl_center)^2 gama
|
||||
! !
|
||||
! ! into
|
||||
! ! fact_k * [ sum (l_x = 0,i_order(1)) P_new(l_x,1) * (x-P_center(1))^l_x ] exp (- p (x-P_center(1))^2 )
|
||||
! ! * [ sum (l_y = 0,i_order(2)) P_new(l_y,2) * (y-P_center(2))^l_y ] exp (- p (y-P_center(2))^2 )
|
||||
! ! * [ sum (l_z = 0,i_order(3)) P_new(l_z,3) * (z-P_center(3))^l_z ] exp (- p (z-P_center(3))^2 )
|
||||
! END_DOC
|
||||
! implicit none
|
||||
! include 'constants.include.F'
|
||||
! integer, intent(in) :: dim
|
||||
! integer, intent(in) :: a(3),b(3) ! powers : (x-xa)**a_x = (x-A(1))**a(1)
|
||||
! double precision, intent(in) :: alpha, beta, gama ! exponents
|
||||
! double precision, intent(in) :: A_center(3) ! A center
|
||||
! double precision, intent(in) :: B_center (3) ! B center
|
||||
! double precision, intent(in) :: Nucl_center(3) ! B center
|
||||
! double precision, intent(out) :: P_center(3) ! new center
|
||||
! double precision, intent(out) :: p ! new exponent
|
||||
! double precision, intent(out) :: fact_k ! constant factor
|
||||
! double precision, intent(out) :: P_new(0:max_dim,3)! polynomial
|
||||
! integer , intent(out) :: iorder(3) ! i_order(i) = order of the polynomials
|
||||
!
|
||||
! double precision :: P_center_tmp(3) ! new center
|
||||
! double precision :: p_tmp ! new exponent
|
||||
! double precision :: fact_k_tmp,fact_k_bis ! constant factor
|
||||
! double precision :: P_new_tmp(0:max_dim,3)! polynomial
|
||||
! integer :: i,j
|
||||
! double precision :: binom_func
|
||||
!
|
||||
! ! First you transform the two primitives into a sum of primitive with the same center P_center_tmp and gaussian exponent p_tmp
|
||||
! call give_explicit_cpoly_and_cgaussian(P_new_tmp,P_center_tmp,p_tmp,fact_k_tmp,iorder,alpha,beta,a,b,A_center,B_center,dim)
|
||||
! ! Then you create the new gaussian from the product of the new one per the Nuclei one
|
||||
! call cgaussian_product(p_tmp,P_center_tmp,gama,Nucl_center,fact_k_bis,p,P_center)
|
||||
! fact_k = fact_k_bis * fact_k_tmp
|
||||
!
|
||||
! ! Then you build the coefficient of the new polynom
|
||||
! do i = 0, iorder(1)
|
||||
! P_new(i,1) = 0.d0
|
||||
! do j = i,iorder(1)
|
||||
! P_new(i,1) = P_new(i,1) + P_new_tmp(j,1) * binom_func(j,j-i) * (P_center(1) - P_center_tmp(1))**(j-i)
|
||||
! enddo
|
||||
! enddo
|
||||
! do i = 0, iorder(2)
|
||||
! P_new(i,2) = 0.d0
|
||||
! do j = i,iorder(2)
|
||||
! P_new(i,2) = P_new(i,2) + P_new_tmp(j,2) * binom_func(j,j-i) * (P_center(2) - P_center_tmp(2))**(j-i)
|
||||
! enddo
|
||||
! enddo
|
||||
! do i = 0, iorder(3)
|
||||
! P_new(i,3) = 0.d0
|
||||
! do j = i,iorder(3)
|
||||
! P_new(i,3) = P_new(i,3) + P_new_tmp(j,3) * binom_func(j,j-i) * (P_center(3) - P_center_tmp(3))**(j-i)
|
||||
! enddo
|
||||
! enddo
|
||||
!
|
||||
!end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine cgaussian_product(a, xa, b, xb, k, p, xp)
|
||||
|
||||
BEGIN_DOC
|
||||
@ -237,7 +175,7 @@ subroutine cgaussian_product(a, xa, b, xb, k, p, xp)
|
||||
ab = a * b * p_inv
|
||||
|
||||
k = ab * (xab(1)*xab(1) + xab(2)*xab(2) + xab(3)*xab(3))
|
||||
tmp_mod = dsqrt(REAL(k)*REAL(k) + AIMAG(k)*AIMAG(k))
|
||||
tmp_mod = dsqrt(real(k)*real(k) + aimag(k)*aimag(k))
|
||||
if(tmp_mod .gt. 40.d0) then
|
||||
k = (0.d0, 0.d0)
|
||||
xp(1:3) = (0.d0, 0.d0)
|
||||
@ -245,9 +183,9 @@ subroutine cgaussian_product(a, xa, b, xb, k, p, xp)
|
||||
endif
|
||||
|
||||
k = zexp(-k)
|
||||
xp(1) = ( a * xa(1) + b * xb(1) ) * p_inv
|
||||
xp(2) = ( a * xa(2) + b * xb(2) ) * p_inv
|
||||
xp(3) = ( a * xa(3) + b * xb(3) ) * p_inv
|
||||
xp(1) = (a * xa(1) + b * xb(1)) * p_inv
|
||||
xp(2) = (a * xa(2) + b * xb(2)) * p_inv
|
||||
xp(3) = (a * xa(3) + b * xb(3)) * p_inv
|
||||
|
||||
end
|
||||
|
||||
@ -309,8 +247,6 @@ subroutine multiply_cpoly(b, nb, c, nc, d, nd)
|
||||
integer, intent(out) :: nd
|
||||
|
||||
integer :: ndtmp, ib, ic
|
||||
double precision :: tmp_mod
|
||||
complex*16 :: tmp
|
||||
|
||||
if(ior(nc, nb) >= 0) then ! True if nc>=0 and nb>=0
|
||||
continue
|
||||
@ -332,9 +268,7 @@ subroutine multiply_cpoly(b, nb, c, nc, d, nd)
|
||||
enddo
|
||||
|
||||
do nd = ndtmp, 0, -1
|
||||
tmp = d(nd)
|
||||
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
||||
if(tmp_mod .lt. 1.d-15) cycle
|
||||
if(abs(d(nd)) .lt. 1.d-15) cycle
|
||||
exit
|
||||
enddo
|
||||
|
||||
@ -432,47 +366,42 @@ subroutine recentered_cpoly2(P_A, x_A, x_P, a, P_B, x_B, x_Q, b)
|
||||
complex*16, intent(in) :: x_A, x_P, x_B, x_Q
|
||||
complex*16, intent(out) :: P_A(0:a), P_B(0:b)
|
||||
|
||||
integer :: i, minab, maxab
|
||||
complex*16 :: pows_a(-2:a+b+4), pows_b(-2:a+b+4)
|
||||
integer :: i
|
||||
integer :: maxbinom
|
||||
complex*16 :: pows_a(0:a+b+2), pows_b(0:a+b+2)
|
||||
|
||||
double precision :: binom_func
|
||||
|
||||
if((a<0) .or. (b<0)) return
|
||||
if((a < 0) .or. (b < 0)) return
|
||||
|
||||
maxab = max(a, b)
|
||||
minab = max(min(a, b), 0)
|
||||
maxbinom = size(binom_transp, 1)
|
||||
|
||||
pows_a(0) = (1.d0, 0.d0)
|
||||
pows_a(1) = x_P - x_A
|
||||
do i = 2, a
|
||||
pows_a(i) = pows_a(i-1) * pows_a(1)
|
||||
enddo
|
||||
|
||||
pows_b(0) = (1.d0, 0.d0)
|
||||
pows_b(1) = x_Q - x_B
|
||||
|
||||
do i = 2, maxab
|
||||
pows_a(i) = pows_a(i-1) * pows_a(1)
|
||||
do i = 2, b
|
||||
pows_b(i) = pows_b(i-1) * pows_b(1)
|
||||
enddo
|
||||
|
||||
P_A(0) = pows_a(a)
|
||||
do i = 1, min(a, maxbinom)
|
||||
P_A(i) = binom_transp(i,a) * pows_a(a-i)
|
||||
enddo
|
||||
do i = maxbinom+1, a
|
||||
P_A(i) = binom_func(a, i) * pows_a(a-i)
|
||||
enddo
|
||||
|
||||
P_B(0) = pows_b(b)
|
||||
|
||||
do i = 1, min(minab, 20)
|
||||
P_A(i) = binom_transp(a-i,a) * pows_a(a-i)
|
||||
P_B(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||||
do i = 1, min(b, maxbinom)
|
||||
P_B(i) = binom_transp(i,b) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
do i = minab+1, min(a, 20)
|
||||
P_A(i) = binom_transp(a-i,a) * pows_a(a-i)
|
||||
enddo
|
||||
do i = minab+1, min(b, 20)
|
||||
P_B(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
do i = 101, a
|
||||
P_A(i) = binom_func(a,a-i) * pows_a(a-i)
|
||||
enddo
|
||||
do i = 101, b
|
||||
P_B(i) = binom_func(b,b-i) * pows_b(b-i)
|
||||
do i = maxbinom+1, b
|
||||
P_B(i) = binom_func(b, i) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
end
|
||||
|
||||
@ -68,66 +68,6 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
complex*16 function crint_quad(n, rho)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n
|
||||
complex*16, intent(in) :: rho
|
||||
|
||||
integer :: i_quad, n_quad
|
||||
double precision :: tmp_inv, tmp
|
||||
|
||||
n_quad = 1000000000
|
||||
tmp_inv = 1.d0 / dble(n_quad)
|
||||
|
||||
!crint_quad = 0.5d0 * zexp(-rho)
|
||||
!do i_quad = 1, n_quad - 1
|
||||
! tmp = tmp_inv * dble(i_quad)
|
||||
! tmp = tmp * tmp
|
||||
! crint_quad += zexp(-rho*tmp) * tmp**n
|
||||
!enddo
|
||||
!crint_quad = crint_quad * tmp_inv
|
||||
|
||||
!crint_quad = 0.5d0 * zexp(-rho)
|
||||
!do i_quad = 1, n_quad - 1
|
||||
! tmp = tmp_inv * dble(i_quad)
|
||||
! crint_quad += zexp(-rho*tmp) * tmp**n / dsqrt(tmp)
|
||||
!enddo
|
||||
!crint_quad = crint_quad * 0.5d0 * tmp_inv
|
||||
|
||||
! Composite Boole's Rule
|
||||
crint_quad = 7.d0 * zexp(-rho)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp = tmp_inv * dble(i_quad)
|
||||
tmp = tmp * tmp
|
||||
if(modulo(i_quad, 4) .eq. 0) then
|
||||
crint_quad += 14.d0 * zexp(-rho*tmp) * tmp**n
|
||||
else if(modulo(i_quad, 2) .eq. 0) then
|
||||
crint_quad += 12.d0 * zexp(-rho*tmp) * tmp**n
|
||||
else
|
||||
crint_quad += 32.d0 * zexp(-rho*tmp) * tmp**n
|
||||
endif
|
||||
enddo
|
||||
crint_quad = crint_quad * 2.d0 * tmp_inv / 45.d0
|
||||
|
||||
! Composite Simpson's 3/8 rule
|
||||
!crint_quad = zexp(-rho)
|
||||
!do i_quad = 1, n_quad - 1
|
||||
! tmp = tmp_inv * dble(i_quad)
|
||||
! tmp = tmp * tmp
|
||||
! if(modulo(i_quad, 3) .eq. 0) then
|
||||
! crint_quad += 2.d0 * zexp(-rho*tmp) * tmp**n
|
||||
! else
|
||||
! crint_quad += 3.d0 * zexp(-rho*tmp) * tmp**n
|
||||
! endif
|
||||
!enddo
|
||||
!crint_quad = crint_quad * 3.d0 * tmp_inv / 8.d0
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
complex*16 function crint_sum_1(n_pt_out, rho, d1)
|
||||
|
||||
implicit none
|
||||
@ -283,20 +223,21 @@ complex*16 function crint_2(n, rho)
|
||||
integer, intent(in) :: n
|
||||
complex*16, intent(in) :: rho
|
||||
|
||||
double precision :: tmp
|
||||
complex*16 :: rho2
|
||||
complex*16 :: vals(0:n)
|
||||
complex*16, external :: crint_smallz
|
||||
double precision :: tmp
|
||||
complex*16 :: rho2
|
||||
complex*16 :: vals(0:n)
|
||||
|
||||
complex*16, external :: crint_smallz
|
||||
|
||||
if(abs(rho) < 10.d0) then
|
||||
|
||||
if(abs(rho) .lt. 1d-6) then
|
||||
tmp = 2.d0 * dble(n)
|
||||
tmp = dble(n + n)
|
||||
rho2 = rho * rho
|
||||
crint_2 = 1.d0 / (tmp + 1.d0) &
|
||||
- rho / (tmp + 3.d0) &
|
||||
+ 0.5d0 * rho2 / (tmp + 5.d0) &
|
||||
- 0.16666666666666666d0 * rho * rho2 / (tmp + 7.d0)
|
||||
crint_2 = - 0.16666666666666666d0 * rho * rho2 / (tmp + 7.d0) &
|
||||
+ 0.5d0 * rho2 / (tmp + 5.d0) &
|
||||
- rho / (tmp + 3.d0) &
|
||||
+ 1.d0 / (tmp + 1.d0)
|
||||
else
|
||||
crint_2 = crint_smallz(n, rho)
|
||||
endif
|
||||
@ -328,6 +269,9 @@ subroutine zboysfun(n_max, x, vals)
|
||||
! Input: x --- argument, complex*16, Re(x) >= 0
|
||||
! Output: vals --- values of the Boys function, n = 0, 1, ..., n_max
|
||||
!
|
||||
! Beylkin & Sharma, J. Chem. Phys. 155, 174117 (2021)
|
||||
! https://doi.org/10.1063/5.0062444
|
||||
!
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
@ -363,6 +307,9 @@ subroutine zboysfunnrp(n_max, x, vals)
|
||||
! Input: x --- argument, complex *16 Re(x)<=0
|
||||
! Output: vals --- values of e^z F(n,z), n = 0, 1, ..., n_max
|
||||
!
|
||||
! Beylkin & Sharma, J. Chem. Phys. 155, 174117 (2021)
|
||||
! https://doi.org/10.1063/5.0062444
|
||||
!
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
@ -398,17 +345,12 @@ complex*16 function crint_sum_2(n_pt_out, rho, d1)
|
||||
|
||||
complex*16, allocatable :: vals(:)
|
||||
|
||||
!complex*16, external :: crint_2
|
||||
!crint_sum_2 = (0.d0, 0.d0)
|
||||
!do i = 0, n_pt_out, 2
|
||||
! n = shiftr(i, 1)
|
||||
! crint_sum_2 = crint_sum_2 + d1(i) * crint_2(n, rho)
|
||||
!enddo
|
||||
|
||||
n_max = shiftr(n_pt_out, 1)
|
||||
|
||||
allocate(vals(0:n_max))
|
||||
|
||||
call crint_2_vec(n_max, rho, vals)
|
||||
! FOR DEBUG
|
||||
!call crint_quad_12_vec(n_max, rho, vals)
|
||||
|
||||
crint_sum_2 = d1(0) * vals(0)
|
||||
do i = 2, n_pt_out, 2
|
||||
@ -444,16 +386,22 @@ subroutine crint_2_vec(n_max, rho, vals)
|
||||
|
||||
! use finite expansion for very small rho
|
||||
|
||||
! rho^2 / 2
|
||||
rho2 = 0.5d0 * rho * rho
|
||||
! rho^3 / 6
|
||||
rho3 = 0.3333333333333333d0 * rho * rho2
|
||||
!! rho^2 / 2
|
||||
!rho2 = 0.5d0 * rho * rho
|
||||
!! rho^3 / 6
|
||||
!rho3 = 0.3333333333333333d0 * rho * rho2
|
||||
!vals(0) = 1.d0 - 0.3333333333333333d0 * rho + 0.2d0 * rho2 - 0.14285714285714285d0 * rho3
|
||||
!do n = 1, n_max
|
||||
! tmp = 2.d0 * dble(n)
|
||||
! vals(n) = 1.d0 / (tmp + 1.d0) - rho / (tmp + 3.d0) &
|
||||
! + rho2 / (tmp + 5.d0) - rho3 / (tmp + 7.d0)
|
||||
!enddo
|
||||
|
||||
vals(0) = 1.d0 - 0.3333333333333333d0 * rho + 0.2d0 * rho2 - 0.14285714285714285d0 * rho3
|
||||
! TODO (last term)
|
||||
vals(0) = 1.d0 + rho * (-0.3333333333333333d0 + rho*(0.1d0 - 0.047619047619047616d0*rho))
|
||||
do n = 1, n_max
|
||||
tmp = 2.d0 * dble(n)
|
||||
vals(n) = 1.d0 / (tmp + 1.d0) - rho / (tmp + 3.d0) &
|
||||
+ rho2 / (tmp + 5.d0) - rho3 / (tmp + 7.d0)
|
||||
vals(n) = 1.d0 / (tmp + 1.d0) + rho * (-1.d0/(tmp+3.d0) + rho*(0.5d0/(tmp+5.d0) - 0.3333333333333333d0*rho/(tmp+7.d0)))
|
||||
enddo
|
||||
|
||||
else
|
||||
@ -541,3 +489,268 @@ end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine crint_quad_1(n, rho, n_quad, crint_quad)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, n_quad
|
||||
complex*16, intent(in) :: rho
|
||||
complex*16, intent(out) :: crint_quad
|
||||
|
||||
integer :: i_quad
|
||||
double precision :: tmp_inv, tmp0, tmp1, tmp2
|
||||
double precision :: coef(0:3) = (/14.d0, 32.d0, 12.d0, 32.d0 /)
|
||||
|
||||
tmp_inv = 1.d0 / dble(n_quad)
|
||||
|
||||
crint_quad = 7.d0 * zexp(-rho)
|
||||
|
||||
tmp0 = 0.d0
|
||||
select case (n)
|
||||
|
||||
case (0)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1)
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case (1)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1) * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case (2)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1) * tmp1 * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case (3)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1) * tmp1 * tmp1 * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case (4)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
tmp2 = tmp1 * tmp1
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1) * tmp2 * tmp2
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case default
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1) * tmp1**n
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
end select
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine crint_quad_2(n, rho, n_quad, crint_quad)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, n_quad
|
||||
complex*16, intent(in) :: rho
|
||||
complex*16, intent(out) :: crint_quad
|
||||
|
||||
integer :: i_quad
|
||||
double precision :: tmp_inv, tmp0, tmp1, tmp2
|
||||
double precision :: coef(0:3) = (/14.d0, 32.d0, 12.d0, 32.d0 /)
|
||||
complex*16 :: rhoc, rhoe
|
||||
|
||||
tmp_inv = 1.d0 / dble(n_quad)
|
||||
|
||||
crint_quad = 7.d0 * zexp(-rho)
|
||||
|
||||
tmp0 = 0.d0
|
||||
rhoc = zexp(-rho*tmp_inv)
|
||||
rhoe = (1.d0, 0.d0)
|
||||
select case (n)
|
||||
|
||||
case (0)
|
||||
!do i_quad = 1, n_quad - 1
|
||||
! tmp0 = tmp0 + tmp_inv
|
||||
! rhoe = rhoe * rhoc
|
||||
! tmp1 = (rhoe - 1.d0) / dsqrt(tmp0)
|
||||
! crint_quad = crint_quad + coef(iand(i_quad, 3)) * tmp1
|
||||
!enddo
|
||||
!crint_quad = 1.d0 + crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe / dsqrt(tmp0)
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (1)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (2)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (3)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0 * tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (4)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
tmp2 = tmp1 * tmp1 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp2
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case default
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0**n / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
end select
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine crint_quad_12(n, rho, n_quad, crint_quad)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, n_quad
|
||||
complex*16, intent(in) :: rho
|
||||
complex*16, intent(out) :: crint_quad
|
||||
|
||||
integer :: i_quad
|
||||
double precision :: tmp_inv, tmp0, tmp1, tmp2
|
||||
double precision :: coef(0:3) = (/14.d0, 32.d0, 12.d0, 32.d0 /)
|
||||
complex*16 :: rhoc, rhoe
|
||||
|
||||
tmp_inv = 1.d0 / dble(n_quad)
|
||||
|
||||
crint_quad = 7.d0 * zexp(-rho)
|
||||
|
||||
tmp0 = 0.d0
|
||||
rhoc = zexp(-rho*tmp_inv)
|
||||
rhoe = (1.d0, 0.d0)
|
||||
select case (n)
|
||||
|
||||
case (0)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * zexp(-rho*tmp1)
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.044444444444444446d0 * tmp_inv
|
||||
|
||||
case (1)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (2)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (3)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0 * tmp0 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case (4)
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0 * tmp0
|
||||
tmp2 = tmp1 * tmp1 / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp2
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
case default
|
||||
do i_quad = 1, n_quad - 1
|
||||
tmp0 = tmp0 + tmp_inv
|
||||
tmp1 = tmp0**n / dsqrt(tmp0)
|
||||
rhoe = rhoe * rhoc
|
||||
crint_quad = crint_quad + coef(iand(i_quad, 3)) * rhoe * tmp1
|
||||
enddo
|
||||
crint_quad = crint_quad * 0.022222222222222223d0 * tmp_inv
|
||||
|
||||
end select
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine crint_quad_12_vec(n_max, rho, vals)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n_max
|
||||
complex*16, intent(in) :: rho
|
||||
complex*16, intent(out) :: vals(0:n_max)
|
||||
|
||||
integer :: n
|
||||
double precision :: tmp, abs_rho
|
||||
complex*16 :: rho2, rho3, erho
|
||||
|
||||
do n = 1, n_max
|
||||
call crint_quad_12(n, rho, 10000000, vals(n))
|
||||
enddo
|
||||
|
||||
return
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
|
||||
@ -143,7 +143,7 @@ complex*16 function erf_G(x, yabs)
|
||||
idble = dble(i)
|
||||
tmp0 = 0.5d0 * idble
|
||||
tmp1 = tmp0 * tmp0 + x2
|
||||
tmp2 = dexp( idble * yabs - tmp1 - dlog(tmp1) - dlog_2pi) * (x - (0.d0, 1.d0)*tmp0)
|
||||
tmp2 = dexp(idble * yabs - tmp1 - dlog(tmp1) - dlog_2pi) * (x - (0.d0, 1.d0)*tmp0)
|
||||
|
||||
erf_G = erf_G + tmp2
|
||||
|
||||
@ -340,8 +340,8 @@ subroutine zboysfun00(z, val)
|
||||
if(abs(z) .ge. 100.0d0) then
|
||||
|
||||
! large |z|
|
||||
z1 = 1.0d0 / zsqrt(z)
|
||||
y = 1.0d0 / z
|
||||
z1 = (1.0d0, 0.d0) / zsqrt(z)
|
||||
y = (1.0d0, 0.d0) / z
|
||||
val = asymcoef(7)
|
||||
do k = 6, 1, -1
|
||||
val = val * y + asymcoef(k)
|
||||
@ -389,6 +389,8 @@ subroutine zboysfun00nrp(z, val)
|
||||
!
|
||||
END_DOC
|
||||
|
||||
include 'constants.include.F'
|
||||
|
||||
implicit none
|
||||
|
||||
double precision, parameter :: asymcoef(1:7) = (/ -0.499999999999999799d0, &
|
||||
@ -413,7 +415,6 @@ subroutine zboysfun00nrp(z, val)
|
||||
|
||||
double precision, parameter :: tol = 1.0d-03
|
||||
double precision, parameter :: sqpio2 = 0.886226925452758014d0 ! sqrt(pi)/2
|
||||
double precision, parameter :: pi = 3.14159265358979324d0
|
||||
double precision, parameter :: etmax = 25.7903399171930621d0
|
||||
double precision, parameter :: etmax1 = 26.7903399171930621d0
|
||||
complex*16, parameter :: ima = (0.d0, 1.d0)
|
||||
@ -452,40 +453,40 @@ subroutine zboysfun00nrp(z, val)
|
||||
0.03112676196932382d0, &
|
||||
0.013576229705876844d0 /)
|
||||
|
||||
double precision, parameter :: qq (1:16) = (/ 0.0007243228510223928d0, &
|
||||
0.01980651726441906d0, &
|
||||
0.11641097769229371d0, &
|
||||
0.38573968881461146d0, &
|
||||
0.9414671037609641d0, &
|
||||
1.8939510935716377d0, &
|
||||
3.3275564293459383d0, &
|
||||
5.280587297262129d0, &
|
||||
7.730992222360452d0, &
|
||||
10.590207725831563d0, &
|
||||
13.706359477128965d0, &
|
||||
16.876705473663804d0, &
|
||||
19.867876155236257d0, &
|
||||
22.441333930203022d0, &
|
||||
24.380717439613566d0, &
|
||||
25.51771075067431d0 /)
|
||||
double precision, parameter :: qq(1:16) = (/ 0.0007243228510223928d0, &
|
||||
0.01980651726441906d0, &
|
||||
0.11641097769229371d0, &
|
||||
0.38573968881461146d0, &
|
||||
0.9414671037609641d0, &
|
||||
1.8939510935716377d0, &
|
||||
3.3275564293459383d0, &
|
||||
5.280587297262129d0, &
|
||||
7.730992222360452d0, &
|
||||
10.590207725831563d0, &
|
||||
13.706359477128965d0, &
|
||||
16.876705473663804d0, &
|
||||
19.867876155236257d0, &
|
||||
22.441333930203022d0, &
|
||||
24.380717439613566d0, &
|
||||
25.51771075067431d0 /)
|
||||
|
||||
|
||||
double precision, parameter :: qq1 (1:16) = (/ 0.0007524078957852004d0,&
|
||||
0.020574499281252233d0, &
|
||||
0.12092472113522865d0, &
|
||||
0.40069643967765295d0, &
|
||||
0.9779717449089211d0, &
|
||||
1.9673875468969015d0, &
|
||||
3.4565797939091802d0, &
|
||||
5.485337886599723d0, &
|
||||
8.030755321535683d0, &
|
||||
11.000834641174064d0, &
|
||||
14.237812708111456d0, &
|
||||
17.531086359214406d0, &
|
||||
20.6382373144543d0, &
|
||||
23.31147887603379d0, &
|
||||
25.326060444703632d0, &
|
||||
26.507139770710722d0 /)
|
||||
double precision, parameter :: qq1(1:16) = (/ 0.0007524078957852004d0,&
|
||||
0.020574499281252233d0, &
|
||||
0.12092472113522865d0, &
|
||||
0.40069643967765295d0, &
|
||||
0.9779717449089211d0, &
|
||||
1.9673875468969015d0, &
|
||||
3.4565797939091802d0, &
|
||||
5.485337886599723d0, &
|
||||
8.030755321535683d0, &
|
||||
11.000834641174064d0, &
|
||||
14.237812708111456d0, &
|
||||
17.531086359214406d0, &
|
||||
20.6382373144543d0, &
|
||||
23.31147887603379d0, &
|
||||
25.326060444703632d0, &
|
||||
26.507139770710722d0 /)
|
||||
|
||||
double precision, parameter :: uu(1:16) = (/ 0.9992759394074501d0, &
|
||||
0.9803883431758104d0, &
|
||||
@ -532,8 +533,8 @@ subroutine zboysfun00nrp(z, val)
|
||||
|
||||
if(abs(z) .ge. 100.0d0) then
|
||||
! large |z|
|
||||
z1 = 1.0d0 / zsqrt(z)
|
||||
y = 1.0d0 / z
|
||||
z1 = (1.0d0, 0.d0) / zsqrt(z)
|
||||
y = (1.0d0, 0.d0) / z
|
||||
val = asymcoef(7)
|
||||
do k = 6, 1, -1
|
||||
val = val * y + asymcoef(k)
|
||||
@ -560,13 +561,13 @@ subroutine zboysfun00nrp(z, val)
|
||||
zsum = zsum + ww(k) * (zz - uu(k)) / (qq(k) + z)
|
||||
else
|
||||
q = z + qq(k)
|
||||
p = 1.0d0 - 0.5d0*q + q*q/6.0d0 - q*q*q/24.0d0 + q*q*q*q/120.0d0
|
||||
zsum = zsum + ww(k) * p *zz
|
||||
p = q * (0.041666666666666664d0*q * (q * (0.2d0*q - 1.d0) + 4.d0) - 0.5d0) + 1.d0
|
||||
zsum = zsum + ww(k) * p * zz
|
||||
endif
|
||||
enddo
|
||||
zt = ima * sqrt(z / etmax)
|
||||
zt = ima * zsqrt(z / etmax)
|
||||
tmp = 0.5d0 * ima * log((1.0d0 - zt) / (1.0d0 + zt))
|
||||
val = sqrt(etmax) * zsum / sqrt(pi) + zz * tmp / sqrt(pi*z)
|
||||
val = dsqrt(etmax) * zsum * inv_sq_pi + zz * tmp / zsqrt(pi*z)
|
||||
else
|
||||
zsum = (0.d0, 0.d0)
|
||||
do k = 1, 16
|
||||
@ -574,13 +575,14 @@ subroutine zboysfun00nrp(z, val)
|
||||
zsum = zsum + ww(k) * (zz - uu1(k)) / (qq1(k) + z)
|
||||
else
|
||||
q = z + qq1(k)
|
||||
p = 1.0d0 - 0.5d0*q + q*q/6.0d0 - q*q*q/24.0d0 + q*q*q*q/120.0d0
|
||||
!p = 1.0d0 - 0.5d0*q + q*q/6.0d0 - q*q*q/24.0d0 + q*q*q*q/120.0d0
|
||||
p = q * (0.041666666666666664d0*q * (q * (0.2d0*q - 1.d0) + 4.d0) - 0.5d0) + 1.d0
|
||||
zsum = zsum + ww(k) * p * zz
|
||||
endif
|
||||
enddo
|
||||
zt = ima * zsqrt(z / etmax1)
|
||||
tmp = 0.5d0 * ima * log((1.0d0 - zt) / (1.0d0 + zt))
|
||||
val = dsqrt(etmax1) * zsum / dsqrt(pi) + zz * tmp / zsqrt(pi*z)
|
||||
val = dsqrt(etmax1) * zsum * inv_sq_pi + zz * tmp / zsqrt(pi*z)
|
||||
endif
|
||||
|
||||
return
|
||||
|
||||
@ -1008,50 +1008,78 @@ subroutine recentered_poly2_v0(P_new, lda, x_A, LD_xA, x_P, a, n_points)
|
||||
deallocate(pows_a)
|
||||
!deallocate(pows_b)
|
||||
|
||||
end subroutine recentered_poly2_v0
|
||||
|
||||
subroutine recentered_poly2(P_new,x_A,x_P,a,P_new2,x_B,x_Q,b)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Recenter two polynomials
|
||||
END_DOC
|
||||
integer, intent(in) :: a,b
|
||||
double precision, intent(in) :: x_A,x_P,x_B,x_Q
|
||||
double precision, intent(out) :: P_new(0:a),P_new2(0:b)
|
||||
double precision :: pows_a(-2:a+b+4), pows_b(-2:a+b+4)
|
||||
double precision :: binom_func
|
||||
integer :: i,j,k,l, minab, maxab
|
||||
if ((a<0).or.(b<0) ) return
|
||||
maxab = max(a,b)
|
||||
minab = max(min(a,b),0)
|
||||
pows_a(0) = 1.d0
|
||||
pows_a(1) = (x_P - x_A)
|
||||
pows_b(0) = 1.d0
|
||||
pows_b(1) = (x_Q - x_B)
|
||||
do i = 2,maxab
|
||||
pows_a(i) = pows_a(i-1)*pows_a(1)
|
||||
pows_b(i) = pows_b(i-1)*pows_b(1)
|
||||
enddo
|
||||
P_new (0) = pows_a(a)
|
||||
P_new2(0) = pows_b(b)
|
||||
do i = 1,min(minab,20)
|
||||
P_new (i) = binom_transp(a-i,a) * pows_a(a-i)
|
||||
P_new2(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||||
enddo
|
||||
do i = minab+1,min(a,20)
|
||||
P_new (i) = binom_transp(a-i,a) * pows_a(a-i)
|
||||
enddo
|
||||
do i = minab+1,min(b,20)
|
||||
P_new2(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||||
enddo
|
||||
do i = 101,a
|
||||
P_new(i) = binom_func(a,a-i) * pows_a(a-i)
|
||||
enddo
|
||||
do i = 101,b
|
||||
P_new2(i) = binom_func(b,b-i) * pows_b(b-i)
|
||||
enddo
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine recentered_poly2(P_new, x_A, x_P, a, Q_new, x_B, x_Q, b)
|
||||
|
||||
BEGIN_DOC
|
||||
!
|
||||
! Recenter two polynomials:
|
||||
!
|
||||
! (x - x_A)^a -> \sum_{i=0}^{a} \binom{a}{i} (x_A - x_P)^{a-i} (x - x_P)^i
|
||||
! (x - x_B)^b -> \sum_{i=0}^{b} \binom{b}{i} (x_B - x_Q)^{b-i} (x - x_Q)^i
|
||||
!
|
||||
! where:
|
||||
! \binom{a}{i} = \binom{a}{a-i} = a! / [i! (a-i)!]
|
||||
!
|
||||
END_DOC
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: a, b
|
||||
double precision, intent(in) :: x_A, x_P, x_B, x_Q
|
||||
double precision, intent(out) :: P_new(0:a), Q_new(0:b)
|
||||
|
||||
double precision :: pows_a(-2:a+b+4), pows_b(-2:a+b+4)
|
||||
integer :: i, minab, maxab
|
||||
integer :: maxbinom
|
||||
|
||||
double precision, external :: binom_func
|
||||
|
||||
if((a < 0) .or. (b < 0)) return
|
||||
|
||||
maxbinom = size(binom_transp, 1)
|
||||
|
||||
maxab = max(a, b)
|
||||
minab = min(min(a, b), maxbinom)
|
||||
|
||||
pows_a(0) = 1.d0
|
||||
pows_a(1) = x_P - x_A
|
||||
pows_b(0) = 1.d0
|
||||
pows_b(1) = x_Q - x_B
|
||||
|
||||
do i = 2, maxab
|
||||
pows_a(i) = pows_a(i-1) * pows_a(1)
|
||||
pows_b(i) = pows_b(i-1) * pows_b(1)
|
||||
enddo
|
||||
|
||||
P_new(0) = pows_a(a)
|
||||
Q_new(0) = pows_b(b)
|
||||
do i = 1, minab
|
||||
P_new(i) = binom_transp(i,a) * pows_a(a-i)
|
||||
Q_new(i) = binom_transp(i,b) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
do i = minab+1, min(a, maxbinom)
|
||||
P_new(i) = binom_transp(i,a) * pows_a(a-i)
|
||||
enddo
|
||||
do i = minab+1, min(b, maxbinom)
|
||||
Q_new(i) = binom_transp(i,b) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
do i = maxbinom+1, a
|
||||
P_new(i) = binom_func(a, i) * pows_a(a-i)
|
||||
enddo
|
||||
do i = maxbinom+1, b
|
||||
Q_new(i) = binom_func(b, i) * pows_b(b-i)
|
||||
enddo
|
||||
|
||||
end
|
||||
|
||||
! ---
|
||||
|
||||
subroutine pol_modif_center(A_center, B_center, iorder, A_pol, B_pol)
|
||||
|
||||
BEGIN_DOC
|
||||
|
||||
Loading…
Reference in New Issue
Block a user