Source code for pysisyphus.wavefunction.ints_numba.diag_quadrupole3d

"""
Molecular integrals over Gaussian basis functions generated by sympleints.
See https://github.com/eljost/sympleints for more information.

sympleints version: 0.1.dev103+g56f68c5.d20240122
sympy version: 1.12

sympleints was executed with the following arguments:
	/home/johannes/.pyenv/versions/sympleints/bin/sympleints --norm cgto --keys ~2c2e ~3c2e_sph ~coul --opt-basic --prefix opt_new

	lmax = 4
	lauxmax = 6
	out_dir = .
	prefix = opt_new
	keys = ['~2c2e', '~3c2e_sph', '~coul']
	sph = False
	opt_basic = True
	boys_func = sympleints.testing.boys
	normalize = cgto
"""

"""

        Diagonal of the quadrupole moment matrix with operators x², y², z².

        for rr in (xx, yy, zz):
            for bf_a in basis_functions_a:
                for bf_b in basis_functions_b:
                        quadrupole_integrals(bf_a, bf_b, rr)
        
"""

import numba
from numba import i8, f8
import numpy


func_type = numba.types.FunctionType(
    numba.types.void(f8, f8, f8[:], f8, f8, f8[:], f8[:], f8[::1])
)


[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_00(ax, da, A, bx, db, B, R, result): """Cartesian 3D (ss) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = 0.5 * x0 x2 = ax * bx * x0 x3 = ( 5.56832799683170785 * da * db * x0**1.5 * numpy.exp(-x2 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) # 3 item(s) result[0] += x3 * (x1 + (-x0 * (ax * A[0] + bx * B[0]) + R[0]) ** 2) result[1] += x3 * (x1 + (-x0 * (ax * A[1] + bx * B[1]) + R[1]) ** 2) result[2] += x3 * (x1 + (-x0 * (ax * A[2] + bx * B[2]) + R[2]) ** 2)
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_10(ax, da, A, bx, db, B, R, result): """Cartesian 3D (ps) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + R[0] x4 = x2 + A[0] x5 = 0.5 * x0 x6 = ax * bx * x0 x7 = ( 5.56832799683170785 * da * db * numpy.sqrt(x0) * numpy.exp(-x6 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x8 = x5 * x7 x9 = x0 * (ax * A[1] + bx * B[1]) x10 = -x9 x11 = x10 + A[1] x12 = x0 * x7 x13 = x12 * (x3**2 + x5) x14 = x0 * (ax * A[2] + bx * B[2]) x15 = -x14 x16 = x15 + A[2] x17 = x10 + R[1] x18 = x12 * (x17**2 + x5) x19 = x15 + R[2] x20 = x12 * (x19**2 + x5) # 9 item(s) result[0] += -x8 * (x0 * (-2.0 * x1 + A[0] + R[0]) + x3 * (x0 + 2.0 * x3 * x4)) result[1] += -x11 * x13 result[2] += -x13 * x16 result[3] += -x18 * x4 result[4] += -x8 * (x0 * (-2.0 * x9 + A[1] + R[1]) + x17 * (x0 + 2.0 * x11 * x17)) result[5] += -x16 * x18 result[6] += -x20 * x4 result[7] += -x11 * x20 result[8] += -x8 * (x0 * (-2.0 * x14 + A[2] + R[2]) + x19 * (x0 + 2.0 * x16 * x19))
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_01(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_10.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_10(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 3, 1), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_20(ax, da, A, bx, db, B, R, result): """Cartesian 3D (ds) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + R[0] x4 = x3**2 x5 = 3.0 * x0 x6 = x2 + A[0] x7 = x3 * x6 x8 = x0 * (-2.0 * x1 + A[0] + R[0]) + x3 * (x0 + 2.0 * x7) x9 = 1.73205080756887729 x10 = 5.56832799683170785 x11 = ax * bx * x0 x12 = numpy.exp(-x11 * (A[0] - B[0]) ** 2) x13 = numpy.exp(-x11 * (A[1] - B[1]) ** 2) x14 = numpy.exp(-x11 * (A[2] - B[2]) ** 2) x15 = da * db * numpy.sqrt(x0) * x10 * x12 * x13 * x14 x16 = x0 * x15 x17 = 0.0833333333333333333 * x16 * x9 x18 = x0 * (ax * A[1] + bx * B[1]) x19 = -x18 x20 = x19 + A[1] x21 = 0.5 * x0 x22 = x15 * x21 x23 = x22 * x8 x24 = x0 * (ax * A[2] + bx * B[2]) x25 = -x24 x26 = x25 + A[2] x27 = x20**2 + x21 x28 = x21 + x4 x29 = 0.333333333333333333 * da * db * x0**1.5 * x10 * x12 * x13 * x14 * x9 x30 = x28 * x29 x31 = x16 * x26 x32 = x21 + x26**2 x33 = x21 + x6**2 x34 = x19 + R[1] x35 = x34**2 x36 = x21 + x35 x37 = x29 * x36 x38 = x20 * x34 x39 = x0 * (-2.0 * x18 + A[1] + R[1]) + x34 * (x0 + 2.0 * x38) x40 = x22 * x39 x41 = x25 + R[2] x42 = x41**2 x43 = x21 + x42 x44 = x29 * x43 x45 = x26 * x41 x46 = x0 * (-2.0 * x24 + A[2] + R[2]) + x41 * (x0 + 2.0 * x45) x47 = x22 * x46 # 18 item(s) result[0] += x17 * (x0 * (2.0 * x4 + x5 + 4.0 * x7) + 2.0 * x6 * x8) result[1] += x20 * x23 result[2] += x23 * x26 result[3] += x27 * x30 result[4] += x20 * x28 * x31 result[5] += x30 * x32 result[6] += x33 * x37 result[7] += x40 * x6 result[8] += x31 * x36 * x6 result[9] += x17 * (x0 * (2.0 * x35 + 4.0 * x38 + x5) + 2.0 * x20 * x39) result[10] += x26 * x40 result[11] += x32 * x37 result[12] += x33 * x44 result[13] += x16 * x20 * x43 * x6 result[14] += x47 * x6 result[15] += x27 * x44 result[16] += x20 * x47 result[17] += x17 * (x0 * (2.0 * x42 + 4.0 * x45 + x5) + 2.0 * x26 * x46)
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_02(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_20.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_20(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 6, 1), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_30(ax, da, A, bx, db, B, R, result): """Cartesian 3D (fs) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + A[0] x4 = x2 + R[0] x5 = x4**2 x6 = 3.0 * x0 x7 = x3 * x4 x8 = x0 * (-2.0 * x1 + A[0] + R[0]) x9 = x0 + 2.0 * x7 x10 = x4 * x9 x11 = x10 + x8 x12 = x0 * (2.0 * x5 + x6 + 4.0 * x7) + 2.0 * x11 * x3 x13 = 2.0 * x0 x14 = 3.87298334620741689 x15 = ax * bx * x0 x16 = ( 5.56832799683170785 * da * db * numpy.exp(-x15 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x17 = numpy.sqrt(x0) * x16 x18 = x0 * x17 x19 = 0.0166666666666666667 * x14 * x18 x20 = x0 * (ax * A[1] + bx * B[1]) x21 = -x20 x22 = x21 + A[1] x23 = 1.73205080756887729 x24 = 0.0833333333333333333 * x18 * x23 x25 = x12 * x24 x26 = x0 * (ax * A[2] + bx * B[2]) x27 = -x26 x28 = x27 + A[2] x29 = x22**2 x30 = 0.5 * x0 x31 = x29 + x30 x32 = x0**1.5 * x16 x33 = x23 * x32 x34 = 0.166666666666666667 * x33 x35 = x11 * x34 x36 = x17 * x28 * x30 x37 = x28**2 x38 = x30 + x37 x39 = x30 + x5 x40 = x22 * x39 x41 = 1.5 * x0 x42 = 0.0666666666666666667 * x14 * x32 x43 = x42 * (x29 + x41) x44 = x28 * x39 x45 = 0.333333333333333333 * x33 x46 = x31 * x45 x47 = x38 * x45 x48 = x42 * (x37 + x41) x49 = x21 + R[1] x50 = x49**2 x51 = x30 + x50 x52 = x3 * x51 x53 = x3**2 x54 = x42 * (x41 + x53) x55 = x30 + x53 x56 = x0 * (-2.0 * x20 + A[1] + R[1]) x57 = x22 * x49 x58 = x0 + 2.0 * x57 x59 = x49 * x58 x60 = x56 + x59 x61 = x34 * x60 x62 = x28 * x51 x63 = x45 * x55 x64 = x0 * (2.0 * x50 + 4.0 * x57 + x6) + 2.0 * x22 * x60 x65 = x24 * x64 x66 = x27 + R[2] x67 = x66**2 x68 = x30 + x67 x69 = x3 * x68 x70 = x22 * x68 x71 = x0 * (-2.0 * x26 + A[2] + R[2]) x72 = x28 * x66 x73 = x0 + 2.0 * x72 x74 = x66 * x73 x75 = x71 + x74 x76 = x34 * x75 x77 = x0 * (x6 + 2.0 * x67 + 4.0 * x72) + 2.0 * x28 * x75 x78 = x24 * x77 # 30 item(s) result[0] += -x19 * (x12 * x3 + x13 * (x10 + x3 * x9 + 2.0 * x8)) result[1] += -x22 * x25 result[2] += -x25 * x28 result[3] += -x31 * x35 result[4] += -x11 * x22 * x36 result[5] += -x35 * x38 result[6] += -x40 * x43 result[7] += -x44 * x46 result[8] += -x40 * x47 result[9] += -x44 * x48 result[10] += -x52 * x54 result[11] += -x55 * x61 result[12] += -x62 * x63 result[13] += -x3 * x65 result[14] += -x3 * x36 * x60 result[15] += -x47 * x52 result[16] += -x19 * (x13 * (x22 * x58 + 2.0 * x56 + x59) + x22 * x64) result[17] += -x28 * x65 result[18] += -x38 * x61 result[19] += -x48 * x62 result[20] += -x54 * x69 result[21] += -x63 * x70 result[22] += -x55 * x76 result[23] += -x46 * x69 result[24] += -x17 * x22 * x3 * x30 * x75 result[25] += -x3 * x78 result[26] += -x43 * x70 result[27] += -x31 * x76 result[28] += -x22 * x78 result[29] += -x19 * (x13 * (x28 * x73 + 2.0 * x71 + x74) + x28 * x77)
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_03(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_30.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_30(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 10, 1), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_40(ax, da, A, bx, db, B, R, result): """Cartesian 3D (gs) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = 0.5 / (ax + bx) x1 = (ax + bx) ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - A[0] x4 = ax * bx * x1 x5 = numpy.exp(-x4 * (A[0] - B[0]) ** 2) x6 = 1.77245385090551603 * numpy.sqrt(x1) x7 = x5 * x6 x8 = x3**2 * x7 x9 = x0 * x7 x10 = 3.0 * x9 x11 = 2.0 * x3 x12 = -x2 - R[0] x13 = x12 * x7 x14 = x10 + x11 * x13 x15 = 2.0 * x0 x16 = x3 * x7 x17 = x0 * (x13 + x16) x18 = x12 * x16 + x9 x19 = x18 * x3 x20 = x12**2 * x7 x21 = x0 * (x14 + x20) x22 = x12 * x18 x23 = x17 + x22 x24 = x23 * x3 x25 = x21 + x24 x26 = 2.0 * x0 * (2.0 * x17 + x19 + x22) + x25 * x3 x27 = da * db x28 = 0.0975900072948533179 * x27 x29 = numpy.exp(-x4 * (A[1] - B[1]) ** 2) x30 = numpy.exp(-x4 * (A[2] - B[2]) ** 2) x31 = 3.14159265358979324 * x1 * x30 x32 = x29 * x31 x33 = -x1 * (ax * A[1] + bx * B[1]) x34 = -x33 - A[1] x35 = 0.258198889747161126 * x27 x36 = x34 * x35 x37 = x26 * x32 x38 = -x1 * (ax * A[2] + bx * B[2]) x39 = -x38 - A[2] x40 = x35 * x39 x41 = x30 * x6 x42 = x29 * x6 x43 = x34**2 * x42 x44 = x0 * x42 x45 = x43 + x44 x46 = 0.333333333333333333 * x27 x47 = x45 * x46 x48 = 1.73205080756887729 x49 = x39 * x46 * x48 x50 = x39**2 * x41 x51 = x0 * x41 x52 = x50 + x51 x53 = x46 * x52 x54 = x34 * x42 x55 = x15 * x54 + x34 * x45 x56 = x23 * x35 x57 = x39 * x41 x58 = x23 * x48 x59 = x15 * x57 + x39 * x52 x60 = 3.0 * x44 x61 = x0 * (3.0 * x43 + x60) + x34 * x55 x62 = x20 + x9 x63 = x28 * x62 x64 = x35 * x62 x65 = 3.0 * x51 x66 = x0 * (3.0 * x50 + x65) + x39 * x59 x67 = x8 + x9 x68 = x15 * x16 + x3 * x67 x69 = x0 * (x10 + 3.0 * x8) + x3 * x68 x70 = -x33 - R[1] x71 = x42 * x70**2 x72 = x44 + x71 x73 = x28 * x72 x74 = x42 * x70 x75 = x0 * (x54 + x74) x76 = x44 + x54 * x70 x77 = x70 * x76 x78 = x75 + x77 x79 = x35 * x78 x80 = x35 * x72 x81 = 2.0 * x34 x82 = x60 + x74 * x81 x83 = x0 * (x71 + x82) x84 = x34 * x78 x85 = x83 + x84 x86 = x46 * x67 x87 = x48 * x78 x88 = x34 * x76 x89 = 2.0 * x0 * (2.0 * x75 + x77 + x88) + x34 * x85 x90 = x31 * x89 x91 = x3 * x5 x92 = x35 * x91 x93 = x28 * x5 x94 = -x38 - R[2] x95 = x41 * x94**2 x96 = x51 + x95 x97 = x28 * x96 x98 = x35 * x96 x99 = x41 * x94 x100 = x0 * (x57 + x99) x101 = x51 + x57 * x94 x102 = x101 * x94 x103 = x100 + x102 x104 = x103 * x35 x105 = x103 * x48 x106 = 2.0 * x39 x107 = x106 * x99 + x65 x108 = x0 * (x107 + x95) x109 = x103 * x39 x110 = x108 + x109 x111 = 3.14159265358979324 * x1 * x29 x112 = x101 * x39 x113 = 2.0 * x0 * (2.0 * x100 + x102 + x112) + x110 * x39 x114 = x111 * x113 # 45 item(s) result[0] += ( x28 * x32 * (x0 * (x11 * (x17 + x19) + x15 * (x14 + x8) + 3.0 * x21 + 3.0 * x24) + x26 * x3) ) result[1] += x36 * x37 result[2] += x37 * x40 result[3] += x25 * x41 * x47 result[4] += x25 * x32 * x34 * x49 result[5] += x25 * x42 * x53 result[6] += x41 * x55 * x56 result[7] += x47 * x57 * x58 result[8] += x53 * x54 * x58 result[9] += x42 * x56 * x59 result[10] += x41 * x61 * x63 result[11] += x55 * x57 * x64 result[12] += x45 * x53 * x62 result[13] += x54 * x59 * x64 result[14] += x42 * x63 * x66 result[15] += x41 * x69 * x73 result[16] += x41 * x68 * x79 result[17] += x57 * x68 * x80 result[18] += x41 * x85 * x86 result[19] += x57 * x86 * x87 result[20] += x53 * x67 * x72 result[21] += x90 * x92 result[22] += x31 * x49 * x85 * x91 result[23] += x16 * x53 * x87 result[24] += x16 * x59 * x80 result[25] += ( x31 * x93 * ( x0 * (x15 * (x43 + x82) + x81 * (x75 + x88) + 3.0 * x83 + 3.0 * x84) + x34 * x89 ) ) result[26] += x40 * x5 * x90 result[27] += x53 * x7 * x85 result[28] += x59 * x7 * x79 result[29] += x66 * x7 * x73 result[30] += x42 * x69 * x97 result[31] += x54 * x68 * x98 result[32] += x104 * x42 * x68 result[33] += x47 * x67 * x96 result[34] += x105 * x54 * x86 result[35] += x110 * x42 * x86 result[36] += x16 * x55 * x98 result[37] += x105 * x16 * x47 result[38] += x110 * x111 * x34 * x46 * x48 * x91 result[39] += x114 * x92 result[40] += x61 * x7 * x97 result[41] += x104 * x55 * x7 result[42] += x110 * x47 * x7 result[43] += x114 * x36 * x5 result[44] += ( x111 * x93 * ( x0 * (x106 * (x100 + x112) + 3.0 * x108 + 3.0 * x109 + x15 * (x107 + x50)) + x113 * x39 ) )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_04(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_40.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_40(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 15, 1), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_11(ax, da, A, bx, db, B, R, result): """Cartesian 3D (pp) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = 3.0 * x0 x2 = x0 * (ax * A[0] + bx * B[0]) x3 = -x2 x4 = x3 + A[0] x5 = x3 + B[0] x6 = x4 * x5 x7 = x3 + R[0] x8 = 2.0 * x7 x9 = x4 * x8 x10 = x5 * x8 x11 = -2.0 * x2 + R[0] x12 = x0 * (x11 + B[0]) x13 = x0 + x10 x14 = ax * bx * x0 x15 = ( 5.56832799683170785 * da * db * numpy.exp(-x14 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x16 = numpy.sqrt(x0) * x15 x17 = x0 * x16 x18 = 0.25 * x17 x19 = x0 * (ax * A[1] + bx * B[1]) x20 = -x19 x21 = x20 + B[1] x22 = 0.5 * x0 x23 = x16 * x22 x24 = x23 * (x0 * (x11 + A[0]) + x7 * (x0 + x9)) x25 = x0 * (ax * A[2] + bx * B[2]) x26 = -x25 x27 = x26 + B[2] x28 = x20 + A[1] x29 = x23 * (x12 + x13 * x7) x30 = x21 * x28 x31 = x22 + x30 x32 = x22 + x7**2 x33 = x0**1.5 * x15 x34 = x32 * x33 x35 = x17 * x32 x36 = x26 + A[2] x37 = x27 * x36 x38 = x22 + x37 x39 = x22 + x6 x40 = x20 + R[1] x41 = x22 + x40**2 x42 = x33 * x41 x43 = -2.0 * x19 + R[1] x44 = x0 * (x43 + B[1]) x45 = 2.0 * x40 x46 = x21 * x45 x47 = x0 + x46 x48 = x23 * (x40 * x47 + x44) x49 = x17 * x41 x50 = x28 * x45 x51 = x23 * (x0 * (x43 + A[1]) + x40 * (x0 + x50)) x52 = x26 + R[2] x53 = x22 + x52**2 x54 = x33 * x53 x55 = x17 * x53 x56 = -2.0 * x25 + R[2] x57 = x0 * (x56 + B[2]) x58 = 2.0 * x52 x59 = x27 * x58 x60 = x0 + x59 x61 = x23 * (x52 * x60 + x57) x62 = x36 * x58 x63 = x23 * (x0 * (x56 + A[2]) + x52 * (x0 + x62)) # 27 item(s) result[0] += x18 * (x0 * (x1 + x10 + 2.0 * x6 + x9) + x8 * (x12 + x13 * x4)) result[1] += x21 * x24 result[2] += x24 * x27 result[3] += x28 * x29 result[4] += x31 * x34 result[5] += x27 * x28 * x35 result[6] += x29 * x36 result[7] += x21 * x35 * x36 result[8] += x34 * x38 result[9] += x39 * x42 result[10] += x4 * x48 result[11] += x27 * x4 * x49 result[12] += x5 * x51 result[13] += x18 * (x0 * (x1 + 2.0 * x30 + x46 + x50) + x45 * (x28 * x47 + x44)) result[14] += x27 * x51 result[15] += x36 * x49 * x5 result[16] += x36 * x48 result[17] += x38 * x42 result[18] += x39 * x54 result[19] += x21 * x4 * x55 result[20] += x4 * x61 result[21] += x28 * x5 * x55 result[22] += x31 * x54 result[23] += x28 * x61 result[24] += x5 * x63 result[25] += x21 * x63 result[26] += x18 * (x0 * (x1 + 2.0 * x37 + x59 + x62) + x58 * (x36 * x60 + x57))
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_21(ax, da, A, bx, db, B, R, result): """Cartesian 3D (dp) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + R[0] x4 = x2 + B[0] x5 = 2.0 * x3 x6 = x4 * x5 x7 = x0 + x6 x8 = x3 * x7 x9 = x2 + A[0] x10 = x7 * x9 x11 = -2.0 * x1 x12 = x11 + R[0] x13 = x12 + B[0] x14 = 3.0 * x0 x15 = x5 * x9 x16 = x0 * (x12 + A[0]) + x3 * (x0 + x15) x17 = x4 * x9 x18 = 2.0 * x17 x19 = x0 * x13 x20 = x0 * (x14 + x15 + x18 + x6) + x5 * (x10 + x19) x21 = 1.73205080756887729 x22 = ax * bx * x0 x23 = ( 5.56832799683170785 * da * db * numpy.exp(-x22 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x24 = numpy.sqrt(x0) * x23 x25 = x0 * x24 x26 = 0.0833333333333333333 * x21 * x25 x27 = x0 * (ax * A[1] + bx * B[1]) x28 = -x27 x29 = x28 + B[1] x30 = x3**2 x31 = x26 * (x0 * (x14 + 4.0 * x3 * x9 + 2.0 * x30) + 2.0 * x16 * x9) x32 = x0 * (ax * A[2] + bx * B[2]) x33 = -x32 x34 = x33 + B[2] x35 = x28 + A[1] x36 = 0.25 * x25 x37 = x20 * x36 x38 = 0.5 * x0 x39 = x29 * x35 x40 = x0**1.5 * x23 x41 = x40 * (x38 + x39) x42 = 0.5 * x16 x43 = x24 * x38 x44 = x16 * x43 x45 = x33 + A[2] x46 = x34 * x45 x47 = x40 * (x38 + x46) x48 = x35**2 + x38 x49 = x19 + x8 x50 = x21 * x40 x51 = 0.166666666666666667 * x50 x52 = x49 * x51 x53 = -2.0 * x27 x54 = x53 + B[1] x55 = 2.0 * x39 x56 = x0 * (x54 + A[1]) + x35 * (x0 + x55) x57 = x30 + x38 x58 = x51 * x57 x59 = 0.333333333333333333 * x50 x60 = x57 * x59 x61 = x43 * x45 x62 = x38 + x45**2 x63 = -2.0 * x32 x64 = x63 + B[2] x65 = 2.0 * x46 x66 = x0 * (x64 + A[2]) + x45 * (x0 + x65) x67 = x0 * (x11 + A[0] + B[0]) + x9 * (x0 + x18) x68 = x28 + R[1] x69 = x68**2 x70 = x38 + x69 x71 = x51 * x70 x72 = x38 + x9**2 x73 = x54 + R[1] x74 = x0 * x73 x75 = 2.0 * x68 x76 = x29 * x75 x77 = x0 + x76 x78 = x68 * x77 x79 = x74 + x78 x80 = x51 * x79 x81 = x59 * x70 x82 = x40 * (x17 + x38) x83 = x35 * x75 x84 = x0 * (x53 + A[1] + R[1]) + x68 * (x0 + x83) x85 = 0.5 * x84 x86 = x35 * x77 x87 = x0 * (x14 + x55 + x76 + x83) + x75 * (x74 + x86) x88 = x36 * x87 x89 = x43 * x9 x90 = x26 * (x0 * (x14 + 4.0 * x35 * x68 + 2.0 * x69) + 2.0 * x35 * x84) x91 = x33 + R[2] x92 = x91**2 x93 = x38 + x92 x94 = x51 * x93 x95 = x59 * x93 x96 = x64 + R[2] x97 = x0 * x96 x98 = 2.0 * x91 x99 = x34 * x98 x100 = x0 + x99 x101 = x100 * x91 x102 = x101 + x97 x103 = x102 * x51 x104 = x45 * x98 x105 = x0 * (x63 + A[2] + R[2]) + x91 * (x0 + x104) x106 = 0.5 * x105 x107 = x100 * x45 x108 = x0 * (x104 + x14 + x65 + x99) + x98 * (x107 + x97) x109 = x108 * x36 x110 = x26 * (x0 * (x14 + 4.0 * x45 * x91 + 2.0 * x92) + 2.0 * x105 * x45) # 54 item(s) result[0] += -x26 * (x0 * (2.0 * x10 + x13 * x14 + x16 + x8) + x20 * x9) result[1] += -x29 * x31 result[2] += -x31 * x34 result[3] += -x35 * x37 result[4] += -x41 * x42 result[5] += -x34 * x35 * x44 result[6] += -x37 * x45 result[7] += -x29 * x44 * x45 result[8] += -x42 * x47 result[9] += -x48 * x52 result[10] += -x56 * x58 result[11] += -x34 * x48 * x60 result[12] += -x35 * x49 * x61 result[13] += -x41 * x45 * x57 result[14] += -x35 * x47 * x57 result[15] += -x52 * x62 result[16] += -x29 * x60 * x62 result[17] += -x58 * x66 result[18] += -x67 * x71 result[19] += -x72 * x80 result[20] += -x34 * x72 * x81 result[21] += -x82 * x85 result[22] += -x88 * x9 result[23] += -x34 * x84 * x89 result[24] += -x45 * x70 * x82 result[25] += -x61 * x79 * x9 result[26] += -x47 * x70 * x9 result[27] += -x4 * x90 result[28] += -x26 * (x0 * (x14 * x73 + x78 + x84 + 2.0 * x86) + x35 * x87) result[29] += -x34 * x90 result[30] += -x4 * x61 * x84 result[31] += -x45 * x88 result[32] += -x47 * x85 result[33] += -x4 * x62 * x81 result[34] += -x62 * x80 result[35] += -x66 * x71 result[36] += -x67 * x94 result[37] += -x29 * x72 * x95 result[38] += -x103 * x72 result[39] += -x35 * x82 * x93 result[40] += -x41 * x9 * x93 result[41] += -x102 * x35 * x89 result[42] += -x106 * x82 result[43] += -x105 * x29 * x89 result[44] += -x109 * x9 result[45] += -x4 * x48 * x95 result[46] += -x56 * x94 result[47] += -x103 * x48 result[48] += -x105 * x35 * x4 * x43 result[49] += -x106 * x41 result[50] += -x109 * x35 result[51] += -x110 * x4 result[52] += -x110 * x29 result[53] += -x26 * (x0 * (x101 + x105 + 2.0 * x107 + x14 * x96) + x108 * x45)
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_12(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_21.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_21(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 6, 3), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_31(ax, da, A, bx, db, B, R, result): """Cartesian 3D (fp) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = 3.0 * x0 x2 = x0 * (ax * A[0] + bx * B[0]) x3 = -x2 x4 = x3 + A[0] x5 = x3 + B[0] x6 = x4 * x5 x7 = 2.0 * x6 x8 = x3 + R[0] x9 = x4 * x8 x10 = 2.0 * x9 x11 = 2.0 * x8 x12 = x11 * x5 x13 = x0 * (x1 + x10 + x12 + x7) x14 = -2.0 * x2 x15 = x14 + R[0] x16 = x15 + B[0] x17 = x0 * x16 x18 = x0 + x12 x19 = x18 * x4 x20 = x17 + x19 x21 = 4.0 * x20 x22 = x8**2 x23 = x0 * (x15 + A[0]) x24 = x0 + x10 x25 = x24 * x8 x26 = x23 + x25 x27 = 2.0 * x4 x28 = x0 * (x1 + 2.0 * x22 + 4.0 * x9) + x26 * x27 x29 = x18 * x8 x30 = x11 * x20 + x13 x31 = x0 * (x1 * x16 + 2.0 * x19 + x26 + x29) + x30 * x4 x32 = ax * bx * x0 x33 = ( 5.56832799683170785 * da * db * numpy.exp(-x32 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x34 = 3.87298334620741689 * x33 x35 = x0**1.5 x36 = x34 * x35 x37 = 0.00833333333333333333 * x36 x38 = x0 * (ax * A[1] + bx * B[1]) x39 = -x38 x40 = x39 + B[1] x41 = 2.0 * x0 x42 = 0.0166666666666666667 * x36 x43 = x42 * (x28 * x4 + x41 * (2.0 * x23 + x24 * x4 + x25)) x44 = x0 * (ax * A[2] + bx * B[2]) x45 = -x44 x46 = x45 + B[2] x47 = x39 + A[1] x48 = x33 * x35 x49 = x47 * x48 x50 = 1.73205080756887729 x51 = 0.0833333333333333333 * x50 x52 = x31 * x51 x53 = 0.5 * x0 x54 = x40 * x47 x55 = x0**1.5 x56 = x33 * x55 x57 = x56 * (x53 + x54) x58 = x28 * x51 x59 = x45 + A[2] x60 = x48 * x59 x61 = x46 * x59 x62 = x56 * (x53 + x61) x63 = x47**2 x64 = x53 + x63 x65 = x51 * x56 x66 = x30 * x65 x67 = -2.0 * x38 x68 = x67 + B[1] x69 = 2.0 * x54 x70 = x0 * (x68 + A[1]) + x47 * (x0 + x69) x71 = x26 * x65 x72 = 0.166666666666666667 * x50 x73 = x64 * x72 x74 = x26 * x56 x75 = 0.25 * x49 x76 = 0.5 * x26 x77 = x59**2 x78 = x53 + x77 x79 = x72 * x78 x80 = -2.0 * x44 x81 = x80 + B[2] x82 = 2.0 * x61 x83 = x0 * (x81 + A[2]) + x59 * (x0 + x82) x84 = x17 + x29 x85 = x34 * x55 x86 = 0.0333333333333333333 * x85 x87 = x84 * x86 x88 = 1.5 * x0 x89 = x47 * (x63 + x88) x90 = 2.0 * x47 x91 = x0 * (x1 + 4.0 * x54 + 2.0 * x63) + x70 * x90 x92 = x22 + x53 x93 = 0.0166666666666666667 * x85 x94 = x92 * x93 x95 = 0.0666666666666666667 * x85 x96 = x92 * x95 x97 = x56 * x59 x98 = x72 * x92 x99 = 0.333333333333333333 * x50 x100 = x92 * x99 x101 = x47 * x56 x102 = x59 * (x77 + x88) x103 = 2.0 * x59 x104 = x0 * (x1 + 4.0 * x61 + 2.0 * x77) + x103 * x83 x105 = x4**2 x106 = x0 * (x14 + A[0] + B[0]) + x4 * (x0 + x7) x107 = x0 * (x1 + 2.0 * x105 + 4.0 * x6) + x106 * x27 x108 = x39 + R[1] x109 = x108**2 x110 = x109 + x53 x111 = x110 * x93 x112 = x68 + R[1] x113 = x0 * x112 x114 = 2.0 * x108 x115 = x114 * x40 x116 = x0 + x115 x117 = x108 * x116 x118 = x113 + x117 x119 = x118 * x4 x120 = x105 + x88 x121 = x120 * x86 x122 = x110 * x95 x123 = x120 * x4 x124 = x0 * (x67 + A[1] + R[1]) x125 = x108 * x90 x126 = x0 + x125 x127 = x108 * x126 x128 = x124 + x127 x129 = x128 * x65 x130 = x105 + x53 x131 = x0 * (x1 + x115 + x125 + x69) x132 = x116 * x47 x133 = x113 + x132 x134 = x114 * x133 + x131 x135 = x134 * x65 x136 = x130 * x72 x137 = x128 * x56 x138 = x110 * x72 x139 = x110 * x99 x140 = 4.0 * x47 x141 = x0 * (x1 + x108 * x140 + 2.0 * x109) + x128 * x90 x142 = x53 + x6 x143 = x142 * x65 x144 = x0 * (x1 * x112 + x117 + x128 + 2.0 * x132) + x134 * x47 x145 = x144 * x51 x146 = x4 * x48 x147 = x141 * x51 x148 = 0.5 * x128 x149 = x142 * x56 x150 = x4 * x56 x151 = x42 * (x141 * x47 + x41 * (2.0 * x124 + x126 * x47 + x127)) x152 = x45 + R[2] x153 = x152**2 x154 = x153 + x53 x155 = x154 * x93 x156 = x154 * x95 x157 = x81 + R[2] x158 = x0 * x157 x159 = 2.0 * x152 x160 = x159 * x46 x161 = x0 + x160 x162 = x152 * x161 x163 = x158 + x162 x164 = x154 * x72 x165 = x154 * x99 x166 = x0 * (x80 + A[2] + R[2]) x167 = x103 * x152 x168 = x0 + x167 x169 = x152 * x168 x170 = x166 + x169 x171 = x170 * x65 x172 = x170 * x56 x173 = x0 * (x1 + x160 + x167 + x82) x174 = x161 * x59 x175 = x158 + x174 x176 = x159 * x175 + x173 x177 = x176 * x65 x178 = 0.5 * x170 x179 = 4.0 * x59 x180 = x0 * (x1 + x152 * x179 + 2.0 * x153) + x103 * x170 x181 = x180 * x51 x182 = x0 * (x1 * x157 + x162 + x170 + 2.0 * x174) + x176 * x59 x183 = x182 * x51 x184 = x42 * (x180 * x59 + x41 * (2.0 * x166 + x168 * x59 + x169)) # 90 item(s) result[0] += x37 * (x0 * (4.0 * x13 + x21 * x4 + x21 * x8 + x28) + x27 * x31) result[1] += x40 * x43 result[2] += x43 * x46 result[3] += x49 * x52 result[4] += x57 * x58 result[5] += x46 * x49 * x58 result[6] += x52 * x60 result[7] += x40 * x58 * x60 result[8] += x58 * x62 result[9] += x64 * x66 result[10] += x70 * x71 result[11] += x46 * x73 * x74 result[12] += x30 * x59 * x75 result[13] += x57 * x59 * x76 result[14] += x47 * x62 * x76 result[15] += x66 * x78 result[16] += x40 * x74 * x79 result[17] += x71 * x83 result[18] += x87 * x89 result[19] += x91 * x94 result[20] += x46 * x89 * x96 result[21] += x73 * x84 * x97 result[22] += x70 * x97 * x98 result[23] += x100 * x62 * x64 result[24] += x101 * x79 * x84 result[25] += x100 * x57 * x78 result[26] += x101 * x83 * x98 result[27] += x102 * x87 result[28] += x102 * x40 * x96 result[29] += x104 * x94 result[30] += x107 * x111 result[31] += x119 * x121 result[32] += x122 * x123 * x46 result[33] += x106 * x129 result[34] += x130 * x135 result[35] += x136 * x137 * x46 result[36] += x106 * x138 * x97 result[37] += x118 * x136 * x97 result[38] += x130 * x139 * x62 result[39] += x141 * x143 result[40] += x145 * x146 result[41] += x146 * x147 * x46 result[42] += x142 * x148 * x97 result[43] += 0.25 * x134 * x4 * x60 result[44] += x148 * x4 * x62 result[45] += x139 * x149 * x78 result[46] += x119 * x56 * x79 result[47] += x138 * x150 * x83 result[48] += x151 * x5 result[49] += x37 * ( x0 * (4.0 * x108 * x133 + 4.0 * x131 + x133 * x140 + x141) + x144 * x90 ) result[50] += x151 * x46 result[51] += x147 * x5 * x60 result[52] += x145 * x60 result[53] += x147 * x62 result[54] += x137 * x5 * x79 result[55] += x135 * x78 result[56] += x129 * x83 result[57] += x102 * x122 * x5 result[58] += x102 * x118 * x86 result[59] += x104 * x111 result[60] += x107 * x155 result[61] += x123 * x156 * x40 result[62] += x121 * x163 * x4 result[63] += x101 * x106 * x164 result[64] += x130 * x165 * x57 result[65] += x101 * x136 * x163 result[66] += x106 * x171 result[67] += x136 * x172 * x40 result[68] += x130 * x177 result[69] += x149 * x165 * x64 result[70] += x150 * x164 * x70 result[71] += x150 * x163 * x73 result[72] += x101 * x142 * x178 result[73] += x178 * x4 * x57 result[74] += x176 * x4 * x75 result[75] += x143 * x180 result[76] += x146 * x181 * x40 result[77] += x146 * x183 result[78] += x156 * x5 * x89 result[79] += x155 * x91 result[80] += x163 * x86 * x89 result[81] += x172 * x5 * x73 result[82] += x171 * x70 result[83] += x177 * x64 result[84] += x181 * x49 * x5 result[85] += x181 * x57 result[86] += x183 * x49 result[87] += x184 * x5 result[88] += x184 * x40 result[89] += x37 * ( x0 * (4.0 * x152 * x175 + 4.0 * x173 + x175 * x179 + x180) + x103 * x182 )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_13(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_31.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_31(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 10, 3), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_41(ax, da, A, bx, db, B, R, result): """Cartesian 3D (gp) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = 0.5 / (ax + bx) x1 = (ax + bx) ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - A[0] x4 = ax * bx * x1 x5 = numpy.exp(-x4 * (A[0] - B[0]) ** 2) x6 = 1.77245385090551603 * numpy.sqrt(x1) x7 = x5 * x6 x8 = x0 * x7 x9 = -x2 - B[0] x10 = -x2 - R[0] x11 = x10 * x7 x12 = x11 * x9 x13 = x12 + x8 x14 = x13 * x3 x15 = 2.0 * x14 x16 = x7 * x9 x17 = x0 * (x11 + x16) x18 = x3 * x7 x19 = x0 * (x11 + x18) x20 = x10 * x18 x21 = x20 + x8 x22 = x21 * x3 x23 = x19 + x22 x24 = x0 * (x16 + x18) x25 = x18 * x9 x26 = x25 + x8 x27 = x26 * x3 x28 = x24 + x27 x29 = 2.0 * x0 x30 = 3.0 * x8 x31 = x0 * (x12 + x20 + x25 + x30) x32 = x14 + x17 x33 = x3 * x32 x34 = 2.0 * x3 x35 = x10 * x13 x36 = x10 * x21 x37 = x19 + x36 x38 = x0 * (x15 + 3.0 * x17 + x35 + x37) x39 = x10 * x32 x40 = x31 + x39 x41 = x3 * x40 x42 = x10**2 * x7 x43 = x11 * x34 + x30 x44 = x0 * (x42 + x43) x45 = x3 * x37 x46 = x44 + x45 x47 = 2.0 * x0 * (2.0 * x19 + x22 + x36) + x3 * x46 x48 = x38 + x41 x49 = x0 * (4.0 * x31 + 2.0 * x33 + 2.0 * x39 + x46) + x3 * x48 x50 = da * db x51 = 0.0975900072948533179 x52 = x50 * x51 x53 = numpy.exp(-x4 * (A[1] - B[1]) ** 2) x54 = numpy.exp(-x4 * (A[2] - B[2]) ** 2) x55 = 3.14159265358979324 * x1 * x54 x56 = x53 * x55 x57 = x52 * x56 x58 = -x1 * (ax * A[1] + bx * B[1]) x59 = -x58 - B[1] x60 = x3**2 * x7 x61 = x57 * (x0 * (x23 * x34 + x29 * (x43 + x60) + 3.0 * x44 + 3.0 * x45) + x3 * x47) x62 = -x1 * (ax * A[2] + bx * B[2]) x63 = -x62 - B[2] x64 = -x58 - A[1] x65 = 0.258198889747161126 x66 = x50 * x65 x67 = x64 * x66 x68 = x49 * x56 x69 = x0 * x6 x70 = x53 * x69 x71 = x53 * x6 x72 = x64 * x71 x73 = x59 * x72 x74 = x70 + x73 x75 = x54 * x6 x76 = x47 * x66 x77 = x56 * x76 x78 = -x62 - A[2] x79 = x66 * x78 x80 = x54 * x69 x81 = x75 * x78 x82 = x63 * x81 x83 = x80 + x82 x84 = x64**2 * x71 x85 = x70 + x84 x86 = 0.333333333333333333 * x50 x87 = x85 * x86 x88 = x59 * x71 x89 = x0 * (x72 + x88) x90 = x64 * x74 x91 = x89 + x90 x92 = x75 * x86 x93 = x63 * x75 x94 = 1.73205080756887729 x95 = x78 * x86 * x94 x96 = x81 * x94 x97 = x46 * x86 x98 = x72 * x94 x99 = x75 * x78**2 x100 = x80 + x99 x101 = x100 * x86 x102 = x0 * (x81 + x93) x103 = x78 * x83 x104 = x102 + x103 x105 = x104 * x86 x106 = x29 * x72 + x64 * x85 x107 = x66 * x75 x108 = 2.0 * x64 x109 = 3.0 * x70 x110 = x109 + x84 x111 = x0 * (x108 * x88 + x110) + x64 * x91 x112 = x37 * x66 x113 = x37 * x94 x114 = x81 * x86 x115 = x100 * x78 + x29 * x81 x116 = x66 * x71 x117 = 2.0 * x78 x118 = 3.0 * x80 x119 = x118 + x99 x120 = x0 * (x117 * x93 + x119) + x104 * x78 x121 = x0 * (x109 + 3.0 * x84) + x106 * x64 x122 = x17 + x35 x123 = x122 * x52 x124 = x0 * (x106 + 3.0 * x89 + 3.0 * x90) + x111 * x64 x125 = x42 + x8 x126 = x125 * x50 x127 = x126 * x51 x128 = x122 * x66 x129 = x126 * x65 x130 = x0 * (x118 + 3.0 * x99) + x115 * x78 x131 = x0 * (3.0 * x102 + 3.0 * x103 + x115) + x120 * x78 x132 = -x58 - R[1] x133 = x132**2 * x71 x134 = x133 + x70 x135 = x60 + x8 x136 = x135 * x3 + x18 * x29 x137 = x0 * (x16 * x34 + x30 + x60) + x28 * x3 x138 = x0 * (x136 + 3.0 * x24 + 3.0 * x27) + x137 * x3 x139 = x52 * x75 x140 = x132 * x71 x141 = x0 * (x140 + x88) x142 = x132 * x88 x143 = x142 + x70 x144 = x132 * x143 x145 = x141 + x144 x146 = x0 * (x30 + 3.0 * x60) + x136 * x3 x147 = x134 * x52 x148 = x0 * (x140 + x72) x149 = x132 * x72 x150 = x149 + x70 x151 = x132 * x150 x152 = x148 + x151 x153 = x0 * (x109 + x142 + x149 + x73) x154 = x143 * x64 x155 = x141 + x154 x156 = x132 * x155 x157 = x153 + x156 x158 = x136 * x66 x159 = x134 * x66 x160 = x108 * x140 x161 = x0 * (x109 + x133 + x160) x162 = x152 * x64 x163 = x161 + x162 x164 = 2.0 * x154 x165 = x0 * (3.0 * x141 + x144 + x152 + x164) x166 = x157 * x64 x167 = x165 + x166 x168 = x135 * x86 x169 = x152 * x94 x170 = x150 * x64 x171 = 2.0 * x0 * (2.0 * x148 + x151 + x170) + x163 * x64 x172 = x155 * x64 x173 = x0 * (4.0 * x153 + 2.0 * x156 + x163 + 2.0 * x172) + x167 * x64 x174 = x5 * x55 x175 = x173 * x174 x176 = x3 * x66 x177 = x171 * x174 x178 = x163 * x86 x179 = x18 * x94 x180 = x115 * x66 x181 = x148 + x170 x182 = x5 * x52 x183 = x182 * x55 x184 = x183 * ( x0 * (x108 * x181 + 3.0 * x161 + 3.0 * x162 + x29 * (x110 + x160)) + x171 * x64 ) x185 = x66 * x7 x186 = x52 * x7 x187 = -x62 - R[2] x188 = x187**2 * x75 x189 = x188 + x80 x190 = x52 * x71 x191 = x189 * x52 x192 = x187 * x75 x193 = x0 * (x192 + x93) x194 = x187 * x93 x195 = x194 + x80 x196 = x187 * x195 x197 = x193 + x196 x198 = x189 * x66 x199 = x0 * (x192 + x81) x200 = x187 * x81 x201 = x200 + x80 x202 = x187 * x201 x203 = x199 + x202 x204 = x0 * (x118 + x194 + x200 + x82) x205 = x195 * x78 x206 = x193 + x205 x207 = x187 * x206 x208 = x204 + x207 x209 = x189 * x86 x210 = x203 * x94 x211 = x210 * x86 x212 = x117 * x192 x213 = x0 * (x118 + x188 + x212) x214 = x203 * x78 x215 = x213 + x214 x216 = x215 * x86 x217 = 2.0 * x205 x218 = x0 * (3.0 * x193 + x196 + x203 + x217) x219 = x208 * x78 x220 = x218 + x219 x221 = x106 * x66 x222 = 3.14159265358979324 * x1 * x53 x223 = x222 * x5 x224 = x201 * x78 x225 = 2.0 * x0 * (2.0 * x199 + x202 + x224) + x215 * x78 x226 = x223 * x225 x227 = x206 * x78 x228 = x0 * (4.0 * x204 + 2.0 * x207 + x215 + 2.0 * x227) + x220 * x78 x229 = x223 * x228 x230 = x199 + x224 x231 = x182 * x222 x232 = x231 * ( x0 * (x117 * x230 + 3.0 * x213 + 3.0 * x214 + x29 * (x119 + x212)) + x225 * x78 ) # 135 item(s) result[0] += x57 * ( x0 * ( x29 * (x15 + 2.0 * x17 + x23 + x28) + x34 * (x31 + x33) + 3.0 * x38 + 3.0 * x41 + x47 ) + x3 * x49 ) result[1] += x59 * x61 result[2] += x61 * x63 result[3] += x67 * x68 result[4] += x74 * x75 * x76 result[5] += x63 * x64 * x77 result[6] += x68 * x79 result[7] += x59 * x77 * x78 result[8] += x71 * x76 * x83 result[9] += x48 * x75 * x87 result[10] += x46 * x91 * x92 result[11] += x46 * x87 * x93 result[12] += x48 * x56 * x64 * x95 result[13] += x74 * x96 * x97 result[14] += x83 * x97 * x98 result[15] += x101 * x48 * x71 result[16] += x101 * x46 * x88 result[17] += x105 * x46 * x71 result[18] += x106 * x107 * x40 result[19] += x107 * x111 * x37 result[20] += x106 * x112 * x93 result[21] += x40 * x87 * x96 result[22] += x113 * x114 * x91 result[23] += x113 * x83 * x87 result[24] += x101 * x40 * x98 result[25] += x101 * x113 * x74 result[26] += x105 * x113 * x72 result[27] += x115 * x116 * x40 result[28] += x112 * x115 * x88 result[29] += x116 * x120 * x37 result[30] += x121 * x123 * x75 result[31] += x124 * x127 * x75 result[32] += x121 * x127 * x93 result[33] += x106 * x128 * x81 result[34] += x111 * x129 * x81 result[35] += x106 * x129 * x83 result[36] += x101 * x122 * x85 result[37] += x101 * x125 * x91 result[38] += x105 * x125 * x85 result[39] += x115 * x128 * x72 result[40] += x115 * x129 * x74 result[41] += x120 * x129 * x72 result[42] += x123 * x130 * x71 result[43] += x127 * x130 * x88 result[44] += x127 * x131 * x71 result[45] += x134 * x138 * x139 result[46] += x139 * x145 * x146 result[47] += x146 * x147 * x93 result[48] += x107 * x137 * x152 result[49] += x107 * x136 * x157 result[50] += x152 * x158 * x93 result[51] += x137 * x159 * x81 result[52] += x145 * x158 * x81 result[53] += x136 * x159 * x83 result[54] += x163 * x28 * x92 result[55] += x167 * x168 * x75 result[56] += x163 * x168 * x93 result[57] += x114 * x169 * x28 result[58] += x157 * x168 * x96 result[59] += x168 * x169 * x83 result[60] += x101 * x134 * x28 result[61] += x101 * x135 * x145 result[62] += x105 * x134 * x135 result[63] += x107 * x171 * x26 result[64] += x175 * x176 result[65] += x176 * x177 * x63 result[66] += x178 * x26 * x96 result[67] += x167 * x174 * x3 * x95 result[68] += x178 * x179 * x83 result[69] += x101 * x169 * x26 result[70] += x101 * x157 * x179 result[71] += x105 * x169 * x18 result[72] += x115 * x159 * x26 result[73] += x145 * x18 * x180 result[74] += x120 * x159 * x18 result[75] += x184 * x9 result[76] += x183 * ( x0 * ( x108 * (x153 + x172) + 3.0 * x165 + 3.0 * x166 + x171 + x29 * (2.0 * x141 + x164 + x181 + x91) ) + x173 * x64 ) result[77] += x184 * x63 result[78] += x177 * x79 * x9 result[79] += x175 * x79 result[80] += x171 * x185 * x83 result[81] += x101 * x16 * x163 result[82] += x101 * x167 * x7 result[83] += x105 * x163 * x7 result[84] += x152 * x16 * x180 result[85] += x115 * x157 * x185 result[86] += x120 * x152 * x185 result[87] += x130 * x147 * x16 result[88] += x130 * x145 * x186 result[89] += x131 * x134 * x186 result[90] += x138 * x189 * x190 result[91] += x146 * x191 * x88 result[92] += x146 * x190 * x197 result[93] += x137 * x198 * x72 result[94] += x136 * x198 * x74 result[95] += x158 * x197 * x72 result[96] += x116 * x137 * x203 result[97] += x158 * x203 * x88 result[98] += x116 * x136 * x208 result[99] += x209 * x28 * x85 result[100] += x135 * x209 * x91 result[101] += x135 * x197 * x87 result[102] += x211 * x28 * x72 result[103] += x168 * x210 * x74 result[104] += x168 * x208 * x98 result[105] += x216 * x28 * x71 result[106] += x168 * x215 * x88 result[107] += x168 * x220 * x71 result[108] += x106 * x198 * x26 result[109] += x111 * x18 * x198 result[110] += x18 * x197 * x221 result[111] += x210 * x26 * x87 result[112] += x18 * x211 * x91 result[113] += x179 * x208 * x87 result[114] += x216 * x26 * x98 result[115] += x179 * x216 * x74 result[116] += x220 * x223 * x3 * x64 * x86 * x94 result[117] += x116 * x225 * x26 result[118] += x176 * x226 * x59 result[119] += x176 * x229 result[120] += x121 * x16 * x191 result[121] += x124 * x186 * x189 result[122] += x121 * x186 * x197 result[123] += x16 * x203 * x221 result[124] += x111 * x185 * x203 result[125] += x106 * x185 * x208 result[126] += x16 * x215 * x87 result[127] += x216 * x7 * x91 result[128] += x220 * x7 * x87 result[129] += x226 * x67 * x9 result[130] += x185 * x225 * x74 result[131] += x229 * x67 result[132] += x232 * x9 result[133] += x232 * x59 result[134] += x231 * ( x0 * ( x117 * (x204 + x227) + 3.0 * x218 + 3.0 * x219 + x225 + x29 * (x104 + 2.0 * x193 + x217 + x230) ) + x228 * x78 )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_14(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_41.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_41(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 15, 3), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_22(ax, da, A, bx, db, B, R, result): """Cartesian 3D (dd) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = 3.0 * x0 x2 = x0 * (ax * A[0] + bx * B[0]) x3 = -x2 x4 = x3 + A[0] x5 = x3 + B[0] x6 = x4 * x5 x7 = 2.0 * x6 x8 = x3 + R[0] x9 = 2.0 * x8 x10 = x4 * x9 x11 = x5 * x8 x12 = 2.0 * x11 x13 = x0 * (x1 + x10 + x12 + x7) x14 = -2.0 * x2 x15 = x14 + R[0] x16 = x15 + B[0] x17 = x0 * x16 x18 = x0 + x12 x19 = x18 * x4 x20 = x17 + x19 x21 = 4.0 * x20 x22 = x8**2 x23 = x1 + 2.0 * x22 x24 = x18 * x8 x25 = x17 + x24 x26 = x0 * (4.0 * x11 + x23) + 2.0 * x25 * x5 x27 = x0 * (x15 + A[0]) + x8 * (x0 + x10) x28 = x0 * (x1 * x16 + 2.0 * x19 + x24 + x27) x29 = x13 + x20 * x9 x30 = x28 + x29 * x5 x31 = 2.0 * x4 x32 = ax * bx * x0 x33 = ( 5.56832799683170785 * da * db * numpy.exp(-x32 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x34 = x0**1.5 * x33 x35 = 0.0416666666666666667 * x34 x36 = x0 * (ax * A[1] + bx * B[1]) x37 = -x36 x38 = x37 + B[1] x39 = x34 * x38 x40 = 1.73205080756887729 x41 = 0.0833333333333333333 * x40 x42 = x41 * (x28 + x29 * x4) x43 = x0 * (ax * A[2] + bx * B[2]) x44 = -x43 x45 = x44 + B[2] x46 = x34 * x45 x47 = ( 0.0833333333333333333 * x0 * (x23 + 4.0 * x4 * x8) + 0.0833333333333333333 * x27 * x31 ) x48 = x38**2 x49 = 0.5 * x0 x50 = x0**1.5 * x33 x51 = x50 * (x48 + x49) x52 = x39 * x40 x53 = x45**2 x54 = x50 * (x49 + x53) x55 = x37 + A[1] x56 = x34 * x41 x57 = x30 * x56 x58 = x38 * x55 x59 = x50 * (x49 + x58) x60 = 0.25 * x29 x61 = -2.0 * x36 x62 = x61 + B[1] x63 = x0 * (x62 + A[1]) x64 = 2.0 * x58 x65 = x0 + x64 x66 = x38 * x65 + x63 x67 = 0.0833333333333333333 * x50 x68 = x40 * x67 x69 = x27 * x68 x70 = 0.5 * x27 x71 = 0.166666666666666667 * x40 x72 = x27 * x71 x73 = x44 + A[2] x74 = x45 * x73 x75 = x49 + x74 x76 = x50 * x75 x77 = -2.0 * x43 x78 = x77 + B[2] x79 = x0 * (x78 + A[2]) x80 = 2.0 * x74 x81 = x0 + x80 x82 = x45 * x81 + x79 x83 = x49 + x55**2 x84 = x26 * x67 x85 = x55 * x65 + x63 x86 = x25 * x68 x87 = x50 * x71 x88 = x45 * x87 x89 = 2.0 * x55 x90 = x0 * (x1 + 2.0 * x48 + 4.0 * x58) + x66 * x89 x91 = x22 + x49 x92 = x67 * x91 x93 = 0.333333333333333333 * x91 x94 = x56 * x73 x95 = 0.5 * x25 x96 = x87 * x91 x97 = x49 + x73**2 x98 = x87 * x97 x99 = x73 * x81 + x79 x100 = 2.0 * x73 x101 = x0 * (x1 + 2.0 * x53 + 4.0 * x74) + x100 * x82 x102 = x5**2 x103 = x0 * (x14 + A[0] + B[0]) x104 = x0 + x7 x105 = x103 + x104 * x5 x106 = x0 * (x1 + 2.0 * x102 + 4.0 * x6) + x105 * x31 x107 = x37 + R[1] x108 = x107**2 x109 = x108 + x49 x110 = x109 * x67 x111 = x103 + x104 * x4 x112 = x62 + R[1] x113 = x0 * x112 x114 = x107 * x38 x115 = 2.0 * x114 x116 = x0 + x115 x117 = x107 * x116 x118 = x113 + x117 x119 = x118 * x68 x120 = x4**2 + x49 x121 = x1 + 2.0 * x108 x122 = x0 * (4.0 * x114 + x121) + 2.0 * x118 * x38 x123 = x122 * x67 x124 = 0.333333333333333333 * x109 x125 = x107 * x89 x126 = x0 * (x61 + A[1] + R[1]) + x107 * (x0 + x125) x127 = x126 * x68 x128 = x0 * (x1 + x115 + x125 + x64) x129 = x116 * x55 x130 = x113 + x129 x131 = x107 * x130 x132 = x128 + 2.0 * x131 x133 = 0.25 * x132 x134 = x49 + x6 x135 = x134 * x50 x136 = 0.5 * x135 x137 = x0 * (x1 * x112 + x117 + x126 + 2.0 * x129) x138 = x132 * x38 + x137 x139 = x138 * x56 x140 = x126 * x71 x141 = x109 * x87 x142 = 0.5 * x76 x143 = x0 * (4.0 * x107 * x55 + x121) + x126 * x89 x144 = x102 + x49 x145 = x144 * x67 x146 = x132 * x55 + x137 x147 = x5 * x56 x148 = 0.0833333333333333333 * x143 x149 = x144 * x50 x150 = x34 * x5 x151 = x44 + R[2] x152 = x151**2 x153 = x152 + x49 x154 = x153 * x67 x155 = x38 * x87 x156 = x78 + R[2] x157 = x0 * x156 x158 = x151 * x45 x159 = 2.0 * x158 x160 = x0 + x159 x161 = x151 * x160 x162 = x157 + x161 x163 = x162 * x68 x164 = 0.333333333333333333 * x153 x165 = x1 + 2.0 * x152 x166 = x0 * (4.0 * x158 + x165) + 2.0 * x162 * x45 x167 = x166 * x67 x168 = x153 * x87 x169 = 0.5 * x59 x170 = x100 * x151 x171 = x0 * (x77 + A[2] + R[2]) + x151 * (x0 + x170) x172 = x171 * x68 x173 = x0 * (x1 + x159 + x170 + x80) x174 = x160 * x73 x175 = x157 + x174 x176 = x151 * x175 x177 = x173 + 2.0 * x176 x178 = 0.25 * x177 x179 = x171 * x71 x180 = x0 * (x1 * x156 + x161 + x171 + 2.0 * x174) x181 = x177 * x45 + x180 x182 = x181 * x56 x183 = x0 * (4.0 * x151 * x73 + x165) + x100 * x171 x184 = 0.0833333333333333333 * x183 x185 = x177 * x73 + x180 # 108 item(s) result[0] += x35 * (x0 * (4.0 * x13 + x21 * x5 + x21 * x8 + x26) + x30 * x31) result[1] += x39 * x42 result[2] += x42 * x46 result[3] += x47 * x51 result[4] += x45 * x47 * x52 result[5] += x47 * x54 result[6] += x55 * x57 result[7] += x59 * x60 result[8] += x46 * x55 * x60 result[9] += x66 * x69 result[10] += x45 * x59 * x70 result[11] += x54 * x55 * x72 result[12] += x57 * x73 result[13] += x39 * x60 * x73 result[14] += x60 * x76 result[15] += x51 * x72 * x73 result[16] += x38 * x70 * x76 result[17] += x69 * x82 result[18] += x83 * x84 result[19] += x85 * x86 result[20] += x25 * x83 * x88 result[21] += x90 * x92 result[22] += x85 * x88 * x91 result[23] += x54 * x83 * x93 result[24] += x26 * x55 * x94 result[25] += x59 * x73 * x95 result[26] += x55 * x76 * x95 result[27] += x66 * x73 * x96 result[28] += x59 * x75 * x91 result[29] += x55 * x82 * x96 result[30] += x84 * x97 result[31] += x25 * x38 * x98 result[32] += x86 * x99 result[33] += x51 * x93 * x97 result[34] += x38 * x96 * x99 result[35] += x101 * x92 result[36] += x106 * x110 result[37] += x111 * x119 result[38] += x109 * x111 * x88 result[39] += x120 * x123 result[40] += x118 * x120 * x88 result[41] += x120 * x124 * x54 result[42] += x105 * x127 result[43] += x133 * x135 result[44] += x126 * x136 * x45 result[45] += x139 * x4 result[46] += x133 * x4 * x46 result[47] += x140 * x4 * x54 result[48] += x105 * x141 * x73 result[49] += x118 * x136 * x73 result[50] += x109 * x134 * x76 result[51] += x122 * x4 * x94 result[52] += x118 * x142 * x4 result[53] += x141 * x4 * x82 result[54] += x143 * x145 result[55] += x146 * x147 result[56] += x148 * x40 * x46 * x5 result[57] += x35 * ( x0 * (x122 + 4.0 * x128 + 4.0 * x130 * x38 + 4.0 * x131) + x138 * x89 ) result[58] += x146 * x41 * x46 result[59] += x148 * x54 result[60] += x140 * x149 * x73 result[61] += x133 * x150 * x73 result[62] += x126 * x142 * x5 result[63] += x139 * x73 result[64] += x133 * x76 result[65] += x127 * x82 result[66] += x124 * x149 * x97 result[67] += x118 * x5 * x98 result[68] += x141 * x5 * x99 result[69] += x123 * x97 result[70] += x119 * x99 result[71] += x101 * x110 result[72] += x106 * x154 result[73] += x111 * x153 * x155 result[74] += x111 * x163 result[75] += x120 * x164 * x51 result[76] += x120 * x155 * x162 result[77] += x120 * x167 result[78] += x105 * x168 * x55 result[79] += x134 * x153 * x59 result[80] += x136 * x162 * x55 result[81] += x168 * x4 * x66 result[82] += x162 * x169 * x4 result[83] += x166 * x4 * x55 * x56 result[84] += x105 * x172 result[85] += x136 * x171 * x38 result[86] += x135 * x178 result[87] += x179 * x4 * x51 result[88] += x178 * x39 * x4 result[89] += x182 * x4 result[90] += x149 * x164 * x83 result[91] += x168 * x5 * x85 result[92] += x162 * x5 * x83 * x87 result[93] += x154 * x90 result[94] += x163 * x85 result[95] += x167 * x83 result[96] += x149 * x179 * x55 result[97] += x169 * x171 * x5 result[98] += x150 * x178 * x55 result[99] += x172 * x66 result[100] += x178 * x59 result[101] += x182 * x55 result[102] += x145 * x183 result[103] += x184 * x5 * x52 result[104] += x147 * x185 result[105] += x184 * x51 result[106] += x185 * x39 * x41 result[107] += x35 * ( x0 * (x166 + 4.0 * x173 + 4.0 * x175 * x45 + 4.0 * x176) + x100 * x181 )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_32(ax, da, A, bx, db, B, R, result): """Cartesian 3D (fd) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + A[0] x4 = x2 + B[0] x5 = -2.0 * x1 x6 = x5 + R[0] x7 = x6 + B[0] x8 = x0 * x7 x9 = x2 + R[0] x10 = x4 * x9 x11 = 2.0 * x10 x12 = x0 + x11 x13 = x12 * x3 x14 = x13 + x8 x15 = 4.0 * x14 x16 = x9**2 x17 = 3.0 * x0 x18 = 2.0 * x16 + x17 x19 = x12 * x9 x20 = x19 + x8 x21 = 2.0 * x4 x22 = x0 * (4.0 * x10 + x18) + x20 * x21 x23 = x3 * x4 x24 = 2.0 * x23 x25 = 2.0 * x9 x26 = x25 * x3 x27 = x0 * (x11 + x17 + x24 + x26) x28 = x15 * x9 + 4.0 * x27 x29 = x0 * (x6 + A[0]) x30 = x0 + x26 x31 = x30 * x9 x32 = x29 + x31 x33 = 2.0 * x13 + x17 * x7 x34 = x0 * (x19 + x32 + x33) x35 = x14 * x25 + x27 x36 = x35 * x4 x37 = x34 + x36 x38 = 2.0 * x3 x39 = x0 * (x15 * x4 + x22 + x28) + x37 * x38 x40 = x0 * (x5 + A[0] + B[0]) x41 = x0 + x24 x42 = x4 * x41 x43 = x40 + x42 x44 = x3 * x35 x45 = 2.0 * x0 x46 = 2.2360679774997897 x47 = ax * bx * x0 x48 = ( 5.56832799683170785 * da * db * numpy.exp(-x47 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x49 = x0**1.5 * x48 x50 = 0.00833333333333333333 * x49 x51 = x46 * x50 x52 = x0 * (ax * A[1] + bx * B[1]) x53 = -x52 x54 = x53 + B[1] x55 = x0 * (x18 + 4.0 * x3 * x9) + x32 * x38 x56 = x34 + x44 x57 = 3.87298334620741689 x58 = x50 * x57 x59 = x58 * (x0 * (x15 * x3 + x28 + x55) + x38 * x56) x60 = x0 * (ax * A[2] + bx * B[2]) x61 = -x60 x62 = x61 + B[2] x63 = 0.0166666666666666667 * x3 * x55 + 0.0166666666666666667 * x45 * ( 2.0 * x29 + x3 * x30 + x31 ) x64 = x54**2 x65 = 0.5 * x0 x66 = x64 + x65 x67 = x0**1.5 * x48 x68 = x66 * x67 x69 = x46 * x68 x70 = x49 * x62 x71 = x57 * x70 x72 = x62**2 x73 = x65 + x72 x74 = x67 * x73 x75 = x46 * x74 x76 = x53 + A[1] x77 = 0.0416666666666666667 * x49 x78 = x39 * x77 x79 = x54 * x76 x80 = x65 + x79 x81 = 1.73205080756887729 x82 = 0.0833333333333333333 * x67 x83 = x81 * x82 x84 = x56 * x83 x85 = 0.0833333333333333333 * x81 x86 = x56 * x85 x87 = -2.0 * x52 x88 = x87 + B[1] x89 = x0 * (x88 + A[1]) x90 = 2.0 * x79 x91 = x0 + x90 x92 = x54 * x91 x93 = x89 + x92 x94 = 0.0416666666666666667 * x67 x95 = x55 * x94 x96 = x55 * x83 x97 = x55 * x82 x98 = x61 + A[2] x99 = x49 * x98 x100 = x62 * x98 x101 = x100 + x65 x102 = -2.0 * x60 x103 = x102 + B[2] x104 = x0 * (x103 + A[2]) x105 = 2.0 * x100 x106 = x0 + x105 x107 = x106 * x62 x108 = x104 + x107 x109 = x76**2 x110 = x109 + x65 x111 = x37 * x82 x112 = x76 * x91 x113 = x112 + x89 x114 = x81 * x94 x115 = x114 * x35 x116 = x62 * x83 x117 = x17 + 4.0 * x79 x118 = 2.0 * x76 x119 = x0 * (x117 + 2.0 * x64) + x118 * x93 x120 = x32 * x94 x121 = 0.166666666666666667 * x32 x122 = x85 * x99 x123 = x67 * x80 x124 = 0.25 * x35 x125 = x101 * x67 x126 = x32 * x83 x127 = 0.5 * x123 x128 = x98**2 x129 = x128 + x65 x130 = x129 * x83 x131 = x106 * x98 x132 = x104 + x131 x133 = 4.0 * x100 + x17 x134 = 2.0 * x98 x135 = x0 * (x133 + 2.0 * x72) + x108 * x134 x136 = 0.0166666666666666667 * x46 x137 = x136 * x22 x138 = 1.5 * x0 x139 = x109 + x138 x140 = x67 * x76 x141 = x139 * x140 x142 = x0 * (2.0 * x109 + x117) + x113 * x118 x143 = x57 * x67 x144 = 0.00833333333333333333 * x143 x145 = x144 * x20 x146 = x139 * x76 x147 = 0.0333333333333333333 * x143 x148 = x147 * x20 x149 = x119 * x76 + x45 * (x112 + 2.0 * x89 + x92) x150 = x16 + x65 x151 = x150 * x67 x152 = x136 * x151 x153 = 0.0166666666666666667 * x143 x154 = x150 * x153 x155 = 0.0666666666666666667 * x150 x156 = x82 * x98 x157 = x20 * x83 x158 = 0.166666666666666667 * x110 x159 = x125 * x81 x160 = 0.166666666666666667 * x150 x161 = 0.166666666666666667 * x151 x162 = x76 * x82 x163 = 0.166666666666666667 * x129 x164 = x123 * x81 x165 = x128 + x138 x166 = x67 * x98 x167 = x165 * x166 x168 = x165 * x98 x169 = x0 * (2.0 * x128 + x133) + x132 * x134 x170 = x135 * x98 + x45 * (2.0 * x104 + x107 + x131) x171 = x4**2 x172 = x17 + 4.0 * x23 x173 = x0 * (2.0 * x171 + x172) + x38 * x43 x174 = x3 * x41 x175 = x173 * x3 + x45 * (x174 + 2.0 * x40 + x42) x176 = x53 + R[1] x177 = x176**2 x178 = x177 + x65 x179 = x178 * x67 x180 = x136 * x179 x181 = x3**2 x182 = x174 + x40 x183 = x0 * (x172 + 2.0 * x181) + x182 * x38 x184 = x88 + R[1] x185 = x0 * x184 x186 = x176 * x54 x187 = 2.0 * x186 x188 = x0 + x187 x189 = x176 * x188 x190 = x185 + x189 x191 = x144 * x190 x192 = x153 * x178 x193 = x17 + 2.0 * x177 x194 = 2.0 * x54 x195 = x0 * (4.0 * x186 + x193) + x190 * x194 x196 = x136 * x195 x197 = x3 * (x138 + x181) x198 = x197 * x67 x199 = x147 * x190 x200 = 0.0666666666666666667 * x197 x201 = x0 * (x87 + A[1] + R[1]) x202 = x118 * x176 x203 = x0 + x202 x204 = x176 * x203 x205 = x201 + x204 x206 = x205 * x94 x207 = x0 * (x17 + x187 + x202 + x90) x208 = x188 * x76 x209 = x185 + x208 x210 = x176 * x209 x211 = x207 + 2.0 * x210 x212 = x114 * x211 x213 = x181 + x65 x214 = x17 * x184 + 2.0 * x208 x215 = x0 * (x189 + x205 + x214) x216 = x211 * x54 x217 = x215 + x216 x218 = x217 * x82 x219 = 0.166666666666666667 * x213 x220 = x83 * x98 x221 = 0.166666666666666667 * x182 x222 = 4.0 * x76 x223 = x0 * (x176 * x222 + x193) + x118 * x205 x224 = x223 * x94 x225 = x23 + x65 x226 = x211 * x76 x227 = x215 + x226 x228 = x227 * x83 x229 = 4.0 * x207 + 4.0 * x210 x230 = x0 * (x195 + 4.0 * x209 * x54 + x229) + x118 * x217 x231 = x230 * x77 x232 = x3 * x85 x233 = x3 * x82 x234 = 0.25 * x211 x235 = x3 * x83 x236 = x225 * x81 x237 = x236 * x67 x238 = 0.166666666666666667 * x236 x239 = x223 * x76 + x45 * (2.0 * x201 + x203 * x76 + x204) x240 = x171 + x65 x241 = x240 * x67 x242 = x136 * x241 x243 = x58 * (x0 * (x209 * x222 + x223 + x229) + x118 * x227) x244 = 0.0166666666666666667 * x239 x245 = x4 * x83 x246 = 0.0666666666666666667 * x46 x247 = x61 + R[2] x248 = x247**2 x249 = x248 + x65 x250 = x249 * x67 x251 = x136 * x250 x252 = x153 * x249 x253 = x103 + R[2] x254 = x0 * x253 x255 = x247 * x62 x256 = 2.0 * x255 x257 = x0 + x256 x258 = x247 * x257 x259 = x254 + x258 x260 = x144 * x259 x261 = x17 + 2.0 * x248 x262 = 2.0 * x62 x263 = x0 * (4.0 * x255 + x261) + x259 * x262 x264 = x136 * x263 x265 = x182 * x83 x266 = x259 * x76 x267 = x0 * (x102 + A[2] + R[2]) x268 = x134 * x247 x269 = x0 + x268 x270 = x247 * x269 x271 = x267 + x270 x272 = x271 * x94 x273 = x0 * (x105 + x17 + x256 + x268) x274 = x257 * x98 x275 = x254 + x274 x276 = x247 * x275 x277 = x273 + 2.0 * x276 x278 = x114 * x277 x279 = x54 * x83 x280 = x17 * x253 + 2.0 * x274 x281 = x0 * (x258 + x271 + x280) x282 = x277 * x62 x283 = x281 + x282 x284 = x283 * x82 x285 = 0.25 * x277 x286 = x232 * x49 x287 = 4.0 * x98 x288 = x0 * (x247 * x287 + x261) + x134 * x271 x289 = x288 * x94 x290 = x277 * x98 x291 = x281 + x290 x292 = x291 * x83 x293 = 4.0 * x273 + 4.0 * x276 x294 = x0 * (x263 + 4.0 * x275 * x62 + x293) + x134 * x283 x295 = x294 * x77 x296 = x4 * x49 x297 = x288 * x98 + x45 * (2.0 * x267 + x269 * x98 + x270) x298 = 0.0166666666666666667 * x297 x299 = x58 * (x0 * (x275 * x287 + x288 + x293) + x134 * x291) # 180 item(s) result[0] += -x51 * ( x3 * x39 + x45 * (x0 * (x12 * x4 + x33 + x43) + x3 * (x14 * x21 + x27) + 2.0 * x34 + x36 + x44) ) result[1] += -x54 * x59 result[2] += -x59 * x62 result[3] += -x63 * x69 result[4] += -x54 * x63 * x71 result[5] += -x63 * x75 result[6] += -x76 * x78 result[7] += -x80 * x84 result[8] += -x70 * x76 * x86 result[9] += -x93 * x95 result[10] += -x62 * x80 * x96 result[11] += -x73 * x76 * x97 result[12] += -x78 * x98 result[13] += -x54 * x86 * x99 result[14] += -x101 * x84 result[15] += -x66 * x97 * x98 result[16] += -x101 * x54 * x96 result[17] += -x108 * x95 result[18] += -x110 * x111 result[19] += -x113 * x115 result[20] += -x110 * x116 * x35 result[21] += -x119 * x120 result[22] += -x113 * x116 * x32 result[23] += -x110 * x121 * x74 result[24] += -x122 * x37 * x76 result[25] += -x123 * x124 * x98 result[26] += -x124 * x125 * x76 result[27] += -x126 * x93 * x98 result[28] += -x101 * x127 * x32 result[29] += -x108 * x126 * x76 result[30] += -x111 * x129 result[31] += -x130 * x35 * x54 result[32] += -x115 * x132 result[33] += -x121 * x129 * x68 result[34] += -x126 * x132 * x54 result[35] += -x120 * x135 result[36] += -x137 * x141 result[37] += -x142 * x145 result[38] += -x146 * x148 * x62 result[39] += -x149 * x152 result[40] += -x142 * x154 * x62 result[41] += -x146 * x155 * x75 result[42] += -x110 * x156 * x22 result[43] += -x113 * x157 * x98 result[44] += -x158 * x159 * x20 result[45] += -x119 * x150 * x156 result[46] += -x113 * x159 * x160 result[47] += -x108 * x110 * x161 result[48] += -x129 * x162 * x22 result[49] += -x163 * x164 * x20 result[50] += -x132 * x157 * x76 result[51] += -x129 * x161 * x93 result[52] += -x132 * x160 * x164 result[53] += -x135 * x150 * x162 result[54] += -x137 * x167 result[55] += -x148 * x168 * x54 result[56] += -x145 * x169 result[57] += -x155 * x168 * x69 result[58] += -x154 * x169 * x54 result[59] += -x152 * x170 result[60] += -x175 * x180 result[61] += -x183 * x191 result[62] += -x183 * x192 * x62 result[63] += -x196 * x198 result[64] += -x197 * x199 * x62 result[65] += -x178 * x200 * x75 result[66] += -x173 * x206 result[67] += -x182 * x212 result[68] += -x116 * x182 * x205 result[69] += -x213 * x218 result[70] += -x116 * x211 * x213 result[71] += -x205 * x219 * x74 result[72] += -x156 * x173 * x178 result[73] += -x182 * x190 * x220 result[74] += -x159 * x178 * x221 result[75] += -x156 * x195 * x213 result[76] += -x159 * x190 * x219 result[77] += -x108 * x179 * x219 result[78] += -x224 * x43 result[79] += -x225 * x228 result[80] += -x116 * x223 * x225 result[81] += -x231 * x3 result[82] += -x227 * x232 * x70 result[83] += -x223 * x233 * x73 result[84] += -x205 * x220 * x43 result[85] += -x166 * x225 * x234 result[86] += -0.5 * x125 * x205 * x225 result[87] += -x122 * x217 * x3 result[88] += -x125 * x234 * x3 result[89] += -x108 * x205 * x235 result[90] += -x163 * x179 * x43 result[91] += -x163 * x190 * x237 result[92] += -x132 * x179 * x238 result[93] += -x129 * x195 * x233 result[94] += -x132 * x190 * x235 result[95] += -x135 * x178 * x233 result[96] += -x239 * x242 result[97] += -x243 * x4 result[98] += -x244 * x4 * x71 result[99] += -x51 * ( x230 * x76 + x45 * ( x0 * (x188 * x54 + x214 + x93) + 2.0 * x215 + x216 + x226 + x76 * (x194 * x209 + x207) ) ) result[100] += -x243 * x62 result[101] += -x244 * x75 result[102] += -x156 * x223 * x240 result[103] += -x122 * x227 * x4 result[104] += -x101 * x223 * x245 result[105] += -x231 * x98 result[106] += -x101 * x228 result[107] += -x108 * x224 result[108] += -x163 * x205 * x241 result[109] += -x130 * x211 * x4 result[110] += -x132 * x205 * x245 result[111] += -x129 * x218 result[112] += -x132 * x212 result[113] += -x135 * x206 result[114] += -x168 * x179 * x240 * x246 result[115] += -x168 * x199 * x4 result[116] += -x169 * x192 * x4 result[117] += -x167 * x196 result[118] += -x169 * x191 result[119] += -x170 * x180 result[120] += -x175 * x251 result[121] += -x183 * x252 * x54 result[122] += -x183 * x260 result[123] += -x200 * x249 * x69 result[124] += -x147 * x197 * x259 * x54 result[125] += -x198 * x264 result[126] += -x162 * x173 * x249 result[127] += -x164 * x221 * x249 result[128] += -x265 * x266 result[129] += -x219 * x250 * x93 result[130] += -x164 * x219 * x259 result[131] += -x162 * x213 * x263 result[132] += -x173 * x272 result[133] += -x265 * x271 * x54 result[134] += -x182 * x278 result[135] += -x219 * x271 * x68 result[136] += -x213 * x277 * x279 result[137] += -x213 * x284 result[138] += -x158 * x250 * x43 result[139] += -x113 * x238 * x250 result[140] += -x158 * x237 * x259 result[141] += -x119 * x233 * x249 result[142] += -x113 * x235 * x259 result[143] += -x110 * x233 * x263 result[144] += -x271 * x43 * x76 * x83 result[145] += -x127 * x225 * x271 result[146] += -x140 * x225 * x285 result[147] += -x235 * x271 * x93 result[148] += -x123 * x285 * x3 result[149] += -x283 * x286 * x76 result[150] += -x289 * x43 result[151] += -x225 * x279 * x288 result[152] += -x225 * x292 result[153] += -x233 * x288 * x66 result[154] += -x286 * x291 * x54 result[155] += -x295 * x3 result[156] += -x146 * x241 * x246 * x249 result[157] += -x142 * x252 * x4 result[158] += -x139 * x147 * x266 * x4 result[159] += -x149 * x251 result[160] += -x142 * x260 result[161] += -x141 * x264 result[162] += -x158 * x241 * x271 result[163] += -x113 * x245 * x271 result[164] += -x110 * x245 * x277 result[165] += -x119 * x272 result[166] += -x113 * x278 result[167] += -x110 * x284 result[168] += -x162 * x240 * x288 result[169] += -x245 * x288 * x80 result[170] += -x291 * x296 * x76 * x85 result[171] += -x289 * x93 result[172] += -x292 * x80 result[173] += -x295 * x76 result[174] += -x242 * x297 result[175] += -x296 * x298 * x54 * x57 result[176] += -x299 * x4 result[177] += -x298 * x69 result[178] += -x299 * x54 result[179] += -x51 * ( x294 * x98 + x45 * ( x0 * (x108 + x257 * x62 + x280) + 2.0 * x281 + x282 + x290 + x98 * (x262 * x275 + x273) ) )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_23(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_32.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_32(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 10, 6), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_42(ax, da, A, bx, db, B, R, result): """Cartesian 3D (gd) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = 0.5 / (ax + bx) x1 = (ax + bx) ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - B[0] x4 = ax * bx * x1 x5 = numpy.exp(-x4 * (A[0] - B[0]) ** 2) x6 = 1.77245385090551603 * numpy.sqrt(x1) x7 = x5 * x6 x8 = x3 * x7 x9 = -x2 - R[0] x10 = x7 * x9 x11 = x0 * (x10 + x8) x12 = -x2 - A[0] x13 = x0 * x7 x14 = x8 * x9 x15 = x13 + x14 x16 = x12 * x15 x17 = x11 + x16 x18 = x17 * x3 x19 = 2.0 * x18 x20 = x3**2 * x7 x21 = 3.0 * x13 x22 = 2.0 * x12 x23 = x21 + x22 * x8 x24 = x0 * (x20 + x23) x25 = x12 * x7 x26 = x0 * (x25 + x8) x27 = x25 * x3 x28 = x13 + x27 x29 = x28 * x3 x30 = x26 + x29 x31 = x12 * x30 x32 = x24 + x31 x33 = x12 * x17 x34 = x25 * x9 x35 = x0 * (x14 + x21 + x27 + x34) x36 = 4.0 * x35 x37 = 2.0 * x33 + x36 x38 = 2.0 * x0 x39 = x17 * x9 x40 = 2.0 * x39 x41 = x10 * x22 x42 = x7 * x9**2 x43 = x21 + x42 x44 = x0 * (x41 + x43) x45 = x0 * (x10 + x25) x46 = x13 + x34 x47 = x46 * x9 x48 = x45 + x47 x49 = x12 * x48 x50 = x44 + x49 x51 = x0 * (x37 + x40 + x50) x52 = 2.0 * x16 x53 = 3.0 * x11 + x52 x54 = x0 * (x15 * x3 + x30 + x53) x55 = x12 * (x18 + x35) x56 = x15 * x9 x57 = x0 * (x48 + x53 + x56) x58 = x35 + x39 x59 = x12 * x58 x60 = x57 + x59 x61 = x12 * x60 x62 = x11 + x56 x63 = x0 * (2.0 * x14 + x43) + x3 * x62 x64 = x0 * (x19 + x36 + x40 + x63) x65 = x3 * x58 x66 = x57 + x65 x67 = x12 * x66 x68 = x64 + x67 x69 = 2.0 * x0 * (x54 + x55 + 2.0 * x57 + x59 + x65) + x12 * x68 x70 = da * db x71 = 0.0563436169819011052 x72 = x70 * x71 x73 = numpy.exp(-x4 * (A[1] - B[1]) ** 2) x74 = numpy.exp(-x4 * (A[2] - B[2]) ** 2) x75 = 3.14159265358979324 * x1 * x74 x76 = x73 * x75 x77 = -x1 * (ax * A[1] + bx * B[1]) x78 = -x77 - B[1] x79 = 0.0975900072948533179 x80 = x78 * x79 x81 = x12 * x46 x82 = x45 + x81 x83 = x12 * x28 x84 = x26 + x83 x85 = 2.0 * x0 * (2.0 * x45 + x47 + x81) + x12 * x50 x86 = x51 + x61 x87 = x70 * x76 x88 = x87 * ( x0 * ( x22 * (x33 + x35) + x38 * (2.0 * x11 + x52 + x82 + x84) + 3.0 * x57 + 3.0 * x59 + x85 ) + x12 * x86 ) x89 = -x1 * (ax * A[2] + bx * B[2]) x90 = -x89 - B[2] x91 = x79 * x90 x92 = x6 * x74 x93 = x6 * x73 x94 = x78**2 * x93 x95 = x0 * x93 x96 = x70 * (x94 + x95) x97 = x12**2 * x7 x98 = x0 * (x22 * x82 + x38 * (x21 + x41 + x97) + 3.0 * x44 + 3.0 * x49) + x12 * x85 x99 = x71 * x98 x100 = x87 * x90 x101 = x90**2 * x92 x102 = x0 * x92 x103 = x70 * (x101 + x102) x104 = -x77 - A[1] x105 = 2.2360679774997897 x106 = 0.0666666666666666667 * x105 x107 = x104 * x106 x108 = x69 * x87 x109 = x104 * x93 x110 = x109 * x78 x111 = x110 + x95 x112 = 3.87298334620741689 x113 = x111 * x112 x114 = 0.0666666666666666667 * x113 x115 = x70 * x92 x116 = 0.0666666666666666667 * x104 x117 = x112 * x86 x118 = x78 * x93 x119 = x0 * (x109 + x118) x120 = x111 * x78 x121 = x119 + x120 x122 = x105 * x121 x123 = 0.0666666666666666667 * x85 x124 = x90 * x92 x125 = x124 * x70 x126 = x105 * x123 x127 = -x89 - A[2] x128 = x106 * x127 x129 = 0.0666666666666666667 * x78 x130 = x127 * x92 x131 = x130 * x90 x132 = x102 + x131 x133 = x112 * x132 x134 = x133 * x70 x135 = 0.0666666666666666667 * x93 x136 = x0 * (x124 + x130) x137 = x132 * x90 x138 = x136 + x137 x139 = x105 * x138 x140 = x70 * x93 x141 = x104**2 * x93 x142 = x141 + x95 x143 = 1.73205080756887729 x144 = 0.111111111111111111 * x143 x145 = x142 * x144 x146 = x104 * x111 x147 = x119 + x146 x148 = 0.333333333333333333 * x70 x149 = x147 * x148 x150 = x142 * x148 x151 = 3.0 * x95 x152 = 2.0 * x104 x153 = x118 * x152 + x151 x154 = x0 * (x153 + x94) x155 = x104 * x121 x156 = x154 + x155 x157 = x143 * x50 x158 = 0.111111111111111111 * x157 x159 = x127 * x148 x160 = x111 * x148 x161 = x130 * x143 x162 = x132 * x143 x163 = x148 * x162 x164 = x148 * x50 x165 = x127**2 * x92 x166 = x102 + x165 x167 = x143 * x166 x168 = 0.111111111111111111 * x167 x169 = x168 * x70 x170 = x148 * x166 x171 = x127 * x132 x172 = x136 + x171 x173 = x148 * x172 x174 = 3.0 * x102 x175 = 2.0 * x127 x176 = x124 * x175 + x174 x177 = x0 * (x101 + x176) x178 = x127 * x138 x179 = x177 + x178 x180 = x104 * x142 + x109 * x38 x181 = 0.0666666666666666667 * x180 x182 = x181 * x70 x183 = x105 * x66 x184 = x0 * (x141 + x153) x185 = x104 * x147 x186 = x184 + x185 x187 = 0.0666666666666666667 * x186 x188 = x112 * x58 x189 = 2.0 * x0 * (2.0 * x119 + x120 + x146) + x104 * x156 x190 = x105 * x48 x191 = 0.0666666666666666667 * x115 x192 = x112 * x48 x193 = x143 * x147 x194 = x148 * x193 x195 = x148 * x48 x196 = x143 * x173 x197 = x111 * x143 x198 = x127 * x166 + x130 * x38 x199 = 0.0666666666666666667 * x198 x200 = x199 * x70 x201 = x0 * (x165 + x176) x202 = x127 * x172 x203 = x201 + x202 x204 = x135 * x70 x205 = x118 * x70 x206 = 0.0666666666666666667 * x203 x207 = 2.0 * x0 * (2.0 * x136 + x137 + x171) + x127 * x179 x208 = x0 * (3.0 * x141 + x151) + x104 * x180 x209 = x63 * x70 x210 = x209 * x71 x211 = x0 * (3.0 * x119 + 3.0 * x146 + x180) + x104 * x186 x212 = x62 * x79 x213 = x0 * (3.0 * x154 + 3.0 * x155 + 2.0 * x184 + 2.0 * x185) + x104 * x189 x214 = x13 + x42 x215 = x214 * x71 x216 = x214 * x70 x217 = x216 * x79 x218 = x105 * x130 x219 = x112 * x70 x220 = x219 * x62 x221 = 0.0666666666666666667 * x216 x222 = x148 * x62 x223 = x144 * x179 x224 = x105 * x109 x225 = x0 * (3.0 * x165 + x174) + x127 * x198 x226 = x0 * (3.0 * x136 + 3.0 * x171 + x198) + x127 * x203 x227 = x0 * (3.0 * x177 + 3.0 * x178 + 2.0 * x201 + 2.0 * x202) + x127 * x207 x228 = x0 * (x23 + x97) x229 = x12 * x84 x230 = 2.0 * x0 * (2.0 * x26 + x29 + x83) + x12 * x32 x231 = x0 * (2.0 * x228 + 2.0 * x229 + 3.0 * x24 + 3.0 * x31) + x12 * x230 x232 = -x77 - R[1] x233 = x232**2 * x93 x234 = x233 + x95 x235 = x234 * x71 x236 = x13 + x97 x237 = x12 * x236 + x25 * x38 x238 = x228 + x229 x239 = x0 * (x237 + 3.0 * x26 + 3.0 * x83) + x12 * x238 x240 = x232 * x93 x241 = x0 * (x118 + x240) x242 = x118 * x232 x243 = x242 + x95 x244 = x232 * x243 x245 = x241 + x244 x246 = x245 * x79 x247 = x234 * x70 x248 = x247 * x79 x249 = x0 * (x21 + 3.0 * x97) + x12 * x237 x250 = x151 + x233 x251 = x0 * (2.0 * x242 + x250) + x245 * x78 x252 = x251 * x72 x253 = x0 * (x109 + x240) x254 = x109 * x232 x255 = x254 + x95 x256 = x232 * x255 x257 = x253 + x256 x258 = x105 * x257 x259 = x0 * (x110 + x151 + x242 + x254) x260 = x104 * x243 x261 = x241 + x260 x262 = x232 * x261 x263 = x259 + x262 x264 = x112 * x263 x265 = 0.0666666666666666667 * x238 x266 = x112 * x265 x267 = 0.0666666666666666667 * x237 x268 = x267 * x70 x269 = 2.0 * x260 x270 = 3.0 * x241 + x269 x271 = x0 * (x244 + x257 + x270) x272 = x263 * x78 x273 = x271 + x272 x274 = x105 * x273 x275 = 0.0666666666666666667 * x234 x276 = x275 * x70 x277 = x219 * x245 x278 = x152 * x240 x279 = x0 * (x250 + x278) x280 = x104 * x257 x281 = x279 + x280 x282 = x144 * x32 x283 = x104 * x263 x284 = x271 + x283 x285 = x148 * x84 x286 = x261 * x78 x287 = 2.0 * x286 x288 = 4.0 * x259 x289 = 2.0 * x262 + x288 x290 = x0 * (x251 + x287 + x289) x291 = x104 * x273 x292 = x290 + x291 x293 = x144 * x236 x294 = x293 * x70 x295 = x148 * x236 x296 = x148 * x257 x297 = x104 * x255 x298 = 2.0 * x0 * (2.0 * x253 + x256 + x297) + x104 * x281 x299 = x105 * x30 x300 = x112 * x28 x301 = x300 * x70 x302 = x104 * x261 x303 = 2.0 * x302 x304 = x0 * (x281 + x289 + x303) x305 = x104 * x284 x306 = x304 + x305 x307 = 0.0666666666666666667 * x306 x308 = 0.0666666666666666667 * x298 x309 = x12 * x5 x310 = x309 * x75 x311 = x0 * (x121 + x243 * x78 + x270) x312 = x104 * (x259 + x286) x313 = 2.0 * x0 * (2.0 * x271 + x272 + x283 + x311 + x312) + x104 * x292 x314 = x313 * x70 x315 = x219 * x307 x316 = x105 * x25 x317 = x148 * x281 x318 = x148 * x28 x319 = x143 * x28 x320 = x13 + x20 x321 = x320 * x70 x322 = x253 + x297 x323 = ( x0 * (x152 * x322 + 3.0 * x279 + 3.0 * x280 + x38 * (x141 + x151 + x278)) + x104 * x298 ) x324 = x323 * x71 x325 = x5 * x75 x326 = x3 * x325 x327 = x70 * ( x0 * ( x152 * (x259 + x302) + 3.0 * x271 + 3.0 * x283 + x298 + x38 * (x147 + 2.0 * x241 + x269 + x322) ) + x104 * x306 ) x328 = x5 * x72 x329 = x7 * x70 x330 = x219 * x8 x331 = 0.0666666666666666667 * x329 x332 = x70 * x8 x333 = -x89 - R[2] x334 = x333**2 * x92 x335 = x102 + x334 x336 = x335 * x71 x337 = x335 * x70 x338 = x337 * x79 x339 = x333 * x92 x340 = x0 * (x124 + x339) x341 = x124 * x333 x342 = x102 + x341 x343 = x333 * x342 x344 = x340 + x343 x345 = x344 * x79 x346 = x174 + x334 x347 = x0 * (2.0 * x341 + x346) + x344 * x90 x348 = x347 * x72 x349 = x106 * x337 x350 = x219 * x344 x351 = x0 * (x130 + x339) x352 = x130 * x333 x353 = x102 + x352 x354 = x333 * x353 x355 = x351 + x354 x356 = x105 * x355 x357 = x0 * (x131 + x174 + x341 + x352) x358 = x127 * x342 x359 = x340 + x358 x360 = x333 * x359 x361 = x357 + x360 x362 = x112 * x361 x363 = 2.0 * x358 x364 = 3.0 * x340 + x363 x365 = x0 * (x343 + x355 + x364) x366 = x361 * x90 x367 = x365 + x366 x368 = x105 * x367 x369 = x148 * x355 x370 = x109 * x143 x371 = x175 * x339 x372 = x0 * (x346 + x371) x373 = x127 * x355 x374 = x372 + x373 x375 = x127 * x361 x376 = x365 + x375 x377 = x359 * x90 x378 = 2.0 * x377 x379 = 4.0 * x357 x380 = 2.0 * x360 + x379 x381 = x0 * (x347 + x378 + x380) x382 = x127 * x367 x383 = x381 + x382 x384 = x148 * x374 x385 = 3.14159265358979324 * x1 * x73 x386 = x309 * x385 x387 = x127 * x353 x388 = 2.0 * x0 * (2.0 * x351 + x354 + x387) + x127 * x374 x389 = x127 * x359 x390 = 2.0 * x389 x391 = x0 * (x374 + x380 + x390) x392 = x127 * x376 x393 = x391 + x392 x394 = x106 * x388 x395 = x219 * x393 x396 = x0 * (x138 + x342 * x90 + x364) x397 = x127 * (x357 + x377) x398 = 2.0 * x0 * (2.0 * x365 + x366 + x375 + x396 + x397) + x127 * x383 x399 = x398 * x70 x400 = x385 * x5 x401 = x3 * x400 x402 = x351 + x387 x403 = ( x0 * (x175 * x402 + 3.0 * x372 + 3.0 * x373 + x38 * (x165 + x174 + x371)) + x127 * x388 ) x404 = x403 * x71 x405 = x70 * ( x0 * ( x175 * (x357 + x389) + 3.0 * x365 + 3.0 * x375 + x38 * (x172 + 2.0 * x340 + x363 + x402) + x388 ) + x127 * x393 ) # 270 item(s) result[0] += ( x72 * x76 * ( x0 * ( x22 * (x54 + x55) + x38 * (x19 + x32 + x37) + 2.0 * x51 + 2.0 * x61 + 3.0 * x64 + 3.0 * x67 ) + x12 * x69 ) ) result[1] += x80 * x88 result[2] += x88 * x91 result[3] += x92 * x96 * x99 result[4] += x100 * x80 * x98 result[5] += x103 * x93 * x99 result[6] += x107 * x108 result[7] += x114 * x115 * x86 result[8] += x100 * x116 * x117 result[9] += x115 * x122 * x123 result[10] += x114 * x125 * x85 result[11] += x103 * x109 * x126 result[12] += x108 * x128 result[13] += x117 * x127 * x129 * x87 result[14] += x134 * x135 * x86 result[15] += x126 * x130 * x96 result[16] += x118 * x123 * x134 result[17] += x123 * x139 * x140 result[18] += x115 * x145 * x68 result[19] += x149 * x60 * x92 result[20] += x124 * x150 * x60 result[21] += x115 * x156 * x158 result[22] += x124 * x149 * x50 result[23] += x103 * x142 * x158 result[24] += x104 * x159 * x68 * x76 result[25] += x160 * x161 * x60 result[26] += x109 * x163 * x60 result[27] += x121 * x130 * x164 result[28] += x132 * x157 * x160 result[29] += x109 * x138 * x164 result[30] += x169 * x68 * x93 result[31] += x118 * x170 * x60 result[32] += x173 * x60 * x93 result[33] += x158 * x166 * x96 result[34] += x118 * x173 * x50 result[35] += x140 * x158 * x179 result[36] += x182 * x183 * x92 result[37] += x115 * x187 * x188 result[38] += x124 * x182 * x188 result[39] += x189 * x190 * x191 result[40] += x125 * x187 * x192 result[41] += x103 * x181 * x190 result[42] += x130 * x150 * x66 result[43] += x130 * x194 * x58 result[44] += x150 * x162 * x58 result[45] += x130 * x156 * x195 result[46] += x147 * x162 * x195 result[47] += x138 * x142 * x195 result[48] += x109 * x170 * x66 result[49] += x160 * x167 * x58 result[50] += x109 * x196 * x58 result[51] += x121 * x166 * x195 result[52] += x172 * x195 * x197 result[53] += x109 * x179 * x195 result[54] += x183 * x200 * x93 result[55] += x118 * x188 * x200 result[56] += x188 * x203 * x204 result[57] += x190 * x199 * x96 result[58] += x192 * x205 * x206 result[59] += x190 * x204 * x207 result[60] += x208 * x210 * x92 result[61] += x115 * x211 * x212 result[62] += x125 * x208 * x212 result[63] += x115 * x213 * x215 result[64] += x124 * x211 * x217 result[65] += x103 * x208 * x215 result[66] += x182 * x218 * x63 result[67] += x130 * x187 * x220 result[68] += x133 * x182 * x62 result[69] += x189 * x218 * x221 result[70] += x133 * x186 * x221 result[71] += x139 * x182 * x214 result[72] += x142 * x168 * x209 result[73] += x147 * x166 * x222 result[74] += x142 * x172 * x222 result[75] += x156 * x168 * x216 result[76] += x147 * x173 * x214 result[77] += x142 * x216 * x223 result[78] += x199 * x209 * x224 result[79] += x113 * x200 * x62 result[80] += x109 * x206 * x220 result[81] += x122 * x199 * x216 result[82] += x113 * x203 * x221 result[83] += x207 * x221 * x224 result[84] += x210 * x225 * x93 result[85] += x205 * x212 * x225 result[86] += x140 * x212 * x226 result[87] += x215 * x225 * x96 result[88] += x118 * x217 * x226 result[89] += x140 * x215 * x227 result[90] += x115 * x231 * x235 result[91] += x115 * x239 * x246 result[92] += x124 * x239 * x248 result[93] += x249 * x252 * x92 result[94] += x125 * x246 * x249 result[95] += x103 * x235 * x249 result[96] += x191 * x230 * x258 result[97] += x191 * x238 * x264 result[98] += x125 * x257 * x266 result[99] += x268 * x274 * x92 result[100] += x124 * x264 * x268 result[101] += x103 * x258 * x267 result[102] += x218 * x230 * x276 result[103] += x130 * x265 * x277 result[104] += x134 * x238 * x275 result[105] += x218 * x251 * x268 result[106] += x134 * x245 * x267 result[107] += x139 * x247 * x267 result[108] += x115 * x281 * x282 result[109] += x284 * x285 * x92 result[110] += x124 * x281 * x285 result[111] += x292 * x294 * x92 result[112] += x124 * x284 * x295 result[113] += x103 * x281 * x293 result[114] += x130 * x296 * x32 result[115] += x161 * x263 * x285 result[116] += x162 * x296 * x84 result[117] += x130 * x273 * x295 result[118] += x162 * x263 * x295 result[119] += x138 * x236 * x296 result[120] += x168 * x247 * x32 result[121] += x166 * x245 * x285 result[122] += x173 * x234 * x84 result[123] += x169 * x236 * x251 result[124] += x173 * x236 * x245 result[125] += x223 * x236 * x247 result[126] += x191 * x298 * x299 result[127] += x301 * x307 * x92 result[128] += x124 * x301 * x308 result[129] += x106 * x310 * x314 result[130] += x310 * x315 * x90 result[131] += x103 * x308 * x316 result[132] += x130 * x30 * x317 result[133] += x161 * x284 * x318 result[134] += x162 * x281 * x318 result[135] += x159 * x292 * x310 result[136] += x163 * x25 * x284 result[137] += x138 * x25 * x317 result[138] += x166 * x296 * x30 result[139] += x167 * x263 * x318 result[140] += x173 * x257 * x319 result[141] += x170 * x25 * x273 result[142] += x196 * x25 * x263 result[143] += x179 * x25 * x296 result[144] += x200 * x234 * x299 result[145] += x200 * x245 * x300 result[146] += x203 * x275 * x301 result[147] += x200 * x251 * x316 result[148] += x206 * x25 * x277 result[149] += x207 * x276 * x316 result[150] += x321 * x324 * x92 result[151] += x326 * x327 * x79 result[152] += x323 * x326 * x70 * x91 result[153] += ( x328 * x75 * ( x0 * ( x152 * (x311 + x312) + 3.0 * x290 + 3.0 * x291 + 2.0 * x304 + 2.0 * x305 + x38 * (x156 + x287 + x288 + x303) ) + x104 * x313 ) ) result[154] += x325 * x327 * x91 result[155] += x103 * x324 * x7 result[156] += x218 * x308 * x321 result[157] += x127 * x315 * x326 result[158] += x134 * x308 * x8 result[159] += x128 * x314 * x325 result[160] += x134 * x307 * x7 result[161] += x139 * x308 * x329 result[162] += x169 * x281 * x320 result[163] += x170 * x284 * x8 result[164] += x173 * x281 * x8 result[165] += x169 * x292 * x7 result[166] += x173 * x284 * x7 result[167] += x223 * x281 * x329 result[168] += x200 * x258 * x320 result[169] += x200 * x264 * x8 result[170] += x206 * x257 * x330 result[171] += x200 * x274 * x7 result[172] += x203 * x264 * x331 result[173] += x207 * x258 * x331 result[174] += x225 * x235 * x321 result[175] += x225 * x246 * x332 result[176] += x226 * x248 * x8 result[177] += x225 * x252 * x7 result[178] += x226 * x246 * x329 result[179] += x227 * x235 * x329 result[180] += x140 * x231 * x336 result[181] += x118 * x239 * x338 result[182] += x140 * x239 * x345 result[183] += x249 * x336 * x96 result[184] += x205 * x249 * x345 result[185] += x249 * x348 * x93 result[186] += x109 * x230 * x349 result[187] += x114 * x238 * x337 result[188] += x109 * x265 * x350 result[189] += x122 * x267 * x337 result[190] += x113 * x268 * x344 result[191] += x224 * x268 * x347 result[192] += x204 * x230 * x356 result[193] += x205 * x266 * x355 result[194] += x204 * x238 * x362 result[195] += x267 * x356 * x96 result[196] += x118 * x268 * x362 result[197] += x268 * x368 * x93 result[198] += x145 * x32 * x337 result[199] += x147 * x285 * x335 result[200] += x142 * x285 * x344 result[201] += x156 * x293 * x337 result[202] += x147 * x295 * x344 result[203] += x142 * x294 * x347 result[204] += x109 * x32 * x369 result[205] += x197 * x285 * x355 result[206] += x285 * x361 * x370 result[207] += x121 * x295 * x355 result[208] += x197 * x295 * x361 result[209] += x109 * x295 * x367 result[210] += x140 * x282 * x374 result[211] += x118 * x285 * x374 result[212] += x285 * x376 * x93 result[213] += x293 * x374 * x96 result[214] += x118 * x295 * x376 result[215] += x294 * x383 * x93 result[216] += x182 * x299 * x335 result[217] += x187 * x301 * x335 result[218] += x182 * x300 * x344 result[219] += x189 * x25 * x349 result[220] += x187 * x25 * x350 result[221] += x182 * x316 * x347 result[222] += x150 * x30 * x355 result[223] += x193 * x318 * x355 result[224] += x150 * x319 * x361 result[225] += x156 * x25 * x369 result[226] += x194 * x25 * x361 result[227] += x150 * x25 * x367 result[228] += x109 * x30 * x384 result[229] += x160 * x319 * x374 result[230] += x318 * x370 * x376 result[231] += x121 * x25 * x384 result[232] += x143 * x160 * x25 * x376 result[233] += x104 * x148 * x383 * x386 result[234] += x204 * x299 * x388 result[235] += 0.0666666666666666667 * x118 * x301 * x388 result[236] += x135 * x301 * x393 result[237] += x25 * x394 * x96 result[238] += x129 * x386 * x395 result[239] += x106 * x386 * x399 result[240] += x208 * x321 * x336 result[241] += x211 * x338 * x8 result[242] += x208 * x332 * x345 result[243] += x213 * x329 * x336 result[244] += x211 * x329 * x345 result[245] += x208 * x348 * x7 result[246] += x182 * x320 * x356 result[247] += x187 * x330 * x355 result[248] += x182 * x362 * x8 result[249] += x189 * x331 * x356 result[250] += x187 * x329 * x362 result[251] += x182 * x368 * x7 result[252] += x145 * x321 * x374 result[253] += x149 * x374 * x8 result[254] += x150 * x376 * x8 result[255] += x144 * x156 * x329 * x374 result[256] += x149 * x376 * x7 result[257] += x145 * x329 * x383 result[258] += x109 * x321 * x394 result[259] += x114 * x332 * x388 result[260] += x116 * x395 * x401 result[261] += x122 * x331 * x388 result[262] += x114 * x329 * x393 result[263] += x107 * x399 * x400 result[264] += x321 * x404 * x93 result[265] += x401 * x403 * x70 * x80 result[266] += x401 * x405 * x79 result[267] += x404 * x7 * x96 result[268] += x400 * x405 * x80 result[269] += ( x328 * x385 * ( x0 * ( x175 * (x396 + x397) + x38 * (x179 + x378 + x379 + x390) + 3.0 * x381 + 3.0 * x382 + 2.0 * x391 + 2.0 * x392 ) + x127 * x398 ) )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_24(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_42.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_42(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 15, 6), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_33(ax, da, A, bx, db, B, R, result): """Cartesian 3D (ff) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = (ax + bx) ** (-1.0) x1 = x0 * (ax * A[0] + bx * B[0]) x2 = -x1 x3 = x2 + A[0] x4 = -2.0 * x1 x5 = x4 + B[0] x6 = x5 + R[0] x7 = x0 * x6 x8 = x2 + R[0] x9 = x2 + B[0] x10 = 2.0 * x9 x11 = x10 * x8 x12 = x0 + x11 x13 = x12 * x3 x14 = x13 + x7 x15 = 4.0 * x14 x16 = x15 * x3 x17 = x9**2 x18 = 3.0 * x0 x19 = x3 * x9 x20 = x18 + 4.0 * x19 x21 = x0 * (2.0 * x17 + x20) x22 = x0 * (x5 + A[0]) x23 = 2.0 * x19 x24 = x0 + x23 x25 = x24 * x9 x26 = x22 + x25 x27 = 2.0 * x3 x28 = x21 + x26 * x27 x29 = x27 * x8 x30 = x0 * (x11 + x18 + x23 + x29) x31 = 4.0 * x30 x32 = x15 * x9 + x31 x33 = 2.0 * x0 x34 = x12 * x9 x35 = 2.0 * x13 + x18 * x6 x36 = x0 * (x26 + x34 + x35) + x3 * (x10 * x14 + x30) x37 = 4.0 * x9 x38 = x12 * x8 x39 = x0 * (x4 + A[0] + R[0]) x40 = x0 + x29 x41 = x40 * x8 x42 = x39 + x41 x43 = x0 * (x35 + x38 + x42) x44 = 2.0 * x14 * x8 + x30 x45 = x44 * x9 x46 = x43 + x45 x47 = x15 * x8 x48 = x8**2 x49 = x18 + 2.0 * x48 x50 = x38 + x7 x51 = x0 * (x37 * x8 + x49) + x10 * x50 x52 = x0 * (x32 + x47 + x51) x53 = 6.0 * x3 x54 = x27 * x46 + x52 x55 = x3 * x44 x56 = x33 * (x36 + 2.0 * x43 + x45 + x55) x57 = x54 * x9 + x56 x58 = ax * bx * x0 x59 = ( 5.56832799683170785 * da * db * numpy.exp(-x58 * ((A[0] - B[0]) ** 2 + (A[1] - B[1]) ** 2 + (A[2] - B[2]) ** 2)) ) x60 = 0.00416666666666666667 * x59 x61 = x0**1.5 x62 = x60 * x61 x63 = x0 * (ax * A[1] + bx * B[1]) x64 = -x63 x65 = x64 + B[1] x66 = x59 * x61 x67 = x65 * x66 x68 = 2.2360679774997897 x69 = 0.00833333333333333333 * x68 x70 = x69 * (x3 * x54 + x56) x71 = x0 * (ax * A[2] + bx * B[2]) x72 = -x71 x73 = x72 + B[2] x74 = x66 * x73 x75 = x65**2 x76 = 0.5 * x0 x77 = x75 + x76 x78 = x0 * (4.0 * x3 * x8 + x49) + x27 * x42 x79 = x43 + x55 x80 = x0 * (x16 + x31 + x47 + x78) + x27 * x79 x81 = x0**1.5 x82 = x59 * x81 x83 = 0.00833333333333333333 * x82 x84 = x68 * x83 x85 = x80 * x84 x86 = 3.87298334620741689 x87 = 0.00833333333333333333 * x86 x88 = x67 * x87 x89 = x73**2 x90 = x76 + x89 x91 = 0.0166666666666666667 * x3 * x78 + 0.0166666666666666667 * x33 * ( x3 * x40 + 2.0 * x39 + x41 ) x92 = 1.5 * x0 x93 = x65 * x82 x94 = x93 * (x75 + x92) x95 = x73 * x82 x96 = x68 * x91 x97 = x95 * (x89 + x92) x98 = x64 + A[1] x99 = x66 * x69 x100 = x57 * x99 x101 = x65 * x98 x102 = x101 + x76 x103 = 0.0416666666666666667 * x82 x104 = x103 * x54 x105 = 0.0416666666666666667 * x54 x106 = -2.0 * x63 x107 = x106 + B[1] x108 = x0 * (x107 + A[1]) x109 = 2.0 * x101 x110 = x0 + x109 x111 = x110 * x65 x112 = x108 + x111 x113 = x103 * x79 x114 = 1.73205080756887729 x115 = x102 * x114 x116 = 0.0833333333333333333 * x79 x117 = 0.0833333333333333333 * x82 x118 = x117 * x90 x119 = 4.0 * x101 + x18 x120 = x0 * (x119 + 2.0 * x75) x121 = 2.0 * x112 x122 = x120 + x121 * x65 x123 = x122 * x68 x124 = x60 * x81 x125 = x124 * x78 x126 = x103 * x78 x127 = x68 * x97 x128 = 0.0166666666666666667 * x78 x129 = x72 + A[2] x130 = x129 * x73 x131 = x130 + x76 x132 = x117 * x77 x133 = x114 * x131 x134 = -2.0 * x71 x135 = x134 + B[2] x136 = x0 * (x135 + A[2]) x137 = 2.0 * x130 x138 = x0 + x137 x139 = x138 * x73 x140 = x136 + x139 x141 = x68 * x94 x142 = 4.0 * x130 + x18 x143 = x0 * (x142 + 2.0 * x89) x144 = 2.0 * x140 x145 = x143 + x144 * x73 x146 = x145 * x68 x147 = x98**2 x148 = x147 + x76 x149 = x10 * x46 + x52 x150 = x149 * x84 x151 = x110 * x98 x152 = x108 + x151 x153 = x103 * x46 x154 = 0.0833333333333333333 * x46 x155 = x120 + x121 * x98 x156 = 0.0208333333333333333 * x82 x157 = x156 * x44 x158 = x103 * x73 x159 = x114 * x44 x160 = x33 * (2.0 * x108 + x111 + x151) x161 = x155 * x65 + x160 x162 = x42 * x84 x163 = x103 * x42 x164 = 0.0333333333333333333 * x42 x165 = x129 * x66 * x87 x166 = x117 * x46 x167 = x103 * x129 x168 = 0.25 * x131 * x82 x169 = x103 * x98 x170 = x83 * x86 x171 = x170 * x42 x172 = x117 * x42 x173 = x129**2 x174 = x173 + x76 x175 = x129 * x138 x176 = x136 + x175 x177 = x103 * x65 x178 = x129 * x144 + x143 x179 = x33 * (2.0 * x136 + x139 + x175) x180 = x178 * x73 + x179 x181 = x98 * (x147 + x92) x182 = 0.0166666666666666667 * x82 x183 = x182 * (x33 * (x34 + x38 + 2.0 * x7) + x51 * x9) x184 = 2.0 * x98 x185 = x0 * (x119 + 2.0 * x147) + x152 * x184 x186 = x124 * x68 x187 = x186 * x51 x188 = x181 * x68 x189 = 0.0166666666666666667 * x51 x190 = x155 * x98 + x160 x191 = x50 * x84 x192 = x170 * x50 x193 = 0.0333333333333333333 * x82 x194 = x193 * x50 x195 = 4.0 * x65 x196 = 6.0 * x98 x197 = x0 * (x112 * x195 + x112 * x196 + 5.0 * x120) + x161 * x184 x198 = x48 + x76 x199 = x198 * x83 x200 = x198 * x68 x201 = 0.0166666666666666667 * x200 x202 = x182 * x200 x203 = 0.0666666666666666667 * x198 x204 = x183 * x68 x205 = x117 * x148 x206 = x117 * x50 x207 = x117 * x198 x208 = x182 * x198 x209 = x117 * x174 x210 = x129 * (x173 + x92) x211 = x210 * x68 x212 = 2.0 * x129 x213 = x0 * (x142 + 2.0 * x173) + x176 * x212 x214 = x129 * x178 + x179 x215 = 4.0 * x73 x216 = 6.0 * x129 x217 = x0 * (x140 * x215 + x140 * x216 + 5.0 * x143) + x180 * x212 x218 = x24 * x3 x219 = x33 * (x218 + 2.0 * x22 + x25) x220 = x219 + x28 * x9 x221 = x0 * (5.0 * x21 + x26 * x37 + x26 * x53) + x220 * x27 x222 = x64 + R[1] x223 = x222**2 x224 = x223 + x76 x225 = x224 * x83 x226 = x219 + x28 * x3 x227 = x107 + R[1] x228 = x0 * x227 x229 = 2.0 * x65 x230 = x222 * x229 x231 = x0 + x230 x232 = x222 * x231 x233 = x228 + x232 x234 = x233 * x84 x235 = x224 * x68 x236 = 0.0166666666666666667 * x226 x237 = x3**2 x238 = x218 + x22 x239 = x0 * (x20 + 2.0 * x237) + x238 * x27 x240 = x18 + 2.0 * x223 x241 = x0 * (x195 * x222 + x240) + x229 * x233 x242 = x186 * x241 x243 = x170 * x233 x244 = x182 * x235 x245 = x231 * x65 x246 = x182 * (x241 * x65 + x33 * (2.0 * x228 + x232 + x245)) x247 = x3 * (x237 + x92) x248 = x247 * x68 x249 = 0.0166666666666666667 * x248 x250 = x193 * x233 x251 = 0.0666666666666666667 * x224 x252 = x0 * (x106 + A[1] + R[1]) x253 = x184 * x222 x254 = x0 + x253 x255 = x222 * x254 x256 = x252 + x255 x257 = x256 * x84 x258 = x0 * (x109 + x18 + x230 + x253) x259 = x231 * x98 x260 = x228 + x259 x261 = x222 * x260 x262 = x258 + 2.0 * x261 x263 = x156 * x262 x264 = x18 * x227 + 2.0 * x259 x265 = x0 * (x232 + x256 + x264) x266 = x262 * x65 x267 = x265 + x266 x268 = x103 * x267 x269 = x114 * x262 x270 = x237 + x76 x271 = x195 * x260 x272 = 4.0 * x258 x273 = 4.0 * x261 + x272 x274 = x0 * (x241 + x271 + x273) x275 = x229 * x267 + x274 x276 = x275 * x84 x277 = 0.0833333333333333333 * x270 x278 = 0.0333333333333333333 * x270 x279 = x117 * x224 x280 = x117 * x133 x281 = x246 * x68 x282 = x117 * x270 x283 = x182 * x270 x284 = 4.0 * x98 x285 = x0 * (x222 * x284 + x240) + x184 * x256 x286 = x10 * x26 + x21 x287 = x186 * x286 x288 = x262 * x98 x289 = x265 + x288 x290 = x103 * x289 x291 = x19 + x76 x292 = x184 * x267 + x274 x293 = x103 * x292 x294 = x114 * x291 x295 = 0.0833333333333333333 * x294 x296 = x0 * (x112 + x245 + x264) + x98 * (x229 * x260 + x258) x297 = x33 * (2.0 * x265 + x266 + x288 + x296) x298 = x292 * x65 + x297 x299 = x298 * x99 x300 = 0.0416666666666666667 * x292 x301 = 0.0166666666666666667 * x3 x302 = x170 * x256 x303 = x117 * x294 x304 = x103 * x3 x305 = x285 * x98 + x33 * (2.0 * x252 + x254 * x98 + x255) x306 = x17 + x92 x307 = x182 * x9 x308 = x306 * x307 x309 = x17 + x76 x310 = x260 * x284 x311 = x0 * (x273 + x285 + x310) + x184 * x289 x312 = x311 * x84 x313 = 0.0166666666666666667 * x305 x314 = x309 * x68 x315 = x292 * x98 + x297 x316 = x9 * x99 x317 = x307 * x68 x318 = x308 * x68 x319 = x117 * x309 x320 = x66 * x9 x321 = x103 * x9 x322 = x306 * x9 x323 = x193 * x322 * x68 x324 = x322 * x82 x325 = x72 + R[2] x326 = x325**2 x327 = x326 + x76 x328 = x327 * x83 x329 = x327 * x68 x330 = x135 + R[2] x331 = x0 * x330 x332 = 2.0 * x73 x333 = x325 * x332 x334 = x0 + x333 x335 = x325 * x334 x336 = x331 + x335 x337 = x336 * x84 x338 = x182 * x329 x339 = x170 * x336 x340 = x18 + 2.0 * x326 x341 = x0 * (x215 * x325 + x340) + x332 * x336 x342 = x186 * x341 x343 = 0.0666666666666666667 * x327 x344 = x193 * x336 x345 = x334 * x73 x346 = x182 * (x33 * (2.0 * x331 + x335 + x345) + x341 * x73) x347 = x117 * x327 x348 = x115 * x117 x349 = x346 * x68 x350 = x0 * (x134 + A[2] + R[2]) x351 = x212 * x325 x352 = x0 + x351 x353 = x325 * x352 x354 = x350 + x353 x355 = x354 * x84 x356 = x0 * (x137 + x18 + x333 + x351) x357 = x129 * x334 x358 = x331 + x357 x359 = x325 * x358 x360 = x356 + 2.0 * x359 x361 = x156 * x360 x362 = x114 * x360 x363 = x18 * x330 + 2.0 * x357 x364 = x0 * (x335 + x354 + x363) x365 = x360 * x73 x366 = x364 + x365 x367 = x103 * x366 x368 = x215 * x358 x369 = 4.0 * x356 x370 = 4.0 * x359 + x369 x371 = x0 * (x341 + x368 + x370) x372 = x332 * x366 + x371 x373 = x372 * x84 x374 = x170 * x354 x375 = 4.0 * x129 x376 = x0 * (x325 * x375 + x340) + x212 * x354 x377 = x129 * x360 x378 = x364 + x377 x379 = x103 * x378 x380 = x212 * x366 + x371 x381 = x103 * x380 x382 = 0.0416666666666666667 * x380 x383 = x0 * (x140 + x345 + x363) + x129 * (x332 * x358 + x356) x384 = x33 * (2.0 * x364 + x365 + x377 + x383) x385 = x380 * x73 + x384 x386 = x385 * x99 x387 = x129 * x376 + x33 * (x129 * x352 + 2.0 * x350 + x353) x388 = 0.0166666666666666667 * x387 x389 = x358 * x375 x390 = x0 * (x370 + x376 + x389) + x212 * x378 x391 = x390 * x84 x392 = x129 * x380 + x384 # 300 item(s) result[0] += x62 * ( x0 * (x33 * (x16 + x28 + x32) + x36 * x37 + x37 * x46 + x46 * x53 + 5.0 * x52) + x27 * x57 ) result[1] += x67 * x70 result[2] += x70 * x74 result[3] += x77 * x85 result[4] += x73 * x80 * x88 result[5] += x85 * x90 result[6] += x91 * x94 result[7] += x77 * x95 * x96 result[8] += x90 * x93 * x96 result[9] += x91 * x97 result[10] += x100 * x98 result[11] += x102 * x104 result[12] += x105 * x74 * x98 result[13] += x112 * x113 result[14] += x115 * x116 * x95 result[15] += x118 * x79 * x98 result[16] += x123 * x125 result[17] += x112 * x126 * x73 result[18] += x102 * x118 * x78 result[19] += x127 * x128 * x98 result[20] += x100 * x129 result[21] += x105 * x129 * x67 result[22] += x104 * x131 result[23] += x129 * x132 * x79 result[24] += x116 * x133 * x93 result[25] += x113 * x140 result[26] += x128 * x129 * x141 result[27] += x131 * x132 * x78 result[28] += x126 * x140 * x65 result[29] += x125 * x146 result[30] += x148 * x150 result[31] += x152 * x153 result[32] += x148 * x154 * x95 result[33] += x155 * x157 result[34] += x152 * x158 * x159 result[35] += x118 * x148 * x44 result[36] += x161 * x162 result[37] += x155 * x163 * x73 result[38] += x118 * x152 * x42 result[39] += x127 * x148 * x164 result[40] += x149 * x165 * x98 result[41] += x115 * x129 * x166 result[42] += x133 * x166 * x98 result[43] += x112 * x159 * x167 result[44] += x102 * x168 * x44 result[45] += x140 * x159 * x169 result[46] += x122 * x129 * x171 result[47] += x112 * x133 * x172 result[48] += x115 * x140 * x172 result[49] += x145 * x171 * x98 result[50] += x150 * x174 result[51] += x154 * x174 * x93 result[52] += x153 * x176 result[53] += x132 * x174 * x44 result[54] += x159 * x176 * x177 result[55] += x157 * x178 result[56] += x141 * x164 * x174 result[57] += x132 * x176 * x42 result[58] += x163 * x178 * x65 result[59] += x162 * x180 result[60] += x181 * x183 result[61] += x185 * x187 result[62] += x188 * x189 * x95 result[63] += x190 * x191 result[64] += x185 * x192 * x73 result[65] += x188 * x194 * x90 result[66] += x197 * x199 result[67] += x190 * x201 * x95 result[68] += x185 * x202 * x90 result[69] += x181 * x203 * x97 result[70] += x129 * x148 * x204 result[71] += x152 * x167 * x51 result[72] += x131 * x205 * x51 result[73] += x155 * x167 * x50 result[74] += x133 * x152 * x206 result[75] += x140 * x205 * x50 result[76] += x129 * x161 * x202 result[77] += x131 * x155 * x207 result[78] += x140 * x152 * x207 result[79] += x146 * x148 * x208 result[80] += x174 * x204 * x98 result[81] += x102 * x209 * x51 result[82] += x169 * x176 * x51 result[83] += x112 * x209 * x50 result[84] += x115 * x176 * x206 result[85] += x169 * x178 * x50 result[86] += x123 * x174 * x208 result[87] += x112 * x176 * x207 result[88] += x102 * x178 * x207 result[89] += x180 * x202 * x98 result[90] += x183 * x210 result[91] += x189 * x211 * x93 result[92] += x187 * x213 result[93] += x194 * x211 * x77 result[94] += x192 * x213 * x65 result[95] += x191 * x214 result[96] += x203 * x210 * x94 result[97] += x202 * x213 * x77 result[98] += x201 * x214 * x93 result[99] += x199 * x217 result[100] += x221 * x225 result[101] += x226 * x234 result[102] += x235 * x236 * x95 result[103] += x239 * x242 result[104] += x239 * x243 * x73 result[105] += x239 * x244 * x90 result[106] += x246 * x247 result[107] += x241 * x249 * x95 result[108] += x248 * x250 * x90 result[109] += x247 * x251 * x97 result[110] += x220 * x257 result[111] += x263 * x28 result[112] += x158 * x256 * x28 result[113] += x238 * x268 result[114] += x158 * x238 * x269 result[115] += x118 * x238 * x256 result[116] += x270 * x276 result[117] += x267 * x277 * x95 result[118] += x118 * x262 * x270 result[119] += x127 * x256 * x278 result[120] += x129 * x220 * x244 result[121] += x167 * x233 * x28 result[122] += x131 * x279 * x28 result[123] += x167 * x238 * x241 result[124] += x233 * x238 * x280 result[125] += x140 * x238 * x279 result[126] += x129 * x270 * x281 result[127] += x131 * x241 * x282 result[128] += x140 * x233 * x282 result[129] += x146 * x224 * x283 result[130] += x285 * x287 result[131] += x26 * x290 result[132] += x158 * x26 * x285 result[133] += x291 * x293 result[134] += x289 * x295 * x95 result[135] += x118 * x285 * x291 result[136] += x299 * x3 result[137] += x3 * x300 * x74 result[138] += x118 * x289 * x3 result[139] += x127 * x285 * x301 result[140] += x129 * x286 * x302 result[141] += x167 * x26 * x269 result[142] += x256 * x26 * x280 result[143] += x129 * x267 * x303 result[144] += x168 * x262 * x291 result[145] += x140 * x256 * x303 result[146] += x165 * x275 * x3 result[147] += x267 * x280 * x3 result[148] += x140 * x269 * x304 result[149] += x145 * x3 * x302 result[150] += x174 * x244 * x286 result[151] += x209 * x233 * x26 result[152] += x176 * x26 * x279 result[153] += x209 * x241 * x291 result[154] += x176 * x233 * x303 result[155] += x178 * x279 * x291 result[156] += x174 * x281 * x3 result[157] += x176 * x241 * x304 result[158] += x178 * x233 * x304 result[159] += x180 * x244 * x3 result[160] += x305 * x308 result[161] += x309 * x312 result[162] += x313 * x314 * x95 result[163] += x315 * x316 result[164] += x311 * x74 * x87 * x9 result[165] += x305 * x317 * x90 result[166] += x62 * ( x0 * ( x195 * x267 + x195 * x296 + x196 * x267 + 5.0 * x274 + x33 * (x155 + x271 + x272 + x310) ) + x184 * x298 ) result[167] += x315 * x69 * x74 result[168] += x312 * x90 result[169] += x313 * x97 result[170] += x129 * x285 * x318 result[171] += x129 * x289 * x319 result[172] += x131 * x285 * x319 result[173] += x129 * x300 * x320 result[174] += x280 * x289 * x9 result[175] += x140 * x285 * x321 result[176] += x129 * x299 result[177] += x131 * x293 result[178] += x140 * x290 result[179] += x124 * x146 * x285 result[180] += x174 * x256 * x323 result[181] += x209 * x262 * x309 result[182] += x176 * x256 * x319 result[183] += x209 * x267 * x9 result[184] += x176 * x269 * x321 result[185] += x178 * x256 * x321 result[186] += x174 * x276 result[187] += x176 * x268 result[188] += x178 * x263 result[189] += x180 * x257 result[190] += x210 * x251 * x324 result[191] += x210 * x250 * x314 result[192] += x213 * x244 * x309 result[193] += x210 * x241 * x317 result[194] += x213 * x243 * x9 result[195] += x214 * x235 * x307 result[196] += x210 * x246 result[197] += x213 * x242 result[198] += x214 * x234 result[199] += x217 * x225 result[200] += x221 * x328 result[201] += x236 * x329 * x93 result[202] += x226 * x337 result[203] += x239 * x338 * x77 result[204] += x239 * x339 * x65 result[205] += x239 * x342 result[206] += x247 * x343 * x94 result[207] += x248 * x344 * x77 result[208] += x249 * x341 * x93 result[209] += x247 * x346 result[210] += x220 * x338 * x98 result[211] += x102 * x28 * x347 result[212] += x169 * x28 * x336 result[213] += x112 * x238 * x347 result[214] += x238 * x336 * x348 result[215] += x169 * x238 * x341 result[216] += x123 * x283 * x327 result[217] += x112 * x282 * x336 result[218] += x102 * x282 * x341 result[219] += x270 * x349 * x98 result[220] += x220 * x355 result[221] += x177 * x28 * x354 result[222] += x28 * x361 result[223] += x132 * x238 * x354 result[224] += x177 * x238 * x362 result[225] += x238 * x367 result[226] += x141 * x278 * x354 result[227] += x132 * x270 * x360 result[228] += x277 * x366 * x93 result[229] += x270 * x373 result[230] += x148 * x286 * x338 result[231] += x152 * x26 * x347 result[232] += x205 * x26 * x336 result[233] += x155 * x291 * x347 result[234] += x152 * x303 * x336 result[235] += x205 * x291 * x341 result[236] += x161 * x3 * x338 result[237] += x155 * x304 * x336 result[238] += x152 * x304 * x341 result[239] += x148 * x3 * x349 result[240] += x286 * x374 * x98 result[241] += x26 * x348 * x354 result[242] += x169 * x26 * x362 result[243] += x112 * x303 * x354 result[244] += 0.25 * x102 * x291 * x360 * x82 result[245] += x303 * x366 * x98 result[246] += x122 * x3 * x374 result[247] += x112 * x304 * x362 result[248] += x3 * x348 * x366 result[249] += x3 * x372 * x66 * x87 * x98 result[250] += x287 * x376 result[251] += x177 * x26 * x376 result[252] += x26 * x379 result[253] += x132 * x291 * x376 result[254] += x295 * x378 * x93 result[255] += x291 * x381 result[256] += x141 * x301 * x376 result[257] += x132 * x3 * x378 result[258] += x3 * x382 * x67 result[259] += x3 * x386 result[260] += x181 * x324 * x343 result[261] += x182 * x185 * x314 * x327 result[262] += x181 * x314 * x344 result[263] += x190 * x317 * x327 result[264] += x185 * x339 * x9 result[265] += x181 * x317 * x341 result[266] += x197 * x328 result[267] += x190 * x337 result[268] += x185 * x342 result[269] += x181 * x346 result[270] += x148 * x323 * x354 result[271] += x152 * x319 * x354 result[272] += x205 * x309 * x360 result[273] += x155 * x321 * x354 result[274] += x152 * x321 * x362 result[275] += x205 * x366 * x9 result[276] += x161 * x355 result[277] += x155 * x361 result[278] += x152 * x367 result[279] += x148 * x373 result[280] += x318 * x376 * x98 result[281] += x102 * x319 * x376 result[282] += x319 * x378 * x98 result[283] += x112 * x321 * x376 result[284] += x348 * x378 * x9 result[285] += x320 * x382 * x98 result[286] += x123 * x124 * x376 result[287] += x112 * x379 result[288] += x102 * x381 result[289] += x386 * x98 result[290] += x308 * x387 result[291] += x314 * x388 * x93 result[292] += x309 * x391 result[293] += x317 * x387 * x77 result[294] += x390 * x88 * x9 result[295] += x316 * x392 result[296] += x388 * x94 result[297] += x391 * x77 result[298] += x392 * x67 * x69 result[299] += x62 * ( x0 * ( x215 * x366 + x215 * x383 + x216 * x366 + x33 * (x178 + x368 + x369 + x389) + 5.0 * x371 ) + x212 * x385 )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_43(ax, da, A, bx, db, B, R, result): """Cartesian 3D (gf) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = 0.5 / (ax + bx) x1 = (ax + bx) ** (-1.0) x2 = ax * bx * x1 x3 = numpy.exp(-x2 * (A[0] - B[0]) ** 2) x4 = 1.77245385090551603 * numpy.sqrt(x1) x5 = x3 * x4 x6 = x0 * x5 x7 = 3.0 * x6 x8 = -x1 * (ax * A[0] + bx * B[0]) x9 = -x8 - B[0] x10 = -x8 - A[0] x11 = x10 * x5 x12 = x11 * x9 x13 = -x8 - R[0] x14 = x11 * x13 x15 = x5 * x9 x16 = x13 * x15 x17 = x0 * (x12 + x14 + x16 + x7) x18 = x13 * x5 x19 = x0 * (x15 + x18) x20 = x16 + x6 x21 = x10 * x20 x22 = x19 + x21 x23 = x22 * x9 x24 = x17 + x23 x25 = 2.0 * x9 x26 = x10 * x24 x27 = x20 * x9 x28 = x0 * (x11 + x15) x29 = x12 + x6 x30 = x29 * x9 x31 = x28 + x30 x32 = 2.0 * x21 x33 = 3.0 * x19 + x32 x34 = x0 * (x27 + x31 + x33) x35 = x10 * x29 x36 = 2.0 * x0 * (2.0 * x28 + x30 + x35) x37 = x5 * x9**2 x38 = x11 * x25 + x7 x39 = x0 * (x37 + x38) x40 = x10 * x31 x41 = x39 + x40 x42 = x41 * x9 x43 = x36 + x42 x44 = 2.0 * x0 x45 = x10 * x22 x46 = 2.0 * x45 x47 = 4.0 * x17 x48 = 2.0 * x23 + x47 x49 = x0 * (x41 + x46 + x48) x50 = x26 + x34 x51 = x50 * x9 x52 = 2.0 * x10 x53 = x13 * x22 x54 = 2.0 * x53 x55 = x13**2 * x5 x56 = x55 + x7 x57 = x13 * x20 x58 = x19 + x57 x59 = x0 * (x18 * x25 + x56) + x58 * x9 x60 = x0 * (x48 + x54 + x59) x61 = x0 * (x11 + x18) x62 = x14 + x6 x63 = x13 * x62 x64 = x61 + x63 x65 = x0 * (x33 + x57 + x64) x66 = x17 + x53 x67 = x66 * x9 x68 = x65 + x67 x69 = x10 * x68 x70 = x60 + x69 x71 = x10 * x70 x72 = x70 * x9 x73 = x10 * x66 x74 = 2.0 * x0 * (x26 + x34 + 2.0 * x65 + x67 + x73) x75 = x68 * x9 x76 = 2.0 * x49 + 3.0 * x69 x77 = x72 + x74 x78 = x0 * (2.0 * x51 + 5.0 * x60 + 2.0 * x75 + x76) + x10 * x77 x79 = 2.64575131106459059 x80 = da * db x81 = 0.00952380952380952381 * x80 x82 = x79 * x81 x83 = numpy.exp(-x2 * (A[1] - B[1]) ** 2) x84 = numpy.exp(-x2 * (A[2] - B[2]) ** 2) x85 = 3.14159265358979324 * x1 * x84 x86 = x83 * x85 x87 = -x1 * (ax * A[1] + bx * B[1]) x88 = -x87 - B[1] x89 = 5.91607978309961604 x90 = x81 * x89 x91 = x88 * x90 x92 = x18 * x52 x93 = x0 * (x56 + x92) x94 = x10 * x64 x95 = x93 + x94 x96 = x0 * (x46 + x47 + x54 + x95) x97 = x65 + x73 x98 = x10 * x97 x99 = x71 + x74 x100 = x86 * (x0 * (x50 * x52 + 3.0 * x60 + x76 + 2.0 * x96 + 2.0 * x98) + x10 * x99) x101 = -x1 * (ax * A[2] + bx * B[2]) x102 = -x101 - B[2] x103 = x102 * x90 x104 = x10 * x62 x105 = x104 + x61 x106 = x28 + x35 x107 = 2.0 * x0 * (x104 + 2.0 * x61 + x63) + x10 * x95 x108 = x96 + x98 x109 = ( x0 * ( x107 + x44 * (x105 + x106 + 2.0 * x19 + x32) + x52 * (x17 + x45) + 3.0 * x65 + 3.0 * x73 ) + x10 * x108 ) x110 = x4 * x84 x111 = x4 * x83 x112 = x111 * x88**2 x113 = x0 * x111 x114 = x112 + x113 x115 = x114 * x89 x116 = x115 * x81 x117 = x102 * x86 x118 = 10.2469507659595984 x119 = x118 * x81 x120 = x119 * x88 x121 = x102**2 * x110 x122 = x0 * x110 x123 = x121 + x122 x124 = x123 * x89 x125 = x124 * x81 x126 = x111 * x88 x127 = x114 * x88 + x126 * x44 x128 = x127 * x79 x129 = x10**2 * x5 x130 = ( x0 * (x105 * x52 + x44 * (x129 + x7 + x92) + 3.0 * x93 + 3.0 * x94) + x10 * x107 ) x131 = x130 * x81 x132 = x102 * x110 x133 = x102 * x123 + x132 * x44 x134 = x133 * x79 x135 = -x87 - A[1] x136 = 0.0666666666666666667 * x80 x137 = x135 * x136 x138 = x78 * x86 x139 = x111 * x135 x140 = x139 * x88 x141 = x113 + x140 x142 = x136 * x141 x143 = 2.2360679774997897 x144 = x143 * x99 x145 = x136 * x143 x146 = x145 * x99 x147 = x0 * (x126 + x139) x148 = x141 * x88 x149 = x147 + x148 x150 = x108 * x145 x151 = 3.87298334620741689 x152 = x108 * x151 x153 = x123 * x143 x154 = x108 * x136 x155 = 3.0 * x113 x156 = 2.0 * x135 x157 = x126 * x156 + x155 x158 = x0 * (x112 + x157) x159 = x149 * x88 x160 = x158 + x159 x161 = x107 * x136 x162 = x107 * x145 x163 = -x101 - A[2] x164 = x136 * x163 x165 = x163 * x86 x166 = x110 * x163 x167 = x102 * x166 x168 = x122 + x167 x169 = x136 * x168 x170 = x114 * x143 x171 = x0 * (x132 + x166) x172 = x102 * x168 x173 = x171 + x172 x174 = 3.0 * x122 x175 = 2.0 * x163 x176 = x132 * x175 + x174 x177 = x0 * (x121 + x176) x178 = x102 * x173 x179 = x177 + x178 x180 = x111 * x135**2 x181 = x113 + x180 x182 = x181 * x80 x183 = 0.0222222222222222222 * x151 x184 = x182 * x183 x185 = x135 * x141 x186 = x147 + x185 x187 = 1.73205080756887729 x188 = x186 * x187 x189 = x110 * x80 x190 = 0.111111111111111111 * x70 x191 = x132 * x187 x192 = x187 * x97 x193 = x135 * x149 x194 = x158 + x193 x195 = 0.111111111111111111 * x194 x196 = 0.333333333333333333 * x80 x197 = x196 * x97 x198 = 0.111111111111111111 * x123 x199 = 2.0 * x0 * (2.0 * x147 + x148 + x185) x200 = x194 * x88 x201 = x199 + x200 x202 = x80 * x95 x203 = x183 * x202 x204 = x135 * x145 x205 = x166 * x196 x206 = x168 * x196 x207 = x145 * x95 x208 = x196 * x95 x209 = x110 * x163**2 x210 = x122 + x209 x211 = x210 * x80 x212 = x183 * x211 x213 = x126 * x187 x214 = x163 * x168 x215 = x171 + x214 x216 = x187 * x215 x217 = x111 * x80 x218 = 0.111111111111111111 * x114 x219 = x196 * x215 x220 = x163 * x173 x221 = x177 + x220 x222 = 0.111111111111111111 * x221 x223 = x127 * x183 x224 = 2.0 * x0 * (2.0 * x171 + x172 + x214) x225 = x102 * x221 x226 = x224 + x225 x227 = x60 + x75 x228 = x135 * x181 + x139 * x44 x229 = x136 * x228 x230 = x0 * (x157 + x180) x231 = x135 * x186 x232 = x230 + x231 x233 = x110 * x145 x234 = x143 * x229 x235 = x135 * x194 x236 = x199 + x235 x237 = x151 * x66 x238 = x136 * x232 x239 = 3.0 * x193 x240 = x0 * (5.0 * x158 + 2.0 * x159 + x239) + x135 * x201 x241 = x136 * x64 x242 = x143 * x241 x243 = x145 * x227 x244 = x181 * x196 x245 = x196 * x64 x246 = x196 * x210 x247 = x187 * x219 x248 = x196 * x221 x249 = x163 * x210 + x166 * x44 x250 = x136 * x249 x251 = x143 * x250 x252 = x0 * (x176 + x209) x253 = x163 * x215 x254 = x252 + x253 x255 = x111 * x145 x256 = x136 * x254 x257 = x163 * x221 x258 = x224 + x257 x259 = 3.0 * x220 x260 = x0 * (5.0 * x177 + 2.0 * x178 + x259) + x163 * x226 x261 = 2.0 * x0 * (2.0 * x19 + x27 + x57) + x59 * x9 x262 = x81 * (x0 * (x155 + 3.0 * x180) + x135 * x228) x263 = x110 * x79 x264 = x0 * (3.0 * x147 + 3.0 * x185 + x228) + x135 * x232 x265 = x110 * x90 x266 = x132 * x89 x267 = x0 * (3.0 * x158 + 2.0 * x230 + 2.0 * x231 + x239) + x135 * x236 x268 = x132 * x81 x269 = x118 * x58 x270 = 3.0 * x0 * (2.0 * x199 + x200 + x235) + x135 * x240 x271 = x55 + x6 x272 = x271 * x81 x273 = x145 * x166 x274 = x151 * x58 x275 = x136 * x271 x276 = x143 * x275 x277 = 0.111111111111111111 * x59 x278 = x187 * x58 x279 = x271 * x80 x280 = x139 * x145 x281 = x0 * (x174 + 3.0 * x209) + x163 * x249 x282 = x281 * x81 x283 = x111 * x79 x284 = x126 * x89 x285 = x0 * (3.0 * x171 + 3.0 * x214 + x249) + x163 * x254 x286 = x111 * x90 x287 = x285 * x81 x288 = x0 * (3.0 * x177 + 2.0 * x252 + 2.0 * x253 + x259) + x163 * x258 x289 = 3.0 * x0 * (2.0 * x224 + x225 + x257) + x163 * x260 x290 = x10 * x41 x291 = x31 * x9 x292 = 3.0 * x40 x293 = x0 * (2.0 * x291 + x292 + 5.0 * x39) + x10 * x43 x294 = 3.0 * x0 * (x290 + 2.0 * x36 + x42) + x10 * x293 x295 = -x87 - R[1] x296 = x111 * x295**2 x297 = x113 + x296 x298 = x297 * x81 x299 = x111 * x295 x300 = x0 * (x126 + x299) x301 = x126 * x295 x302 = x113 + x301 x303 = x295 * x302 x304 = x300 + x303 x305 = x0 * (x129 + x38) x306 = x10 * x106 x307 = x290 + x36 x308 = x0 * (x292 + 2.0 * x305 + 2.0 * x306 + 3.0 * x39) + x10 * x307 x309 = 2.0 * x88 x310 = x155 + x296 x311 = x0 * (x299 * x309 + x310) + x304 * x88 x312 = x129 + x6 x313 = x10 * x312 + x11 * x44 x314 = x305 + x306 x315 = x0 * (3.0 * x28 + x313 + 3.0 * x35) + x10 * x314 x316 = x118 * x304 x317 = x302 * x88 x318 = 2.0 * x0 * (2.0 * x300 + x303 + x317) + x311 * x88 x319 = x0 * (3.0 * x129 + x7) + x10 * x313 x320 = x319 * x82 x321 = x319 * x90 x322 = x0 * (x139 + x299) x323 = x139 * x295 x324 = x113 + x323 x325 = x295 * x324 x326 = x322 + x325 x327 = x110 * x136 x328 = x0 * (x140 + x155 + x301 + x323) x329 = x135 * x302 x330 = x300 + x329 x331 = x295 * x330 x332 = x328 + x331 x333 = x145 * x326 x334 = 2.0 * x329 x335 = 3.0 * x300 + x334 x336 = x0 * (x303 + x326 + x335) x337 = x332 * x88 x338 = x336 + x337 x339 = x136 * x314 x340 = x143 * x339 x341 = x132 * x151 x342 = x330 * x88 x343 = 2.0 * x342 x344 = 4.0 * x328 x345 = 2.0 * x331 + x344 x346 = x0 * (x311 + x343 + x345) x347 = x338 * x88 x348 = x346 + x347 x349 = x136 * x313 x350 = x143 * x349 x351 = x136 * x297 x352 = x143 * x297 x353 = x151 * x304 x354 = x156 * x299 x355 = x0 * (x310 + x354) x356 = x135 * x326 x357 = x355 + x356 x358 = x357 * x80 x359 = x183 * x358 x360 = x135 * x332 x361 = x336 + x360 x362 = x187 * x361 x363 = 0.111111111111111111 * x41 x364 = x106 * x187 x365 = x135 * x338 x366 = x346 + x365 x367 = 0.111111111111111111 * x366 x368 = x106 * x196 x369 = x0 * (x149 + x317 + x335) x370 = x328 + x342 x371 = x135 * x370 x372 = 2.0 * x0 * (2.0 * x336 + x337 + x360 + x369 + x371) x373 = x366 * x88 x374 = x372 + x373 x375 = x312 * x80 x376 = x183 * x375 x377 = x196 * x326 x378 = x187 * x368 x379 = x196 * x312 x380 = x187 * x304 x381 = x297 * x80 x382 = 0.111111111111111111 * x311 x383 = x135 * x324 x384 = 2.0 * x0 * (2.0 * x322 + x325 + x383) + x135 * x357 x385 = x291 + x39 x386 = x135 * x330 x387 = 2.0 * x386 x388 = x0 * (x345 + x357 + x387) x389 = x135 * x361 x390 = x388 + x389 x391 = x145 * x384 x392 = x135 * x366 x393 = x372 + x392 x394 = x136 * x29 x395 = x369 + x371 x396 = x395 * x88 x397 = x0 * (x194 + x343 + x344 + x387) x398 = 3.0 * x365 + 2.0 * x397 x399 = x0 * (5.0 * x346 + 2.0 * x347 + 2.0 * x396 + x398) + x135 * x374 x400 = x3 * x85 x401 = x399 * x400 x402 = x10 * x136 x403 = x102 * x400 x404 = x10 * x145 x405 = x11 * x136 x406 = x136 * x384 x407 = x196 * x357 x408 = x196 * x29 x409 = x163 * x400 x410 = x11 * x196 x411 = x11 * x145 x412 = x322 + x383 x413 = ( x0 * (x156 * x412 + 3.0 * x355 + 3.0 * x356 + x44 * (x155 + x180 + x354)) + x135 * x384 ) x414 = x37 + x6 x415 = x25 * x6 + x414 * x9 x416 = x415 * x79 x417 = x110 * x81 x418 = ( x0 * ( x156 * (x328 + x386) + 3.0 * x336 + 3.0 * x360 + x384 + x44 * (x186 + 2.0 * x300 + x334 + x412) ) + x135 * x390 ) x419 = x414 * x89 x420 = x400 * ( x0 * (x156 * x395 + 3.0 * x346 + 2.0 * x388 + 2.0 * x389 + x398) + x135 * x393 ) x421 = x9 * x90 x422 = x5 * x81 x423 = x143 * x414 x424 = x15 * x151 x425 = x143 * x5 x426 = x145 * x5 x427 = x136 * x5 x428 = 0.111111111111111111 * x414 x429 = x15 * x187 x430 = x5 * x80 x431 = x15 * x89 x432 = x5 * x79 x433 = x5 * x90 x434 = -x101 - R[2] x435 = x110 * x434**2 x436 = x122 + x435 x437 = x436 * x81 x438 = x110 * x434 x439 = x0 * (x132 + x438) x440 = x132 * x434 x441 = x122 + x440 x442 = x434 * x441 x443 = x439 + x442 x444 = x126 * x81 x445 = x118 * x443 x446 = 2.0 * x102 x447 = x174 + x435 x448 = x0 * (x438 * x446 + x447) + x102 * x443 x449 = x102 * x441 x450 = 2.0 * x0 * (2.0 * x439 + x442 + x449) + x102 * x448 x451 = x136 * x436 x452 = x143 * x436 x453 = x151 * x443 x454 = x0 * (x166 + x438) x455 = x166 * x434 x456 = x122 + x455 x457 = x434 * x456 x458 = x454 + x457 x459 = x111 * x136 x460 = x145 * x458 x461 = x0 * (x167 + x174 + x440 + x455) x462 = x163 * x441 x463 = x439 + x462 x464 = x434 * x463 x465 = x461 + x464 x466 = x126 * x151 x467 = 2.0 * x462 x468 = 3.0 * x439 + x467 x469 = x0 * (x442 + x458 + x468) x470 = x102 * x465 x471 = x469 + x470 x472 = x102 * x463 x473 = 2.0 * x472 x474 = 4.0 * x461 x475 = 2.0 * x464 + x474 x476 = x0 * (x448 + x473 + x475) x477 = x102 * x471 x478 = x476 + x477 x479 = x436 * x80 x480 = x187 * x443 x481 = 0.111111111111111111 * x448 x482 = x196 * x458 x483 = x139 * x196 x484 = x175 * x438 x485 = x0 * (x447 + x484) x486 = x163 * x458 x487 = x485 + x486 x488 = x487 * x80 x489 = x183 * x488 x490 = x163 * x465 x491 = x469 + x490 x492 = x187 * x491 x493 = x163 * x471 x494 = x476 + x493 x495 = 0.111111111111111111 * x494 x496 = x0 * (x173 + x449 + x468) x497 = x461 + x472 x498 = x163 * x497 x499 = 2.0 * x0 * (2.0 * x469 + x470 + x490 + x496 + x498) x500 = x102 * x494 x501 = x499 + x500 x502 = x145 * x436 x503 = x196 * x487 x504 = 3.14159265358979324 * x1 * x3 * x83 x505 = x204 * x504 x506 = x163 * x456 x507 = 2.0 * x0 * (2.0 * x454 + x457 + x506) + x163 * x487 x508 = x145 * x507 x509 = x163 * x463 x510 = 2.0 * x509 x511 = x0 * (x475 + x487 + x510) x512 = x163 * x491 x513 = x511 + x512 x514 = x163 * x494 x515 = x499 + x514 x516 = x136 * x507 x517 = x496 + x498 x518 = x102 * x517 x519 = x0 * (x221 + x473 + x474 + x510) x520 = 3.0 * x493 + 2.0 * x519 x521 = x0 * (5.0 * x476 + 2.0 * x477 + 2.0 * x518 + x520) + x163 * x501 x522 = x504 * x521 x523 = x454 + x506 x524 = ( x0 * (x175 * x523 + x44 * (x174 + x209 + x484) + 3.0 * x485 + 3.0 * x486) + x163 * x507 ) x525 = x111 * x81 x526 = ( x0 * ( x175 * (x461 + x509) + x44 * (x215 + 2.0 * x439 + x467 + x523) + 3.0 * x469 + 3.0 * x490 + x507 ) + x163 * x513 ) x527 = x504 * ( x0 * (x175 * x517 + 3.0 * x476 + 2.0 * x511 + 2.0 * x512 + x520) + x163 * x515 ) # 450 item(s) result[0] += ( x82 * x86 * ( x0 * ( x44 * (x24 * x25 + 3.0 * x26 + 5.0 * x34 + x43) + x52 * (x49 + x51) + 3.0 * x71 + 3.0 * x72 + 6.0 * x74 ) + x10 * x78 ) ) result[1] += x100 * x91 result[2] += x100 * x103 result[3] += x109 * x110 * x116 result[4] += x109 * x117 * x120 result[5] += x109 * x111 * x125 result[6] += x110 * x128 * x131 result[7] += x116 * x130 * x132 result[8] += x125 * x126 * x130 result[9] += x111 * x131 * x134 result[10] += x137 * x138 result[11] += x110 * x142 * x144 result[12] += x117 * x135 * x146 result[13] += x110 * x149 * x150 result[14] += x132 * x142 * x152 result[15] += x139 * x153 * x154 result[16] += x110 * x160 * x161 result[17] += x132 * x149 * x162 result[18] += x107 * x142 * x153 result[19] += x133 * x139 * x161 result[20] += x138 * x164 result[21] += x146 * x165 * x88 result[22] += x111 * x144 * x169 result[23] += x154 * x166 * x170 result[24] += x126 * x152 * x169 result[25] += x111 * x150 * x173 result[26] += x127 * x161 * x166 result[27] += x107 * x169 * x170 result[28] += x126 * x162 * x173 result[29] += x111 * x161 * x179 result[30] += x110 * x184 * x77 result[31] += x188 * x189 * x190 result[32] += x182 * x190 * x191 result[33] += x189 * x192 * x195 result[34] += x132 * x186 * x197 result[35] += x182 * x192 * x198 result[36] += x110 * x201 * x203 result[37] += x191 * x195 * x202 result[38] += x188 * x198 * x202 result[39] += x133 * x184 * x95 result[40] += x165 * x204 * x77 result[41] += x141 * x205 * x70 result[42] += x139 * x206 * x70 result[43] += x149 * x166 * x197 result[44] += x141 * x192 * x206 result[45] += x139 * x173 * x197 result[46] += x160 * x166 * x207 result[47] += x149 * x168 * x208 result[48] += x141 * x173 * x208 result[49] += x139 * x179 * x207 result[50] += x111 * x212 * x77 result[51] += x190 * x211 * x213 result[52] += x190 * x216 * x217 result[53] += x192 * x211 * x218 result[54] += x126 * x219 * x97 result[55] += x192 * x217 * x222 result[56] += x202 * x210 * x223 result[57] += x202 * x216 * x218 result[58] += x202 * x213 * x222 result[59] += x111 * x203 * x226 result[60] += x110 * x227 * x229 result[61] += x232 * x233 * x68 result[62] += x132 * x234 * x68 result[63] += x233 * x236 * x66 result[64] += x132 * x237 * x238 result[65] += x153 * x229 * x66 result[66] += x110 * x240 * x241 result[67] += x132 * x236 * x242 result[68] += x153 * x232 * x241 result[69] += x133 * x228 * x241 result[70] += x166 * x181 * x243 result[71] += x186 * x205 * x68 result[72] += x168 * x244 * x68 result[73] += x194 * x205 * x66 result[74] += x188 * x206 * x66 result[75] += x173 * x244 * x66 result[76] += x166 * x201 * x242 result[77] += x168 * x194 * x245 result[78] += x173 * x186 * x245 result[79] += x179 * x181 * x242 result[80] += x139 * x210 * x243 result[81] += x141 * x246 * x68 result[82] += x139 * x219 * x68 result[83] += x149 * x246 * x66 result[84] += x141 * x247 * x66 result[85] += x139 * x248 * x66 result[86] += x160 * x210 * x242 result[87] += x149 * x215 * x245 result[88] += x141 * x221 * x245 result[89] += x139 * x226 * x242 result[90] += x111 * x227 * x250 result[91] += x126 * x251 * x68 result[92] += x254 * x255 * x68 result[93] += x170 * x250 * x66 result[94] += x126 * x237 * x256 result[95] += x255 * x258 * x66 result[96] += x127 * x241 * x249 result[97] += x170 * x241 * x254 result[98] += x126 * x242 * x258 result[99] += x111 * x241 * x260 result[100] += x261 * x262 * x263 result[101] += x264 * x265 * x59 result[102] += x262 * x266 * x59 result[103] += x265 * x267 * x58 result[104] += x264 * x268 * x269 result[105] += x124 * x262 * x58 result[106] += x263 * x270 * x272 result[107] += x266 * x267 * x272 result[108] += x124 * x264 * x272 result[109] += x134 * x262 * x271 result[110] += x166 * x229 * x261 result[111] += x232 * x273 * x59 result[112] += x168 * x234 * x59 result[113] += x236 * x273 * x58 result[114] += x169 * x232 * x274 result[115] += x173 * x234 * x58 result[116] += x166 * x240 * x275 result[117] += x168 * x236 * x276 result[118] += x173 * x232 * x276 result[119] += x179 * x228 * x275 result[120] += x184 * x210 * x261 result[121] += x188 * x211 * x277 result[122] += x182 * x216 * x277 result[123] += x195 * x211 * x278 result[124] += x186 * x219 * x58 result[125] += x182 * x222 * x278 result[126] += x201 * x212 * x271 result[127] += x195 * x216 * x279 result[128] += x188 * x222 * x279 result[129] += x184 * x226 * x271 result[130] += x139 * x250 * x261 result[131] += x141 * x251 * x59 result[132] += x254 * x280 * x59 result[133] += x149 * x251 * x58 result[134] += x142 * x254 * x274 result[135] += x258 * x280 * x58 result[136] += x160 * x249 * x275 result[137] += x149 * x254 * x276 result[138] += x141 * x258 * x276 result[139] += x139 * x260 * x275 result[140] += x261 * x282 * x283 result[141] += x282 * x284 * x59 result[142] += x285 * x286 * x59 result[143] += x115 * x282 * x58 result[144] += x126 * x269 * x287 result[145] += x286 * x288 * x58 result[146] += x128 * x272 * x281 result[147] += x115 * x272 * x285 result[148] += x272 * x284 * x288 result[149] += x272 * x283 * x289 result[150] += x263 * x294 * x298 result[151] += x265 * x304 * x308 result[152] += x266 * x298 * x308 result[153] += x265 * x311 * x315 result[154] += x268 * x315 * x316 result[155] += x125 * x297 * x315 result[156] += x110 * x318 * x320 result[157] += x132 * x311 * x321 result[158] += x125 * x304 * x319 result[159] += x134 * x298 * x319 result[160] += x293 * x326 * x327 result[161] += x233 * x307 * x332 result[162] += x132 * x307 * x333 result[163] += x110 * x338 * x340 result[164] += x332 * x339 * x341 result[165] += x153 * x326 * x339 result[166] += x110 * x348 * x349 result[167] += x132 * x338 * x350 result[168] += x153 * x332 * x349 result[169] += x133 * x326 * x349 result[170] += x166 * x293 * x351 result[171] += x273 * x304 * x307 result[172] += x169 * x307 * x352 result[173] += x166 * x311 * x340 result[174] += x169 * x314 * x353 result[175] += x173 * x339 * x352 result[176] += x166 * x318 * x349 result[177] += x168 * x311 * x350 result[178] += x173 * x304 * x350 result[179] += x179 * x297 * x349 result[180] += x110 * x359 * x43 result[181] += x189 * x362 * x363 result[182] += x191 * x358 * x363 result[183] += x189 * x364 * x367 result[184] += x132 * x361 * x368 result[185] += x198 * x358 * x364 result[186] += x110 * x374 * x376 result[187] += x191 * x367 * x375 result[188] += x198 * x362 * x375 result[189] += x133 * x312 * x359 result[190] += x166 * x333 * x43 result[191] += x205 * x332 * x41 result[192] += x168 * x377 * x41 result[193] += x166 * x338 * x368 result[194] += x168 * x332 * x378 result[195] += x106 * x173 * x377 result[196] += x273 * x312 * x348 result[197] += x168 * x338 * x379 result[198] += x173 * x332 * x379 result[199] += x179 * x312 * x333 result[200] += x212 * x297 * x43 result[201] += x211 * x363 * x380 result[202] += x216 * x363 * x381 result[203] += x211 * x364 * x382 result[204] += x106 * x219 * x304 result[205] += x222 * x364 * x381 result[206] += x212 * x312 * x318 result[207] += x216 * x375 * x382 result[208] += x222 * x375 * x380 result[209] += x226 * x297 * x376 result[210] += x327 * x384 * x385 result[211] += x233 * x31 * x390 result[212] += x132 * x31 * x391 result[213] += x233 * x29 * x393 result[214] += x341 * x390 * x394 result[215] += x153 * x384 * x394 result[216] += x401 * x402 result[217] += x393 * x403 * x404 result[218] += x153 * x390 * x405 result[219] += x11 * x133 * x406 result[220] += x273 * x357 * x385 result[221] += x205 * x31 * x361 result[222] += x168 * x31 * x407 result[223] += x166 * x366 * x408 result[224] += x206 * x29 * x362 result[225] += x173 * x29 * x407 result[226] += x374 * x404 * x409 result[227] += x11 * x206 * x366 result[228] += x173 * x361 * x410 result[229] += x179 * x357 * x411 result[230] += x210 * x333 * x385 result[231] += x246 * x31 * x332 result[232] += x219 * x31 * x326 result[233] += x246 * x29 * x338 result[234] += x247 * x29 * x332 result[235] += x221 * x29 * x377 result[236] += x210 * x348 * x411 result[237] += x11 * x219 * x338 result[238] += x11 * x248 * x332 result[239] += x11 * x226 * x333 result[240] += x250 * x297 * x385 result[241] += x251 * x304 * x31 result[242] += x256 * x31 * x352 result[243] += x251 * x29 * x311 result[244] += x254 * x353 * x394 result[245] += x258 * x352 * x394 result[246] += x11 * x250 * x318 result[247] += x254 * x311 * x411 result[248] += x258 * x304 * x411 result[249] += x11 * x260 * x351 result[250] += x413 * x416 * x417 result[251] += x417 * x418 * x419 result[252] += x268 * x413 * x419 result[253] += x420 * x421 result[254] += x119 * x403 * x418 * x9 result[255] += x125 * x15 * x413 result[256] += ( x400 * x82 * ( x0 * ( x156 * (x396 + x397) + 6.0 * x372 + 3.0 * x373 + 3.0 * x392 + x44 * (x201 + x309 * x370 + 5.0 * x369 + 3.0 * x371) ) + x135 * x399 ) ) result[257] += x103 * x420 result[258] += x125 * x418 * x5 result[259] += x134 * x413 * x422 result[260] += x166 * x406 * x415 result[261] += x273 * x390 * x414 result[262] += x169 * x384 * x423 result[263] += x145 * x393 * x409 * x9 result[264] += x169 * x390 * x424 result[265] += x15 * x173 * x391 result[266] += x164 * x401 result[267] += x169 * x393 * x425 result[268] += x173 * x390 * x426 result[269] += x179 * x384 * x427 result[270] += x212 * x357 * x415 result[271] += x211 * x362 * x428 result[272] += x216 * x358 * x428 result[273] += x211 * x367 * x429 result[274] += x15 * x219 * x361 result[275] += x222 * x358 * x429 result[276] += x212 * x374 * x5 result[277] += x216 * x367 * x430 result[278] += x222 * x362 * x430 result[279] += x226 * x359 * x5 result[280] += x250 * x326 * x415 result[281] += x251 * x332 * x414 result[282] += x254 * x333 * x414 result[283] += x15 * x251 * x338 result[284] += x256 * x332 * x424 result[285] += x15 * x258 * x333 result[286] += x250 * x348 * x5 result[287] += x254 * x338 * x426 result[288] += x258 * x332 * x426 result[289] += x260 * x326 * x427 result[290] += x282 * x297 * x416 result[291] += x282 * x304 * x419 result[292] += x285 * x298 * x419 result[293] += x282 * x311 * x431 result[294] += x15 * x287 * x316 result[295] += x288 * x298 * x431 result[296] += x282 * x318 * x432 result[297] += x285 * x311 * x433 result[298] += x288 * x304 * x433 result[299] += x289 * x298 * x432 result[300] += x283 * x294 * x437 result[301] += x284 * x308 * x437 result[302] += x286 * x308 * x443 result[303] += x115 * x315 * x437 result[304] += x315 * x444 * x445 result[305] += x286 * x315 * x448 result[306] += x128 * x319 * x437 result[307] += x116 * x319 * x443 result[308] += x126 * x321 * x448 result[309] += x111 * x320 * x450 result[310] += x139 * x293 * x451 result[311] += x142 * x307 * x452 result[312] += x280 * x307 * x443 result[313] += x149 * x339 * x452 result[314] += x142 * x314 * x453 result[315] += x139 * x340 * x448 result[316] += x160 * x349 * x436 result[317] += x149 * x350 * x443 result[318] += x141 * x350 * x448 result[319] += x139 * x349 * x450 result[320] += x293 * x458 * x459 result[321] += x126 * x307 * x460 result[322] += x255 * x307 * x465 result[323] += x170 * x339 * x458 result[324] += x339 * x465 * x466 result[325] += x111 * x340 * x471 result[326] += x127 * x349 * x458 result[327] += x170 * x349 * x465 result[328] += x126 * x350 * x471 result[329] += x111 * x349 * x478 result[330] += x184 * x43 * x436 result[331] += x188 * x363 * x479 result[332] += x182 * x363 * x480 result[333] += x195 * x364 * x479 result[334] += x186 * x368 * x443 result[335] += x182 * x364 * x481 result[336] += x201 * x376 * x436 result[337] += x195 * x375 * x480 result[338] += x188 * x375 * x481 result[339] += x184 * x312 * x450 result[340] += x139 * x43 * x460 result[341] += x141 * x41 * x482 result[342] += x41 * x465 * x483 result[343] += x149 * x368 * x458 result[344] += x141 * x378 * x465 result[345] += x139 * x368 * x471 result[346] += x160 * x312 * x460 result[347] += x149 * x379 * x465 result[348] += x141 * x379 * x471 result[349] += x280 * x312 * x478 result[350] += x111 * x43 * x489 result[351] += x213 * x363 * x488 result[352] += x217 * x363 * x492 result[353] += x218 * x364 * x488 result[354] += x126 * x368 * x491 result[355] += x217 * x364 * x495 result[356] += x223 * x375 * x487 result[357] += x218 * x375 * x492 result[358] += x213 * x375 * x495 result[359] += x111 * x376 * x501 result[360] += x229 * x385 * x436 result[361] += x232 * x31 * x502 result[362] += x234 * x31 * x443 result[363] += x236 * x29 * x502 result[364] += x232 * x394 * x453 result[365] += x234 * x29 * x448 result[366] += x11 * x240 * x451 result[367] += x236 * x411 * x443 result[368] += x232 * x411 * x448 result[369] += x11 * x229 * x450 result[370] += x181 * x385 * x460 result[371] += x186 * x31 * x482 result[372] += x244 * x31 * x465 result[373] += x194 * x29 * x482 result[374] += x188 * x408 * x465 result[375] += x244 * x29 * x471 result[376] += x11 * x201 * x460 result[377] += x194 * x410 * x465 result[378] += x186 * x410 * x471 result[379] += x181 * x411 * x478 result[380] += x280 * x385 * x487 result[381] += x141 * x31 * x503 result[382] += x31 * x483 * x491 result[383] += x149 * x29 * x503 result[384] += x141 * x408 * x492 result[385] += x139 * x408 * x494 result[386] += x160 * x411 * x487 result[387] += x149 * x410 * x491 result[388] += x141 * x410 * x494 result[389] += x10 * x501 * x505 result[390] += x385 * x459 * x507 result[391] += x126 * x31 * x508 result[392] += x255 * x31 * x513 result[393] += x170 * x394 * x507 result[394] += x394 * x466 * x513 result[395] += x255 * x29 * x515 result[396] += x11 * x127 * x516 result[397] += x170 * x405 * x513 result[398] += x404 * x504 * x515 * x88 result[399] += x402 * x522 result[400] += x262 * x416 * x436 result[401] += x264 * x419 * x437 result[402] += x262 * x419 * x443 result[403] += x267 * x431 * x437 result[404] += x15 * x264 * x445 * x81 result[405] += x262 * x431 * x448 result[406] += x270 * x432 * x437 result[407] += x267 * x433 * x443 result[408] += x264 * x433 * x448 result[409] += x262 * x432 * x450 result[410] += x229 * x415 * x458 result[411] += x232 * x414 * x460 result[412] += x234 * x414 * x465 result[413] += x15 * x236 * x460 result[414] += x238 * x424 * x465 result[415] += x15 * x234 * x471 result[416] += x240 * x427 * x458 result[417] += x236 * x426 * x465 result[418] += x232 * x426 * x471 result[419] += x229 * x478 * x5 result[420] += x184 * x415 * x487 result[421] += x188 * x428 * x488 result[422] += x182 * x428 * x492 result[423] += x195 * x429 * x488 result[424] += x15 * x186 * x196 * x491 result[425] += x182 * x429 * x495 result[426] += x201 * x489 * x5 result[427] += x195 * x430 * x492 result[428] += x188 * x430 * x495 result[429] += x184 * x5 * x501 result[430] += x139 * x415 * x516 result[431] += x142 * x423 * x507 result[432] += x280 * x414 * x513 result[433] += x149 * x15 * x508 result[434] += x142 * x424 * x513 result[435] += x505 * x515 * x9 result[436] += x160 * x427 * x507 result[437] += x149 * x426 * x513 result[438] += x142 * x425 * x515 result[439] += x137 * x522 result[440] += x416 * x524 * x525 result[441] += x419 * x444 * x524 result[442] += x419 * x525 * x526 result[443] += x116 * x15 * x524 result[444] += x120 * x504 * x526 * x9 result[445] += x421 * x527 result[446] += x128 * x422 * x524 result[447] += x116 * x5 * x526 result[448] += x527 * x91 result[449] += ( x504 * x82 * ( x0 * ( x175 * (x518 + x519) + x44 * (x226 + x446 * x497 + 5.0 * x496 + 3.0 * x498) + 6.0 * x499 + 3.0 * x500 + 3.0 * x514 ) + x163 * x521 ) )
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_34(ax, da, A, bx, db, B, R, result): """See docstring of diag_quadrupole3d_43.""" # Call equivalent function and write to result tmp = numpy.zeros_like(result) diag_quadrupole3d_43(bx, db, B, ax, da, A, R, tmp) result[:] += numpy.transpose(tmp.reshape(3, 15, 10), axes=(0, 2, 1)).flatten()
[docs] @numba.jit( func_type.signature, nopython=True, nogil=True, fastmath=True, cache=True, ) def diag_quadrupole3d_44(ax, da, A, bx, db, B, R, result): """Cartesian 3D (gg) quadrupole moment integrals for operators x², y² and z². The origin is at R. Generated code; DO NOT modify by hand!""" x0 = 0.5 / (ax + bx) x1 = (ax + bx) ** (-1.0) x2 = -x1 * (ax * A[0] + bx * B[0]) x3 = -x2 - A[0] x4 = -x2 - B[0] x5 = ax * bx * x1 x6 = numpy.exp(-x5 * (A[0] - B[0]) ** 2) x7 = 1.77245385090551603 * numpy.sqrt(x1) x8 = x6 * x7 x9 = x0 * x8 x10 = -x2 - R[0] x11 = x4 * x8 x12 = x10 * x11 x13 = x12 + x9 x14 = x13 * x4 x15 = x3 * x6 x16 = x15 * x7 x17 = x0 * (x11 + x16) x18 = x16 * x4 x19 = x18 + x9 x20 = x19 * x4 x21 = x17 + x20 x22 = x13 * x3 x23 = 2.0 * x22 x24 = x10 * x8 x25 = x0 * (x11 + x24) x26 = x23 + 3.0 * x25 x27 = x0 * (x14 + x21 + x26) x28 = 3.0 * x9 x29 = x10 * x16 x30 = x0 * (x12 + x18 + x28 + x29) x31 = x22 + x25 x32 = x31 * x4 x33 = x30 + x32 x34 = x3 * x33 x35 = x27 + x34 x36 = x3 * x35 x37 = x35 * x4 x38 = x3 * x31 x39 = 2.0 * x38 x40 = 2.0 * x4 x41 = x16 * x40 x42 = x4**2 * x8 x43 = x28 + x42 x44 = x0 * (x41 + x43) x45 = x21 * x3 x46 = x44 + x45 x47 = 4.0 * x30 x48 = 2.0 * x32 + x47 x49 = x0 * (x39 + x46 + x48) x50 = x21 * x4 x51 = 3.0 * x45 x52 = x0 * (5.0 * x44 + 2.0 * x50 + x51) x53 = x19 * x3 x54 = 2.0 * x0 * (2.0 * x17 + x20 + x53) x55 = x4 * x46 x56 = x54 + x55 x57 = x3 * x56 x58 = x52 + x57 x59 = 2.0 * x0 x60 = x33 * x40 x61 = x0 * (5.0 * x27 + 3.0 * x34 + x56 + x60) x62 = x3 * (x37 + x49) x63 = 2.0 * x27 x64 = x10 * x31 x65 = x30 + x64 x66 = x3 * x65 x67 = x4 * x65 x68 = x10 * x13 x69 = x0 * (x16 + x24) x70 = x29 + x9 x71 = x10 * x70 x72 = x69 + x71 x73 = x0 * (x26 + x68 + x72) x74 = x0 * (2.0 * x34 + x63 + 2.0 * x66 + 2.0 * x67 + 4.0 * x73) x75 = 2.0 * x64 x76 = x24 * x40 x77 = x10**2 * x8 x78 = x28 + x77 x79 = x0 * (x76 + x78) x80 = x25 + x68 x81 = x4 * x80 x82 = x79 + x81 x83 = x0 * (x48 + x75 + x82) x84 = x67 + x73 x85 = x3 * x84 x86 = x83 + x85 x87 = x4 * x86 x88 = x74 + x87 x89 = x4 * x88 x90 = x3 * x88 x91 = x4 * x84 x92 = 2.0 * x49 + 3.0 * x85 x93 = x0 * (2.0 * x37 + 5.0 * x83 + 2.0 * x91 + x92) x94 = x3 * x86 x95 = x0 * (2.0 * x61 + 2.0 * x62 + 6.0 * x74 + 3.0 * x87 + 3.0 * x94) x96 = x90 + x93 x97 = x4 * x96 + x95 x98 = numpy.exp(-x5 * (A[1] - B[1]) ** 2) x99 = da * db x100 = 0.00952380952380952381 * x99 x101 = numpy.exp(-x5 * (A[2] - B[2]) ** 2) x102 = 3.14159265358979324 * x1 * x101 x103 = x100 * x102 x104 = x103 * x98 x105 = -x1 * (ax * A[1] + bx * B[1]) x106 = -x105 - B[1] x107 = 2.64575131106459059 x108 = x104 * x107 x109 = x108 * (x3 * x96 + x95) x110 = -x1 * (ax * A[2] + bx * B[2]) x111 = -x110 - B[2] x112 = 2.0 * x3 x113 = x112 * x24 x114 = x0 * (x113 + x78) x115 = x3 * x72 x116 = x114 + x115 x117 = x0 * (x116 + x39 + x47 + x75) x118 = x66 + x73 x119 = x118 * x3 x120 = x74 + x94 x121 = x0 * (2.0 * x117 + 2.0 * x119 + 2.0 * x36 + 3.0 * x83 + x92) + x120 * x3 x122 = x101 * x7 x123 = 0.0325300024316177726 x124 = x7 * x98 x125 = x106**2 * x124 x126 = x0 * x124 x127 = x125 + x126 x128 = x127 * x99 x129 = x123 * x128 x130 = 5.91607978309961604 x131 = x104 * x130 x132 = x111**2 * x122 x133 = x0 * x122 x134 = x132 + x133 x135 = x134 * x99 x136 = x123 * x135 x137 = x3 * x70 x138 = x137 + x69 x139 = x17 + x53 x140 = 3.0 * x73 x141 = 2.0 * x0 * (x137 + 2.0 * x69 + x71) + x116 * x3 x142 = x117 + x119 x143 = ( x0 * ( x112 * (x30 + x38) + x140 + x141 + x59 * (x138 + x139 + x23 + 2.0 * x25) + 3.0 * x66 ) + x142 * x3 ) x144 = x106 * x124 x145 = x106 * x127 + x144 * x59 x146 = x107 * x145 x147 = x100 * x122 x148 = x111 * x122 x149 = x100 * x130 x150 = x143 * x149 x151 = x111 * x134 + x148 * x59 x152 = x107 * x151 x153 = x100 * x124 x154 = 3.0 * x126 x155 = x0 * (3.0 * x125 + x154) + x106 * x145 x156 = x3**2 * x8 x157 = x156 + x28 x158 = x0 * (x112 * x138 + 3.0 * x114 + 3.0 * x115 + x59 * (x113 + x157)) + x141 * x3 x159 = x100 * x158 x160 = 3.0 * x133 x161 = x0 * (3.0 * x132 + x160) + x111 * x151 x162 = -x105 - A[1] x163 = x108 * x97 x164 = x124 * x162 x165 = x106 * x164 x166 = x126 + x165 x167 = x166 * x99 x168 = 0.0666666666666666667 * x167 x169 = 0.0666666666666666667 * x99 x170 = x102 * x169 x171 = x111 * x170 x172 = x96 * x98 x173 = x0 * (x144 + x164) x174 = x106 * x166 x175 = x173 + x174 x176 = 0.0860662965823870419 x177 = x176 * x99 x178 = x175 * x177 x179 = 2.2360679774997897 x180 = x168 * x179 x181 = x135 * x176 x182 = 2.0 * x106 x183 = x154 + x164 * x182 x184 = x0 * (x125 + x183) x185 = x106 * x175 x186 = x184 + x185 x187 = x169 * x186 x188 = x142 * x179 x189 = x151 * x169 x190 = 3.0 * x173 x191 = x0 * (x145 + 3.0 * x174 + x190) + x106 * x186 x192 = x107 * x141 x193 = 0.0666666666666666667 * x141 x194 = x193 * x99 x195 = x141 * x176 x196 = x100 * x192 x197 = -x110 - A[2] x198 = x170 * x197 x199 = x122 * x197 x200 = x111 * x199 x201 = x133 + x200 x202 = x201 * x99 x203 = 0.0666666666666666667 * x202 x204 = x128 * x176 x205 = x179 * x203 x206 = x0 * (x148 + x199) x207 = x111 * x201 x208 = x206 + x207 x209 = x177 * x208 x210 = x145 * x169 x211 = x144 * x169 x212 = 2.0 * x111 x213 = x160 + x199 * x212 x214 = x0 * (x132 + x213) x215 = x111 * x208 x216 = x214 + x215 x217 = x169 * x216 x218 = 3.0 * x206 x219 = x0 * (x151 + 3.0 * x207 + x218) + x111 * x216 x220 = x89 + x93 x221 = x124 * x162**2 x222 = x126 + x221 x223 = x222 * x99 x224 = x123 * x223 x225 = x162 * x166 x226 = x173 + x225 x227 = x122 * x177 x228 = x176 * x223 x229 = x162 * x175 x230 = x184 + x229 x231 = 0.111111111111111111 * x99 x232 = x230 * x231 x233 = 1.73205080756887729 x234 = x226 * x233 x235 = x231 * x234 x236 = x134 * x231 x237 = 2.0 * x0 * (2.0 * x173 + x174 + x225) x238 = x106 * x230 x239 = x237 + x238 x240 = x118 * x233 x241 = x151 * x176 x242 = 3.0 * x229 x243 = x0 * (5.0 * x184 + 2.0 * x185 + x242) x244 = x106 * x239 x245 = x243 + x244 x246 = x116 * x99 x247 = x123 * x246 x248 = x176 * x246 x249 = x175 * x233 x250 = x231 * x249 x251 = 0.333333333333333333 * x167 x252 = x208 * x233 x253 = x231 * x252 x254 = x179 * x187 x255 = 0.333333333333333333 * x202 x256 = x179 * x217 x257 = x116 * x149 x258 = x116 * x179 x259 = x122 * x197**2 x260 = x133 + x259 x261 = x260 * x99 x262 = x123 * x261 x263 = x176 * x261 x264 = x197 * x201 x265 = x206 + x264 x266 = x124 * x177 x267 = x127 * x231 x268 = x233 * x265 x269 = x231 * x268 x270 = x197 * x208 x271 = x214 + x270 x272 = x231 * x271 x273 = x145 * x176 x274 = 2.0 * x0 * (2.0 * x206 + x207 + x264) x275 = x111 * x271 x276 = x274 + x275 x277 = x123 * x155 x278 = 3.0 * x270 x279 = x0 * (5.0 * x214 + 2.0 * x215 + x278) x280 = x111 * x276 x281 = x279 + x280 x282 = 2.0 * x0 * (x14 + 2.0 * x25 + x68) + x4 * x82 x283 = x83 + x91 x284 = x0 * (x140 + x282 + x60 + x63 + 3.0 * x67) + x283 * x4 x285 = x162 * x222 + x164 * x59 x286 = x107 * x285 x287 = x0 * (x183 + x221) x288 = x162 * x226 x289 = x287 + x288 x290 = x169 * x283 x291 = 0.0666666666666666667 * x285 x292 = x291 * x99 x293 = x162 * x230 x294 = x237 + x293 x295 = x179 * x289 x296 = x169 * x295 x297 = x162 * x239 x298 = x243 + x297 x299 = x65 * x99 x300 = 0.0666666666666666667 * x299 x301 = x179 * x300 x302 = 3.0 * x0 * (2.0 * x237 + x238 + x293) x303 = x106 * x298 + x302 x304 = x100 * x72 x305 = x107 * x304 x306 = x169 * x72 x307 = x149 * x284 x308 = x169 * x179 x309 = x283 * x308 x310 = x179 * x222 x311 = x199 * x233 x312 = x222 * x231 x313 = 0.333333333333333333 * x299 x314 = x130 * x304 x315 = x179 * x72 x316 = x179 * x306 x317 = x179 * x260 x318 = x231 * x260 x319 = x233 * x272 x320 = x197 * x260 + x199 * x59 x321 = x107 * x320 x322 = x169 * x320 x323 = x0 * (x213 + x259) x324 = x197 * x265 x325 = x323 + x324 x326 = x179 * x325 x327 = x197 * x271 x328 = x274 + x327 x329 = 0.0666666666666666667 * x320 x330 = x197 * x276 x331 = x279 + x330 x332 = 3.0 * x0 * (2.0 * x274 + x275 + x327) x333 = x111 * x331 + x332 x334 = x0 * (x154 + 3.0 * x221) + x162 * x285 x335 = ( x0 * (x40 * (x14 + x25) + x59 * (x43 + x76) + 3.0 * x79 + 3.0 * x81) + x282 * x4 ) x336 = x100 * x335 x337 = x0 * (x190 + 3.0 * x225 + x285) + x162 * x289 x338 = x107 * x282 x339 = x100 * x338 x340 = x0 * (3.0 * x184 + x242 + 2.0 * x287 + 2.0 * x288) + x162 * x294 x341 = x123 * x99 x342 = x341 * x82 x343 = x149 * x82 x344 = x162 * x298 + x302 x345 = x100 * x80 x346 = x107 * x345 x347 = x130 * x345 x348 = x0 * (7.0 * x243 + 3.0 * x244 + 4.0 * x297) + x162 * x303 x349 = x77 + x9 x350 = x100 * x349 x351 = x107 * x350 x352 = x169 * x282 x353 = x177 * x82 x354 = x169 * x80 x355 = x179 * x80 x356 = 0.0666666666666666667 * x349 x357 = x169 * x349 x358 = x176 * x282 x359 = x231 * x82 x360 = x176 * x80 x361 = x123 * x349 x362 = x177 * x349 x363 = x177 * x320 x364 = x0 * (x160 + 3.0 * x259) + x197 * x320 x365 = x0 * (x218 + 3.0 * x264 + x320) + x197 * x325 x366 = x123 * x364 x367 = x0 * (3.0 * x214 + x278 + 2.0 * x323 + 2.0 * x324) + x197 * x328 x368 = x197 * x331 + x332 x369 = x0 * (7.0 * x279 + 3.0 * x280 + 4.0 * x330) + x197 * x333 x370 = x4 * x56 x371 = x3 * x46 x372 = 3.0 * x0 * (x371 + 2.0 * x54 + x55) x373 = x372 + x4 * x58 x374 = x0 * (3.0 * x370 + 7.0 * x52 + 4.0 * x57) + x3 * x373 x375 = -x105 - R[1] x376 = x124 * x375**2 x377 = x126 + x376 x378 = x100 * x377 x379 = x3 * x58 + x372 x380 = x124 * x375 x381 = x0 * (x144 + x380) x382 = x144 * x375 x383 = x126 + x382 x384 = x375 * x383 x385 = x381 + x384 x386 = x100 * x385 x387 = x107 * x122 x388 = x107 * x148 x389 = x154 + x182 * x380 x390 = x0 * (x376 + x389) x391 = x106 * x385 x392 = x390 + x391 x393 = x0 * (x157 + x41) x394 = x139 * x3 x395 = x371 + x54 x396 = x0 * (2.0 * x393 + 2.0 * x394 + 3.0 * x44 + x51) + x3 * x395 x397 = x122 * x341 x398 = x130 * x386 x399 = x106 * x383 x400 = 2.0 * x0 * (2.0 * x381 + x384 + x399) + x106 * x392 x401 = 3.0 * x17 x402 = x156 + x9 x403 = x16 * x59 + x3 * x402 x404 = x393 + x394 x405 = x0 * (x401 + x403 + 3.0 * x53) + x3 * x404 x406 = x107 * x147 x407 = x148 * x149 x408 = x0 * (3.0 * x156 + x28) + x3 * x403 x409 = ( x0 * (x182 * (x381 + x399) + 3.0 * x390 + 3.0 * x391 + x59 * (x125 + x389)) + x106 * x400 ) x410 = x100 * x400 x411 = x0 * (x164 + x380) x412 = x164 * x375 x413 = x126 + x412 x414 = x375 * x413 x415 = x411 + x414 x416 = x100 * x415 x417 = x0 * (x154 + x165 + x382 + x412) x418 = x162 * x383 x419 = x381 + x418 x420 = x375 * x419 x421 = x417 + x420 x422 = x169 * x421 x423 = x169 * x415 x424 = 2.0 * x418 x425 = 3.0 * x381 + x424 x426 = x0 * (x384 + x415 + x425) x427 = x106 * x421 x428 = x426 + x427 x429 = x179 * x422 x430 = 2.0 * x420 x431 = x106 * x419 x432 = 4.0 * x417 x433 = 2.0 * x431 + x432 x434 = x0 * (x392 + x430 + x433) x435 = x106 * x428 x436 = x434 + x435 x437 = x169 * x436 x438 = x179 * x404 x439 = x169 * x438 x440 = x0 * (x175 + x399 + x425) x441 = 2.0 * x440 x442 = x417 + x431 x443 = x182 * x442 x444 = 3.0 * x426 x445 = x0 * (x400 + 3.0 * x427 + x441 + x443 + x444) + x106 * x436 x446 = x107 * x403 x447 = x107 * x378 x448 = x169 * x385 x449 = x177 * x392 x450 = x169 * x400 x451 = x100 * x409 x452 = 2.0 * x162 x453 = x154 + x380 * x452 x454 = x0 * (x376 + x453) x455 = x162 * x415 x456 = x454 + x455 x457 = x370 + x52 x458 = x162 * x421 x459 = x426 + x458 x460 = x177 * x456 x461 = x162 * x428 x462 = x434 + x461 x463 = x231 * x46 x464 = x233 * x463 x465 = x162 * x442 x466 = x0 * (4.0 * x426 + 2.0 * x427 + x441 + 2.0 * x458 + 2.0 * x465) x467 = x106 * x462 x468 = x466 + x467 x469 = x139 * x233 x470 = x231 * x469 x471 = x241 * x99 x472 = x440 + x465 x473 = x106 * x472 x474 = x162 * x419 x475 = 2.0 * x474 x476 = x0 * (x230 + x433 + x475) x477 = 3.0 * x461 + 2.0 * x476 x478 = x0 * (5.0 * x434 + 2.0 * x435 + 2.0 * x473 + x477) x479 = x106 * x468 x480 = x478 + x479 x481 = x123 * x402 x482 = x481 * x99 x483 = x177 * x402 x484 = x130 * x416 x485 = x308 * x436 x486 = 0.333333333333333333 * x99 x487 = x208 * x486 x488 = x149 * x199 x489 = x177 * x377 x490 = x162 * x413 x491 = 2.0 * x0 * (2.0 * x411 + x414 + x490) + x162 * x456 x492 = x42 + x9 x493 = x11 * x59 + x4 * x492 x494 = x44 + x50 x495 = x0 * (3.0 * x20 + x401 + x493) + x4 * x494 x496 = x0 * (x430 + x432 + x456 + x475) x497 = x162 * x459 x498 = x496 + x497 x499 = x169 * x494 x500 = x162 * x462 x501 = x466 + x500 x502 = x177 * x21 x503 = x308 * x498 x504 = x162 * x468 x505 = x478 + x504 x506 = x169 * x19 x507 = x19 * x308 x508 = x0 * (x239 + 5.0 * x440 + x443 + 3.0 * x465) x509 = x162 * (x473 + x476) x510 = x0 * (6.0 * x466 + 3.0 * x467 + 3.0 * x500 + 2.0 * x508 + 2.0 * x509) x511 = x106 * x505 + x510 x512 = x107 * x511 x513 = x103 * x15 x514 = x100 * x107 x515 = x491 * x514 x516 = x308 * x494 x517 = x21 * x233 x518 = x231 * x517 x519 = x149 * x16 x520 = x265 * x486 x521 = x19 * x486 x522 = x169 * x377 x523 = x179 * x19 x524 = x0 * (x28 + 3.0 * x42) + x4 * x493 x525 = x411 + x490 x526 = ( x0 * (x452 * x525 + 3.0 * x454 + 3.0 * x455 + x59 * (x221 + x453)) + x162 * x491 ) x527 = ( x0 * ( x444 + x452 * (x417 + x474) + 3.0 * x458 + x491 + x59 * (x226 + 2.0 * x381 + x424 + x525) ) + x162 * x498 ) x528 = x107 * x493 x529 = x100 * x526 x530 = x0 * (3.0 * x434 + x452 * x472 + x477 + 2.0 * x496 + 2.0 * x497) + x162 * x501 x531 = x492 * x99 x532 = x123 * x531 x533 = x107 * x4 x534 = x103 * x6 x535 = x534 * (x162 * x505 + x510) x536 = x130 * x4 x537 = x11 * x149 x538 = x100 * x8 x539 = x169 * x493 x540 = x177 * x492 x541 = x4 * x6 x542 = x107 * x538 x543 = x177 * x493 x544 = x177 * x8 x545 = x341 * x8 x546 = x11 * x169 x547 = x107 * x8 x548 = x107 * x11 x549 = -x110 - R[2] x550 = x122 * x549**2 x551 = x133 + x550 x552 = x100 * x551 x553 = x107 * x552 x554 = x122 * x549 x555 = x0 * (x148 + x554) x556 = x148 * x549 x557 = x133 + x556 x558 = x549 * x557 x559 = x555 + x558 x560 = x100 * x559 x561 = x107 * x124 x562 = x130 * x560 x563 = x160 + x212 * x554 x564 = x0 * (x550 + x563) x565 = x111 * x559 x566 = x564 + x565 x567 = x144 * x149 x568 = x111 * x557 x569 = 2.0 * x0 * (2.0 * x555 + x558 + x568) + x111 * x566 x570 = x107 * x153 x571 = x514 * x569 x572 = ( x0 * (x212 * (x555 + x568) + 3.0 * x564 + 3.0 * x565 + x59 * (x132 + x563)) + x111 * x569 ) x573 = x164 * x169 x574 = x177 * x566 x575 = x100 * x572 x576 = x0 * (x199 + x554) x577 = x199 * x549 x578 = x133 + x577 x579 = x549 * x578 x580 = x576 + x579 x581 = x100 * x580 x582 = x0 * (x160 + x200 + x556 + x577) x583 = x197 * x557 x584 = x555 + x583 x585 = x549 * x584 x586 = x582 + x585 x587 = x124 * x169 x588 = x308 * x586 x589 = 2.0 * x583 x590 = 3.0 * x555 + x589 x591 = x0 * (x558 + x580 + x590) x592 = x111 * x586 x593 = x591 + x592 x594 = 2.0 * x585 x595 = x111 * x584 x596 = 4.0 * x582 x597 = 2.0 * x595 + x596 x598 = x0 * (x566 + x594 + x597) x599 = x111 * x593 x600 = x598 + x599 x601 = x0 * (x208 + x568 + x590) x602 = 2.0 * x601 x603 = x582 + x595 x604 = x212 * x603 x605 = 3.0 * x591 x606 = x0 * (x569 + 3.0 * x592 + x602 + x604 + x605) + x111 * x600 x607 = x177 * x551 x608 = x130 * x581 x609 = x486 * x586 x610 = x308 * x600 x611 = x149 * x164 x612 = 2.0 * x197 x613 = x160 + x554 * x612 x614 = x0 * (x550 + x613) x615 = x197 * x580 x616 = x614 + x615 x617 = x616 * x99 x618 = x123 * x617 x619 = x177 * x616 x620 = x197 * x586 x621 = x591 + x620 x622 = x197 * x593 x623 = x598 + x622 x624 = x197 * x603 x625 = x0 * (4.0 * x591 + 2.0 * x592 + x602 + 2.0 * x620 + 2.0 * x624) x626 = x111 * x623 x627 = x625 + x626 x628 = x601 + x624 x629 = x111 * x628 x630 = x197 * x584 x631 = 2.0 * x630 x632 = x0 * (x271 + x597 + x631) x633 = 3.0 * x622 + 2.0 * x632 x634 = x0 * (5.0 * x598 + 2.0 * x599 + 2.0 * x629 + x633) x635 = x111 * x627 x636 = x634 + x635 x637 = x169 * x551 x638 = x16 * x169 x639 = x232 * x233 x640 = 3.14159265358979324 * x1 * x98 x641 = x100 * x640 x642 = x15 * x641 x643 = x197 * x578 x644 = 2.0 * x0 * (2.0 * x576 + x579 + x643) + x197 * x616 x645 = x0 * (x594 + x596 + x616 + x631) x646 = x197 * x621 x647 = x645 + x646 x648 = x308 * x647 x649 = x197 * x623 x650 = x625 + x649 x651 = x197 * x627 x652 = x634 + x651 x653 = x514 * x644 x654 = x169 * x640 * x652 x655 = x0 * (x276 + 5.0 * x601 + x604 + 3.0 * x624) x656 = x197 * (x629 + x632) x657 = x0 * (6.0 * x625 + 3.0 * x626 + 3.0 * x649 + 2.0 * x655 + 2.0 * x656) x658 = x111 * x652 + x657 x659 = x107 * x658 x660 = x169 * x8 x661 = x6 * x641 x662 = x576 + x643 x663 = ( x0 * (x59 * (x259 + x613) + x612 * x662 + 3.0 * x614 + 3.0 * x615) + x197 * x644 ) x664 = x100 * x663 x665 = ( x0 * ( x59 * (x265 + 2.0 * x555 + x589 + x662) + x605 + x612 * (x582 + x630) + 3.0 * x620 + x644 ) + x197 * x647 ) x666 = x0 * (3.0 * x598 + x612 * x628 + x633 + 2.0 * x645 + 2.0 * x646) + x197 * x650 x667 = x661 * (x197 * x652 + x657) # 675 item(s) result[0] += x104 * ( x0 * ( x40 * (x61 + x62) + x59 * (3.0 * x36 + 3.0 * x37 + 6.0 * x49 + x58) + 3.0 * x89 + 4.0 * x90 + 7.0 * x93 ) + x3 * x97 ) result[1] += x106 * x109 result[2] += x109 * x111 result[3] += x121 * x122 * x129 result[4] += x106 * x111 * x121 * x131 result[5] += x121 * x124 * x136 result[6] += x143 * x146 * x147 result[7] += x127 * x148 * x150 result[8] += x134 * x144 * x150 result[9] += x143 * x152 * x153 result[10] += x122 * x155 * x159 result[11] += x146 * x148 * x159 result[12] += x127 * x136 * x158 result[13] += x144 * x152 * x159 result[14] += x124 * x159 * x161 result[15] += x162 * x163 result[16] += x122 * x168 * x96 result[17] += x162 * x171 * x172 result[18] += x120 * x122 * x178 result[19] += x120 * x148 * x180 result[20] += x120 * x164 * x181 result[21] += x122 * x142 * x187 result[22] += x148 * x169 * x175 * x188 result[23] += x134 * x168 * x188 result[24] += x142 * x164 * x189 result[25] += x147 * x191 * x192 result[26] += x148 * x186 * x194 result[27] += x135 * x175 * x195 result[28] += x151 * x167 * x193 result[29] += x161 * x164 * x196 result[30] += x163 * x197 result[31] += x106 * x172 * x198 result[32] += x124 * x203 * x96 result[33] += x120 * x199 * x204 result[34] += x120 * x144 * x205 result[35] += x120 * x124 * x209 result[36] += x142 * x199 * x210 result[37] += x127 * x188 * x203 result[38] += x188 * x208 * x211 result[39] += x124 * x142 * x217 result[40] += x155 * x196 * x199 result[41] += x145 * x193 * x202 result[42] += x128 * x195 * x208 result[43] += x144 * x194 * x216 result[44] += x153 * x192 * x219 result[45] += x122 * x220 * x224 result[46] += x226 * x227 * x88 result[47] += x148 * x228 * x88 result[48] += x122 * x232 * x86 result[49] += x148 * x235 * x86 result[50] += x222 * x236 * x86 result[51] += x118 * x227 * x239 result[52] += x148 * x232 * x240 result[53] += x226 * x236 * x240 result[54] += x118 * x223 * x241 result[55] += x122 * x245 * x247 result[56] += x148 * x239 * x248 result[57] += x116 * x230 * x236 result[58] += x226 * x241 * x246 result[59] += x116 * x161 * x224 result[60] += x131 * x162 * x197 * x220 result[61] += x180 * x199 * x88 result[62] += x164 * x205 * x88 result[63] += x199 * x250 * x86 result[64] += x201 * x251 * x86 result[65] += x164 * x253 * x86 result[66] += x118 * x199 * x254 result[67] += x118 * x175 * x255 result[68] += x118 * x208 * x251 result[69] += x118 * x164 * x256 result[70] += x191 * x199 * x257 result[71] += x186 * x203 * x258 result[72] += x116 * x175 * x253 result[73] += x168 * x216 * x258 result[74] += x164 * x219 * x257 result[75] += x124 * x220 * x262 result[76] += x144 * x263 * x88 result[77] += x265 * x266 * x88 result[78] += x260 * x267 * x86 result[79] += x144 * x269 * x86 result[80] += x124 * x272 * x86 result[81] += x118 * x261 * x273 result[82] += x240 * x265 * x267 result[83] += x144 * x240 * x272 result[84] += x118 * x266 * x276 result[85] += x246 * x260 * x277 result[86] += x246 * x265 * x273 result[87] += x116 * x267 * x271 result[88] += x144 * x248 * x276 result[89] += x124 * x247 * x281 result[90] += x147 * x284 * x286 result[91] += x122 * x289 * x290 result[92] += x148 * x283 * x292 result[93] += x227 * x294 * x84 result[94] += x148 * x296 * x84 result[95] += x181 * x285 * x84 result[96] += x122 * x298 * x300 result[97] += x148 * x294 * x301 result[98] += x134 * x295 * x300 result[99] += x151 * x291 * x299 result[100] += x122 * x303 * x305 result[101] += x148 * x298 * x306 result[102] += x181 * x294 * x72 result[103] += x151 * x289 * x306 result[104] += x161 * x286 * x304 result[105] += x199 * x222 * x307 result[106] += x199 * x226 * x309 result[107] += x203 * x283 * x310 result[108] += x232 * x311 * x84 result[109] += x226 * x255 * x84 result[110] += x252 * x312 * x84 result[111] += x199 * x239 * x301 result[112] += x230 * x255 * x65 result[113] += x208 * x226 * x313 result[114] += x216 * x300 * x310 result[115] += x199 * x245 * x314 result[116] += x203 * x239 * x315 result[117] += x232 * x252 * x72 result[118] += x216 * x226 * x316 result[119] += x219 * x222 * x314 result[120] += x164 * x260 * x307 result[121] += x168 * x283 * x317 result[122] += x164 * x265 * x309 result[123] += x249 * x318 * x84 result[124] += x251 * x265 * x84 result[125] += x164 * x319 * x84 result[126] += x186 * x300 * x317 result[127] += x175 * x265 * x313 result[128] += x251 * x271 * x65 result[129] += x164 * x276 * x301 result[130] += x191 * x260 * x314 result[131] += x186 * x265 * x316 result[132] += x249 * x272 * x72 result[133] += x168 * x276 * x315 result[134] += x164 * x281 * x314 result[135] += x153 * x284 * x321 result[136] += x144 * x283 * x322 result[137] += x124 * x290 * x325 result[138] += x204 * x320 * x84 result[139] += x211 * x326 * x84 result[140] += x266 * x328 * x84 result[141] += x145 * x299 * x329 result[142] += x127 * x300 * x326 result[143] += x144 * x301 * x328 result[144] += x124 * x300 * x331 result[145] += x155 * x304 * x321 result[146] += x145 * x306 * x325 result[147] += x204 * x328 * x72 result[148] += x144 * x306 * x331 result[149] += x124 * x305 * x333 result[150] += x122 * x334 * x336 result[151] += x147 * x337 * x338 result[152] += x148 * x334 * x339 result[153] += x122 * x340 * x342 result[154] += x148 * x337 * x343 result[155] += x136 * x334 * x82 result[156] += x122 * x344 * x346 result[157] += x148 * x340 * x347 result[158] += x134 * x337 * x347 result[159] += x152 * x334 * x345 result[160] += x122 * x348 * x350 result[161] += x148 * x344 * x351 result[162] += x136 * x340 * x349 result[163] += x152 * x337 * x350 result[164] += x161 * x334 * x350 result[165] += x199 * x286 * x336 result[166] += x199 * x289 * x352 result[167] += x202 * x282 * x291 result[168] += x199 * x294 * x353 result[169] += x203 * x295 * x82 result[170] += x209 * x285 * x82 result[171] += x199 * x298 * x354 result[172] += x203 * x294 * x355 result[173] += x208 * x295 * x354 result[174] += x216 * x292 * x80 result[175] += x199 * x303 * x351 result[176] += x202 * x298 * x356 result[177] += x209 * x294 * x349 result[178] += x216 * x289 * x357 result[179] += x219 * x286 * x350 result[180] += x224 * x260 * x335 result[181] += x226 * x261 * x358 result[182] += x223 * x265 * x358 result[183] += x230 * x260 * x359 result[184] += x226 * x268 * x359 result[185] += x222 * x271 * x359 result[186] += x239 * x261 * x360 result[187] += x232 * x268 * x80 result[188] += x226 * x319 * x80 result[189] += x223 * x276 * x360 result[190] += x245 * x261 * x361 result[191] += x239 * x265 * x362 result[192] += x230 * x272 * x349 result[193] += x226 * x276 * x362 result[194] += x224 * x281 * x349 result[195] += x164 * x321 * x336 result[196] += x167 * x282 * x329 result[197] += x164 * x325 * x352 result[198] += x175 * x363 * x82 result[199] += x168 * x326 * x82 result[200] += x164 * x328 * x353 result[201] += x186 * x322 * x80 result[202] += x175 * x326 * x354 result[203] += x168 * x328 * x355 result[204] += x164 * x331 * x354 result[205] += x191 * x321 * x350 result[206] += x186 * x325 * x357 result[207] += x175 * x328 * x362 result[208] += x167 * x331 * x356 result[209] += x164 * x333 * x351 result[210] += x124 * x336 * x364 result[211] += x144 * x339 * x364 result[212] += x153 * x338 * x365 result[213] += x128 * x366 * x82 result[214] += x144 * x343 * x365 result[215] += x124 * x342 * x367 result[216] += x146 * x345 * x364 result[217] += x127 * x347 * x365 result[218] += x144 * x347 * x367 result[219] += x124 * x346 * x368 result[220] += x155 * x350 * x364 result[221] += x146 * x350 * x365 result[222] += x128 * x361 * x367 result[223] += x144 * x351 * x368 result[224] += x124 * x350 * x369 result[225] += x122 * x374 * x378 result[226] += x379 * x386 * x387 result[227] += x378 * x379 * x388 result[228] += x392 * x396 * x397 result[229] += x148 * x396 * x398 result[230] += x136 * x377 * x396 result[231] += x400 * x405 * x406 result[232] += x392 * x405 * x407 result[233] += x134 * x398 * x405 result[234] += x152 * x378 * x405 result[235] += x147 * x408 * x409 result[236] += x388 * x408 * x410 result[237] += x136 * x392 * x408 result[238] += x152 * x386 * x408 result[239] += x161 * x378 * x408 result[240] += x373 * x387 * x416 result[241] += x122 * x422 * x58 result[242] += x148 * x423 * x58 result[243] += x227 * x395 * x428 result[244] += x148 * x395 * x429 result[245] += x181 * x395 * x415 result[246] += x122 * x404 * x437 result[247] += x148 * x428 * x439 result[248] += x134 * x422 * x438 result[249] += x189 * x404 * x415 result[250] += x147 * x445 * x446 result[251] += x148 * x403 * x437 result[252] += x181 * x403 * x428 result[253] += x189 * x403 * x421 result[254] += x161 * x416 * x446 result[255] += x199 * x373 * x447 result[256] += x199 * x448 * x58 result[257] += x203 * x377 * x58 result[258] += x199 * x395 * x449 result[259] += x205 * x385 * x395 result[260] += x209 * x377 * x395 result[261] += x199 * x404 * x450 result[262] += x203 * x392 * x438 result[263] += x208 * x438 * x448 result[264] += x217 * x377 * x404 result[265] += x199 * x446 * x451 result[266] += x203 * x400 * x403 result[267] += x209 * x392 * x403 result[268] += x217 * x385 * x403 result[269] += x219 * x378 * x446 result[270] += x397 * x456 * x457 result[271] += x227 * x459 * x56 result[272] += x148 * x460 * x56 result[273] += x122 * x462 * x463 result[274] += x148 * x459 * x464 result[275] += x236 * x456 * x46 result[276] += x139 * x227 * x468 result[277] += x148 * x462 * x470 result[278] += x236 * x459 * x469 result[279] += x139 * x456 * x471 result[280] += x122 * x480 * x482 result[281] += x148 * x468 * x483 result[282] += x236 * x402 * x462 result[283] += x402 * x459 * x471 result[284] += x161 * x456 * x482 result[285] += x199 * x457 * x484 result[286] += x199 * x429 * x56 result[287] += x205 * x415 * x56 result[288] += x311 * x428 * x463 result[289] += x255 * x421 * x46 result[290] += x252 * x415 * x463 result[291] += x139 * x199 * x485 result[292] += x139 * x255 * x428 result[293] += x139 * x421 * x487 result[294] += x139 * x256 * x415 result[295] += x402 * x445 * x488 result[296] += x205 * x402 * x436 result[297] += x253 * x402 * x428 result[298] += x256 * x402 * x421 result[299] += x219 * x402 * x484 result[300] += x262 * x377 * x457 result[301] += x263 * x385 * x56 result[302] += x265 * x489 * x56 result[303] += x318 * x392 * x46 result[304] += x268 * x385 * x463 result[305] += x272 * x377 * x46 result[306] += x139 * x263 * x400 result[307] += x139 * x269 * x392 result[308] += x139 * x319 * x385 result[309] += x139 * x276 * x489 result[310] += x261 * x409 * x481 result[311] += x265 * x400 * x483 result[312] += x272 * x392 * x402 result[313] += x276 * x385 * x483 result[314] += x281 * x377 * x482 result[315] += x406 * x491 * x495 result[316] += x122 * x498 * x499 result[317] += x148 * x491 * x499 result[318] += x122 * x501 * x502 result[319] += x148 * x21 * x503 result[320] += x181 * x21 * x491 result[321] += x122 * x505 * x506 result[322] += x148 * x501 * x507 result[323] += x134 * x498 * x507 result[324] += x189 * x19 * x491 result[325] += x512 * x513 result[326] += x15 * x171 * x505 result[327] += x16 * x181 * x501 result[328] += x16 * x189 * x498 result[329] += x16 * x161 * x515 result[330] += x456 * x488 * x495 result[331] += x199 * x459 * x516 result[332] += x205 * x456 * x494 result[333] += x199 * x462 * x518 result[334] += x21 * x255 * x459 result[335] += x21 * x253 * x456 result[336] += x199 * x468 * x507 result[337] += x19 * x255 * x462 result[338] += x19 * x459 * x487 result[339] += x19 * x256 * x456 result[340] += x130 * x197 * x480 * x513 result[341] += x16 * x205 * x468 result[342] += x16 * x253 * x462 result[343] += x16 * x256 * x459 result[344] += x219 * x456 * x519 result[345] += x260 * x484 * x495 result[346] += x317 * x422 * x494 result[347] += x265 * x415 * x516 result[348] += x318 * x428 * x517 result[349] += x21 * x421 * x520 result[350] += x21 * x319 * x415 result[351] += x317 * x436 * x506 result[352] += x19 * x428 * x520 result[353] += x271 * x421 * x521 result[354] += x276 * x415 * x507 result[355] += x260 * x445 * x519 result[356] += x16 * x265 * x485 result[357] += x16 * x319 * x428 result[358] += x16 * x276 * x429 result[359] += x16 * x281 * x484 result[360] += x321 * x378 * x495 result[361] += x322 * x385 * x494 result[362] += x325 * x494 * x522 result[363] += x21 * x363 * x392 result[364] += x21 * x326 * x448 result[365] += x21 * x328 * x489 result[366] += x19 * x322 * x400 result[367] += x326 * x392 * x506 result[368] += x328 * x448 * x523 result[369] += x19 * x331 * x522 result[370] += x16 * x321 * x451 result[371] += x16 * x325 * x450 result[372] += x16 * x328 * x449 result[373] += x16 * x331 * x448 result[374] += x16 * x333 * x447 result[375] += x147 * x524 * x526 result[376] += x147 * x527 * x528 result[377] += x148 * x528 * x529 result[378] += x122 * x530 * x532 result[379] += x407 * x492 * x527 result[380] += x136 * x492 * x526 result[381] += x533 * x535 result[382] += x111 * x530 * x534 * x536 result[383] += x134 * x527 * x537 result[384] += x11 * x152 * x529 result[385] += x534 * ( x0 * ( x182 * (x508 + x509) + 7.0 * x478 + 3.0 * x479 + 4.0 * x504 + x59 * (3.0 * x162 * x472 + x298 + 3.0 * x473 + 6.0 * x476) ) + x162 * x511 ) result[386] += x107 * x111 * x535 result[387] += x136 * x530 * x8 result[388] += x152 * x527 * x538 result[389] += x161 * x526 * x538 result[390] += x199 * x515 * x524 result[391] += x199 * x498 * x539 result[392] += x203 * x491 * x493 result[393] += x199 * x501 * x540 result[394] += x205 * x492 * x498 result[395] += x209 * x491 * x492 result[396] += x198 * x505 * x541 result[397] += x11 * x205 * x501 result[398] += x11 * x208 * x503 result[399] += x11 * x217 * x491 result[400] += x197 * x512 * x534 result[401] += x203 * x505 * x8 result[402] += x209 * x501 * x8 result[403] += x217 * x498 * x8 result[404] += x219 * x491 * x542 result[405] += x262 * x456 * x524 result[406] += x263 * x459 * x493 result[407] += x265 * x456 * x543 result[408] += x318 * x462 * x492 result[409] += x269 * x459 * x492 result[410] += x272 * x456 * x492 result[411] += x11 * x263 * x468 result[412] += x11 * x269 * x462 result[413] += x11 * x319 * x459 result[414] += x11 * x276 * x460 result[415] += x262 * x480 * x8 result[416] += x265 * x468 * x544 result[417] += x272 * x462 * x8 result[418] += x276 * x459 * x544 result[419] += x281 * x456 * x545 result[420] += x321 * x416 * x524 result[421] += x322 * x421 * x493 result[422] += x325 * x415 * x539 result[423] += x363 * x428 * x492 result[424] += x326 * x422 * x492 result[425] += x328 * x415 * x540 result[426] += x11 * x322 * x436 result[427] += x326 * x428 * x546 result[428] += x11 * x328 * x429 result[429] += x11 * x331 * x423 result[430] += x321 * x445 * x538 result[431] += x325 * x437 * x8 result[432] += x328 * x428 * x544 result[433] += x331 * x422 * x8 result[434] += x333 * x416 * x547 result[435] += x364 * x378 * x524 result[436] += x364 * x386 * x528 result[437] += x365 * x378 * x528 result[438] += x366 * x392 * x531 result[439] += x365 * x398 * x492 result[440] += x367 * x377 * x532 result[441] += x364 * x410 * x548 result[442] += x365 * x392 * x537 result[443] += x11 * x367 * x398 result[444] += x11 * x368 * x447 result[445] += x364 * x409 * x538 result[446] += x365 * x400 * x542 result[447] += x367 * x392 * x545 result[448] += x368 * x386 * x547 result[449] += x369 * x378 * x8 result[450] += x124 * x374 * x552 result[451] += x144 * x379 * x553 result[452] += x379 * x560 * x561 result[453] += x129 * x396 * x551 result[454] += x144 * x396 * x562 result[455] += x124 * x341 * x396 * x566 result[456] += x146 * x405 * x552 result[457] += x127 * x405 * x562 result[458] += x405 * x566 * x567 result[459] += x405 * x569 * x570 result[460] += x155 * x408 * x552 result[461] += x146 * x408 * x560 result[462] += x129 * x408 * x566 result[463] += x144 * x408 * x571 result[464] += x153 * x408 * x572 result[465] += x164 * x373 * x553 result[466] += x168 * x551 * x58 result[467] += x559 * x573 * x58 result[468] += x178 * x395 * x551 result[469] += x180 * x395 * x559 result[470] += x164 * x395 * x574 result[471] += x187 * x404 * x551 result[472] += x175 * x439 * x559 result[473] += x168 * x438 * x566 result[474] += x404 * x569 * x573 result[475] += x191 * x446 * x552 result[476] += x187 * x403 * x559 result[477] += x178 * x403 * x566 result[478] += x168 * x403 * x569 result[479] += x164 * x446 * x575 result[480] += x373 * x561 * x581 result[481] += x211 * x58 * x580 result[482] += x58 * x586 * x587 result[483] += x204 * x395 * x580 result[484] += x144 * x395 * x588 result[485] += x266 * x395 * x593 result[486] += x210 * x404 * x580 result[487] += x127 * x439 * x586 result[488] += x144 * x439 * x593 result[489] += x404 * x587 * x600 result[490] += x155 * x446 * x581 result[491] += x210 * x403 * x586 result[492] += x204 * x403 * x593 result[493] += x211 * x403 * x600 result[494] += x153 * x446 * x606 result[495] += x224 * x457 * x551 result[496] += x226 * x56 * x607 result[497] += x228 * x559 * x56 result[498] += x230 * x463 * x551 result[499] += x234 * x463 * x559 result[500] += x222 * x463 * x566 result[501] += x139 * x239 * x607 result[502] += x232 * x469 * x559 result[503] += x226 * x470 * x566 result[504] += x139 * x228 * x569 result[505] += x245 * x482 * x551 result[506] += x239 * x483 * x559 result[507] += x232 * x402 * x566 result[508] += x226 * x483 * x569 result[509] += x224 * x402 * x572 result[510] += x164 * x457 * x608 result[511] += x180 * x56 * x580 result[512] += x164 * x56 * x588 result[513] += x249 * x463 * x580 result[514] += x251 * x46 * x586 result[515] += x164 * x464 * x593 result[516] += x139 * x254 * x580 result[517] += x139 * x175 * x609 result[518] += x139 * x251 * x593 result[519] += x139 * x164 * x610 result[520] += x191 * x402 * x608 result[521] += x254 * x402 * x586 result[522] += x250 * x402 * x593 result[523] += x180 * x402 * x600 result[524] += x402 * x606 * x611 result[525] += x124 * x457 * x618 result[526] += x144 * x56 * x619 result[527] += x266 * x56 * x621 result[528] += x267 * x46 * x616 result[529] += x144 * x464 * x621 result[530] += x124 * x463 * x623 result[531] += x139 * x273 * x617 result[532] += x267 * x469 * x621 result[533] += x144 * x470 * x623 result[534] += x139 * x266 * x627 result[535] += x277 * x402 * x617 result[536] += x273 * x402 * x621 * x99 result[537] += x267 * x402 * x623 result[538] += x144 * x483 * x627 result[539] += x124 * x482 * x636 result[540] += x286 * x495 * x552 result[541] += x289 * x494 * x637 result[542] += x292 * x494 * x559 result[543] += x21 * x294 * x607 result[544] += x21 * x296 * x559 result[545] += x285 * x502 * x566 result[546] += x19 * x298 * x637 result[547] += x294 * x507 * x559 result[548] += x295 * x506 * x566 result[549] += x19 * x292 * x569 result[550] += x16 * x303 * x553 result[551] += x298 * x559 * x638 result[552] += x16 * x294 * x574 result[553] += x289 * x569 * x638 result[554] += x16 * x286 * x575 result[555] += x222 * x495 * x608 result[556] += x226 * x516 * x580 result[557] += x310 * x499 * x586 result[558] += x232 * x517 * x580 result[559] += x21 * x226 * x609 result[560] += x312 * x517 * x593 result[561] += x239 * x507 * x580 result[562] += x230 * x521 * x586 result[563] += x226 * x521 * x593 result[564] += x310 * x506 * x600 result[565] += x16 * x245 * x608 result[566] += x16 * x239 * x588 result[567] += x16 * x593 * x639 result[568] += x16 * x226 * x610 result[569] += x222 * x519 * x606 result[570] += x495 * x611 * x616 result[571] += x180 * x494 * x616 result[572] += x164 * x516 * x621 result[573] += x21 * x250 * x616 result[574] += x21 * x251 * x621 result[575] += x164 * x518 * x623 result[576] += x187 * x523 * x616 result[577] += x175 * x521 * x621 result[578] += x19 * x251 * x623 result[579] += x164 * x507 * x627 result[580] += x191 * x519 * x616 result[581] += x16 * x254 * x621 result[582] += x16 * x250 * x623 result[583] += x16 * x180 * x627 result[584] += x130 * x162 * x636 * x642 result[585] += x495 * x570 * x644 result[586] += x144 * x499 * x644 result[587] += x124 * x499 * x647 result[588] += x204 * x21 * x644 result[589] += x144 * x21 * x648 result[590] += x124 * x502 * x650 result[591] += x19 * x210 * x644 result[592] += x127 * x507 * x647 result[593] += x144 * x507 * x650 result[594] += x124 * x506 * x652 result[595] += x155 * x16 * x653 result[596] += x16 * x210 * x647 result[597] += x16 * x204 * x650 result[598] += x106 * x15 * x654 result[599] += x642 * x659 result[600] += x334 * x524 * x552 result[601] += x337 * x528 * x552 result[602] += x334 * x528 * x560 result[603] += x340 * x532 * x551 result[604] += x337 * x492 * x562 result[605] += x334 * x532 * x566 result[606] += x344 * x548 * x552 result[607] += x11 * x340 * x562 result[608] += x337 * x537 * x566 result[609] += x11 * x334 * x571 result[610] += x348 * x552 * x8 result[611] += x344 * x547 * x560 result[612] += x340 * x545 * x566 result[613] += x337 * x542 * x569 result[614] += x334 * x538 * x572 result[615] += x286 * x524 * x581 result[616] += x289 * x539 * x580 result[617] += x292 * x493 * x586 result[618] += x294 * x540 * x580 result[619] += x296 * x492 * x586 result[620] += x285 * x540 * x593 result[621] += x298 * x546 * x580 result[622] += x11 * x294 * x588 result[623] += x11 * x296 * x593 result[624] += x11 * x292 * x600 result[625] += x303 * x547 * x581 result[626] += x298 * x586 * x660 result[627] += x294 * x544 * x593 result[628] += x289 * x600 * x660 result[629] += x286 * x538 * x606 result[630] += x224 * x524 * x616 result[631] += x226 * x543 * x616 result[632] += x228 * x493 * x621 result[633] += x232 * x492 * x616 result[634] += x235 * x492 * x621 result[635] += x312 * x492 * x623 result[636] += x11 * x239 * x619 result[637] += x11 * x621 * x639 result[638] += x11 * x235 * x623 result[639] += x11 * x228 * x627 result[640] += x245 * x618 * x8 result[641] += x239 * x544 * x621 result[642] += x232 * x623 * x8 result[643] += x226 * x544 * x627 result[644] += x224 * x636 * x8 result[645] += x164 * x524 * x653 result[646] += x168 * x493 * x644 result[647] += x164 * x539 * x647 result[648] += x175 * x540 * x644 result[649] += x180 * x492 * x647 result[650] += x164 * x540 * x650 result[651] += x11 * x187 * x644 result[652] += x11 * x175 * x648 result[653] += x11 * x180 * x650 result[654] += x162 * x541 * x654 result[655] += x191 * x542 * x644 result[656] += x187 * x647 * x8 result[657] += x178 * x650 * x8 result[658] += x168 * x652 * x8 result[659] += x162 * x659 * x661 result[660] += x153 * x524 * x663 result[661] += x144 * x528 * x664 result[662] += x153 * x528 * x665 result[663] += x129 * x492 * x663 result[664] += x492 * x567 * x665 result[665] += x124 * x532 * x666 result[666] += x11 * x146 * x664 result[667] += x127 * x537 * x665 result[668] += x106 * x536 * x661 * x666 result[669] += x533 * x667 result[670] += x155 * x538 * x663 result[671] += x146 * x538 * x665 result[672] += x129 * x666 * x8 result[673] += x106 * x107 * x667 result[674] += x661 * ( x0 * ( x212 * (x655 + x656) + x59 * (3.0 * x197 * x628 + x331 + 3.0 * x629 + 6.0 * x632) + 7.0 * x634 + 3.0 * x635 + 4.0 * x651 ) + x197 * x658 )
int_tuple_type = numba.types.UniTuple(i8, 2) func_dict_type = numba.types.DictType(int_tuple_type, func_type) # Sadly, this function can't be cached.
[docs] @numba.jit(func_dict_type(), nopython=True, cache=True) def get_func_dict(): # Can we somehow utilize the 'func_dict_type' definition above?! # # This definition below does not work but leads to strange errors. # func_dict = numba.typed.Dict.empty( # key_type=func_dict_type.key_type, # value_type=func_dict_type.value_type, # ) # numba plzzz func_dict = numba.typed.Dict.empty( key_type=int_tuple_type, value_type=func_type, ) func_dict[(0, 0)] = diag_quadrupole3d_00 func_dict[(1, 0)] = diag_quadrupole3d_10 func_dict[(0, 1)] = diag_quadrupole3d_01 func_dict[(2, 0)] = diag_quadrupole3d_20 func_dict[(0, 2)] = diag_quadrupole3d_02 func_dict[(3, 0)] = diag_quadrupole3d_30 func_dict[(0, 3)] = diag_quadrupole3d_03 func_dict[(4, 0)] = diag_quadrupole3d_40 func_dict[(0, 4)] = diag_quadrupole3d_04 func_dict[(1, 1)] = diag_quadrupole3d_11 func_dict[(2, 1)] = diag_quadrupole3d_21 func_dict[(1, 2)] = diag_quadrupole3d_12 func_dict[(3, 1)] = diag_quadrupole3d_31 func_dict[(1, 3)] = diag_quadrupole3d_13 func_dict[(4, 1)] = diag_quadrupole3d_41 func_dict[(1, 4)] = diag_quadrupole3d_14 func_dict[(2, 2)] = diag_quadrupole3d_22 func_dict[(3, 2)] = diag_quadrupole3d_32 func_dict[(2, 3)] = diag_quadrupole3d_23 func_dict[(4, 2)] = diag_quadrupole3d_42 func_dict[(2, 4)] = diag_quadrupole3d_24 func_dict[(3, 3)] = diag_quadrupole3d_33 func_dict[(4, 3)] = diag_quadrupole3d_43 func_dict[(3, 4)] = diag_quadrupole3d_34 func_dict[(4, 4)] = diag_quadrupole3d_44 return func_dict