cdtools/CDTools/tools/atoms.py

"""Contains functions to generate standard object functions for atoms

The atomic scattering factors used to derive these object functions are
pulled from E.J Kirkland, Advanced Computing in Electron Microscopy,
Appendix C. doi: 10.1007/978-1-4419-6533-2_11

They are actually taken from https://github.com/LeBeauGroup/pyMultislicer
written by Jim LeBeau, but above is the original reference.
"""
from __future__ import division, print_function, absolute_import
import numpy as np
import torch as t
from scipy import fftpack


__all__ = ['generate_k_grid','generate_atom']


def fParams(Z):
    # This function ruthlessly plagiarized from pyMultislicer
    fparams = {z: [0 for _ in range(0, 12)] for z in range(1, 104)}
    fparams[1][0] = 4.20298324e-003
    fparams[1][1] = 2.25350888e-001
    fparams[1][2] = 6.27762505e-002
    fparams[1][3] = 2.25366950e-001
    fparams[1][4] = 3.00907347e-002
    fparams[1][5] = 2.25331756e-001
    fparams[1][6] = 6.77756695e-002
    fparams[1][7] = 4.38854001e+000
    fparams[1][8] = 3.56609237e-003
    fparams[1][9] = 4.03884823e-001
    fparams[1][10] = 2.76135815e-002
    fparams[1][11] = 1.44490166e+000
    fparams[2][0] = 1.87543704e-005
    fparams[2][1] = 2.12427997e-001
    fparams[2][2] = 4.10595800e-004
    fparams[2][3] = 3.32212279e-001
    fparams[2][4] = 1.96300059e-001
    fparams[2][5] = 5.17325152e-001
    fparams[2][6] = 8.36015738e-003
    fparams[2][7] = 3.66668239e-001
    fparams[2][8] = 2.95102022e-002
    fparams[2][9] = 1.37171827e+000
    fparams[2][10] = 4.65928982e-007
    fparams[2][11] = 3.75768025e+004
    fparams[3][0] = 7.45843816e-002
    fparams[3][1] = 8.81151424e-001
    fparams[3][2] = 7.15382250e-002
    fparams[3][3] = 4.59142904e-002
    fparams[3][4] = 1.45315229e-001
    fparams[3][5] = 8.81301714e-001
    fparams[3][6] = 1.12125769e+000
    fparams[3][7] = 1.88483665e+001
    fparams[3][8] = 2.51736525e-003
    fparams[3][9] = 1.59189995e-001
    fparams[3][10] = 3.58434971e-001
    fparams[3][11] = 6.12371000e+000
    fparams[4][0] = 6.11642897e-002
    fparams[4][1] = 9.90182132e-002
    fparams[4][2] = 1.25755034e-001
    fparams[4][3] = 9.90272412e-002
    fparams[4][4] = 2.00831548e-001
    fparams[4][5] = 1.87392509e+000
    fparams[4][6] = 7.87242876e-001
    fparams[4][7] = 9.32794929e+000
    fparams[4][8] = 1.58847850e-003
    fparams[4][9] = 8.91900236e-002
    fparams[4][10] = 2.73962031e-001
    fparams[4][11] = 3.20687658e+000
    fparams[5][0] = 1.25716066e-001
    fparams[5][1] = 1.48258830e-001
    fparams[5][2] = 1.73314452e-001
    fparams[5][3] = 1.48257216e-001
    fparams[5][4] = 1.84774811e-001
    fparams[5][5] = 3.34227311e+000
    fparams[5][6] = 1.95250221e-001
    fparams[5][7] = 1.97339463e+000
    fparams[5][8] = 5.29642075e-001
    fparams[5][9] = 5.70035553e+000
    fparams[5][10] = 1.08230500e-003
    fparams[5][11] = 5.64857237e-002
    fparams[6][0] = 2.12080767e-001
    fparams[6][1] = 2.08605417e-001
    fparams[6][2] = 1.99811865e-001
    fparams[6][3] = 2.08610186e-001
    fparams[6][4] = 1.68254385e-001
    fparams[6][5] = 5.57870773e+000
    fparams[6][6] = 1.42048360e-001
    fparams[6][7] = 1.33311887e+000
    fparams[6][8] = 3.63830672e-001
    fparams[6][9] = 3.80800263e+000
    fparams[6][10] = 8.35012044e-004
    fparams[6][11] = 4.03982620e-002
    fparams[7][0] = 5.33015554e-001
    fparams[7][1] = 2.90952515e-001
    fparams[7][2] = 5.29008883e-002
    fparams[7][3] = 1.03547896e+001
    fparams[7][4] = 9.24159648e-002
    fparams[7][5] = 1.03540028e+001
    fparams[7][6] = 2.61799101e-001
    fparams[7][7] = 2.76252723e+000
    fparams[7][8] = 8.80262108e-004
    fparams[7][9] = 3.47681236e-002
    fparams[7][10] = 1.10166555e-001
    fparams[7][11] = 9.93421736e-001
    fparams[8][0] = 3.39969204e-001
    fparams[8][1] = 3.81570280e-001
    fparams[8][2] = 3.07570172e-001
    fparams[8][3] = 3.81571436e-001
    fparams[8][4] = 1.30369072e-001
    fparams[8][5] = 1.91919745e+001
    fparams[8][6] = 8.83326058e-002
    fparams[8][7] = 7.60635525e-001
    fparams[8][8] = 1.96586700e-001
    fparams[8][9] = 2.07401094e+000
    fparams[8][10] = 9.96220028e-004
    fparams[8][11] = 3.03266869e-002
    fparams[9][0] = 2.30560593e-001
    fparams[9][1] = 4.80754213e-001
    fparams[9][2] = 5.26889648e-001
    fparams[9][3] = 4.80763895e-001
    fparams[9][4] = 1.24346755e-001
    fparams[9][5] = 3.95306720e+001
    fparams[9][6] = 1.24616894e-003
    fparams[9][7] = 2.62181803e-002
    fparams[9][8] = 7.20452555e-002
    fparams[9][9] = 5.92495593e-001
    fparams[9][10] = 1.53075777e-001
    fparams[9][11] = 1.59127671e+000
    fparams[10][0] = 4.08371771e-001
    fparams[10][1] = 5.88228627e-001
    fparams[10][2] = 4.54418858e-001
    fparams[10][3] = 5.88288655e-001
    fparams[10][4] = 1.44564923e-001
    fparams[10][5] = 1.21246013e+002
    fparams[10][6] = 5.91531395e-002
    fparams[10][7] = 4.63963540e-001
    fparams[10][8] = 1.24003718e-001
    fparams[10][9] = 1.23413025e+000
    fparams[10][10] = 1.64986037e-003
    fparams[10][11] = 2.05869217e-002
    fparams[11][0] = 1.36471662e-001
    fparams[11][1] = 4.99965301e-002
    fparams[11][2] = 7.70677865e-001
    fparams[11][3] = 8.81899664e-001
    fparams[11][4] = 1.56862014e-001
    fparams[11][5] = 1.61768579e+001
    fparams[11][6] = 9.96821513e-001
    fparams[11][7] = 2.00132610e+001
    fparams[11][8] = 3.80304670e-002
    fparams[11][9] = 2.60516254e-001
    fparams[11][10] = 1.27685089e-001
    fparams[11][11] = 6.99559329e-001
    fparams[12][0] = 3.04384121e-001
    fparams[12][1] = 8.42014377e-002
    fparams[12][2] = 7.56270563e-001
    fparams[12][3] = 1.64065598e+000
    fparams[12][4] = 1.01164809e-001
    fparams[12][5] = 2.97142975e+001
    fparams[12][6] = 3.45203403e-002
    fparams[12][7] = 2.16596094e-001
    fparams[12][8] = 9.71751327e-001
    fparams[12][9] = 1.21236852e+001
    fparams[12][10] = 1.20593012e-001
    fparams[12][11] = 5.60865838e-001
    fparams[13][0] = 7.77419424e-001
    fparams[13][1] = 2.71058227e+000
    fparams[13][2] = 5.78312036e-002
    fparams[13][3] = 7.17532098e+001
    fparams[13][4] = 4.26386499e-001
    fparams[13][5] = 9.13331555e-002
    fparams[13][6] = 1.13407220e-001
    fparams[13][7] = 4.48867451e-001
    fparams[13][8] = 7.90114035e-001
    fparams[13][9] = 8.66366718e+000
    fparams[13][10] = 3.23293496e-002
    fparams[13][11] = 1.78503463e-001
    fparams[14][0] = 1.06543892e+000
    fparams[14][1] = 1.04118455e+000
    fparams[14][2] = 1.20143691e-001
    fparams[14][3] = 6.87113368e+001
    fparams[14][4] = 1.80915263e-001
    fparams[14][5] = 8.87533926e-002
    fparams[14][6] = 1.12065620e+000
    fparams[14][7] = 3.70062619e+000
    fparams[14][8] = 3.05452816e-002
    fparams[14][9] = 2.14097897e-001
    fparams[14][10] = 1.59963502e+000
    fparams[14][11] = 9.99096638e+000
    fparams[15][0] = 1.05284447e+000
    fparams[15][1] = 1.31962590e+000
    fparams[15][2] = 2.99440284e-001
    fparams[15][3] = 1.28460520e-001
    fparams[15][4] = 1.17460748e-001
    fparams[15][5] = 1.02190163e+002
    fparams[15][6] = 9.60643452e-001
    fparams[15][7] = 2.87477555e+000
    fparams[15][8] = 2.63555748e-002
    fparams[15][9] = 1.82076844e-001
    fparams[15][10] = 1.38059330e+000
    fparams[15][11] = 7.49165526e+000
    fparams[16][0] = 1.01646916e+000
    fparams[16][1] = 1.69181965e+000
    fparams[16][2] = 4.41766748e-001
    fparams[16][3] = 1.74180288e-001
    fparams[16][4] = 1.21503863e-001
    fparams[16][5] = 1.67011091e+002
    fparams[16][6] = 8.27966670e-001
    fparams[16][7] = 2.30342810e+000
    fparams[16][8] = 2.33022533e-002
    fparams[16][9] = 1.56954150e-001
    fparams[16][10] = 1.18302846e+000
    fparams[16][11] = 5.85782891e+000
    fparams[17][0] = 9.44221116e-001
    fparams[17][1] = 2.40052374e-001
    fparams[17][2] = 4.37322049e-001
    fparams[17][3] = 9.30510439e+000
    fparams[17][4] = 2.54547926e-001
    fparams[17][5] = 9.30486346e+000
    fparams[17][6] = 5.47763323e-002
    fparams[17][7] = 1.68655688e-001
    fparams[17][8] = 8.00087488e-001
    fparams[17][9] = 2.97849774e+000
    fparams[17][10] = 1.07488641e-002
    fparams[17][11] = 6.84240646e-002
    fparams[18][0] = 1.06983288e+000
    fparams[18][1] = 2.87791022e-001
    fparams[18][2] = 4.24631786e-001
    fparams[18][3] = 1.24156957e+001
    fparams[18][4] = 2.43897949e-001
    fparams[18][5] = 1.24158868e+001
    fparams[18][6] = 4.79446296e-002
    fparams[18][7] = 1.36979796e-001
    fparams[18][8] = 7.64958952e-001
    fparams[18][9] = 2.43940729e+000
    fparams[18][10] = 8.23128431e-003
    fparams[18][11] = 5.27258749e-002
    fparams[19][0] = 6.92717865e-001
    fparams[19][1] = 7.10849990e+000
    fparams[19][2] = 9.65161085e-001
    fparams[19][3] = 3.57532901e-001
    fparams[19][4] = 1.48466588e-001
    fparams[19][5] = 3.93763275e-002
    fparams[19][6] = 2.64645027e-002
    fparams[19][7] = 1.03591321e-001
    fparams[19][8] = 1.80883768e+000
    fparams[19][9] = 3.22845199e+001
    fparams[19][10] = 5.43900018e-001
    fparams[19][11] = 1.67791374e+000
    fparams[20][0] = 3.66902871e-001
    fparams[20][1] = 6.14274129e-002
    fparams[20][2] = 8.66378999e-001
    fparams[20][3] = 5.70881727e-001
    fparams[20][4] = 6.67203300e-001
    fparams[20][5] = 7.82965639e+000
    fparams[20][6] = 4.87743636e-001
    fparams[20][7] = 1.32531318e+000
    fparams[20][8] = 1.82406314e+000
    fparams[20][9] = 2.10056032e+001
    fparams[20][10] = 2.20248453e-002
    fparams[20][11] = 9.11853450e-002
    fparams[21][0] = 3.78871777e-001
    fparams[21][1] = 6.98910162e-002
    fparams[21][2] = 9.00022505e-001
    fparams[21][3] = 5.21061541e-001
    fparams[21][4] = 7.15288914e-001
    fparams[21][5] = 7.87707920e+000
    fparams[21][6] = 1.88640973e-002
    fparams[21][7] = 8.17512708e-002
    fparams[21][8] = 4.07945949e-001
    fparams[21][9] = 1.11141388e+000
    fparams[21][10] = 1.61786540e+000
    fparams[21][11] = 1.80840759e+001
    fparams[22][0] = 3.62383267e-001
    fparams[22][1] = 7.54707114e-002
    fparams[22][2] = 9.84232966e-001
    fparams[22][3] = 4.97757309e-001
    fparams[22][4] = 7.41715642e-001
    fparams[22][5] = 8.17659391e+000
    fparams[22][6] = 3.62555269e-001
    fparams[22][7] = 9.55524906e-001
    fparams[22][8] = 1.49159390e+000
    fparams[22][9] = 1.62221677e+001
    fparams[22][10] = 1.61659509e-002
    fparams[22][11] = 7.33140839e-002
    fparams[23][0] = 3.52961378e-001
    fparams[23][1] = 8.19204103e-002
    fparams[23][2] = 7.46791014e-001
    fparams[23][3] = 8.81189511e+000
    fparams[23][4] = 1.08364068e+000
    fparams[23][5] = 5.10646075e-001
    fparams[23][6] = 1.39013610e+000
    fparams[23][7] = 1.48901841e+001
    fparams[23][8] = 3.31273356e-001
    fparams[23][9] = 8.38543079e-001
    fparams[23][10] = 1.40422612e-002
    fparams[23][11] = 6.57432678e-002
    fparams[24][0] = 1.34348379e+000
    fparams[24][1] = 1.25814353e+000
    fparams[24][2] = 5.07040328e-001
    fparams[24][3] = 1.15042811e+001
    fparams[24][4] = 4.26358955e-001
    fparams[24][5] = 8.53660389e-002
    fparams[24][6] = 1.17241826e-002
    fparams[24][7] = 6.00177061e-002
    fparams[24][8] = 5.11966516e-001
    fparams[24][9] = 1.53772451e+000
    fparams[24][10] = 3.38285828e-001
    fparams[24][11] = 6.62418319e-001
    fparams[25][0] = 3.26697613e-001
    fparams[25][1] = 8.88813083e-002
    fparams[25][2] = 7.17297000e-001
    fparams[25][3] = 1.11300198e+001
    fparams[25][4] = 1.33212464e+000
    fparams[25][5] = 5.82141104e-001
    fparams[25][6] = 2.80801702e-001
    fparams[25][7] = 6.71583145e-001
    fparams[25][8] = 1.15499241e+000
    fparams[25][9] = 1.26825395e+001
    fparams[25][10] = 1.11984488e-002
    fparams[25][11] = 5.32334467e-002
    fparams[26][0] = 3.13454847e-001
    fparams[26][1] = 8.99325756e-002
    fparams[26][2] = 6.89290016e-001
    fparams[26][3] = 1.30366038e+001
    fparams[26][4] = 1.47141531e+000
    fparams[26][5] = 6.33345291e-001
    fparams[26][6] = 1.03298688e+000
    fparams[26][7] = 1.16783425e+001
    fparams[26][8] = 2.58280285e-001
    fparams[26][9] = 6.09116446e-001
    fparams[26][10] = 1.03460690e-002
    fparams[26][11] = 4.81610627e-002
    fparams[27][0] = 3.15878278e-001
    fparams[27][1] = 9.46683246e-002
    fparams[27][2] = 1.60139005e+000
    fparams[27][3] = 6.99436449e-001
    fparams[27][4] = 6.56394338e-001
    fparams[27][5] = 1.56954403e+001
    fparams[27][6] = 9.36746624e-001
    fparams[27][7] = 1.09392410e+001
    fparams[27][8] = 9.77562646e-003
    fparams[27][9] = 4.37446816e-002
    fparams[27][10] = 2.38378578e-001
    fparams[27][11] = 5.56286483e-001
    fparams[28][0] = 1.72254630e+000
    fparams[28][1] = 7.76606908e-001
    fparams[28][2] = 3.29543044e-001
    fparams[28][3] = 1.02262360e-001
    fparams[28][4] = 6.23007200e-001
    fparams[28][5] = 1.94156207e+001
    fparams[28][6] = 9.43496513e-003
    fparams[28][7] = 3.98684596e-002
    fparams[28][8] = 8.54063515e-001
    fparams[28][9] = 1.04078166e+001
    fparams[28][10] = 2.21073515e-001
    fparams[28][11] = 5.10869330e-001
    fparams[29][0] = 3.58774531e-001
    fparams[29][1] = 1.06153463e-001
    fparams[29][2] = 1.76181348e+000
    fparams[29][3] = 1.01640995e+000
    fparams[29][4] = 6.36905053e-001
    fparams[29][5] = 1.53659093e+001
    fparams[29][6] = 7.44930667e-003
    fparams[29][7] = 3.85345989e-002
    fparams[29][8] = 1.89002347e-001
    fparams[29][9] = 3.98427790e-001
    fparams[29][10] = 2.29619589e-001
    fparams[29][11] = 9.01419843e-001
    fparams[30][0] = 5.70893973e-001
    fparams[30][1] = 1.26534614e-001
    fparams[30][2] = 1.98908856e+000
    fparams[30][3] = 2.17781965e+000
    fparams[30][4] = 3.06060585e-001
    fparams[30][5] = 3.78619003e+001
    fparams[30][6] = 2.35600223e-001
    fparams[30][7] = 3.67019041e-001
    fparams[30][8] = 3.97061102e-001
    fparams[30][9] = 8.66419596e-001
    fparams[30][10] = 6.85657228e-003
    fparams[30][11] = 3.35778823e-002
    fparams[31][0] = 6.25528464e-001
    fparams[31][1] = 1.10005650e-001
    fparams[31][2] = 2.05302901e+000
    fparams[31][3] = 2.41095786e+000
    fparams[31][4] = 2.89608120e-001
    fparams[31][5] = 4.78685736e+001
    fparams[31][6] = 2.07910594e-001
    fparams[31][7] = 3.27807224e-001
    fparams[31][8] = 3.45079617e-001
    fparams[31][9] = 7.43139061e-001
    fparams[31][10] = 6.55634298e-003
    fparams[31][11] = 3.09411369e-002
    fparams[32][0] = 5.90952690e-001
    fparams[32][1] = 1.18375976e-001
    fparams[32][2] = 5.39980660e-001
    fparams[32][3] = 7.18937433e+001
    fparams[32][4] = 2.00626188e+000
    fparams[32][5] = 1.39304889e+000
    fparams[32][6] = 7.49705041e-001
    fparams[32][7] = 6.89943350e+000
    fparams[32][8] = 1.83581347e-001
    fparams[32][9] = 3.64667232e-001
    fparams[32][10] = 9.52190743e-003
    fparams[32][11] = 2.69888650e-002
    fparams[33][0] = 7.77875218e-001
    fparams[33][1] = 1.50733157e-001
    fparams[33][2] = 5.93848150e-001
    fparams[33][3] = 1.42882209e+002
    fparams[33][4] = 1.95918751e+000
    fparams[33][5] = 1.74750339e+000
    fparams[33][6] = 1.79880226e-001
    fparams[33][7] = 3.31800852e-001
    fparams[33][8] = 8.63267222e-001
    fparams[33][9] = 5.85490274e+000
    fparams[33][10] = 9.59053427e-003
    fparams[33][11] = 2.33777569e-002
    fparams[34][0] = 9.58390681e-001
    fparams[34][1] = 1.83775557e-001
    fparams[34][2] = 6.03851342e-001
    fparams[34][3] = 1.96819224e+002
    fparams[34][4] = 1.90828931e+000
    fparams[34][5] = 2.15082053e+000
    fparams[34][6] = 1.73885956e-001
    fparams[34][7] = 3.00006024e-001
    fparams[34][8] = 9.35265145e-001
    fparams[34][9] = 4.92471215e+000
    fparams[34][10] = 8.62254658e-003
    fparams[34][11] = 2.12308108e-002
    fparams[35][0] = 1.14136170e+000
    fparams[35][1] = 2.18708710e-001
    fparams[35][2] = 5.18118737e-001
    fparams[35][3] = 1.93916682e+002
    fparams[35][4] = 1.85731975e+000
    fparams[35][5] = 2.65755396e+000
    fparams[35][6] = 1.68217399e-001
    fparams[35][7] = 2.71719918e-001
    fparams[35][8] = 9.75705606e-001
    fparams[35][9] = 4.19482500e+000
    fparams[35][10] = 7.24187871e-003
    fparams[35][11] = 1.99325718e-002
    fparams[36][0] = 3.24386970e-001
    fparams[36][1] = 6.31317973e+001
    fparams[36][2] = 1.31732163e+000
    fparams[36][3] = 2.54706036e-001
    fparams[36][4] = 1.79912614e+000
    fparams[36][5] = 3.23668394e+000
    fparams[36][6] = 4.29961425e-003
    fparams[36][7] = 1.98965610e-002
    fparams[36][8] = 1.00429433e+000
    fparams[36][9] = 3.61094513e+000
    fparams[36][10] = 1.62188197e-001
    fparams[36][11] = 2.45583672e-001
    fparams[37][0] = 2.90445351e-001
    fparams[37][1] = 3.68420227e-002
    fparams[37][2] = 2.44201329e+000
    fparams[37][3] = 1.16013332e+000
    fparams[37][4] = 7.69435449e-001
    fparams[37][5] = 1.69591472e+001
    fparams[37][6] = 1.58687000e+000
    fparams[37][7] = 2.53082574e+000
    fparams[37][8] = 2.81617593e-003
    fparams[37][9] = 1.88577417e-002
    fparams[37][10] = 1.28663830e-001
    fparams[37][11] = 2.10753969e-001
    fparams[38][0] = 1.37373086e-002
    fparams[38][1] = 1.87469061e-002
    fparams[38][2] = 1.97548672e+000
    fparams[38][3] = 6.36079230e+000
    fparams[38][4] = 1.59261029e+000
    fparams[38][5] = 2.21992482e-001
    fparams[38][6] = 1.73263882e-001
    fparams[38][7] = 2.01624958e-001
    fparams[38][8] = 4.66280378e+000
    fparams[38][9] = 2.53027803e+001
    fparams[38][10] = 1.61265063e-003
    fparams[38][11] = 1.53610568e-002
    fparams[39][0] = 6.75302747e-001
    fparams[39][1] = 6.54331847e-002
    fparams[39][2] = 4.70286720e-001
    fparams[39][3] = 1.06108709e+002
    fparams[39][4] = 2.63497677e+000
    fparams[39][5] = 2.06643540e+000
    fparams[39][6] = 1.09621746e-001
    fparams[39][7] = 1.93131925e-001
    fparams[39][8] = 9.60348773e-001
    fparams[39][9] = 1.63310938e+000
    fparams[39][10] = 5.28921555e-003
    fparams[39][11] = 1.66083821e-002
    fparams[40][0] = 2.64365505e+000
    fparams[40][1] = 2.20202699e+000
    fparams[40][2] = 5.54225147e-001
    fparams[40][3] = 1.78260107e+002
    fparams[40][4] = 7.61376625e-001
    fparams[40][5] = 7.67218745e-002
    fparams[40][6] = 6.02946891e-003
    fparams[40][7] = 1.55143296e-002
    fparams[40][8] = 9.91630530e-002
    fparams[40][9] = 1.76175995e-001
    fparams[40][10] = 9.56782020e-001
    fparams[40][11] = 1.54330682e+000
    fparams[41][0] = 6.59532875e-001
    fparams[41][1] = 8.66145490e-002
    fparams[41][2] = 1.84545854e+000
    fparams[41][3] = 5.94774398e+000
    fparams[41][4] = 1.25584405e+000
    fparams[41][5] = 6.40851475e-001
    fparams[41][6] = 1.22253422e-001
    fparams[41][7] = 1.66646050e-001
    fparams[41][8] = 7.06638328e-001
    fparams[41][9] = 1.62853268e+000
    fparams[41][10] = 2.62381591e-003
    fparams[41][11] = 8.26257859e-003
    fparams[42][0] = 6.10160120e-001
    fparams[42][1] = 9.11628054e-002
    fparams[42][2] = 1.26544000e+000
    fparams[42][3] = 5.06776025e-001
    fparams[42][4] = 1.97428762e+000
    fparams[42][5] = 5.89590381e+000
    fparams[42][6] = 6.48028962e-001
    fparams[42][7] = 1.46634108e+000
    fparams[42][8] = 2.60380817e-003
    fparams[42][9] = 7.84336311e-003
    fparams[42][10] = 1.13887493e-001
    fparams[42][11] = 1.55114340e-001
    fparams[43][0] = 8.55189183e-001
    fparams[43][1] = 1.02962151e-001
    fparams[43][2] = 1.66219641e+000
    fparams[43][3] = 7.64907000e+000
    fparams[43][4] = 1.45575475e+000
    fparams[43][5] = 1.01639987e+000
    fparams[43][6] = 1.05445664e-001
    fparams[43][7] = 1.42303338e-001
    fparams[43][8] = 7.71657112e-001
    fparams[43][9] = 1.34659349e+000
    fparams[43][10] = 2.20992635e-003
    fparams[43][11] = 7.90358976e-003
    fparams[44][0] = 4.70847093e-001
    fparams[44][1] = 9.33029874e-002
    fparams[44][2] = 1.58180781e+000
    fparams[44][3] = 4.52831347e-001
    fparams[44][4] = 2.02419818e+000
    fparams[44][5] = 7.11489023e+000
    fparams[44][6] = 1.97036257e-003
    fparams[44][7] = 7.56181595e-003
    fparams[44][8] = 6.26912639e-001
    fparams[44][9] = 1.25399858e+000
    fparams[44][10] = 1.02641320e-001
    fparams[44][11] = 1.33786087e-001
    fparams[45][0] = 4.20051553e-001
    fparams[45][1] = 9.38882628e-002
    fparams[45][2] = 1.76266507e+000
    fparams[45][3] = 4.64441687e-001
    fparams[45][4] = 2.02735641e+000
    fparams[45][5] = 8.19346046e+000
    fparams[45][6] = 1.45487176e-003
    fparams[45][7] = 7.82704517e-003
    fparams[45][8] = 6.22809600e-001
    fparams[45][9] = 1.17194153e+000
    fparams[45][10] = 9.91529915e-002
    fparams[45][11] = 1.24532839e-001
    fparams[46][0] = 2.10475155e+000
    fparams[46][1] = 8.68606470e+000
    fparams[46][2] = 2.03884487e+000
    fparams[46][3] = 3.78924449e-001
    fparams[46][4] = 1.82067264e-001
    fparams[46][5] = 1.42921634e-001
    fparams[46][6] = 9.52040948e-002
    fparams[46][7] = 1.17125900e-001
    fparams[46][8] = 5.91445248e-001
    fparams[46][9] = 1.07843808e+000
    fparams[46][10] = 1.13328676e-003
    fparams[46][11] = 7.80252092e-003
    fparams[47][0] = 2.07981390e+000
    fparams[47][1] = 9.92540297e+000
    fparams[47][2] = 4.43170726e-001
    fparams[47][3] = 1.04920104e-001
    fparams[47][4] = 1.96515215e+000
    fparams[47][5] = 6.40103839e-001
    fparams[47][6] = 5.96130591e-001
    fparams[47][7] = 8.89594790e-001
    fparams[47][8] = 4.78016333e-001
    fparams[47][9] = 1.98509407e+000
    fparams[47][10] = 9.46458470e-002
    fparams[47][11] = 1.12744464e-001
    fparams[48][0] = 1.63657549e+000
    fparams[48][1] = 1.24540381e+001
    fparams[48][2] = 2.17927989e+000
    fparams[48][3] = 1.45134660e+000
    fparams[48][4] = 7.71300690e-001
    fparams[48][5] = 1.26695757e-001
    fparams[48][6] = 6.64193880e-001
    fparams[48][7] = 7.77659202e-001
    fparams[48][8] = 7.64563285e-001
    fparams[48][9] = 1.66075210e+000
    fparams[48][10] = 8.61126689e-002
    fparams[48][11] = 1.05728357e-001
    fparams[49][0] = 2.24820632e+000
    fparams[49][1] = 1.51913507e+000
    fparams[49][2] = 1.64706864e+000
    fparams[49][3] = 1.30113424e+001
    fparams[49][4] = 7.88679265e-001
    fparams[49][5] = 1.06128184e-001
    fparams[49][6] = 8.12579069e-002
    fparams[49][7] = 9.94045620e-002
    fparams[49][8] = 6.68280346e-001
    fparams[49][9] = 1.49742063e+000
    fparams[49][10] = 6.38467475e-001
    fparams[49][11] = 7.18422635e-001
    fparams[50][0] = 2.16644620e+000
    fparams[50][1] = 1.13174909e+001
    fparams[50][2] = 6.88691021e-001
    fparams[50][3] = 1.10131285e-001
    fparams[50][4] = 1.92431751e+000
    fparams[50][5] = 6.74464853e-001
    fparams[50][6] = 5.65359888e-001
    fparams[50][7] = 7.33564610e-001
    fparams[50][8] = 9.18683861e-001
    fparams[50][9] = 1.02310312e+001
    fparams[50][10] = 7.80542213e-002
    fparams[50][11] = 9.31104308e-002
    fparams[51][0] = 1.73662114e+000
    fparams[51][1] = 8.84334719e-001
    fparams[51][2] = 9.99871380e-001
    fparams[51][3] = 1.38462121e-001
    fparams[51][4] = 2.13972409e+000
    fparams[51][5] = 1.19666432e+001
    fparams[51][6] = 5.60566526e-001
    fparams[51][7] = 6.72672880e-001
    fparams[51][8] = 9.93772747e-001
    fparams[51][9] = 8.72330411e+000
    fparams[51][10] = 7.37374982e-002
    fparams[51][11] = 8.78577715e-002
    fparams[52][0] = 2.09383882e+000
    fparams[52][1] = 1.26856869e+001
    fparams[52][2] = 1.56940519e+000
    fparams[52][3] = 1.21236537e+000
    fparams[52][4] = 1.30941993e+000
    fparams[52][5] = 1.66633292e-001
    fparams[52][6] = 6.98067804e-002
    fparams[52][7] = 8.30817576e-002
    fparams[52][8] = 1.04969537e+000
    fparams[52][9] = 7.43147857e+000
    fparams[52][10] = 5.55594354e-001
    fparams[52][11] = 6.17487676e-001
    fparams[53][0] = 1.60186925e+000
    fparams[53][1] = 1.95031538e-001
    fparams[53][2] = 1.98510264e+000
    fparams[53][3] = 1.36976183e+001
    fparams[53][4] = 1.48226200e+000
    fparams[53][5] = 1.80304795e+000
    fparams[53][6] = 5.53807199e-001
    fparams[53][7] = 5.67912340e-001
    fparams[53][8] = 1.11728722e+000
    fparams[53][9] = 6.40879878e+000
    fparams[53][10] = 6.60720847e-002
    fparams[53][11] = 7.86615429e-002
    fparams[54][0] = 1.60015487e+000
    fparams[54][1] = 2.92913354e+000
    fparams[54][2] = 1.71644581e+000
    fparams[54][3] = 1.55882990e+001
    fparams[54][4] = 1.84968351e+000
    fparams[54][5] = 2.22525983e-001
    fparams[54][6] = 6.23813648e-002
    fparams[54][7] = 7.45581223e-002
    fparams[54][8] = 1.21387555e+000
    fparams[54][9] = 5.56013271e+000
    fparams[54][10] = 5.54051946e-001
    fparams[54][11] = 5.21994521e-001
    fparams[55][0] = 2.95236854e+000
    fparams[55][1] = 6.01461952e+000
    fparams[55][2] = 4.28105721e-001
    fparams[55][3] = 4.64151246e+001
    fparams[55][4] = 1.89599233e+000
    fparams[55][5] = 1.80109756e-001
    fparams[55][6] = 5.48012938e-002
    fparams[55][7] = 7.12799633e-002
    fparams[55][8] = 4.70838600e+000
    fparams[55][9] = 4.56702799e+001
    fparams[55][10] = 5.90356719e-001
    fparams[55][11] = 4.70236310e-001
    fparams[56][0] = 3.19434243e+000
    fparams[56][1] = 9.27352241e+000
    fparams[56][2] = 1.98289586e+000
    fparams[56][3] = 2.28741632e-001
    fparams[56][4] = 1.55121052e-001
    fparams[56][5] = 3.82000231e-002
    fparams[56][6] = 6.73222354e-002
    fparams[56][7] = 7.30961745e-002
    fparams[56][8] = 4.48474211e+000
    fparams[56][9] = 2.95703565e+001
    fparams[56][10] = 5.42674414e-001
    fparams[56][11] = 4.08647015e-001
    fparams[57][0] = 2.05036425e+000
    fparams[57][1] = 2.20348417e-001
    fparams[57][2] = 1.42114311e-001
    fparams[57][3] = 3.96438056e-002
    fparams[57][4] = 3.23538151e+000
    fparams[57][5] = 9.56979169e+000
    fparams[57][6] = 6.34683429e-002
    fparams[57][7] = 6.92443091e-002
    fparams[57][8] = 3.97960586e+000
    fparams[57][9] = 2.53178406e+001
    fparams[57][10] = 5.20116711e-001
    fparams[57][11] = 3.83614098e-001
    fparams[58][0] = 3.22990759e+000
    fparams[58][1] = 9.94660135e+000
    fparams[58][2] = 1.57618307e-001
    fparams[58][3] = 4.15378676e-002
    fparams[58][4] = 2.13477838e+000
    fparams[58][5] = 2.40480572e-001
    fparams[58][6] = 5.01907609e-001
    fparams[58][7] = 3.66252019e-001
    fparams[58][8] = 3.80889010e+000
    fparams[58][9] = 2.43275968e+001
    fparams[58][10] = 5.96625028e-002
    fparams[58][11] = 6.59653503e-002
    fparams[59][0] = 1.58189324e-001
    fparams[59][1] = 3.91309056e-002
    fparams[59][2] = 3.18141995e+000
    fparams[59][3] = 1.04139545e+001
    fparams[59][4] = 2.27622140e+000
    fparams[59][5] = 2.81671757e-001
    fparams[59][6] = 3.97705472e+000
    fparams[59][7] = 2.61872978e+001
    fparams[59][8] = 5.58448277e-002
    fparams[59][9] = 6.30921695e-002
    fparams[59][10] = 4.85207954e-001
    fparams[59][11] = 3.54234369e-001
    fparams[60][0] = 1.81379417e-001
    fparams[60][1] = 4.37324793e-002
    fparams[60][2] = 3.17616396e+000
    fparams[60][3] = 1.07842572e+001
    fparams[60][4] = 2.35221519e+000
    fparams[60][5] = 3.05571833e-001
    fparams[60][6] = 3.83125763e+000
    fparams[60][7] = 2.54745408e+001
    fparams[60][8] = 5.25889976e-002
    fparams[60][9] = 6.02676073e-002
    fparams[60][10] = 4.70090742e-001
    fparams[60][11] = 3.39017003e-001
    fparams[61][0] = 1.92986811e-001
    fparams[61][1] = 4.37785970e-002
    fparams[61][2] = 2.43756023e+000
    fparams[61][3] = 3.29336996e-001
    fparams[61][4] = 3.17248504e+000
    fparams[61][5] = 1.11259996e+001
    fparams[61][6] = 3.58105414e+000
    fparams[61][7] = 2.46709586e+001
    fparams[61][8] = 4.56529394e-001
    fparams[61][9] = 3.24990282e-001
    fparams[61][10] = 4.94812177e-002
    fparams[61][11] = 5.76553100e-002
    fparams[62][0] = 2.12002595e-001
    fparams[62][1] = 4.57703608e-002
    fparams[62][2] = 3.16891754e+000
    fparams[62][3] = 1.14536599e+001
    fparams[62][4] = 2.51503494e+000
    fparams[62][5] = 3.55561054e-001
    fparams[62][6] = 4.44080845e-001
    fparams[62][7] = 3.11953363e-001
    fparams[62][8] = 3.36742101e+000
    fparams[62][9] = 2.40291435e+001
    fparams[62][10] = 4.65652543e-002
    fparams[62][11] = 5.52266819e-002
    fparams[63][0] = 2.59355002e+000
    fparams[63][1] = 3.82452612e-001
    fparams[63][2] = 3.16557522e+000
    fparams[63][3] = 1.17675155e+001
    fparams[63][4] = 2.29402652e-001
    fparams[63][5] = 4.76642249e-002
    fparams[63][6] = 4.32257780e-001
    fparams[63][7] = 2.99719833e-001
    fparams[63][8] = 3.17261920e+000
    fparams[63][9] = 2.34462738e+001
    fparams[63][10] = 4.37958317e-002
    fparams[63][11] = 5.29440680e-002
    fparams[64][0] = 3.19144939e+000
    fparams[64][1] = 1.20224655e+001
    fparams[64][2] = 2.55766431e+000
    fparams[64][3] = 4.08338876e-001
    fparams[64][4] = 3.32681934e-001
    fparams[64][5] = 5.85819814e-002
    fparams[64][6] = 4.14243130e-002
    fparams[64][7] = 5.06771477e-002
    fparams[64][8] = 2.61036728e+000
    fparams[64][9] = 1.99344244e+001
    fparams[64][10] = 4.20526863e-001
    fparams[64][11] = 2.85686240e-001
    fparams[65][0] = 2.59407462e-001
    fparams[65][1] = 5.04689354e-002
    fparams[65][2] = 3.16177855e+000
    fparams[65][3] = 1.23140183e+001
    fparams[65][4] = 2.75095751e+000
    fparams[65][5] = 4.38337626e-001
    fparams[65][6] = 2.79247686e+000
    fparams[65][7] = 2.23797309e+001
    fparams[65][8] = 3.85931001e-002
    fparams[65][9] = 4.87920992e-002
    fparams[65][10] = 4.10881708e-001
    fparams[65][11] = 2.77622892e-001
    fparams[66][0] = 3.16055396e+000
    fparams[66][1] = 1.25470414e+001
    fparams[66][2] = 2.82751709e+000
    fparams[66][3] = 4.67899094e-001
    fparams[66][4] = 2.75140255e-001
    fparams[66][5] = 5.23226982e-002
    fparams[66][6] = 4.00967160e-001
    fparams[66][7] = 2.67614884e-001
    fparams[66][8] = 2.63110834e+000
    fparams[66][9] = 2.19498166e+001
    fparams[66][10] = 3.61333817e-002
    fparams[66][11] = 4.68871497e-002
    fparams[67][0] = 2.88642467e-001
    fparams[67][1] = 5.40507687e-002
    fparams[67][2] = 2.90567296e+000
    fparams[67][3] = 4.97581077e-001
    fparams[67][4] = 3.15960159e+000
    fparams[67][5] = 1.27599505e+001
    fparams[67][6] = 3.91280259e-001
    fparams[67][7] = 2.58151831e-001
    fparams[67][8] = 2.48596038e+000
    fparams[67][9] = 2.15400972e+001
    fparams[67][10] = 3.37664478e-002
    fparams[67][11] = 4.50664323e-002
    fparams[68][0] = 3.15573213e+000
    fparams[68][1] = 1.29729009e+001
    fparams[68][2] = 3.11519560e-001
    fparams[68][3] = 5.81399387e-002
    fparams[68][4] = 2.97722406e+000
    fparams[68][5] = 5.31213394e-001
    fparams[68][6] = 3.81563854e-001
    fparams[68][7] = 2.49195776e-001
    fparams[68][8] = 2.40247532e+000
    fparams[68][9] = 2.13627616e+001
    fparams[68][10] = 3.15224214e-002
    fparams[68][11] = 4.33253257e-002
    fparams[69][0] = 3.15591970e+000
    fparams[69][1] = 1.31232407e+001
    fparams[69][2] = 3.22544710e-001
    fparams[69][3] = 5.97223323e-002
    fparams[69][4] = 3.05569053e+000
    fparams[69][5] = 5.61876773e-001
    fparams[69][6] = 2.92845100e-002
    fparams[69][7] = 4.16534255e-002
    fparams[69][8] = 3.72487205e-001
    fparams[69][9] = 2.40821967e-001
    fparams[69][10] = 2.27833695e+000
    fparams[69][11] = 2.10034185e+001
    fparams[70][0] = 3.10794704e+000
    fparams[70][1] = 6.06347847e-001
    fparams[70][2] = 3.14091221e+000
    fparams[70][3] = 1.33705269e+001
    fparams[70][4] = 3.75660454e-001
    fparams[70][5] = 7.29814740e-002
    fparams[70][6] = 3.61901097e-001
    fparams[70][7] = 2.32652051e-001
    fparams[70][8] = 2.45409082e+000
    fparams[70][9] = 2.12695209e+001
    fparams[70][10] = 2.72383990e-002
    fparams[70][11] = 3.99969597e-002
    fparams[71][0] = 3.11446863e+000
    fparams[71][1] = 1.38968881e+001
    fparams[71][2] = 5.39634353e-001
    fparams[71][3] = 8.91708508e-002
    fparams[71][4] = 3.06460915e+000
    fparams[71][5] = 6.79919563e-001
    fparams[71][6] = 2.58563745e-002
    fparams[71][7] = 3.82808522e-002
    fparams[71][8] = 2.13983556e+000
    fparams[71][9] = 1.80078788e+001
    fparams[71][10] = 3.47788231e-001
    fparams[71][11] = 2.22706591e-001
    fparams[72][0] = 3.01166899e+000
    fparams[72][1] = 7.10401889e-001
    fparams[72][2] = 3.16284788e+000
    fparams[72][3] = 1.38262192e+001
    fparams[72][4] = 6.33421771e-001
    fparams[72][5] = 9.48486572e-002
    fparams[72][6] = 3.41417198e-001
    fparams[72][7] = 2.14129678e-001
    fparams[72][8] = 1.53566013e+000
    fparams[72][9] = 1.55298698e+001
    fparams[72][10] = 2.40723773e-002
    fparams[72][11] = 3.67833690e-002
    fparams[73][0] = 3.20236821e+000
    fparams[73][1] = 1.38446369e+001
    fparams[73][2] = 8.30098413e-001
    fparams[73][3] = 1.18381581e-001
    fparams[73][4] = 2.86552297e+000
    fparams[73][5] = 7.66369118e-001
    fparams[73][6] = 2.24813887e-002
    fparams[73][7] = 3.52934622e-002
    fparams[73][8] = 1.40165263e+000
    fparams[73][9] = 1.46148877e+001
    fparams[73][10] = 3.33740596e-001
    fparams[73][11] = 2.05704486e-001
    fparams[74][0] = 9.24906855e-001
    fparams[74][1] = 1.28663377e-001
    fparams[74][2] = 2.75554557e+000
    fparams[74][3] = 7.65826479e-001
    fparams[74][4] = 3.30440060e+000
    fparams[74][5] = 1.34471170e+001
    fparams[74][6] = 3.29973862e-001
    fparams[74][7] = 1.98218895e-001
    fparams[74][8] = 1.09916444e+000
    fparams[74][9] = 1.35087534e+001
    fparams[74][10] = 2.06498883e-002
    fparams[74][11] = 3.38918459e-002
    fparams[75][0] = 1.96952105e+000
    fparams[75][1] = 4.98830620e+001
    fparams[75][2] = 1.21726619e+000
    fparams[75][3] = 1.33243809e-001
    fparams[75][4] = 4.10391685e+000
    fparams[75][5] = 1.84396916e+000
    fparams[75][6] = 2.90791978e-002
    fparams[75][7] = 2.84192813e-002
    fparams[75][8] = 2.30696669e-001
    fparams[75][9] = 1.90968784e-001
    fparams[75][10] = 6.08840299e-001
    fparams[75][11] = 1.37090356e+000
    fparams[76][0] = 2.06385867e+000
    fparams[76][1] = 4.05671697e+001
    fparams[76][2] = 1.29603406e+000
    fparams[76][3] = 1.46559047e-001
    fparams[76][4] = 3.96920673e+000
    fparams[76][5] = 1.82561596e+000
    fparams[76][6] = 2.69835487e-002
    fparams[76][7] = 2.84172045e-002
    fparams[76][8] = 2.31083999e-001
    fparams[76][9] = 1.79765184e-001
    fparams[76][10] = 6.30466774e-001
    fparams[76][11] = 1.38911543e+000
    fparams[77][0] = 2.21522726e+000
    fparams[77][1] = 3.24464090e+001
    fparams[77][2] = 1.37573155e+000
    fparams[77][3] = 1.60920048e-001
    fparams[77][4] = 3.78244405e+000
    fparams[77][5] = 1.78756553e+000
    fparams[77][6] = 2.44643240e-002
    fparams[77][7] = 2.82909938e-002
    fparams[77][8] = 2.36932016e-001
    fparams[77][9] = 1.70692368e-001
    fparams[77][10] = 6.48471412e-001
    fparams[77][11] = 1.37928390e+000
    fparams[78][0] = 9.84697940e-001
    fparams[78][1] = 1.60910839e-001
    fparams[78][2] = 2.73987079e+000
    fparams[78][3] = 7.18971667e-001
    fparams[78][4] = 3.61696715e+000
    fparams[78][5] = 1.29281016e+001
    fparams[78][6] = 3.02885602e-001
    fparams[78][7] = 1.70134854e-001
    fparams[78][8] = 2.78370726e-001
    fparams[78][9] = 1.49862703e+000
    fparams[78][10] = 1.52124129e-002
    fparams[78][11] = 2.83510822e-002
    fparams[79][0] = 9.61263398e-001
    fparams[79][1] = 1.70932277e-001
    fparams[79][2] = 3.69581030e+000
    fparams[79][3] = 1.29335319e+001
    fparams[79][4] = 2.77567491e+000
    fparams[79][5] = 6.89997070e-001
    fparams[79][6] = 2.95414176e-001
    fparams[79][7] = 1.63525510e-001
    fparams[79][8] = 3.11475743e-001
    fparams[79][9] = 1.39200901e+000
    fparams[79][10] = 1.43237267e-002
    fparams[79][11] = 2.71265337e-002
    fparams[80][0] = 1.29200491e+000
    fparams[80][1] = 1.83432865e-001
    fparams[80][2] = 2.75161478e+000
    fparams[80][3] = 9.42368371e-001
    fparams[80][4] = 3.49387949e+000
    fparams[80][5] = 1.46235654e+001
    fparams[80][6] = 2.77304636e-001
    fparams[80][7] = 1.55110144e-001
    fparams[80][8] = 4.30232810e-001
    fparams[80][9] = 1.28871670e+000
    fparams[80][10] = 1.48294351e-002
    fparams[80][11] = 2.61903834e-002
    fparams[81][0] = 3.75964730e+000
    fparams[81][1] = 1.35041513e+001
    fparams[81][2] = 3.21195904e+000
    fparams[81][3] = 6.66330993e-001
    fparams[81][4] = 6.47767825e-001
    fparams[81][5] = 9.22518234e-002
    fparams[81][6] = 2.76123274e-001
    fparams[81][7] = 1.50312897e-001
    fparams[81][8] = 3.18838810e-001
    fparams[81][9] = 1.12565588e+000
    fparams[81][10] = 1.31668419e-002
    fparams[81][11] = 2.48879842e-002
    fparams[82][0] = 1.00795975e+000
    fparams[82][1] = 1.17268427e-001
    fparams[82][2] = 3.09796153e+000
    fparams[82][3] = 8.80453235e-001
    fparams[82][4] = 3.61296864e+000
    fparams[82][5] = 1.47325812e+001
    fparams[82][6] = 2.62401476e-001
    fparams[82][7] = 1.43491014e-001
    fparams[82][8] = 4.05621995e-001
    fparams[82][9] = 1.04103506e+000
    fparams[82][10] = 1.31812509e-002
    fparams[82][11] = 2.39575415e-002
    fparams[83][0] = 1.59826875e+000
    fparams[83][1] = 1.56897471e-001
    fparams[83][2] = 4.38233925e+000
    fparams[83][3] = 2.47094692e+000
    fparams[83][4] = 2.06074719e+000
    fparams[83][5] = 5.72438972e+001
    fparams[83][6] = 1.94426023e-001
    fparams[83][7] = 1.32979109e-001
    fparams[83][8] = 8.22704978e-001
    fparams[83][9] = 9.56532528e-001
    fparams[83][10] = 2.33226953e-002
    fparams[83][11] = 2.23038435e-002
    fparams[84][0] = 1.71463223e+000
    fparams[84][1] = 9.79262841e+001
    fparams[84][2] = 2.14115960e+000
    fparams[84][3] = 2.10193717e-001
    fparams[84][4] = 4.37512413e+000
    fparams[84][5] = 3.66948812e+000
    fparams[84][6] = 2.16216680e-002
    fparams[84][7] = 1.98456144e-002
    fparams[84][8] = 1.97843837e-001
    fparams[84][9] = 1.33758807e-001
    fparams[84][10] = 6.52047920e-001
    fparams[84][11] = 7.80432104e-001
    fparams[85][0] = 1.48047794e+000
    fparams[85][1] = 1.25943919e+002
    fparams[85][2] = 2.09174630e+000
    fparams[85][3] = 1.83803008e-001
    fparams[85][4] = 4.75246033e+000
    fparams[85][5] = 4.19890596e+000
    fparams[85][6] = 1.85643958e-002
    fparams[85][7] = 1.81383503e-002
    fparams[85][8] = 2.05859375e-001
    fparams[85][9] = 1.33035404e-001
    fparams[85][10] = 7.13540948e-001
    fparams[85][11] = 7.03031938e-001
    fparams[86][0] = 6.30022295e-001
    fparams[86][1] = 1.40909762e-001
    fparams[86][2] = 3.80962881e+000
    fparams[86][3] = 3.08515540e+001
    fparams[86][4] = 3.89756067e+000
    fparams[86][5] = 6.51559763e-001
    fparams[86][6] = 2.40755100e-001
    fparams[86][7] = 1.08899672e-001
    fparams[86][8] = 2.62868577e+000
    fparams[86][9] = 6.42383261e+000
    fparams[86][10] = 3.14285931e-002
    fparams[86][11] = 2.42346699e-002
    fparams[87][0] = 5.23288135e+000
    fparams[87][1] = 8.60599536e+000
    fparams[87][2] = 2.48604205e+000
    fparams[87][3] = 3.04543982e-001
    fparams[87][4] = 3.23431354e-001
    fparams[87][5] = 3.87759096e-002
    fparams[87][6] = 2.55403596e-001
    fparams[87][7] = 1.28717724e-001
    fparams[87][8] = 5.53607228e-001
    fparams[87][9] = 5.36977452e-001
    fparams[87][10] = 5.75278889e-003
    fparams[87][11] = 1.29417790e-002
    fparams[88][0] = 1.44192685e+000
    fparams[88][1] = 1.18740873e-001
    fparams[88][2] = 3.55291725e+000
    fparams[88][3] = 1.01739750e+000
    fparams[88][4] = 3.91259586e+000
    fparams[88][5] = 6.31814783e+001
    fparams[88][6] = 2.16173519e-001
    fparams[88][7] = 9.55806441e-002
    fparams[88][8] = 3.94191605e+000
    fparams[88][9] = 3.50602732e+001
    fparams[88][10] = 4.60422605e-002
    fparams[88][11] = 2.20850385e-002
    fparams[89][0] = 1.45864127e+000
    fparams[89][1] = 1.07760494e-001
    fparams[89][2] = 4.18945405e+000
    fparams[89][3] = 8.89090649e+001
    fparams[89][4] = 3.65866182e+000
    fparams[89][5] = 1.05088931e+000
    fparams[89][6] = 2.08479229e-001
    fparams[89][7] = 9.09335557e-002
    fparams[89][8] = 3.16528117e+000
    fparams[89][9] = 3.13297788e+001
    fparams[89][10] = 5.23892556e-002
    fparams[89][11] = 2.08807697e-002
    fparams[90][0] = 1.19014064e+000
    fparams[90][1] = 7.73468729e-002
    fparams[90][2] = 2.55380607e+000
    fparams[90][3] = 6.59693681e-001
    fparams[90][4] = 4.68110181e+000
    fparams[90][5] = 1.28013896e+001
    fparams[90][6] = 2.26121303e-001
    fparams[90][7] = 1.08632194e-001
    fparams[90][8] = 3.58250545e-001
    fparams[90][9] = 4.56765664e-001
    fparams[90][10] = 7.82263950e-003
    fparams[90][11] = 1.62623474e-002
    fparams[91][0] = 4.68537504e+000
    fparams[91][1] = 1.44503632e+001
    fparams[91][2] = 2.98413708e+000
    fparams[91][3] = 5.56438592e-001
    fparams[91][4] = 8.91988061e-001
    fparams[91][5] = 6.69512914e-002
    fparams[91][6] = 2.24825384e-001
    fparams[91][7] = 1.03235396e-001
    fparams[91][8] = 3.04444846e-001
    fparams[91][9] = 4.27255647e-001
    fparams[91][10] = 9.48162708e-003
    fparams[91][11] = 1.77730611e-002
    fparams[92][0] = 4.63343606e+000
    fparams[92][1] = 1.63377267e+001
    fparams[92][2] = 3.18157056e+000
    fparams[92][3] = 5.69517868e-001
    fparams[92][4] = 8.76455075e-001
    fparams[92][5] = 6.88860012e-002
    fparams[92][6] = 2.21685477e-001
    fparams[92][7] = 9.84254550e-002
    fparams[92][8] = 2.72917100e-001
    fparams[92][9] = 4.09470917e-001
    fparams[92][10] = 1.11737298e-002
    fparams[92][11] = 1.86215410e-002
    fparams[93][0] = 4.56773888e+000
    fparams[93][1] = 1.90992795e+001
    fparams[93][2] = 3.40325179e+000
    fparams[93][3] = 5.90099634e-001
    fparams[93][4] = 8.61841923e-001
    fparams[93][5] = 7.03204851e-002
    fparams[93][6] = 2.19728870e-001
    fparams[93][7] = 9.36334280e-002
    fparams[93][8] = 2.38176903e-001
    fparams[93][9] = 3.93554882e-001
    fparams[93][10] = 1.38306499e-002
    fparams[93][11] = 1.94437286e-002
    fparams[94][0] = 5.45671123e+000
    fparams[94][1] = 1.01892720e+001
    fparams[94][2] = 1.11687906e-001
    fparams[94][3] = 3.98131313e-002
    fparams[94][4] = 3.30260343e+000
    fparams[94][5] = 3.14622212e-001
    fparams[94][6] = 1.84568319e-001
    fparams[94][7] = 1.04220860e-001
    fparams[94][8] = 4.93644263e-001
    fparams[94][9] = 4.63080540e-001
    fparams[94][10] = 3.57484743e+000
    fparams[94][11] = 2.19369542e+001
    fparams[95][0] = 5.38321999e+000
    fparams[95][1] = 1.07289857e+001
    fparams[95][2] = 1.23343236e-001
    fparams[95][3] = 4.15137806e-002
    fparams[95][4] = 3.46469090e+000
    fparams[95][5] = 3.39326208e-001
    fparams[95][6] = 1.75437132e-001
    fparams[95][7] = 9.98932346e-002
    fparams[95][8] = 3.39800073e+000
    fparams[95][9] = 2.11601535e+001
    fparams[95][10] = 4.69459519e-001
    fparams[95][11] = 4.51996970e-001
    fparams[96][0] = 5.38402377e+000
    fparams[96][1] = 1.11211419e+001
    fparams[96][2] = 3.49861264e+000
    fparams[96][3] = 3.56750210e-001
    fparams[96][4] = 1.88039547e-001
    fparams[96][5] = 5.39853583e-002
    fparams[96][6] = 1.69143137e-001
    fparams[96][7] = 9.60082633e-002
    fparams[96][8] = 3.19595016e+000
    fparams[96][9] = 1.80694389e+001
    fparams[96][10] = 4.64393059e-001
    fparams[96][11] = 4.36318197e-001
    fparams[97][0] = 3.66090688e+000
    fparams[97][1] = 3.84420906e-001
    fparams[97][2] = 2.03054678e-001
    fparams[97][3] = 5.48547131e-002
    fparams[97][4] = 5.30697515e+000
    fparams[97][5] = 1.17150262e+001
    fparams[97][6] = 1.60934046e-001
    fparams[97][7] = 9.21020329e-002
    fparams[97][8] = 3.04808401e+000
    fparams[97][9] = 1.73525367e+001
    fparams[97][10] = 4.43610295e-001
    fparams[97][11] = 4.27132359e-001
    fparams[98][0] = 3.94150390e+000
    fparams[98][1] = 4.18246722e-001
    fparams[98][2] = 5.16915345e+000
    fparams[98][3] = 1.25201788e+001
    fparams[98][4] = 1.61941074e-001
    fparams[98][5] = 4.81540117e-002
    fparams[98][6] = 4.15299561e-001
    fparams[98][7] = 4.24913856e-001
    fparams[98][8] = 2.91761325e+000
    fparams[98][9] = 1.90899693e+001
    fparams[98][10] = 1.51474927e-001
    fparams[98][11] = 8.81568925e-002
    fparams[99][0] = 4.09780623e+000
    fparams[99][1] = 4.46021145e-001
    fparams[99][2] = 5.10079393e+000
    fparams[99][3] = 1.31768613e+001
    fparams[99][4] = 1.74617289e-001
    fparams[99][5] = 5.02742829e-002
    fparams[99][6] = 2.76774658e+000
    fparams[99][7] = 1.84815393e+001
    fparams[99][8] = 1.44496639e-001
    fparams[99][9] = 8.46232592e-002
    fparams[99][10] = 4.02772109e-001
    fparams[99][11] = 4.17640100e-001
    fparams[100][0] = 4.24934820e+000
    fparams[100][1] = 4.75263933e-001
    fparams[100][2] = 5.03556594e+000
    fparams[100][3] = 1.38570834e+001
    fparams[100][4] = 1.88920613e-001
    fparams[100][5] = 5.26975158e-002
    fparams[100][6] = 3.94356058e-001
    fparams[100][7] = 4.11193751e-001
    fparams[100][8] = 2.61213100e+000
    fparams[100][9] = 1.78537905e+001
    fparams[100][10] = 1.38001927e-001
    fparams[100][11] = 8.12774434e-002
    fparams[101][0] = 2.00942931e-001
    fparams[101][1] = 5.48366518e-002
    fparams[101][2] = 4.40119869e+000
    fparams[101][3] = 5.04248434e-001
    fparams[101][4] = 4.97250102e+000
    fparams[101][5] = 1.45721366e+001
    fparams[101][6] = 2.47530599e+000
    fparams[101][7] = 1.72978308e+001
    fparams[101][8] = 3.86883197e-001
    fparams[101][9] = 4.05043898e-001
    fparams[101][10] = 1.31936095e-001
    fparams[101][11] = 7.80821071e-002
    fparams[102][0] = 2.16052899e-001
    fparams[102][1] = 5.83584058e-002
    fparams[102][2] = 4.91106799e+000
    fparams[102][3] = 1.53264212e+001
    fparams[102][4] = 4.54862870e+000
    fparams[102][5] = 5.34434760e-001
    fparams[102][6] = 2.36114249e+000
    fparams[102][7] = 1.68164803e+001
    fparams[102][8] = 1.26277292e-001
    fparams[102][9] = 7.50304633e-002
    fparams[102][10] = 3.81364501e-001
    fparams[102][11] = 3.99305852e-001
    fparams[103][0] = 4.86738014e+000
    fparams[103][1] = 1.60320520e+001
    fparams[103][2] = 3.19974401e-001
    fparams[103][3] = 6.70871138e-002
    fparams[103][4] = 4.58872425e+000
    fparams[103][5] = 5.77039373e-001
    fparams[103][6] = 1.21482448e-001
    fparams[103][7] = 7.22275899e-002
    fparams[103][8] = 2.31639872e+000
    fparams[103][9] = 1.41279737e+001
    fparams[103][10] = 3.79258137e-001
    fparams[103][11] = 3.89973484e-001
    return fparams[Z]


def generate_k_grid(shape, spacing):
    ki = 2 * np.pi * fftpack.fftfreq(shape[0],spacing[0])
    kj = 2 * np.pi * fftpack.fftfreq(shape[1],spacing[1])
    Kj, Ki = np.meshgrid(kj,ki)
    return Ki, Kj, np.sqrt(Ki**2 + Kj**2)
    
def generate_atom(Z, Ksq):

    coeffs = fParams(Z)
        
    # This will be the k-space representation of the object function
    scattering_factors = np.zeros(Ksq.shape,dtype=np.complex64)

    for m in range(0, 3):
        a = 2*m
        b = a+1
        c = a + 6
        d = b + 6
        # Keep in mind that these constants are in angstrom-related units.
        # for a; m=0,2,4 -> A^-1
        # for b; m=1,3,5 -> A^-2
        # for c; m=6,8,10 -> A
        # for d; m=7,9,11 -> A^2
        
        # This is the functional form of the parameterization
        scattering_factors += (1e10*coeffs[a])/(Ksq+1e20*coeffs[b])
        scattering_factors += 1e-10*coeffs[c]*np.exp(-1e-20*coeffs[d] * Ksq)
        
    # This is the real-space distribution
    return np.fft.ifft2(scattering_factors)