#!/usr/bin/python3
'''!    	
	@Author: wpx
	@File Name: dict.py
	@Mail: wpx15673207315@gmail.com 
	@Created Time: 2022年04月12日 星期二 19时00分08秒
	@bref 
	@ref 
'''  
import numpy as np

phiphi11 = np.array(
        [[[1/6, 1/12, 1/12], [1/12, 1/6, 1/12], [1/12, 1/12, 1/6]]]) 

phiphi12 = np.array(
        [[[1/30, 2/15, 2/15, -1/60, 1/15, -1/60], [-1/60, 2/15, 1/15,
        1/30, 2/15, -1/60], [-1/60, 1/15, 2/15, -1/60, 2/15, 1/30]]])

phiphi13 = np.array(
        [[[1/60, 3/40, 3/40, 0, 3/20, 0, 1/120, 0, 0, 1/120], [1/120, 0,
        0, 3/40, 3/20, 0, 1/60, 3/40, 0, 1/120], [1/120, 0, 0, 0, 3/20, 3/40, 1/120, 0,
        3/40, 1/60]]])

phiphi21 = np.array(
        [[[1/30, -1/60, -1/60], [2/15, 2/15, 1/15], [2/15, 1/15, 2/15],
        [-1/60, 1/30, -1/60], [1/15, 2/15, 2/15], [-1/60, -1/60, 1/30]]])

phiphi22 = np.array(
        [[[1/30, 0, 0, -1/180, -1/45, -1/180], [0, 8/45, 4/45, 0, 4/45, -1/45], [0, 4/45,
        8/45, -1/45, 4/45, 0], [-1/180, 0, -1/45, 1/30, 0, -1/180], [-1/45, 4/45, 4/45,
        0, 8/45, 0], [-1/180, -1/45, 0, -1/180, 0, 1/30]]])

phiphi23 = np.array(
        [[[1/84, 9/280, 9/280, -3/140, -3/140, -3/140, 1/840, -1/140, -1/140, 1/840], [1/210,
        2/35, 1/35, 2/35, 6/35, -1/70, 1/210, 1/35, -1/70, 1/105], [1/210, 1/35, 2/35,
        -1/70, 6/35, 2/35, 1/105, -1/70, 1/35, 1/210], [1/840, -3/140, -1/140, 9/280,
        -3/140, -1/140, 1/84, 9/280, -3/140, 1/840], [1/105, -1/70, -1/70, 1/35,
        6/35, 1/35, 1/210, 2/35, 2/35, 1/210], [1/840, -1/140, -3/140,
        -1/140, -3/140, 9/280, 1/840, -3/140, 9/280, 1/84]]])

phiphi31 = np.array(
        [[[1/60, 1/120, 1/120], [3/40, 0, 0], [3/40, 0, 0], [0, 3/40, 0], [3/20, 3/20, 3/20],
        [0, 0, 3/40], [1/120, 1/60, 1/120], [0, 3/40, 0], [0, 0, 3/40], [1/120, 1/120,
        1/60]]])

phiphi32 = np.array(
        [[[1/84, 1/210, 1/210, 1/840, 1/105, 1/840], [9/280, 2/35, 1/35, -3/140, -1/70,
        -1/140], [9/280, 1/35, 2/35, -1/140, -1/70, -3/140], [-3/140, 2/35, -1/70, 9/280,
        1/35, -1/140], [-3/140, 6/35, 6/35, -3/140, 6/35, -3/140], [-3/140, -1/70,
        2/35, -1/140, 1/35, 9/280], [1/840, 1/210, 1/105, 1/84, 1/210, 1/840],
        [-1/140, 1/35, -1/70, 9/280, 2/35, -3/140], [-1/140, -1/70, 1/35, -3/140,
        2/35, 9/280], [1/840, 1/105, 1/210, 1/840, 1/210, 1/84]]])
phiphi33 = np.array(
        [[[19/1680, 3/1120, 3/1120, 0, 3/560, 0, 11/6720, 9/2240,
        9/2240,11/6720], [3/1120, 9/112, 9/224, -9/320, 27/1120, -9/448, 0, -9/448,
        -9/1120, 9/2240], [3/1120, 9/224, 9/112, -9/448, 27/1120, -9/320, 9/2240,
        -9/1120, -9/448, 0], [0, -9/320, -9/448, 9/112, 27/1120, -9/1120, 3/1120,
        9/224, -9/448, 9/2240], [3/560, 27/1120, 27/1120, 27/1120, 81/280,
        27/1120, 3/560, 27/1120, 27/1120, 3/560], [0, -9/448, -9/320,
        -9/1120, 27/1120, 9/112, 9/2240, -9/448, 9/224, 3/1120],
        [11/6720, 0, 9/2240, 3/1120, 3/560, 9/2240, 19/1680, 3/1120, 0,
        11/6720], [9/2240, -9/448, -9/1120, 9/224, 27/1120, -9/448,
        3/1120, 9/112, -9/320, 0], [9/2240, -9/1120, -9/448,
        -9/448, 27/1120, 9/224, 0, -9/320, 9/112, 3/1120],
        [11/6720, 9/2240, 0, 9/2240, 3/560, 3/1120, 11/6720, 0,
        3/1120, 19/1680]]],dtype=np.float64)


phiphi = {'11':phiphi11, '12':phiphi12 ,'13':phiphi13,
          '21':phiphi21, '22':phiphi22 ,'23':phiphi23,
          '31':phiphi31, '32':phiphi32 ,'33':phiphi33}

gphigphi11 = np.array(
        [[[[1, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 1, 0], [0, 0, 0], [0,
        0, 0]], [[0, 0, 1], [0, 0, 0], [0, 0, 0]]], [[[0, 0, 0], [1, 0, 0], [0, 0, 0]],
        [[0, 0, 0], [0, 1, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 1], [0, 0, 0]]], [[[0,
        0, 0], [0, 0, 0], [1, 0, 0]], [[0, 0, 0], [0, 0, 0], [0, 1, 0]], [[0, 0,
        0], [0, 0, 0], [0, 0, 1]]]])

gphigphi12 = np.array(
        [[[[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[4/3, 4/3, 0], [0, 0, 0], [0, 0, 0]],
        [[4/3, 0, 4/3], [0, 0, 0], [0, 0, 0]], [[0, 1/3, 0], [0, 0, 0], [0, 0,
        0]], [[0, 4/3, 4/3], [0, 0, 0], [0, 0, 0]], [[0, 0, 1/3], [0, 0, 0],
        [0, 0, 0]]], [[[0, 0, 0], [1/3, 0, 0], [0, 0, 0]], [[0, 0, 0],
        [4/3, 4/3, 0], [0, 0, 0]], [[0, 0, 0], [4/3, 0, 4/3], [0, 0,
        0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]], [[0, 0, 0], [0,
        4/3, 4/3], [0, 0, 0]], [[0, 0, 0], [0, 0, 1/3], [0,
        0, 0]]], [[[0, 0, 0], [0, 0, 0], [1/3, 0, 0]],
        [[0, 0, 0], [0, 0, 0], [4/3, 4/3, 0]], [[0,
        0, 0], [0, 0, 0], [4/3, 0, 4/3]], [[0, 0,
        0], [0, 0, 0], [0, 1/3, 0]], [[0, 0,
        0], [0, 0, 0], [0, 4/3, 4/3]],
        [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]]]])

gphigphi21 = np.array(
        [[[[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 1/3, 0], [0, 0, 0],
        [0, 0, 0]], [[0, 0, 1/3], [0, 0, 0], [0, 0, 0]]], [[[4/3, 0, 0], [4/3, 0, 0], [0,
        0, 0]], [[0, 4/3, 0], [0, 4/3, 0], [0, 0, 0]], [[0, 0, 4/3], [0, 0, 4/3], [0,
        0, 0]]], [[[4/3, 0, 0], [0, 0, 0], [4/3, 0, 0]], [[0, 4/3, 0], [0, 0, 0],
        [0, 4/3, 0]], [[0, 0, 4/3], [0, 0, 0], [0, 0, 4/3]]], [[[0, 0, 0],
        [1/3, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]],
        [[0, 0, 0], [0, 0, 1/3], [0, 0, 0]]], [[[0, 0, 0], [4/3, 0, 0],
        [4/3, 0, 0]], [[0, 0, 0], [0, 4/3, 0], [0, 4/3, 0]], [[0, 0,
        0], [0, 0, 4/3], [0, 0, 4/3]]], [[[0, 0, 0], [0, 0, 0],
        [1/3, 0, 0]], [[0, 0, 0], [0, 0, 0], [0, 1/3, 0]],
        [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]]]])

gphigphi22 = np.array([[[[1, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 4/3, 0], [0, 0, 0], [0,
        0, 0]], [[0, 0, 4/3], [0, 0, 0], [0, 0, 0]], [[0, -1/3, 0], [0, 0, 0], [0, 0,0]],
        [[0, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 0, -1/3], [0, 0, 0], [0, 0, 0]]], [[[0,
        0, 0], [4/3, 0, 0], [0, 0, 0]], [[8/3, 4/3, 0], [4/3, 8/3, 0], [0, 0, 0]],
        [[4/3, 0, 4/3], [4/3, 0, 8/3], [0, 0, 0]], [[0, 4/3, 0], [0, 0, 0], [0, 0,
        0]], [[0, 4/3, 8/3], [0, 4/3, 4/3], [0, 0, 0]], [[0, 0, 0], [0, 0, 0],
        [0, 0, 0]]], [[[0, 0, 0], [0, 0, 0], [4/3, 0, 0]], [[4/3, 4/3, 0],
        [0, 0, 0], [4/3, 8/3, 0]], [[8/3, 0, 4/3], [0, 0, 0], [4/3, 0,
        8/3]], [[0, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 8/3, 4/3], [0, 0, 0], [0, 4/3,
        4/3]], [[0, 0, 4/3], [0, 0, 0], [0, 0, 0]]], [[[0, 0, 0], [-1/3, 0, 0],
        [0, 0, 0]], [[0, 0, 0], [4/3, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0,
        0], [0, 0, 0]], [[0, 0, 0], [0, 1, 0], [0, 0, 0]], [[0, 0, 0],
        [0, 0, 4/3], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/3], [0, 0,
        0]]], [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 0, 0],
        [4/3, 4/3, 0], [8/3, 4/3, 0]], [[0, 0, 0], [8/3, 0,
        4/3], [4/3, 0, 4/3]], [[0, 0, 0], [0, 0, 0], [0,
        4/3, 0]], [[0, 0, 0], [0, 8/3, 4/3], [0, 4/3,
        8/3]], [[0, 0, 0], [0, 0, 4/3], [0, 0, 0]]], [[[0, 0, 0], [0, 0, 0], [-1/3,
        0, 0]], [[0, 0, 0], [0, 0, 0], [0, 0, 0]], [[0, 0, 0], [0, 0, 0], [4/3,
        0, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/3, 0]], [[0, 0, 0], [0, 0, 0],
        [0, 4/3, 0]], [[0, 0, 0], [0, 0, 0], [0, 0, 1]]]])

gphigphi = {'11':gphigphi11, '12':gphigphi12, 
        '21':gphigphi21, '22':gphigphi22}

gphiphi11 = np.array(
        [[[1/3, 0, 0], [1/3, 0, 0], [1/3, 0, 0]], [[0, 1/3, 0], [0, 1/3,
        0], [0, 1/3, 0]], [[0, 0, 1/3], [0, 0, 1/3], [0, 0, 1/3]]]) 

gphiphi12 = np.array(
        [[[0, 0, 0], [1/3, 0, 0], [1/3, 0, 0], [0, 0, 0], [1/3, 0, 0],
        [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 1/3, 0], [0, 0, 0], [0, 1/3, 0], [0, 0,
        0]], [[0, 0, 0], [0, 0, 1/3], [0, 0, 1/3], [0, 0, 0], [0, 0, 1/3], [0, 0, 0]]])

gphiphi21 = np.array(
        [[[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[1/3, 2/3, 0], [2/3, 1/3,
        0], [1/3, 1/3, 0]], [[1/3, 0, 2/3], [1/3, 0, 1/3], [2/3, 0, 1/3]], [[0, 0, 0],
        [0, 1/3, 0], [0, 0, 0]], [[0, 1/3, 1/3], [0, 1/3, 2/3], [0, 2/3, 1/3]], [[0,
        0, 0], [0, 0, 0], [0, 0, 1/3]]])

gphiphi22 = np.array(
        [[[2/15, 0, 0], [1/5, 0, 0], [1/5, 0, 0], [-1/15, 0, 0], [-1/15,
        0, 0], [-1/15, 0, 0]], [[-1/15, 2/15, 0], [8/15, 8/15, 0], [4/15, 8/15, 0],
        [2/15, -1/15, 0], [8/15, 4/15, 0], [-1/15, -1/15, 0]], [[-1/15, 0, 2/15],
        [4/15, 0, 8/15], [8/15, 0, 8/15], [-1/15, 0, -1/15], [8/15, 0, 4/15],
        [2/15, 0, -1/15]], [[0, -1/15, 0], [0, 1/5, 0], [0, -1/15, 0], [0, 2/15,
        0], [0, 1/5, 0], [0, -1/15, 0]], [[0, -1/15, -1/15], [0, 4/15, 8/15],
        [0, 8/15, 4/15], [0, -1/15, 2/15], [0, 8/15, 8/15], [0, 2/15,
        -1/15]], [[0, 0, -1/15], [0, 0, -1/15], [0, 0, 1/5], [0, 0,
        -1/15], [0, 0, 1/5], [0, 0, 2/15]]])

gphiphi = {'11':gphiphi11, '12':gphiphi12, 
           '21':gphiphi21, '22':gphiphi22}

phigphiphi222 = np.array(
        [[[[13/210, 0, 0], [4/105, 0, 0], [4/105, 0, 0], [-1/140, 0, 0], [1/105, 0, 0],
        [-1/140, 0, 0]], [[2/105, 2/21, 0], [-8/315, 4/105, 0], [-4/315, 4/105, 0],
        [-4/315, -4/315, 0], [-4/105, -4/315, 0], [1/315, -4/315, 0]], [[2/105, 0,
        2/21], [-4/315, 0, 4/105], [-8/315, 0, 4/105], [1/315, 0, -4/315],
        [-4/105, 0, -4/315], [-4/315, 0, -4/315]], [[0, -1/70, 0], [0, -8/315,
        0], [0, -4/315, 0], [0, -1/140, 0], [0, -1/63, 0], [0, 11/1260, 0]],
        [[0, 2/105, 2/105], [0, -4/315, -8/315], [0, -8/315, -4/315], [0, 1/315,
        -4/315], [0, -4/105, -4/105], [0, -4/315, 1/315]], [[0, 0, -1/70],
        [0, 0, -4/315], [0, 0, -8/315], [0, 0, 11/1260], [0, 0, -1/63],
        [0, 0, -1/140]]], [[[4/105, 0, 0], [8/63, 0, 0], [4/63, 0, 0],
        [-8/315, 0, 0], [4/315, 0, 0], [-1/63, 0, 0]], [[-8/315,
        4/105, 0], [32/105, 32/105, 0], [32/315, 16/105, 0],
        [4/105, -8/315, 0], [16/105, 32/315, 0], [-4/105, -4/105,
        0]], [[-4/315, 0, 4/105], [32/315, 0, 32/105],
        [32/315, 0, 16/105], [-4/315, 0, -8/315],[32/315, 0, 32/315], [-4/315, 0,
        -4/105]], [[0, -8/315, 0], [0, 8/63, 0], [0, 4/315, 0], [0, 4/105, 0],
        [0, 4/63, 0], [0, -1/63, 0]], [[0, -4/315, -8/315], [0, 32/315,
        32/105], [0, 32/315, 32/315], [0, -4/315, 4/105], [0, 32/315,
        16/105], [0, -4/315, -4/105]], [[0, 0, -4/315], [0, 0,
        -8/105], [0, 0, 4/315], [0, 0, -4/315], [0, 0, 4/315],
        [0, 0, 1/105]]], [[[4/105, 0, 0], [4/63, 0, 0], [8/63, 0,
        0], [-1/63, 0, 0], [4/315, 0, 0], [-8/315, 0, 0]],
        [[-4/315, 4/105, 0], [32/315, 16/105, 0], [32/315, 32/105, 0], [-4/315,
        -4/105, 0], [32/315, 32/315, 0], [-4/315, -8/315, 0]], [[-8/315, 0,
        4/105], [32/315, 0, 16/105], [32/105, 0, 32/105], [-4/105, 0,
        -4/105], [16/105, 0, 32/315], [4/105, 0, -8/315]], [[0, -4/315,
        0], [0, 4/315, 0], [0, -8/105, 0], [0, 1/105, 0], [0, 4/315,
        0], [0, -4/315, 0]], [[0, -8/315, -4/315], [0, 32/315,
        32/315], [0, 32/105, 32/315], [0, -4/105, -4/315],
        [0, 16/105, 32/315], [0, 4/105, -4/315]], [[0, 0,
        -8/315], [0, 0, 4/315], [0, 0, 8/63], [0, 0,-1/63], [0, 0, 4/63], [0, 0,
        4/105]]], [[[-1/140, 0, 0], [-8/315, 0, 0], [-1/63, 0, 0], [-1/70, 0, 0],
        [-4/315, 0, 0], [11/1260, 0, 0]], [[-4/315, -4/315, 0], [4/105,
        -8/315, 0], [-4/315, -4/105, 0], [2/21, 2/105, 0], [4/105,
        -4/315, 0], [-4/315, 1/315, 0]], [[1/315, 0, -4/315],
        [-4/315, 0, -8/315], [-4/105, 0, -4/105], [2/105, 0,
        2/105], [-8/315, 0, -4/315], [-4/315, 0, 1/315]],
        [[0, -1/140, 0], [0, 4/105, 0], [0, 1/105, 0], [0,
        13/210, 0], [0, 4/105, 0], [0, -1/140, 0]], [[0,
        1/315, -4/315], [0, -4/315, 4/105], [0, -4/105, -4/315], [0, 2/105, 2/21],
        [0, -8/315, 4/105], [0, -4/315, -4/315]], [[0, 0, 11/1260], [0, 0, -4/315],
        [0, 0, -1/63], [0, 0, -1/70], [0, 0, -8/315], [0, 0, -1/140]]], [[[1/105,
        0, 0], [4/315, 0, 0], [4/315, 0, 0], [-4/315, 0, 0], [-8/105, 0, 0],
        [-4/315, 0, 0]], [[-4/105, -4/315, 0], [16/105, 32/315, 0], [32/315,
        32/315, 0], [4/105, -4/315, 0], [32/105, 32/315, 0], [-8/315,
        -4/315, 0]], [[-4/105, 0, -4/315], [32/315, 0, 32/315],
        [16/105, 0, 32/315], [-8/315, 0, -4/315], [32/105, 0,
        32/315], [4/105, 0, -4/315]], [[0, -1/63, 0], [0,
        4/63, 0], [0, 4/315, 0], [0, 4/105, 0], [0, 8/63,
        0], [0, -8/315, 0]], [[0, -4/105, -4/105], [0, 32/315, 16/105], [0, 16/105,
        32/315], [0, -8/315, 4/105], [0, 32/105, 32/105], [0, 4/105, -8/315]],
        [[0, 0, -1/63], [0, 0, 4/315], [0, 0, 4/63], [0, 0, -8/315], [0, 0, 8/63],
        [0, 0, 4/105]]], [[[-1/140, 0, 0], [-1/63, 0, 0], [-8/315, 0, 0],
        [11/1260, 0, 0], [-4/315, 0, 0], [-1/70, 0, 0]], [[1/315, -4/315, 0],
        [-4/105, -4/105, 0], [-4/315, -8/315, 0], [-4/315, 1/315, 0],
        [-8/315, -4/315, 0], [2/105, 2/105, 0]], [[-4/315, 0, -4/315],
        [-4/315, 0, -4/105], [4/105, 0, -8/315], [-4/315, 0, 1/315],
        [4/105, 0, -4/315], [2/21, 0, 2/105]], [[0, 11/1260, 0], [0,
        -1/63, 0], [0, -4/315, 0], [0, -1/140, 0], [0, -8/315,
        0], [0, -1/70, 0]], [[0, -4/315, 1/315], [0, -4/315,
        -4/105], [0, 4/105, -4/315], [0, -4/315, -4/315], [0, 4/105, -8/315], [0,
            2/21, 2/105]], [[0, 0, -1/140], [0, 0, 1/105], [0, 0, 4/105], [0, 0,
                -1/140], [0, 0, 4/105], [0, 0, 13/210]]]])
phigphiphi = {'222':phigphiphi222}


phiphiphi111 = np.array(
        [[[1/10, 1/30, 1/30], [1/30, 1/30, 1/60], [1/30, 1/60, 1/30]], [[1/30,
        1/30, 1/60], [1/30, 1/10, 1/30], [1/60, 1/30, 1/30]], [[1/30, 1/60,
        1/30], [1/60, 1/30, 1/30], [1/30, 1/30, 1/10]]])



phiphiphi222 = np.array(
        [[[1/70, 1/105, 1/105, -1/630, 1/315, -1/630], [1/105, 0, 0, -1/315,
        -2/315, 0], [1/105, 0, 0, 0, -2/315, -1/315], [-1/630, -1/315, 0,
        -1/630, 0, 1/1260], [1/315, -2/315, -2/315, 0, -4/315, 0],
        [-1/630, 0, -1/315, 1/1260, 0, -1/630]], [[1/105, 0, 0, -1/315,
        -2/315, 0], [0, 4/35, 4/105, 0, 4/105, -4/315], [0, 4/105,
        4/105, -2/315, 8/315, -2/315], [-1/315, 0, -2/315, 1/105, 0,
        0], [-2/315, 4/105, 8/315, 0, 4/105, -2/315], [0, -4/315, -2/315, 0,
        -2/315, 1/315]], [[1/105, 0, 0, 0, -2/315, -1/315], [0, 4/105,
        4/105, -2/315, 8/315, -2/315], [0, 4/105, 4/35, -4/315, 4/105,
        0], [0, -2/315, -4/315, 1/315, -2/315, 0], [-2/315, 8/315,
        4/105, -2/315, 4/105, 0], [-1/315, -2/315, 0, 0, 0, 1/105]], [[-1/630,
        -1/315, 0, -1/630, 0, 1/1260], [-1/315, 0, -2/315, 1/105, 0, 0], [0,
        -2/315, -4/315, 1/315, -2/315, 0], [-1/630, 1/105, 1/315, 1/70,
        1/105, -1/630], [0, 0, -2/315, 1/105, 0, -1/315], [1/1260,
        0, 0, -1/630, -1/315, -1/630]], [[1/315, -2/315, -2/315,
        0, -4/315, 0], [-2/315, 4/105, 8/315, 0, 4/105,
        -2/315], [-2/315, 8/315, 4/105, -2/315, 4/105,
        0], [0, 0, -2/315, 1/105, 0, -1/315],
        [-4/315, 4/105, 4/105, 0, 4/35, 0], [0, -2/315,
        0, -1/315, 0, 1/105]], [[-1/630, 0, -1/315,
        1/1260, 0, -1/630], [0, -4/315, -2/315,
        0, -2/315, 1/315], [-1/315, -2/315,
        0, 0, 0, 1/105], [1/1260, 0, 0,
        -1/630, -1/315, -1/630], [0,
        -2/315, 0, -1/315, 0,
        1/105], [-1/630, 1/315,
        1/105, -1/630,
        1/105, 1/70]]])

phiphiphi = {'111':phiphiphi111, '222':phiphiphi222}

gphigphiphi111 = np.array(
        [[[[[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[1/3, 0, 0], [0, 0, 0], [0, 0, 0]]], [[[0, 1/3, 0], [0, 0, 0], [0, 0, 0]], [[0, 1/3, 0], [0, 0, 0], [0, 0, 0]], [[0, 1/3, 0], [0, 0, 0], [0, 0, 0]]], [[[0, 0, 1/3], [0, 0, 0], [0, 0, 0]], [[0, 0, 1/3], [0, 0, 0], [0, 0, 0]], [[0, 0, 1/3], [0, 0, 0], [0, 0, 0]]]], [[[[0, 0, 0], [1/3, 0, 0], [0, 0, 0]], [[0, 0, 0], [1/3, 0, 0], [0, 0, 0]], [[0, 0, 0], [1/3, 0, 0], [0, 0, 0]]], [[[0, 0, 0], [0, 1/3, 0], [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]]], [[[0, 0, 0], [0, 0, 1/3], [0, 0, 0]], [[0, 0, 0], [0, 0, 1/3], [0, 0, 0]], [[0, 0, 0], [0, 0, 1/3], [0, 0, 0]]]], [[[[0, 0, 0], [0, 0, 0], [1/3, 0, 0]], [[0, 0, 0], [0, 0, 0], [1/3, 0, 0]], [[0, 0, 0], [0, 0, 0], [1/3, 0, 0]]], [[[0, 0, 0], [0, 0, 0], [0, 1/3, 0]], [[0, 0, 0], [0, 0, 0], [0, 1/3, 0]], [[0, 0, 0], [0, 0, 0], [0, 1/3, 0]]], [[[0, 0, 0], [0, 0, 0], [0, 0, 1/3]], [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]], [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]]]]])
gphigphiphi222 = np.array(
        [[[[[4/15, 0, 0], [0, 0, 0], [0, 0, 0]], [[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[1/3, 0, 0], [0, 0, 0], [0, 0, 0]], [[-2/45, 0, 0], [0, 0, 0], [0, 0, 0]], [[7/45, 0, 0], [0, 0, 0], [0, 0, 0]], [[-2/45, 0, 0], [0, 0, 0], [0, 0, 0]]], [[[1/15, 2/5, 0], [0, 0, 0], [0, 0, 0]], [[8/45, 8/15, 0], [0, 0, 0], [0, 0, 0]], [[4/45, 8/15, 0], [0, 0, 0], [0, 0, 0]], [[-2/15, -1/9, 0], [0, 0, 0], [0, 0, 0]], [[-8/45, 4/45, 0], [0, 0, 0], [0, 0, 0]], [[-1/45, -1/9, 0], [0, 0, 0], [0, 0, 0]]], [[[1/15, 0, 2/5], [0, 0, 0], [0, 0, 0]], [[4/45, 0, 8/15], [0, 0, 0], [0, 0, 0]], [[8/45, 0, 8/15], [0, 0, 0], [0, 0, 0]], [[-1/45, 0, -1/9], [0, 0, 0], [0, 0, 0]], [[-8/45, 0, 4/45], [0, 0, 0], [0, 0, 0]], [[-2/15, 0, -1/9], [0, 0, 0], [0, 0, 0]]], [[[0, -1/15, 0], [0, 0, 0], [0, 0, 0]], [[0, -1/45, 0], [0, 0, 0], [0, 0, 0]], [[0, -1/9, 0], [0, 0, 0], [0, 0, 0]], [[0, -1/15, 0], [0, 0, 0], [0, 0, 0]], [[0, -1/9, 0], [0, 0, 0], [0, 0, 0]], [[0, 2/45, 0], [0, 0, 0], [0, 0, 0]]], [[[0, 1/15, 1/15], [0, 0, 0], [0, 0, 0]], [[0, 4/45, 8/45], [0, 0, 0], [0, 0, 0]], [[0, 8/45, 4/45], [0, 0, 0], [0, 0, 0]], [[0, -1/45, -2/15], [0, 0, 0], [0, 0, 0]], [[0, -8/45, -8/45], [0, 0, 0], [0, 0, 0]], [[0, -2/15, -1/45], [0, 0, 0], [0, 0, 0]]], [[[0, 0, -1/15], [0, 0, 0], [0, 0, 0]], [[0, 0, -1/9], [0, 0, 0], [0, 0, 0]], [[0, 0, -1/45], [0, 0, 0], [0, 0, 0]], [[0, 0, 2/45], [0, 0, 0], [0, 0, 0]], [[0, 0, -1/9], [0, 0, 0], [0, 0, 0]], [[0, 0, -1/15], [0, 0, 0], [0, 0, 0]]]], [[[[1/15, 0, 0], [2/5, 0, 0], [0, 0, 0]], [[8/45, 0, 0], [8/15, 0, 0], [0, 0, 0]], [[4/45, 0, 0], [8/15, 0, 0], [0, 0, 0]], [[-2/15, 0, 0], [-1/9, 0, 0], [0, 0, 0]], [[-8/45, 0, 0], [4/45, 0, 0], [0, 0, 0]], [[-1/45, 0, 0], [-1/9, 0, 0], [0, 0, 0]]], [[[-8/45, 0, 0], [0, 8/15, 0], [0, 0, 0]], [[16/15, 32/45, 0], [32/45, 16/15, 0], [0, 0, 0]], [[16/45, 16/45, 0], [16/45, 16/15, 0], [0, 0, 0]], [[8/15, 0, 0], [0, -8/45, 0], [0, 0, 0]], [[16/15, 16/45, 0], [16/45, 16/45, 0], [0, 0, 0]], [[-8/45, -4/45, 0], [-4/45, -8/45, 0], [0, 0, 0]]], [[[-4/45, 0, 0], [0, 0, 8/15], [0, 0, 0]], [[16/45, 0, 32/45], [16/45, 0, 16/15], [0, 0, 0]], [[16/45, 0, 16/45], [32/45, 0, 16/15], [0, 0, 0]], [[0, 0, 0], [-4/45, 0, -8/45], [0, 0, 0]], [[32/45, 0, 16/45], [16/45, 0, 16/45], [0, 0, 0]], [[0, 0, -4/45], [0, 0, -8/45], [0, 0, 0]]], [[[0, -1/9, 0], [0, -2/15, 0], [0, 0, 0]], [[0, 8/15, 0], [0, 8/45, 0], [0, 0, 0]], [[0, 4/45, 0], [0, -8/45, 0], [0, 0, 0]], [[0, 2/5, 0], [0, 1/15, 0], [0, 0, 0]], [[0, 8/15, 0], [0, 4/45, 0], [0, 0, 0]], [[0, -1/9, 0], [0, -1/45, 0], [0, 0, 0]]], [[[0, -4/45, -8/45], [0, 0, 0], [0, 0, 0]], [[0, 16/45, 16/15], [0, 16/45, 32/45], [0, 0, 0]], [[0, 16/45, 16/45], [0, 32/45, 16/45], [0, 0, 0]], [[0, 0, 8/15], [0, -4/45, 0], [0, 0, 0]], [[0, 32/45, 16/15], [0, 16/45, 16/45], [0, 0, 0]], [[0, 0, -8/45], [0, 0, -4/45], [0, 0, 0]]], [[[0, 0, -1/45], [0, 0, -2/15], [0, 0, 0]], [[0, 0, -8/45], [0, 0, -8/45], [0, 0, 0]], [[0, 0, 4/45], [0, 0, 8/45], [0, 0, 0]], [[0, 0, -2/15], [0, 0, -1/45], [0, 0, 0]], [[0, 0, 8/45], [0, 0, 4/45], [0, 0, 0]], [[0, 0, 1/15], [0, 0, 1/15], [0, 0, 0]]]], [[[[1/15, 0, 0], [0, 0, 0], [2/5, 0, 0]], [[4/45, 0, 0], [0, 0, 0], [8/15, 0, 0]], [[8/45, 0, 0], [0, 0, 0], [8/15, 0, 0]], [[-1/45, 0, 0], [0, 0, 0], [-1/9, 0, 0]], [[-8/45, 0, 0], [0, 0, 0], [4/45, 0, 0]], [[-2/15, 0, 0], [0, 0, 0], [-1/9, 0, 0]]], [[[-4/45, 0, 0], [0, 0, 0], [0, 8/15, 0]], [[16/45, 16/45, 0], [0, 0, 0], [32/45, 16/15, 0]], [[16/45, 32/45, 0], [0, 0, 0], [16/45, 16/15, 0]], [[0, -4/45, 0], [0, 0, 0], [0, -8/45, 0]], [[32/45, 16/45, 0], [0, 0, 0], [16/45, 16/45, 0]], [[0, 0, 0], [0, 0, 0], [-4/45, -8/45, 0]]], [[[-8/45, 0, 0], [0, 0, 0], [0, 0, 8/15]], [[16/45, 0, 16/45], [0, 0, 0], [16/45, 0, 16/15]], [[16/15, 0, 32/45], [0, 0, 0], [32/45, 0, 16/15]], [[-8/45, 0, -4/45], [0, 0, 0], [-4/45, 0, -8/45]], [[16/15, 0, 16/45], [0, 0, 0], [16/45, 0, 16/45]], [[8/15, 0, 0], [0, 0, 0], [0, 0, -8/45]]], [[[0, -1/45, 0], [0, 0, 0], [0, -2/15, 0]], [[0, 4/45, 0], [0, 0, 0], [0, 8/45, 0]], [[0, -8/45, 0], [0, 0, 0], [0, -8/45, 0]], [[0, 1/15, 0], [0, 0, 0], [0, 1/15, 0]], [[0, 8/45, 0], [0, 0, 0], [0, 4/45, 0]], [[0, -2/15, 0], [0, 0, 0], [0, -1/45, 0]]], [[[0, -8/45, -4/45], [0, 0, 0], [0, 0, 0]], [[0, 16/45, 16/45], [0, 0, 0], [0, 16/45, 32/45]], [[0, 16/15, 16/45], [0, 0, 0], [0, 32/45, 16/45]], [[0, -8/45, 0], [0, 0, 0], [0, -4/45, 0]], [[0, 16/15, 32/45], [0, 0, 0], [0, 16/45, 16/45]], [[0, 8/15, 0], [0, 0, 0], [0, 0, -4/45]]], [[[0, 0, -1/9], [0, 0, 0], [0, 0, -2/15]], [[0, 0, 4/45], [0, 0, 0], [0, 0, -8/45]], [[0, 0, 8/15], [0, 0, 0], [0, 0, 8/45]], [[0, 0, -1/9], [0, 0, 0], [0, 0, -1/45]], [[0, 0, 8/15], [0, 0, 0], [0, 0, 4/45]], [[0, 0, 2/5], [0, 0, 0], [0, 0, 1/15]]]], [[[[0, 0, 0], [-1/15, 0, 0], [0, 0, 0]], [[0, 0, 0], [-1/45, 0, 0], [0, 0, 0]], [[0, 0, 0], [-1/9, 0, 0], [0, 0, 0]], [[0, 0, 0], [-1/15, 0, 0], [0, 0, 0]], [[0, 0, 0], [-1/9, 0, 0], [0, 0, 0]], [[0, 0, 0], [2/45, 0, 0], [0, 0, 0]]], [[[0, 0, 0], [-1/9, -2/15, 0], [0, 0, 0]], [[0, 0, 0], [8/15, 8/45, 0], [0, 0, 0]], [[0, 0, 0], [4/45, -8/45, 0], [0, 0, 0]], [[0, 0, 0], [2/5, 1/15, 0], [0, 0, 0]], [[0, 0, 0], [8/15, 4/45, 0], [0, 0, 0]], [[0, 0, 0], [-1/9, -1/45, 0], [0, 0, 0]]], [[[0, 0, 0], [-1/45, 0, -2/15], [0, 0, 0]], [[0, 0, 0], [4/45, 0, 8/45], [0, 0, 0]], [[0, 0, 0], [-8/45, 0, -8/45], [0, 0, 0]], [[0, 0, 0], [1/15, 0, 1/15], [0, 0, 0]], [[0, 0, 0], [8/45, 0, 4/45], [0, 0, 0]], [[0, 0, 0], [-2/15, 0, -1/45], [0, 0, 0]]], [[[0, 0, 0], [0, -2/45, 0], [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]], [[0, 0, 0], [0, 7/45, 0], [0, 0, 0]], [[0, 0, 0], [0, 4/15, 0], [0, 0, 0]], [[0, 0, 0], [0, 1/3, 0], [0, 0, 0]], [[0, 0, 0], [0, -2/45, 0], [0, 0, 0]]], [[[0, 0, 0], [0, -1/45, -1/9], [0, 0, 0]], [[0, 0, 0], [0, 4/45, 8/15], [0, 0, 0]], [[0, 0, 0], [0, -8/45, 4/45], [0, 0, 0]], [[0, 0, 0], [0, 1/15, 2/5], [0, 0, 0]], [[0, 0, 0], [0, 8/45, 8/15], [0, 0, 0]], [[0, 0, 0], [0, -2/15, -1/9], [0, 0, 0]]], [[[0, 0, 0], [0, 0, 2/45], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/9], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/9], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/15], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/45], [0, 0, 0]], [[0, 0, 0], [0, 0, -1/15], [0, 0, 0]]]], [[[[0, 0, 0], [1/15, 0, 0], [1/15, 0, 0]], [[0, 0, 0], [4/45, 0, 0], [8/45, 0, 0]], [[0, 0, 0], [8/45, 0, 0], [4/45, 0, 0]], [[0, 0, 0], [-1/45, 0, 0], [-2/15, 0, 0]], [[0, 0, 0], [-8/45, 0, 0], [-8/45, 0, 0]], [[0, 0, 0], [-2/15, 0, 0], [-1/45, 0, 0]]], [[[0, 0, 0], [-4/45, 0, 0], [-8/45, 0, 0]], [[0, 0, 0], [16/45, 16/45, 0], [16/15, 32/45, 0]], [[0, 0, 0], [16/45, 32/45, 0], [16/45, 16/45, 0]], [[0, 0, 0], [0, -4/45, 0], [8/15, 0, 0]], [[0, 0, 0], [32/45, 16/45, 0], [16/15, 16/45, 0]], [[0, 0, 0], [0, 0, 0], [-8/45, -4/45, 0]]], [[[0, 0, 0], [-8/45, 0, 0], [-4/45, 0, 0]], [[0, 0, 0], [16/45, 0, 16/45], [16/45, 0, 32/45]], [[0, 0, 0], [16/15, 0, 32/45], [16/45, 0, 16/45]], [[0, 0, 0], [-8/45, 0, -4/45], [0, 0, 0]], [[0, 0, 0], [16/15, 0, 16/45], [32/45, 0, 16/45]], [[0, 0, 0], [8/15, 0, 0], [0, 0, -4/45]]], [[[0, 0, 0], [0, -1/45, 0], [0, -1/9, 0]], [[0, 0, 0], [0, 4/45, 0], [0, 8/15, 0]], [[0, 0, 0], [0, -8/45, 0], [0, 4/45, 0]], [[0, 0, 0], [0, 1/15, 0], [0, 2/5, 0]], [[0, 0, 0], [0, 8/45, 0], [0, 8/15, 0]], [[0, 0, 0], [0, -2/15, 0], [0, -1/9, 0]]], [[[0, 0, 0], [0, -8/45, -4/45], [0, -4/45, -8/45]], [[0, 0, 0], [0, 16/45, 16/45], [0, 16/45, 16/15]], [[0, 0, 0], [0, 16/15, 16/45], [0, 16/45, 16/45]], [[0, 0, 0], [0, -8/45, 0], [0, 0, 8/15]], [[0, 0, 0], [0, 16/15, 32/45], [0, 32/45, 16/15]], [[0, 0, 0], [0, 8/15, 0], [0, 0, -8/45]]], [[[0, 0, 0], [0, 0, -1/9], [0, 0, -1/45]], [[0, 0, 0], [0, 0, 4/45], [0, 0, -8/45]], [[0, 0, 0], [0, 0, 8/15], [0, 0, 4/45]], [[0, 0, 0], [0, 0, -1/9], [0, 0, -2/15]], [[0, 0, 0], [0, 0, 8/15], [0, 0, 8/45]], [[0, 0, 0], [0, 0, 2/5], [0, 0, 1/15]]]], [[[[0, 0, 0], [0, 0, 0], [-1/15, 0, 0]], [[0, 0, 0], [0, 0, 0], [-1/9, 0, 0]], [[0, 0, 0], [0, 0, 0], [-1/45, 0, 0]], [[0, 0, 0], [0, 0, 0], [2/45, 0, 0]], [[0, 0, 0], [0, 0, 0], [-1/9, 0, 0]], [[0, 0, 0], [0, 0, 0], [-1/15, 0, 0]]], [[[0, 0, 0], [0, 0, 0], [-1/45, -2/15, 0]], [[0, 0, 0], [0, 0, 0], [-8/45, -8/45, 0]], [[0, 0, 0], [0, 0, 0], [4/45, 8/45, 0]], [[0, 0, 0], [0, 0, 0], [-2/15, -1/45, 0]], [[0, 0, 0], [0, 0, 0], [8/45, 4/45, 0]], [[0, 0, 0], [0, 0, 0], [1/15, 1/15, 0]]], [[[0, 0, 0], [0, 0, 0], [-1/9, 0, -2/15]], [[0, 0, 0], [0, 0, 0], [4/45, 0, -8/45]], [[0, 0, 0], [0, 0, 0], [8/15, 0, 8/45]], [[0, 0, 0], [0, 0, 0], [-1/9, 0, -1/45]], [[0, 0, 0], [0, 0, 0], [8/15, 0, 4/45]], [[0, 0, 0], [0, 0, 0], [2/5, 0, 1/15]]], [[[0, 0, 0], [0, 0, 0], [0, 2/45, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/9, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/9, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/15, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/45, 0]], [[0, 0, 0], [0, 0, 0], [0, -1/15, 0]]], [[[0, 0, 0], [0, 0, 0], [0, -1/9, -1/45]], [[0, 0, 0], [0, 0, 0], [0, 4/45, -8/45]], [[0, 0, 0], [0, 0, 0], [0, 8/15, 4/45]], [[0, 0, 0], [0, 0, 0], [0, -1/9, -2/15]], [[0, 0, 0], [0, 0, 0], [0, 8/15, 8/45]], [[0, 0, 0], [0, 0, 0], [0, 2/5, 1/15]]], [[[0, 0, 0], [0, 0, 0], [0, 0, -2/45]], [[0, 0, 0], [0, 0, 0], [0, 0, 7/45]], [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]], [[0, 0, 0], [0, 0, 0], [0, 0, -2/45]], [[0, 0, 0], [0, 0, 0], [0, 0, 1/3]], [[0, 0, 0], [0, 0, 0], [0, 0, 4/15]]]]])        
gphigphiphi = {'111':gphigphiphi111, '222':gphigphiphi222}
