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299 lines
12 KiB
299 lines
12 KiB
# -*- coding: utf-8 -*-
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"""
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Created on Fri Feb 5 21:00:23 2021
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@author: Liangchao Zhu
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"""
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import numpy as np
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def getFilters(Ke):
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Filters = np.zeros((256,9,27))
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for h1 in range(2):
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for h2 in range(2):
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for h3 in range(2):
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for h4 in range(2):
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for h5 in range(2):
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for h6 in range(2):
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for h7 in range(2):
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for h8 in range(2):
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# idx = h1*2**7 + h2*2**6 + h3*2**5 + h4*2**4 + h5*2**3 + h6*2**2 + h7*2**1 + h8*2**0
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idx = h1*2**0 + h2*2**1 + h3*2**2 + h4*2**3 + h5*2**4 + h6*2**5 + h7*2**6 + h8*2**7
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thetaXX,thetaXY,thetaXZ,thetaYX,thetaYY,thetaYZ,thetaZX,thetaZY,thetaZZ = symbolicExec(Ke,h1,h2,h3,h4,h5,h6,h7,h8)
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Filters[idx] = np.concatenate((thetaXX[np.newaxis], thetaXY[np.newaxis],thetaXZ[np.newaxis],thetaYX[np.newaxis],thetaYY[np.newaxis],thetaYZ[np.newaxis],thetaZX[np.newaxis],thetaZY[np.newaxis],thetaZZ[np.newaxis]), axis=0)
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return Filters
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def symbolicExec(Ke,h1,h2,h3,h4,h5,h6,h7,h8):
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for i in range(24):
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for j in range(24):
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exec("global k%d_%d ; k%d_%d = Ke[i,j]"%(i+1,j+1,i+1,j+1))
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thetaXX = np.zeros((27))
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thetaXY = np.zeros((27))
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thetaXZ = np.zeros((27))
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thetaYX = np.zeros((27))
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thetaYY = np.zeros((27))
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thetaYZ = np.zeros((27))
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thetaZX = np.zeros((27))
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thetaZY = np.zeros((27))
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thetaZZ = np.zeros((27))
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thetaXX[0]=h1*k24_1;
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thetaXX[1]=h2*k21_1 + h1*k24_4;
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thetaXX[2]=h2*k21_4;
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thetaXX[3]=h3*k18_1 + h1*k24_7;
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thetaXX[4]=h4*k15_1 + h3*k18_4 + h2*k21_7 + h1*k24_10;
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thetaXX[5]=h4*k15_4 + h2*k21_10;
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thetaXX[6]=h3*k18_7;
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thetaXX[7]=h4*k15_7 + h3*k18_10;
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thetaXX[8]=h4*k15_10;
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thetaXX[9]=h5*k12_1 + h1*k24_13;
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thetaXX[10]=h5*k12_4 + h2*k21_13 + h1*k24_16 + h6*k9_1;
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thetaXX[11]=h2*k21_16 + h6*k9_4;
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thetaXX[12]=h5*k12_7 + h3*k18_13 + h1*k24_19 + h7*k6_1;
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thetaXX[13]=h5*k12_10 + h4*k15_13 + h3*k18_16 + h2*k21_19 + h1*k24_22 + h8*k3_1 + h7*k6_4 + h6*k9_7;
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thetaXX[14]=h4*k15_16 + h2*k21_22 + h8*k3_4 + h6*k9_10;
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thetaXX[15]=h3*k18_19 + h7*k6_7;
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thetaXX[16]=h4*k15_19 + h3*k18_22 + h8*k3_7 + h7*k6_10;
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thetaXX[17]=h4*k15_22 + h8*k3_10;
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thetaXX[18]=h5*k12_13;
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thetaXX[19]=h5*k12_16 + h6*k9_13;
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thetaXX[20]=h6*k9_16;
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thetaXX[21]=h5*k12_19 + h7*k6_13;
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thetaXX[22]=h5*k12_22 + h8*k3_13 + h7*k6_16 + h6*k9_19;
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thetaXX[23]=h8*k3_16 + h6*k9_22;
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thetaXX[24]=h7*k6_19;
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thetaXX[25]=h8*k3_19 + h7*k6_22;
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thetaXX[26]=h8*k3_22;
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thetaXY[0]=h1*k24_2;
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thetaXY[1]=h2*k21_2 + h1*k24_5;
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thetaXY[2]=h2*k21_5;
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thetaXY[3]=h3*k18_2 + h1*k24_8;
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thetaXY[4]=h4*k15_2 + h3*k18_5 + h2*k21_8 + h1*k24_11;
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thetaXY[5]=h4*k15_5 + h2*k21_11;
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thetaXY[6]=h3*k18_8;
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thetaXY[7]=h4*k15_8 + h3*k18_11;
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thetaXY[8]=h4*k15_11;
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thetaXY[9]=h5*k12_2 + h1*k24_14;
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thetaXY[10]=h5*k12_5 + h2*k21_14 + h1*k24_17 + h6*k9_2;
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thetaXY[11]=h2*k21_17 + h6*k9_5;
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thetaXY[12]=h5*k12_8 + h3*k18_14 + h1*k24_20 + h7*k6_2;
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thetaXY[13]=h5*k12_11 + h4*k15_14 + h3*k18_17 + h2*k21_20 + h1*k24_23 + h8*k3_2 + h7*k6_5 + h6*k9_8;
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thetaXY[14]=h4*k15_17 + h2*k21_23 + h8*k3_5 + h6*k9_11;
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thetaXY[15]=h3*k18_20 + h7*k6_8;
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thetaXY[16]=h4*k15_20 + h3*k18_23 + h8*k3_8 + h7*k6_11;
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thetaXY[17]=h4*k15_23 + h8*k3_11;
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thetaXY[18]=h5*k12_14;
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thetaXY[19]=h5*k12_17 + h6*k9_14;
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thetaXY[20]=h6*k9_17;
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thetaXY[21]=h5*k12_20 + h7*k6_14;
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thetaXY[22]=h5*k12_23 + h8*k3_14 + h7*k6_17 + h6*k9_20;
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thetaXY[23]=h8*k3_17 + h6*k9_23;
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thetaXY[24]=h7*k6_20;
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thetaXY[25]=h8*k3_20 + h7*k6_23;
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thetaXY[26]=h8*k3_23;
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thetaXZ[0]=h1*k24_3;
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thetaXZ[1]=h2*k21_3 + h1*k24_6;
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thetaXZ[2]=h2*k21_6;
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thetaXZ[3]=h3*k18_3 + h1*k24_9;
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thetaXZ[4]=h4*k15_3 + h3*k18_6 + h2*k21_9 + h1*k24_12;
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thetaXZ[5]=h4*k15_6 + h2*k21_12;
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thetaXZ[6]=h3*k18_9;
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thetaXZ[7]=h4*k15_9 + h3*k18_12;
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thetaXZ[8]=h4*k15_12;
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thetaXZ[9]=h5*k12_3 + h1*k24_15;
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thetaXZ[10]=h5*k12_6 + h2*k21_15 + h1*k24_18 + h6*k9_3;
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thetaXZ[11]=h2*k21_18 + h6*k9_6;
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thetaXZ[12]=h5*k12_9 + h3*k18_15 + h1*k24_21 + h7*k6_3;
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thetaXZ[13]=h5*k12_12 + h4*k15_15 + h3*k18_18 + h2*k21_21 + h1*k24_24 + h8*k3_3 + h7*k6_6 + h6*k9_9;
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thetaXZ[14]=h4*k15_18 + h2*k21_24 + h8*k3_6 + h6*k9_12;
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thetaXZ[15]=h3*k18_21 + h7*k6_9;
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thetaXZ[16]=h4*k15_21 + h3*k18_24 + h8*k3_9 + h7*k6_12;
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thetaXZ[17]=h4*k15_24 + h8*k3_12;
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thetaXZ[18]=h5*k12_15;
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thetaXZ[19]=h5*k12_18 + h6*k9_15;
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thetaXZ[20]=h6*k9_18;
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thetaXZ[21]=h5*k12_21 + h7*k6_15;
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thetaXZ[22]=h5*k12_24 + h8*k3_15 + h7*k6_18 + h6*k9_21;
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thetaXZ[23]=h8*k3_18 + h6*k9_24;
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thetaXZ[24]=h7*k6_21;
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thetaXZ[25]=h8*k3_21 + h7*k6_24;
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thetaXZ[26]=h8*k3_24;
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thetaYX[0]=h1*k24_1;
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thetaYX[1]=h2*k21_1 + h1*k24_4;
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thetaYX[2]=h2*k21_4;
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thetaYX[3]=h3*k18_1 + h1*k24_7;
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thetaYX[4]=h4*k15_1 + h3*k18_4 + h2*k21_7 + h1*k24_10;
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thetaYX[5]=h4*k15_4 + h2*k21_10;
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thetaYX[6]=h3*k18_7;
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thetaYX[7]=h4*k15_7 + h3*k18_10;
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thetaYX[8]=h4*k15_10;
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thetaYX[9]=h5*k12_1 + h1*k24_13;
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thetaYX[10]=h5*k12_4 + h2*k21_13 + h1*k24_16 + h6*k9_1;
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thetaYX[11]=h2*k21_16 + h6*k9_4;
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thetaYX[12]=h5*k12_7 + h3*k18_13 + h1*k24_19 + h7*k6_1;
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thetaYX[13]=h5*k12_10 + h4*k15_13 + h3*k18_16 + h2*k21_19 + h1*k24_22 + h8*k3_1 + h7*k6_4 + h6*k9_7;
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thetaYX[14]=h4*k15_16 + h2*k21_22 + h8*k3_4 + h6*k9_10;
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thetaYX[15]=h3*k18_19 + h7*k6_7;
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thetaYX[16]=h4*k15_19 + h3*k18_22 + h8*k3_7 + h7*k6_10;
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thetaYX[17]=h4*k15_22 + h8*k3_10;
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thetaYX[18]=h5*k12_13;
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thetaYX[19]=h5*k12_16 + h6*k9_13;
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thetaYX[20]=h6*k9_16;
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thetaYX[21]=h5*k12_19 + h7*k6_13;
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thetaYX[22]=h5*k12_22 + h8*k3_13 + h7*k6_16 + h6*k9_19;
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thetaYX[23]=h8*k3_16 + h6*k9_22;
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thetaYX[24]=h7*k6_19;
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thetaYX[25]=h8*k3_19 + h7*k6_22;
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thetaYX[26]=h8*k3_22;
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thetaYY[0]=h1*k24_2;
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thetaYY[1]=h2*k21_2 + h1*k24_5;
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thetaYY[2]=h2*k21_5;
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thetaYY[3]=h3*k18_2 + h1*k24_8;
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thetaYY[4]=h4*k15_2 + h3*k18_5 + h2*k21_8 + h1*k24_11;
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thetaYY[5]=h4*k15_5 + h2*k21_11;
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thetaYY[6]=h3*k18_8;
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thetaYY[7]=h4*k15_8 + h3*k18_11;
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thetaYY[8]=h4*k15_11;
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thetaYY[9]=h5*k12_2 + h1*k24_14;
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thetaYY[10]=h5*k12_5 + h2*k21_14 + h1*k24_17 + h6*k9_2;
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thetaYY[11]=h2*k21_17 + h6*k9_5;
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thetaYY[12]=h5*k12_8 + h3*k18_14 + h1*k24_20 + h7*k6_2;
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thetaYY[13]=h5*k12_11 + h4*k15_14 + h3*k18_17 + h2*k21_20 + h1*k24_23 + h8*k3_2 + h7*k6_5 + h6*k9_8;
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thetaYY[14]=h4*k15_17 + h2*k21_23 + h8*k3_5 + h6*k9_11;
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thetaYY[15]=h3*k18_20 + h7*k6_8;
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thetaYY[16]=h4*k15_20 + h3*k18_23 + h8*k3_8 + h7*k6_11;
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thetaYY[17]=h4*k15_23 + h8*k3_11;
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thetaYY[18]=h5*k12_14;
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thetaYY[19]=h5*k12_17 + h6*k9_14;
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thetaYY[20]=h6*k9_17;
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thetaYY[21]=h5*k12_20 + h7*k6_14;
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thetaYY[22]=h5*k12_23 + h8*k3_14 + h7*k6_17 + h6*k9_20;
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thetaYY[23]=h8*k3_17 + h6*k9_23;
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thetaYY[24]=h7*k6_20;
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thetaYY[25]=h8*k3_20 + h7*k6_23;
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thetaYY[26]=h8*k3_23;
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thetaYZ[0]=h1*k24_3;
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thetaYZ[1]=h2*k21_3 + h1*k24_6;
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thetaYZ[2]=h2*k21_6;
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thetaYZ[3]=h3*k18_3 + h1*k24_9;
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thetaYZ[4]=h4*k15_3 + h3*k18_6 + h2*k21_9 + h1*k24_12;
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thetaYZ[5]=h4*k15_6 + h2*k21_12;
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thetaYZ[6]=h3*k18_9;
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thetaYZ[7]=h4*k15_9 + h3*k18_12;
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thetaYZ[8]=h4*k15_12;
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thetaYZ[9]=h5*k12_3 + h1*k24_15;
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thetaYZ[10]=h5*k12_6 + h2*k21_15 + h1*k24_18 + h6*k9_3;
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thetaYZ[11]=h2*k21_18 + h6*k9_6;
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thetaYZ[12]=h5*k12_9 + h3*k18_15 + h1*k24_21 + h7*k6_3;
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thetaYZ[13]=h5*k12_12 + h4*k15_15 + h3*k18_18 + h2*k21_21 + h1*k24_24 + h8*k3_3 + h7*k6_6 + h6*k9_9;
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thetaYZ[14]=h4*k15_18 + h2*k21_24 + h8*k3_6 + h6*k9_12;
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thetaYZ[15]=h3*k18_21 + h7*k6_9;
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thetaYZ[16]=h4*k15_21 + h3*k18_24 + h8*k3_9 + h7*k6_12;
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thetaYZ[17]=h4*k15_24 + h8*k3_12;
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thetaYZ[18]=h5*k12_15;
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thetaYZ[19]=h5*k12_18 + h6*k9_15;
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thetaYZ[20]=h6*k9_18;
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thetaYZ[21]=h5*k12_21 + h7*k6_15;
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thetaYZ[22]=h5*k12_24 + h8*k3_15 + h7*k6_18 + h6*k9_21;
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thetaYZ[23]=h8*k3_18 + h6*k9_24;
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thetaYZ[24]=h7*k6_21;
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thetaYZ[25]=h8*k3_21 + h7*k6_24;
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thetaYZ[26]=h8*k3_24;
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thetaZX[0]=h1*k24_1;
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thetaZX[1]=h2*k21_1 + h1*k24_4;
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thetaZX[2]=h2*k21_4;
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thetaZX[3]=h3*k18_1 + h1*k24_7;
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thetaZX[4]=h4*k15_1 + h3*k18_4 + h2*k21_7 + h1*k24_10;
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thetaZX[5]=h4*k15_4 + h2*k21_10;
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thetaZX[6]=h3*k18_7;
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thetaZX[7]=h4*k15_7 + h3*k18_10;
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thetaZX[8]=h4*k15_10;
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thetaZX[9]=h5*k12_1 + h1*k24_13;
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thetaZX[10]=h5*k12_4 + h2*k21_13 + h1*k24_16 + h6*k9_1;
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thetaZX[11]=h2*k21_16 + h6*k9_4;
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thetaZX[12]=h5*k12_7 + h3*k18_13 + h1*k24_19 + h7*k6_1;
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thetaZX[13]=h5*k12_10 + h4*k15_13 + h3*k18_16 + h2*k21_19 + h1*k24_22 + h8*k3_1 + h7*k6_4 + h6*k9_7;
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thetaZX[14]=h4*k15_16 + h2*k21_22 + h8*k3_4 + h6*k9_10;
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thetaZX[15]=h3*k18_19 + h7*k6_7;
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thetaZX[16]=h4*k15_19 + h3*k18_22 + h8*k3_7 + h7*k6_10;
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thetaZX[17]=h4*k15_22 + h8*k3_10;
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thetaZX[18]=h5*k12_13;
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thetaZX[19]=h5*k12_16 + h6*k9_13;
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thetaZX[20]=h6*k9_16;
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thetaZX[21]=h5*k12_19 + h7*k6_13;
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thetaZX[22]=h5*k12_22 + h8*k3_13 + h7*k6_16 + h6*k9_19;
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thetaZX[23]=h8*k3_16 + h6*k9_22;
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thetaZX[24]=h7*k6_19;
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thetaZX[25]=h8*k3_19 + h7*k6_22;
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thetaZX[26]=h8*k3_22;
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thetaZY[0]=h1*k24_2;
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thetaZY[1]=h2*k21_2 + h1*k24_5;
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thetaZY[2]=h2*k21_5;
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thetaZY[3]=h3*k18_2 + h1*k24_8;
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thetaZY[4]=h4*k15_2 + h3*k18_5 + h2*k21_8 + h1*k24_11;
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thetaZY[5]=h4*k15_5 + h2*k21_11;
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thetaZY[6]=h3*k18_8;
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thetaZY[7]=h4*k15_8 + h3*k18_11;
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thetaZY[8]=h4*k15_11;
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thetaZY[9]=h5*k12_2 + h1*k24_14;
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thetaZY[10]=h5*k12_5 + h2*k21_14 + h1*k24_17 + h6*k9_2;
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thetaZY[11]=h2*k21_17 + h6*k9_5;
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thetaZY[12]=h5*k12_8 + h3*k18_14 + h1*k24_20 + h7*k6_2;
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thetaZY[13]=h5*k12_11 + h4*k15_14 + h3*k18_17 + h2*k21_20 + h1*k24_23 + h8*k3_2 + h7*k6_5 + h6*k9_8;
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thetaZY[14]=h4*k15_17 + h2*k21_23 + h8*k3_5 + h6*k9_11;
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thetaZY[15]=h3*k18_20 + h7*k6_8;
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thetaZY[16]=h4*k15_20 + h3*k18_23 + h8*k3_8 + h7*k6_11;
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thetaZY[17]=h4*k15_23 + h8*k3_11;
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thetaZY[18]=h5*k12_14;
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thetaZY[19]=h5*k12_17 + h6*k9_14;
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thetaZY[20]=h6*k9_17;
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thetaZY[21]=h5*k12_20 + h7*k6_14;
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thetaZY[22]=h5*k12_23 + h8*k3_14 + h7*k6_17 + h6*k9_20;
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thetaZY[23]=h8*k3_17 + h6*k9_23;
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thetaZY[24]=h7*k6_20;
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thetaZY[25]=h8*k3_20 + h7*k6_23;
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thetaZY[26]=h8*k3_23;
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thetaZZ[0]=h1*k24_3;
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thetaZZ[1]=h2*k21_3 + h1*k24_6;
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thetaZZ[2]=h2*k21_6;
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thetaZZ[3]=h3*k18_3 + h1*k24_9;
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thetaZZ[4]=h4*k15_3 + h3*k18_6 + h2*k21_9 + h1*k24_12;
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thetaZZ[5]=h4*k15_6 + h2*k21_12;
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thetaZZ[6]=h3*k18_9;
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thetaZZ[7]=h4*k15_9 + h3*k18_12;
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thetaZZ[8]=h4*k15_12;
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thetaZZ[9]=h5*k12_3 + h1*k24_15;
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thetaZZ[10]=h5*k12_6 + h2*k21_15 + h1*k24_18 + h6*k9_3;
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thetaZZ[11]=h2*k21_18 + h6*k9_6;
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thetaZZ[12]=h5*k12_9 + h3*k18_15 + h1*k24_21 + h7*k6_3;
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thetaZZ[13]=h5*k12_12 + h4*k15_15 + h3*k18_18 + h2*k21_21 + h1*k24_24 + h8*k3_3 + h7*k6_6 + h6*k9_9;
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thetaZZ[14]=h4*k15_18 + h2*k21_24 + h8*k3_6 + h6*k9_12;
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thetaZZ[15]=h3*k18_21 + h7*k6_9;
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thetaZZ[16]=h4*k15_21 + h3*k18_24 + h8*k3_9 + h7*k6_12;
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thetaZZ[17]=h4*k15_24 + h8*k3_12;
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thetaZZ[18]=h5*k12_15;
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thetaZZ[19]=h5*k12_18 + h6*k9_15;
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thetaZZ[20]=h6*k9_18;
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thetaZZ[21]=h5*k12_21 + h7*k6_15;
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thetaZZ[22]=h5*k12_24 + h8*k3_15 + h7*k6_18 + h6*k9_21;
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thetaZZ[23]=h8*k3_18 + h6*k9_24;
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thetaZZ[24]=h7*k6_21;
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thetaZZ[25]=h8*k3_21 + h7*k6_24;
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thetaZZ[26]=h8*k3_24;
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return thetaXX,thetaXY,thetaXZ,thetaYX,thetaYY,thetaYZ,thetaZX,thetaZY,thetaZZ
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if __name__ == "__main__":
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Ke = np.eye(24)
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Filters = getFilters(Ke)
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# h1=1;h2=1;h3=1;h4=1;h5=1;h6=1;h7=1;h8=1;
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# thetaXX,thetaXY,thetaXZ,thetaYX,thetaYY,thetaYZ,thetaZX,thetaZY,thetaZZ = symbolicExec(Ke,h1,h2,h3,h4,h5,h6,h7,h8)
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