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helper.py
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helper.py
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import numpy as np
import math
M_PI = 3.14159265358979323846
NUM_IMPLEMENTED_TYPE = 5
IMPLEMENTED_MCSH_TYPE = [0,1,2,3,4]
def calc_C1(A, B, alpha, beta):
temp = np.sqrt(M_PI / (alpha + beta))
return A * B * temp * temp * temp
def calc_C2(alpha, beta):
return -1.0 * (alpha * beta / (alpha + beta))
def calc_lambda( alpha, beta):
return beta / (alpha + beta)
def calc_gamma( alpha, beta):
return alpha + beta
def P1( lamda, x0, gamma):
return lamda * x0
def P2( lamda, x0, gamma):
lambda_x0_2 = lamda * lamda * x0 * x0
return (0.5 / gamma) + lambda_x0_2
def P3( lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_3 = lambda_x0 * lambda_x0 * lambda_x0
return (1.5 * lambda_x0 / gamma) + lambda_x0_3
def P4( lamda, x0, gamma):
lambda_x0_2 = lamda * lamda * x0 * x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
return (0.75 / (gamma * gamma)) + (3.0 * lambda_x0_2 / gamma) + lambda_x0_4
def P5( lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_3 = lambda_x0 * lambda_x0_2
lambda_x0_5 = lambda_x0_3 * lambda_x0_2
return ((15.0 * lambda_x0) / (4.0 * gamma * gamma)) + (5.0 * lambda_x0_3 / gamma) + lambda_x0_5
def P6(lamda, x0, gamma):
lambda_x0_2 = lamda * lamda * x0 * x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
lambda_x0_6 = lambda_x0_4 * lambda_x0_2
return (15.0 / (8.0 * gamma * gamma * gamma)) + ((11.25 * lambda_x0_2) / (gamma * gamma)) + (7.5 * lambda_x0_4 / gamma) + lambda_x0_6
def P7(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_3 = lambda_x0 * lambda_x0_2
lambda_x0_5 = lambda_x0_3 * lambda_x0_2
lambda_x0_7 = lambda_x0_5 * lambda_x0_2
term1 = 105.0 * lambda_x0 / (8.0 * gamma * gamma * gamma)
term2 = 105.0 * lambda_x0_3 / (4.0 * gamma * gamma)
term3 = 10.5 * lambda_x0_5 / gamma
return term1 + term2 + term3 + lambda_x0_7
def P8(lamda, x0, gamma):
lambda_x0_2 = lamda * lamda * x0 * x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
lambda_x0_6 = lambda_x0_4 * lambda_x0_2
lambda_x0_8 = lambda_x0_6 * lambda_x0_2
term1 = 105.0 / (16.0 * gamma * gamma * gamma * gamma)
term2 = 105.0 * lambda_x0_2 / (2.0 * gamma * gamma * gamma)
term3 = 105.0 * lambda_x0_4 / (2.0 * gamma * gamma)
term4 = 14.0 * lambda_x0_6 / gamma
return term1 + term2 + term3 + term4 + lambda_x0_8
def P9(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_3 = lambda_x0 * lambda_x0_2
lambda_x0_5 = lambda_x0_3 * lambda_x0_2
lambda_x0_7 = lambda_x0_5 * lambda_x0_2
lambda_x0_9 = lambda_x0_7 * lambda_x0_2
term1 = 945.0 * lambda_x0 / (16.0 * gamma * gamma * gamma * gamma)
term2 = 315.0 * lambda_x0_3 / (2.0 * gamma * gamma * gamma)
term3 = 189.0 * lambda_x0_5 / (2.0 * gamma * gamma)
term4 = 18.0 * lambda_x0_7 / gamma
return term1 + term2 + term3 + term4 + lambda_x0_9
def dP1(lamda, x0, gamma):
return lamda
def dP2(lamda, x0, gamma):
return 2.0 * lamda * lamda * x0
def dP3(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
return lamda * (3.0 * lambda_x0_2 + (3.0 / (2.0 * gamma)))
def dP4(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_3 = lambda_x0 * lambda_x0 * lambda_x0
return lamda * (4.0 * lambda_x0_3 + ((6.0 * lambda_x0) / gamma))
def dP5(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
return lamda * (5.0 * lambda_x0_4 + ((15.0 * lambda_x0_2) / gamma) + (15.0 / (4.0 * gamma * gamma)))
def dP6(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_3 = lambda_x0 * lambda_x0_2
lambda_x0_5 = lambda_x0_3 * lambda_x0_2
return lamda * (6.0 * lambda_x0_5 + ((30.0 * lambda_x0_3) / gamma) + (45.0 * lambda_x0 / (2.0 * gamma * gamma)))
def dP7(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
lambda_x0_6 = lambda_x0_4 * lambda_x0_2
return lamda * (7.0 * lambda_x0_6 + ((105.0 * lambda_x0_4) / (2.0 * gamma)) + ((315.0 * lambda_x0_2) / (4.0 * gamma * gamma)) + (105.0 / (8.0 * gamma * gamma * gamma)))
def dP8(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_3 = lambda_x0 * lambda_x0_2
lambda_x0_5 = lambda_x0_3 * lambda_x0_2
lambda_x0_7 = lambda_x0_5 * lambda_x0_2
return lamda * (8.0 * lambda_x0_7 + ((84.0 * lambda_x0_5) / gamma) + (210.0 * lambda_x0_3 / (gamma * gamma)) + ((105.0 * lambda_x0) / (gamma * gamma * gamma)))
def dP9(lamda, x0, gamma):
lambda_x0 = lamda * x0
lambda_x0_2 = lambda_x0 * lambda_x0
lambda_x0_4 = lambda_x0_2 * lambda_x0_2
lambda_x0_6 = lambda_x0_4 * lambda_x0_2
lambda_x0_8 = lambda_x0_6 * lambda_x0_2
return lamda * (9.0 * lambda_x0_8 + ((126.0 * lambda_x0_6) / gamma) + ((945.0 * lambda_x0_4) / (2.0 * gamma * gamma)) + ((945.0 * lambda_x0_2) / (2.0 * gamma * gamma * gamma)) + (945.0 / (16.0 * gamma * gamma * gamma * gamma)))
def dP1_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP1(lamda, x0, gamma)
def dP2_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP2(lamda, x0, gamma)
def dP3_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP3(lamda, x0, gamma)
def dP4_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP4(lamda, x0, gamma)
def dP5_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP5(lamda, x0, gamma)
def dP6_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP6(lamda, x0, gamma)
def dP7_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP7(lamda, x0, gamma)
def dP8_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP8(lamda, x0, gamma)
def dP9_exp(P, C2, lamda, x0, gamma):
temp = 2.0 * C2 * x0
return P * temp + dP9(lamda, x0, gamma)
def get_num_groups(mcsh_order):
if (mcsh_order == 0):
return 1
elif (mcsh_order == 1):
return 1
elif (mcsh_order == 2):
return 2
elif (mcsh_order == 3):
return 3
elif (mcsh_order == 4):
return 4
elif (mcsh_order == 5):
return 5
elif (mcsh_order == 6):
return 7
elif (mcsh_order == 7):
return 8
elif (mcsh_order == 8):
return 10
elif (mcsh_order == 9):
return 12
else:
return 0
def get_group_coefficients(mcsh_order, group_num):
if (mcsh_order == 0):
if (group_num == 1):
return 1.0
else:
return 0.0
elif (mcsh_order == 1):
if (group_num == 1):
return 1.0
else:
return 0.0
elif (mcsh_order == 2):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 2.0
else:
return 0.0
elif (mcsh_order == 3):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 3.0
elif (group_num == 3):
return 6.0
else:
return 0.0
elif (mcsh_order == 4):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 4.0
elif (group_num == 3):
return 6.0
elif (group_num == 4):
return 12.0
else:
return 0.0
elif (mcsh_order == 5):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 5.0
elif (group_num == 3):
return 10.0
elif (group_num == 4):
return 20.0
elif (group_num == 5):
return 30.0
else:
return 0.0
elif (mcsh_order == 6):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 6.0
elif (group_num == 3):
return 15.0
elif (group_num == 4):
return 30.0
elif (group_num == 5):
return 20.0
elif (group_num == 6):
return 60.0
elif (group_num == 7):
return 90.0
else:
return 0.0
elif (mcsh_order == 7):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 7.0
elif (group_num == 3):
return 21.0
elif (group_num == 4):
return 42.0
elif (group_num == 5):
return 35.0
elif (group_num == 6):
return 105.0
elif (group_num == 7):
return 140.0
elif (group_num == 8):
return 210.0
else:
return 0.0
elif (mcsh_order == 8):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 8.0
elif (group_num == 3):
return 28.0
elif (group_num == 4):
return 56.0
elif (group_num == 5):
return 56.0
elif (group_num == 6):
return 168.0
elif (group_num == 7):
return 70.0
elif (group_num == 8):
return 280.0
elif (group_num == 9):
return 420.0
elif (group_num == 10):
return 560.0
else:
return 0.0
elif (mcsh_order == 9):
if (group_num == 1):
return 1.0
elif (group_num == 2):
return 9.0
elif (group_num == 3):
return 36.0
elif (group_num == 4):
return 72.0
elif (group_num == 5):
return 84.0
elif (group_num == 6):
return 252.0
elif (group_num == 7):
return 126.0
elif (group_num == 8):
return 504.0
elif (group_num == 9):
return 756.0
elif (group_num == 10):
return 630.0
elif (group_num == 11):
return 1260.0
elif (group_num == 12):
return 1680.0
else:
return 0.0
else:
return 0.0
def get_mcsh_type(mcsh_order, group_num):
if (mcsh_order == 0):
if (group_num == 1):
return 1
else:
return 0
elif (mcsh_order == 1):
if (group_num == 1):
return 2
else:
return 0
elif (mcsh_order == 2):
if (group_num == 1):
return 2
elif (group_num == 2):
return 2
else:
return 0
elif (mcsh_order == 3):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 1
else:
return 0
elif (mcsh_order == 4):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 2
elif (group_num == 4):
return 2
else:
return 0
elif (mcsh_order == 5):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 3
elif (group_num == 4):
return 2
elif (group_num == 5):
return 2
else:
return 0
elif (mcsh_order == 6):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 3
elif (group_num == 4):
return 2
elif (group_num == 5):
return 2
elif (group_num == 6):
return 3
elif (group_num == 7):
return 1
else:
return 0
elif (mcsh_order == 7):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 3
elif (group_num == 4):
return 2
elif (group_num == 5):
return 3
elif (group_num == 6):
return 3
elif (group_num == 7):
return 2
elif (group_num == 8):
return 2
else:
return 0
elif (mcsh_order == 8):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 3
elif (group_num == 4):
return 2
elif (group_num == 5):
return 3
elif (group_num == 6):
return 3
elif (group_num == 7):
return 2
elif (group_num == 8):
return 3
elif (group_num == 9):
return 2
elif (group_num == 10):
return 2
else:
return 0
elif (mcsh_order == 9):
if (group_num == 1):
return 2
elif (group_num == 2):
return 3
elif (group_num == 3):
return 3
elif (group_num == 4):
return 2
elif (group_num == 5):
return 3
elif (group_num == 6):
return 3
elif (group_num == 7):
return 3
elif (group_num == 8):
return 3
elif (group_num == 9):
return 2
elif (group_num == 10):
return 2
elif (group_num == 11):
return 3
elif (group_num == 12):
return 1
else:
return 0
else:
return 0