72 lines
1.9 KiB
Python
72 lines
1.9 KiB
Python
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#!/usr/bin/python
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from scipy.special import j1 , hyp1f1
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from scipy.integrate import simps
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from scipy.stats import norm , gamma
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import numpy as np
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import sys
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import math
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pi=math.pi
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e=math.e
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sys.path.append("/mntdirect/_users/semeraro/python_tools")
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import FitTools
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N_OrAv = 90*2
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N_CapCyl = 50
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###########################################################################################
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###########################################################################################
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""" SPHERICAL BESSEL FUNCTION j0 & j1 """
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def spherical_j0_np(x):
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return np.where(x==0, 1, np.sin(x)/x )
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def spherical_j1_np(x):
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return np.where(x==0, 1./3, (np.sin(x)-x*np.cos(x))/x**2 )
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###########################################################################################
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###########################################################################################
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""" NORMAL DISTRIBUTION """
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def Normal(x,xo,w):
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return np.exp(- (x-xo)**2/(2*w**2) ) / (w*np.sqrt(2*pi))
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###########################################################################################
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###########################################################################################
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""" FORM FACTORS """
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################################ SPHERE
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def Amp_Sphere(q,R):
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if R==0 or q==0:
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A=Vol_Sphere(R)
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else:
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A=Vol_Sphere(R) * 3 * spherical_j1(q*R) / (q*R)
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return A
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################################ SPHERES
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def Sphere( q, PAR ):
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[n,rho,R,C] = PAR
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amp = (4*np.pi*R**3/3) * 3 * spherical_j1_np(q*R) / (q*R)
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return n * (rho * amp)**2 + C
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################################ POLYDISPERSE SPHERES (NORMAl PDF)
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def Sphere_Normal (q,PAR):
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[n,rho,R,w,C] = PAR
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N = 21
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R_array = np.linspace(R-3*w,R+3*w,N)
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Normal = norm.pdf(R_array, R, w)
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I = np.zeros(q.shape[0], dtype=float)
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for r in range(R_array.shape[0]):
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if r==0 or r==N-1 : I+= Sphere(q,[1,1,R_array[r],0]) * Normal[r] / 2
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else : I+= Sphere(q,[1,1,R_array[r],0]) * Normal[r]
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I*= 6*w/(N-1)
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return n*rho**2*I + C
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