| 1 | #/usr/bin/env python |
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| 2 | # -*- coding: utf-8 -*- |
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| 3 | ''' |
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| 4 | *GSASII powder calculation module* |
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| 5 | ================================== |
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| 6 | |
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| 7 | ''' |
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| 8 | ########### SVN repository information ################### |
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| 9 | # $Date: 2016-03-31 20:17:43 +0000 (Thu, 31 Mar 2016) $ |
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| 10 | # $Author: vondreele $ |
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| 11 | # $Revision: 2187 $ |
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| 12 | # $URL: trunk/GSASIIpwd.py $ |
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| 13 | # $Id: GSASIIpwd.py 2187 2016-03-31 20:17:43Z vondreele $ |
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| 14 | ########### SVN repository information ################### |
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| 15 | import sys |
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| 16 | import math |
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| 17 | import time |
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| 18 | import os |
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| 19 | import subprocess as subp |
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| 20 | |
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| 21 | import numpy as np |
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| 22 | import scipy as sp |
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| 23 | import numpy.linalg as nl |
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| 24 | import random as rand |
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| 25 | from numpy.fft import ifft, fft, fftshift |
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| 26 | import scipy.interpolate as si |
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| 27 | import scipy.stats as st |
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| 28 | import scipy.optimize as so |
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| 29 | |
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| 30 | import GSASIIpath |
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| 31 | GSASIIpath.SetVersionNumber("$Revision: 2187 $") |
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| 32 | import GSASIIlattice as G2lat |
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| 33 | import GSASIIspc as G2spc |
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| 34 | import GSASIIElem as G2elem |
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| 35 | import GSASIIgrid as G2gd |
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| 36 | import GSASIIIO as G2IO |
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| 37 | import GSASIImath as G2mth |
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| 38 | import pypowder as pyd |
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| 39 | import pydiffax as pyx |
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| 40 | |
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| 41 | # trig functions in degrees |
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| 42 | sind = lambda x: math.sin(x*math.pi/180.) |
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| 43 | asind = lambda x: 180.*math.asin(x)/math.pi |
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| 44 | tand = lambda x: math.tan(x*math.pi/180.) |
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| 45 | atand = lambda x: 180.*math.atan(x)/math.pi |
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| 46 | atan2d = lambda y,x: 180.*math.atan2(y,x)/math.pi |
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| 47 | cosd = lambda x: math.cos(x*math.pi/180.) |
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| 48 | acosd = lambda x: 180.*math.acos(x)/math.pi |
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| 49 | rdsq2d = lambda x,p: round(1.0/math.sqrt(x),p) |
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| 50 | #numpy versions |
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| 51 | npsind = lambda x: np.sin(x*np.pi/180.) |
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| 52 | npasind = lambda x: 180.*np.arcsin(x)/math.pi |
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| 53 | npcosd = lambda x: np.cos(x*math.pi/180.) |
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| 54 | npacosd = lambda x: 180.*np.arccos(x)/math.pi |
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| 55 | nptand = lambda x: np.tan(x*math.pi/180.) |
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| 56 | npatand = lambda x: 180.*np.arctan(x)/np.pi |
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| 57 | npatan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi |
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| 58 | npT2stl = lambda tth, wave: 2.0*npsind(tth/2.0)/wave |
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| 59 | npT2q = lambda tth,wave: 2.0*np.pi*npT2stl(tth,wave) |
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| 60 | forln2 = 4.0*math.log(2.0) |
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| 61 | |
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| 62 | #GSASII pdf calculation routines |
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| 63 | |
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| 64 | def Transmission(Geometry,Abs,Diam): |
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| 65 | ''' |
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| 66 | Calculate sample transmission |
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| 67 | |
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| 68 | :param str Geometry: one of 'Cylinder','Bragg-Brentano','Tilting flat plate in transmission','Fixed flat plate' |
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| 69 | :param float Abs: absorption coeff in cm-1 |
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| 70 | :param float Diam: sample thickness/diameter in mm |
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| 71 | ''' |
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| 72 | if 'Cylinder' in Geometry: #Lobanov & Alte da Veiga for 2-theta = 0; beam fully illuminates sample |
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| 73 | MuR = Abs*Diam/20.0 |
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| 74 | if MuR <= 3.0: |
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| 75 | T0 = 16/(3.*math.pi) |
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| 76 | T1 = -0.045780 |
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| 77 | T2 = -0.02489 |
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| 78 | T3 = 0.003045 |
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| 79 | T = -T0*MuR-T1*MuR**2-T2*MuR**3-T3*MuR**4 |
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| 80 | if T < -20.: |
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| 81 | return 2.06e-9 |
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| 82 | else: |
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| 83 | return math.exp(T) |
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| 84 | else: |
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| 85 | T1 = 1.433902 |
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| 86 | T2 = 0.013869+0.337894 |
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| 87 | T3 = 1.933433+1.163198 |
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| 88 | T4 = 0.044365-0.04259 |
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| 89 | T = (T1-T4)/(1.0+T2*(MuR-3.0))**T3+T4 |
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| 90 | return T/100. |
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| 91 | elif 'plate' in Geometry: |
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| 92 | MuR = Abs*Diam/10. |
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| 93 | return math.exp(-MuR) |
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| 94 | elif 'Bragg' in Geometry: |
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| 95 | return 0.0 |
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| 96 | |
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| 97 | def SurfaceRough(SRA,SRB,Tth): |
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| 98 | ''' Suortti (J. Appl. Cryst, 5,325-331, 1972) surface roughness correction |
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| 99 | :param float SRA: Suortti surface roughness parameter |
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| 100 | :param float SRB: Suortti surface roughness parameter |
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| 101 | :param float Tth: 2-theta(deg) - can be numpy array |
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| 102 | |
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| 103 | ''' |
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| 104 | sth = npsind(Tth/2.) |
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| 105 | T1 = np.exp(-SRB/sth) |
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| 106 | T2 = SRA+(1.-SRA)*np.exp(-SRB) |
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| 107 | return (SRA+(1.-SRA)*T1)/T2 |
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| 108 | |
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| 109 | def SurfaceRoughDerv(SRA,SRB,Tth): |
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| 110 | ''' Suortti surface roughness correction derivatives |
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| 111 | :param float SRA: Suortti surface roughness parameter (dimensionless) |
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| 112 | :param float SRB: Suortti surface roughness parameter (dimensionless) |
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| 113 | :param float Tth: 2-theta(deg) - can be numpy array |
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| 114 | :return list: [dydSRA,dydSRB] derivatives to be used for intensity derivative |
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| 115 | ''' |
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| 116 | sth = npsind(Tth/2.) |
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| 117 | T1 = np.exp(-SRB/sth) |
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| 118 | T2 = SRA+(1.-SRA)*np.exp(-SRB) |
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| 119 | Trans = (SRA+(1.-SRA)*T1)/T2 |
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| 120 | dydSRA = ((1.-T1)*T2-(1.-np.exp(-SRB))*Trans)/T2**2 |
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| 121 | dydSRB = ((SRA-1.)*T1*T2/sth-Trans*(SRA-T2))/T2**2 |
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| 122 | return [dydSRA,dydSRB] |
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| 123 | |
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| 124 | def Absorb(Geometry,MuR,Tth,Phi=0,Psi=0): |
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| 125 | '''Calculate sample absorption |
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| 126 | :param str Geometry: one of 'Cylinder','Bragg-Brentano','Tilting Flat Plate in transmission','Fixed flat plate' |
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| 127 | :param float MuR: absorption coeff * sample thickness/2 or radius |
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| 128 | :param Tth: 2-theta scattering angle - can be numpy array |
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| 129 | :param float Phi: flat plate tilt angle - future |
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| 130 | :param float Psi: flat plate tilt axis - future |
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| 131 | ''' |
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| 132 | |
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| 133 | def muRunder3(Sth2): |
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| 134 | T0 = 16.0/(3.*np.pi) |
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| 135 | T1 = (25.99978-0.01911*Sth2**0.25)*np.exp(-0.024551*Sth2)+ \ |
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| 136 | 0.109561*np.sqrt(Sth2)-26.04556 |
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| 137 | T2 = -0.02489-0.39499*Sth2+1.219077*Sth2**1.5- \ |
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| 138 | 1.31268*Sth2**2+0.871081*Sth2**2.5-0.2327*Sth2**3 |
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| 139 | T3 = 0.003045+0.018167*Sth2-0.03305*Sth2**2 |
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| 140 | Trns = -T0*MuR-T1*MuR**2-T2*MuR**3-T3*MuR**4 |
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| 141 | return np.exp(Trns) |
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| 142 | |
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| 143 | def muRover3(Sth2): |
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| 144 | T1 = 1.433902+11.07504*Sth2-8.77629*Sth2*Sth2+ \ |
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| 145 | 10.02088*Sth2**3-3.36778*Sth2**4 |
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| 146 | T2 = (0.013869-0.01249*Sth2)*np.exp(3.27094*Sth2)+ \ |
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| 147 | (0.337894+13.77317*Sth2)/(1.0+11.53544*Sth2)**1.555039 |
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| 148 | T3 = 1.933433/(1.0+23.12967*Sth2)**1.686715- \ |
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| 149 | 0.13576*np.sqrt(Sth2)+1.163198 |
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| 150 | T4 = 0.044365-0.04259/(1.0+0.41051*Sth2)**148.4202 |
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| 151 | Trns = (T1-T4)/(1.0+T2*(MuR-3.0))**T3+T4 |
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| 152 | return Trns/100. |
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| 153 | |
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| 154 | Sth2 = npsind(Tth/2.0)**2 |
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| 155 | Cth2 = 1.-Sth2 |
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| 156 | if 'Cylinder' in Geometry: #Lobanov & Alte da Veiga for 2-theta = 0; beam fully illuminates sample |
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| 157 | if MuR <= 3.0: |
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| 158 | return muRunder3(Sth2) |
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| 159 | else: |
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| 160 | return muRover3(Sth2) |
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| 161 | elif 'Bragg' in Geometry: |
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| 162 | return 1.0 |
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| 163 | elif 'Fixed' in Geometry: #assumes sample plane is perpendicular to incident beam |
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| 164 | # and only defined for 2theta < 90 |
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| 165 | MuT = 2.*MuR |
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| 166 | T1 = np.exp(-MuT) |
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| 167 | T2 = np.exp(-MuT/npcosd(Tth)) |
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| 168 | Tb = MuT-MuT/npcosd(Tth) |
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| 169 | return (T2-T1)/Tb |
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| 170 | elif 'Tilting' in Geometry: #assumes symmetric tilt so sample plane is parallel to diffraction vector |
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| 171 | MuT = 2.*MuR |
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| 172 | cth = npcosd(Tth/2.0) |
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| 173 | return np.exp(-MuT/cth)/cth |
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| 174 | |
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| 175 | def AbsorbDerv(Geometry,MuR,Tth,Phi=0,Psi=0): |
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| 176 | 'needs a doc string' |
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| 177 | dA = 0.001 |
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| 178 | AbsP = Absorb(Geometry,MuR+dA,Tth,Phi,Psi) |
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| 179 | if MuR: |
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| 180 | AbsM = Absorb(Geometry,MuR-dA,Tth,Phi,Psi) |
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| 181 | return (AbsP-AbsM)/(2.0*dA) |
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| 182 | else: |
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| 183 | return (AbsP-1.)/dA |
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| 184 | |
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| 185 | def Polarization(Pola,Tth,Azm=0.0): |
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| 186 | """ Calculate angle dependent x-ray polarization correction (not scaled correctly!) |
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| 187 | |
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| 188 | :param Pola: polarization coefficient e.g 1.0 fully polarized, 0.5 unpolarized |
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| 189 | :param Azm: azimuthal angle e.g. 0.0 in plane of polarization |
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| 190 | :param Tth: 2-theta scattering angle - can be numpy array |
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| 191 | which (if either) of these is "right"? |
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| 192 | :return: (pola, dpdPola) |
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| 193 | * pola = ((1-Pola)*npcosd(Azm)**2+Pola*npsind(Azm)**2)*npcosd(Tth)**2+ \ |
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| 194 | (1-Pola)*npsind(Azm)**2+Pola*npcosd(Azm)**2 |
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| 195 | * dpdPola: derivative needed for least squares |
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| 196 | |
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| 197 | """ |
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| 198 | pola = ((1.0-Pola)*npcosd(Azm)**2+Pola*npsind(Azm)**2)*npcosd(Tth)**2+ \ |
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| 199 | (1.0-Pola)*npsind(Azm)**2+Pola*npcosd(Azm)**2 |
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| 200 | dpdPola = -npsind(Tth)**2*(npsind(Azm)**2-npcosd(Azm)**2) |
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| 201 | return pola,dpdPola |
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| 202 | |
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| 203 | def Oblique(ObCoeff,Tth): |
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| 204 | 'currently assumes detector is normal to beam' |
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| 205 | if ObCoeff: |
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| 206 | return (1.-ObCoeff)/(1.0-np.exp(np.log(ObCoeff)/npcosd(Tth))) |
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| 207 | else: |
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| 208 | return 1.0 |
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| 209 | |
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| 210 | def Ruland(RulCoff,wave,Q,Compton): |
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| 211 | 'needs a doc string' |
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| 212 | C = 2.9978e8 |
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| 213 | D = 1.5e-3 |
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| 214 | hmc = 0.024262734687 |
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| 215 | sinth2 = (Q*wave/(4.0*np.pi))**2 |
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| 216 | dlam = (wave**2)*Compton*Q/C |
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| 217 | dlam_c = 2.0*hmc*sinth2-D*wave**2 |
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| 218 | return 1.0/((1.0+dlam/RulCoff)*(1.0+(np.pi*dlam_c/(dlam+RulCoff))**2)) |
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| 219 | |
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| 220 | def LorchWeight(Q): |
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| 221 | 'needs a doc string' |
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| 222 | return np.sin(np.pi*(Q[-1]-Q)/(2.0*Q[-1])) |
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| 223 | |
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| 224 | def GetAsfMean(ElList,Sthl2): |
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| 225 | '''Calculate various scattering factor terms for PDF calcs |
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| 226 | |
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| 227 | :param dict ElList: element dictionary contains scattering factor coefficients, etc. |
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| 228 | :param np.array Sthl2: numpy array of sin theta/lambda squared values |
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| 229 | :returns: mean(f^2), mean(f)^2, mean(compton) |
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| 230 | ''' |
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| 231 | sumNoAtoms = 0.0 |
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| 232 | FF = np.zeros_like(Sthl2) |
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| 233 | FF2 = np.zeros_like(Sthl2) |
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| 234 | CF = np.zeros_like(Sthl2) |
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| 235 | for El in ElList: |
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| 236 | sumNoAtoms += ElList[El]['FormulaNo'] |
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| 237 | for El in ElList: |
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| 238 | el = ElList[El] |
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| 239 | ff2 = (G2elem.ScatFac(el,Sthl2)+el['fp'])**2+el['fpp']**2 |
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| 240 | cf = G2elem.ComptonFac(el,Sthl2) |
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| 241 | FF += np.sqrt(ff2)*el['FormulaNo']/sumNoAtoms |
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| 242 | FF2 += ff2*el['FormulaNo']/sumNoAtoms |
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| 243 | CF += cf*el['FormulaNo']/sumNoAtoms |
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| 244 | return FF2,FF**2,CF |
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| 245 | |
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| 246 | def GetNumDensity(ElList,Vol): |
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| 247 | 'needs a doc string' |
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| 248 | sumNoAtoms = 0.0 |
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| 249 | for El in ElList: |
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| 250 | sumNoAtoms += ElList[El]['FormulaNo'] |
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| 251 | return sumNoAtoms/Vol |
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| 252 | |
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| 253 | def CalcPDF(data,inst,xydata): |
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| 254 | 'needs a doc string' |
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| 255 | auxPlot = [] |
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| 256 | import copy |
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| 257 | import scipy.fftpack as ft |
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| 258 | #subtract backgrounds - if any |
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| 259 | xydata['IofQ'] = copy.deepcopy(xydata['Sample']) |
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| 260 | if data['Sample Bkg.']['Name']: |
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| 261 | xydata['IofQ'][1][1] += (xydata['Sample Bkg.'][1][1]+ |
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| 262 | data['Sample Bkg.']['Add'])*data['Sample Bkg.']['Mult'] |
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| 263 | if data['Container']['Name']: |
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| 264 | xycontainer = (xydata['Container'][1][1]+data['Container']['Add'])*data['Container']['Mult'] |
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| 265 | if data['Container Bkg.']['Name']: |
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| 266 | xycontainer += (xydata['Container Bkg.'][1][1]+ |
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| 267 | data['Container Bkg.']['Add'])*data['Container Bkg.']['Mult'] |
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| 268 | xydata['IofQ'][1][1] += xycontainer |
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| 269 | #get element data & absorption coeff. |
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| 270 | ElList = data['ElList'] |
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| 271 | Abs = G2lat.CellAbsorption(ElList,data['Form Vol']) |
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| 272 | #Apply angle dependent corrections |
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| 273 | Tth = xydata['Sample'][1][0] |
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| 274 | dt = (Tth[1]-Tth[0]) |
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| 275 | MuR = Abs*data['Diam']/20.0 |
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| 276 | xydata['IofQ'][1][1] /= Absorb(data['Geometry'],MuR,Tth) |
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| 277 | if 'X' in inst['Type'][0]: |
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| 278 | xydata['IofQ'][1][1] /= Polarization(inst['Polariz.'][1],Tth,Azm=inst['Azimuth'][1])[0] |
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| 279 | if data['DetType'] == 'Image plate': |
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| 280 | xydata['IofQ'][1][1] *= Oblique(data['ObliqCoeff'],Tth) |
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| 281 | XY = xydata['IofQ'][1] |
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| 282 | #convert to Q |
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| 283 | hc = 12.397639 |
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| 284 | wave = G2mth.getWave(inst) |
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| 285 | keV = hc/wave |
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| 286 | minQ = npT2q(Tth[0],wave) |
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| 287 | maxQ = npT2q(Tth[-1],wave) |
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| 288 | Qpoints = np.linspace(0.,maxQ,len(XY[0]),endpoint=True) |
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| 289 | dq = Qpoints[1]-Qpoints[0] |
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| 290 | XY[0] = npT2q(XY[0],wave) |
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| 291 | # Qdata = np.nan_to_num(si.griddata(XY[0],XY[1],Qpoints,method='linear')) #only OK for scipy 0.9! |
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| 292 | T = si.interp1d(XY[0],XY[1],bounds_error=False,fill_value=0.0) #OK for scipy 0.8 |
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| 293 | Qdata = T(Qpoints) |
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| 294 | |
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| 295 | qLimits = data['QScaleLim'] |
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| 296 | minQ = np.searchsorted(Qpoints,qLimits[0]) |
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| 297 | maxQ = np.searchsorted(Qpoints,qLimits[1]) |
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| 298 | newdata = [] |
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| 299 | xydata['IofQ'][1][0] = Qpoints |
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| 300 | xydata['IofQ'][1][1] = Qdata |
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| 301 | for item in xydata['IofQ'][1]: |
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| 302 | newdata.append(item[:maxQ]) |
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| 303 | xydata['IofQ'][1] = newdata |
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| 304 | |
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| 305 | |
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| 306 | xydata['SofQ'] = copy.deepcopy(xydata['IofQ']) |
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| 307 | FFSq,SqFF,CF = GetAsfMean(ElList,(xydata['SofQ'][1][0]/(4.0*np.pi))**2) #these are <f^2>,<f>^2,Cf |
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| 308 | Q = xydata['SofQ'][1][0] |
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| 309 | ruland = Ruland(data['Ruland'],wave,Q,CF) |
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| 310 | # auxPlot.append([Q,ruland,'Ruland']) |
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| 311 | CF *= ruland |
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| 312 | # auxPlot.append([Q,CF,'CF-Corr']) |
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| 313 | scale = np.sum((FFSq+CF)[minQ:maxQ])/np.sum(xydata['SofQ'][1][1][minQ:maxQ]) |
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| 314 | xydata['SofQ'][1][1] *= scale |
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| 315 | xydata['SofQ'][1][1] -= CF |
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| 316 | xydata['SofQ'][1][1] = xydata['SofQ'][1][1]/SqFF |
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| 317 | scale = len(xydata['SofQ'][1][1][minQ:maxQ])/np.sum(xydata['SofQ'][1][1][minQ:maxQ]) |
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| 318 | xydata['SofQ'][1][1] *= scale |
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| 319 | |
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| 320 | xydata['FofQ'] = copy.deepcopy(xydata['SofQ']) |
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| 321 | xydata['FofQ'][1][1] = xydata['FofQ'][1][0]*(xydata['SofQ'][1][1]-1.0) |
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| 322 | if data['Lorch']: |
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| 323 | xydata['FofQ'][1][1] *= LorchWeight(Q) |
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| 324 | |
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| 325 | xydata['GofR'] = copy.deepcopy(xydata['FofQ']) |
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| 326 | nR = len(xydata['GofR'][1][1]) |
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| 327 | xydata['GofR'][1][1] = -dq*np.imag(ft.fft(xydata['FofQ'][1][1],4*nR)[:nR]) |
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| 328 | xydata['GofR'][1][0] = 0.5*np.pi*np.linspace(0,nR,nR)/qLimits[1] |
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| 329 | |
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| 330 | |
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| 331 | return auxPlot |
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| 332 | |
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| 333 | ################################################################################ |
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| 334 | #GSASII peak fitting routines: Finger, Cox & Jephcoat model |
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| 335 | ################################################################################ |
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| 336 | |
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| 337 | def factorize(num): |
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| 338 | ''' Provide prime number factors for integer num |
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| 339 | :returns: dictionary of prime factors (keys) & power for each (data) |
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| 340 | ''' |
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| 341 | factors = {} |
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| 342 | orig = num |
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| 343 | |
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| 344 | # we take advantage of the fact that (i +1)**2 = i**2 + 2*i +1 |
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| 345 | i, sqi = 2, 4 |
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| 346 | while sqi <= num: |
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| 347 | while not num%i: |
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| 348 | num /= i |
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| 349 | factors[i] = factors.get(i, 0) + 1 |
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| 350 | |
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| 351 | sqi += 2*i + 1 |
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| 352 | i += 1 |
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| 353 | |
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| 354 | if num != 1 and num != orig: |
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| 355 | factors[num] = factors.get(num, 0) + 1 |
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| 356 | |
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| 357 | if factors: |
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| 358 | return factors |
|---|
| 359 | else: |
|---|
| 360 | return {num:1} #a prime number! |
|---|
| 361 | |
|---|
| 362 | def makeFFTsizeList(nmin=1,nmax=1023,thresh=15): |
|---|
| 363 | ''' Provide list of optimal data sizes for FFT calculations |
|---|
| 364 | |
|---|
| 365 | :param int nmin: minimum data size >= 1 |
|---|
| 366 | :param int nmax: maximum data size > nmin |
|---|
| 367 | :param int thresh: maximum prime factor allowed |
|---|
| 368 | :Returns: list of data sizes where the maximum prime factor is < thresh |
|---|
| 369 | ''' |
|---|
| 370 | plist = [] |
|---|
| 371 | nmin = max(1,nmin) |
|---|
| 372 | nmax = max(nmin+1,nmax) |
|---|
| 373 | for p in range(nmin,nmax): |
|---|
| 374 | if max(factorize(p).keys()) < thresh: |
|---|
| 375 | plist.append(p) |
|---|
| 376 | return plist |
|---|
| 377 | |
|---|
| 378 | np.seterr(divide='ignore') |
|---|
| 379 | |
|---|
| 380 | # Normal distribution |
|---|
| 381 | |
|---|
| 382 | # loc = mu, scale = std |
|---|
| 383 | _norm_pdf_C = 1./math.sqrt(2*math.pi) |
|---|
| 384 | class norm_gen(st.rv_continuous): |
|---|
| 385 | 'needs a doc string' |
|---|
| 386 | |
|---|
| 387 | def pdf(self,x,*args,**kwds): |
|---|
| 388 | loc,scale=kwds['loc'],kwds['scale'] |
|---|
| 389 | x = (x-loc)/scale |
|---|
| 390 | return np.exp(-x**2/2.0) * _norm_pdf_C / scale |
|---|
| 391 | |
|---|
| 392 | norm = norm_gen(name='norm',longname='A normal',extradoc=""" |
|---|
| 393 | |
|---|
| 394 | Normal distribution |
|---|
| 395 | |
|---|
| 396 | The location (loc) keyword specifies the mean. |
|---|
| 397 | The scale (scale) keyword specifies the standard deviation. |
|---|
| 398 | |
|---|
| 399 | normal.pdf(x) = exp(-x**2/2)/sqrt(2*pi) |
|---|
| 400 | """) |
|---|
| 401 | |
|---|
| 402 | ## Cauchy |
|---|
| 403 | |
|---|
| 404 | # median = loc |
|---|
| 405 | |
|---|
| 406 | class cauchy_gen(st.rv_continuous): |
|---|
| 407 | 'needs a doc string' |
|---|
| 408 | |
|---|
| 409 | def pdf(self,x,*args,**kwds): |
|---|
| 410 | loc,scale=kwds['loc'],kwds['scale'] |
|---|
| 411 | x = (x-loc)/scale |
|---|
| 412 | return 1.0/np.pi/(1.0+x*x) / scale |
|---|
| 413 | |
|---|
| 414 | cauchy = cauchy_gen(name='cauchy',longname='Cauchy',extradoc=""" |
|---|
| 415 | |
|---|
| 416 | Cauchy distribution |
|---|
| 417 | |
|---|
| 418 | cauchy.pdf(x) = 1/(pi*(1+x**2)) |
|---|
| 419 | |
|---|
| 420 | This is the t distribution with one degree of freedom. |
|---|
| 421 | """) |
|---|
| 422 | |
|---|
| 423 | |
|---|
| 424 | #GSASII peak fitting routine: Finger, Cox & Jephcoat model |
|---|
| 425 | |
|---|
| 426 | |
|---|
| 427 | class fcjde_gen(st.rv_continuous): |
|---|
| 428 | """ |
|---|
| 429 | Finger-Cox-Jephcoat D(2phi,2th) function for S/L = H/L |
|---|
| 430 | Ref: J. Appl. Cryst. (1994) 27, 892-900. |
|---|
| 431 | |
|---|
| 432 | :param x: array -1 to 1 |
|---|
| 433 | :param t: 2-theta position of peak |
|---|
| 434 | :param s: sum(S/L,H/L); S: sample height, H: detector opening, |
|---|
| 435 | L: sample to detector opening distance |
|---|
| 436 | :param dx: 2-theta step size in deg |
|---|
| 437 | |
|---|
| 438 | :returns: for fcj.pdf |
|---|
| 439 | |
|---|
| 440 | * T = x*dx+t |
|---|
| 441 | * s = S/L+H/L |
|---|
| 442 | * if x < 0:: |
|---|
| 443 | |
|---|
| 444 | fcj.pdf = [1/sqrt({cos(T)**2/cos(t)**2}-1) - 1/s]/|cos(T)| |
|---|
| 445 | |
|---|
| 446 | * if x >= 0: fcj.pdf = 0 |
|---|
| 447 | """ |
|---|
| 448 | def _pdf(self,x,t,s,dx): |
|---|
| 449 | T = dx*x+t |
|---|
| 450 | ax2 = abs(npcosd(T)) |
|---|
| 451 | ax = ax2**2 |
|---|
| 452 | bx = npcosd(t)**2 |
|---|
| 453 | bx = np.where(ax>bx,bx,ax) |
|---|
| 454 | fx = np.where(ax>bx,(np.sqrt(bx/(ax-bx))-1./s)/ax2,0.0) |
|---|
| 455 | fx = np.where(fx > 0.,fx,0.0) |
|---|
| 456 | return fx |
|---|
| 457 | |
|---|
| 458 | def pdf(self,x,*args,**kwds): |
|---|
| 459 | loc=kwds['loc'] |
|---|
| 460 | return self._pdf(x-loc,*args) |
|---|
| 461 | |
|---|
| 462 | fcjde = fcjde_gen(name='fcjde',shapes='t,s,dx') |
|---|
| 463 | |
|---|
| 464 | def getWidthsCW(pos,sig,gam,shl): |
|---|
| 465 | '''Compute the peak widths used for computing the range of a peak |
|---|
| 466 | for constant wavelength data. On low-angle side, 10 FWHM are used, |
|---|
| 467 | on high-angle side 15 are used, low angle side extended by axial divergence |
|---|
| 468 | (for peaks above 90 deg, these are reversed.) |
|---|
| 469 | ''' |
|---|
| 470 | widths = [np.sqrt(sig)/100.,gam/100.] |
|---|
| 471 | fwhm = 2.355*widths[0]+widths[1] |
|---|
| 472 | fmin = 10.*(fwhm+shl*abs(npcosd(pos))) |
|---|
| 473 | fmax = 15.0*fwhm |
|---|
| 474 | if pos > 90: |
|---|
| 475 | fmin,fmax = [fmax,fmin] |
|---|
| 476 | return widths,fmin,fmax |
|---|
| 477 | |
|---|
| 478 | def getWidthsTOF(pos,alp,bet,sig,gam): |
|---|
| 479 | '''Compute the peak widths used for computing the range of a peak |
|---|
| 480 | for constant wavelength data. 10 FWHM are used on both sides each |
|---|
| 481 | extended by exponential coeff. |
|---|
| 482 | ''' |
|---|
| 483 | lnf = 3.3 # =log(0.001/2) |
|---|
| 484 | widths = [np.sqrt(sig),gam] |
|---|
| 485 | fwhm = 2.355*widths[0]+2.*widths[1] |
|---|
| 486 | fmin = 10.*fwhm*(1.+1./alp) |
|---|
| 487 | fmax = 10.*fwhm*(1.+1./bet) |
|---|
| 488 | return widths,fmin,fmax |
|---|
| 489 | |
|---|
| 490 | def getFWHM(pos,Inst): |
|---|
| 491 | '''Compute total FWHM from Thompson, Cox & Hastings (1987), J. Appl. Cryst. 20, 79-83 |
|---|
| 492 | via getgamFW(g,s). |
|---|
| 493 | |
|---|
| 494 | :param pos: float peak position in deg 2-theta or tof in musec |
|---|
| 495 | :param Inst: dict instrument parameters |
|---|
| 496 | |
|---|
| 497 | :returns float: total FWHM of pseudoVoigt in deg or musec |
|---|
| 498 | ''' |
|---|
| 499 | |
|---|
| 500 | sig = lambda Th,U,V,W: np.sqrt(max(0.001,U*tand(Th)**2+V*tand(Th)+W)) |
|---|
| 501 | sigTOF = lambda dsp,S0,S1,S2,Sq: S0+S1*dsp**2+S2*dsp**4+Sq/dsp**2 |
|---|
| 502 | gam = lambda Th,X,Y: (X/cosd(Th)+Y*tand(Th)) |
|---|
| 503 | gamTOF = lambda dsp,X,Y: X*dsp+Y*dsp**2 |
|---|
| 504 | if 'C' in Inst['Type'][0]: |
|---|
| 505 | s = sig(pos/2.,Inst['U'][1],Inst['V'][1],Inst['W'][1]) |
|---|
| 506 | g = gam(pos/2.,Inst['X'][1],Inst['Y'][1]) |
|---|
| 507 | return getgamFW(g,s)/100. #returns FWHM in deg |
|---|
| 508 | else: |
|---|
| 509 | dsp = pos/Inst['difC'][0] |
|---|
| 510 | s = sigTOF(dsp,Inst['sig-0'][1],Inst['sig-1'][1],Inst['sig-2'][1],Inst['sig-q'][1]) |
|---|
| 511 | g = gamTOF(dsp,Inst['X'][1],Inst['Y'][1]) |
|---|
| 512 | return getgamFW(g,s) |
|---|
| 513 | |
|---|
| 514 | def getgamFW(g,s): |
|---|
| 515 | '''Compute total FWHM from Thompson, Cox & Hastings (1987), J. Appl. Cryst. 20, 79-83 |
|---|
| 516 | lambda fxn needs FWHM for both Gaussian & Lorentzian components |
|---|
| 517 | |
|---|
| 518 | :param g: float Lorentzian gamma = FWHM(L) |
|---|
| 519 | :param s: float Gaussian sig |
|---|
| 520 | |
|---|
| 521 | :returns float: total FWHM of pseudoVoigt |
|---|
| 522 | ''' |
|---|
| 523 | gamFW = lambda s,g: np.exp(np.log(s**5+2.69269*s**4*g+2.42843*s**3*g**2+4.47163*s**2*g**3+0.07842*s*g**4+g**5)/5.) |
|---|
| 524 | return gamFW(2.35482*s,g) #sqrt(8ln2)*sig = FWHM(G) |
|---|
| 525 | |
|---|
| 526 | def getFCJVoigt(pos,intens,sig,gam,shl,xdata): |
|---|
| 527 | 'needs a doc string' |
|---|
| 528 | DX = xdata[1]-xdata[0] |
|---|
| 529 | widths,fmin,fmax = getWidthsCW(pos,sig,gam,shl) |
|---|
| 530 | x = np.linspace(pos-fmin,pos+fmin,256) |
|---|
| 531 | dx = x[1]-x[0] |
|---|
| 532 | Norm = norm.pdf(x,loc=pos,scale=widths[0]) |
|---|
| 533 | Cauchy = cauchy.pdf(x,loc=pos,scale=widths[1]) |
|---|
| 534 | arg = [pos,shl/57.2958,dx,] |
|---|
| 535 | FCJ = fcjde.pdf(x,*arg,loc=pos) |
|---|
| 536 | if len(np.nonzero(FCJ)[0])>5: |
|---|
| 537 | z = np.column_stack([Norm,Cauchy,FCJ]).T |
|---|
| 538 | Z = fft(z) |
|---|
| 539 | Df = ifft(Z.prod(axis=0)).real |
|---|
| 540 | else: |
|---|
| 541 | z = np.column_stack([Norm,Cauchy]).T |
|---|
| 542 | Z = fft(z) |
|---|
| 543 | Df = fftshift(ifft(Z.prod(axis=0))).real |
|---|
| 544 | Df /= np.sum(Df) |
|---|
| 545 | Df = si.interp1d(x,Df,bounds_error=False,fill_value=0.0) |
|---|
| 546 | return intens*Df(xdata)*DX/dx |
|---|
| 547 | |
|---|
| 548 | def getBackground(pfx,parmDict,bakType,dataType,xdata): |
|---|
| 549 | 'needs a doc string' |
|---|
| 550 | if 'T' in dataType: |
|---|
| 551 | q = 2.*np.pi*parmDict[pfx+'difC']/xdata |
|---|
| 552 | elif 'C' in dataType: |
|---|
| 553 | wave = parmDict.get(pfx+'Lam',parmDict.get(pfx+'Lam1',1.0)) |
|---|
| 554 | q = 2.*np.pi*npsind(xdata/2.)/wave |
|---|
| 555 | yb = np.zeros_like(xdata) |
|---|
| 556 | nBak = 0 |
|---|
| 557 | cw = np.diff(xdata) |
|---|
| 558 | cw = np.append(cw,cw[-1]) |
|---|
| 559 | sumBk = [0.,0.,0] |
|---|
| 560 | while True: |
|---|
| 561 | key = pfx+'Back;'+str(nBak) |
|---|
| 562 | if key in parmDict: |
|---|
| 563 | nBak += 1 |
|---|
| 564 | else: |
|---|
| 565 | break |
|---|
| 566 | #empirical functions |
|---|
| 567 | if bakType in ['chebyschev','cosine']: |
|---|
| 568 | dt = xdata[-1]-xdata[0] |
|---|
| 569 | for iBak in range(nBak): |
|---|
| 570 | key = pfx+'Back;'+str(iBak) |
|---|
| 571 | if bakType == 'chebyschev': |
|---|
| 572 | ybi = parmDict[key]*(2.*(xdata-xdata[0])/dt-1.)**iBak |
|---|
| 573 | elif bakType == 'cosine': |
|---|
| 574 | ybi = parmDict[key]*npcosd(xdata*iBak) |
|---|
| 575 | yb += ybi |
|---|
| 576 | sumBk[0] = np.sum(yb) |
|---|
| 577 | elif bakType in ['Q^2 power series','Q^-2 power series']: |
|---|
| 578 | QT = 1. |
|---|
| 579 | yb += np.ones_like(yb)*parmDict[pfx+'Back;0'] |
|---|
| 580 | for iBak in range(nBak-1): |
|---|
| 581 | key = pfx+'Back;'+str(iBak+1) |
|---|
| 582 | if '-2' in bakType: |
|---|
| 583 | QT *= (iBak+1)*q**-2 |
|---|
| 584 | else: |
|---|
| 585 | QT *= q**2/(iBak+1) |
|---|
| 586 | yb += QT*parmDict[key] |
|---|
| 587 | sumBk[0] = np.sum(yb) |
|---|
| 588 | elif bakType in ['lin interpolate','inv interpolate','log interpolate',]: |
|---|
| 589 | if nBak == 1: |
|---|
| 590 | yb = np.ones_like(xdata)*parmDict[pfx+'Back;0'] |
|---|
| 591 | elif nBak == 2: |
|---|
| 592 | dX = xdata[-1]-xdata[0] |
|---|
| 593 | T2 = (xdata-xdata[0])/dX |
|---|
| 594 | T1 = 1.0-T2 |
|---|
| 595 | yb = parmDict[pfx+'Back;0']*T1+parmDict[pfx+'Back;1']*T2 |
|---|
| 596 | else: |
|---|
| 597 | if bakType == 'lin interpolate': |
|---|
| 598 | bakPos = np.linspace(xdata[0],xdata[-1],nBak,True) |
|---|
| 599 | elif bakType == 'inv interpolate': |
|---|
| 600 | bakPos = 1./np.linspace(1./xdata[-1],1./xdata[0],nBak,True) |
|---|
| 601 | elif bakType == 'log interpolate': |
|---|
| 602 | bakPos = np.exp(np.linspace(np.log(xdata[0]),np.log(xdata[-1]),nBak,True)) |
|---|
| 603 | bakPos[0] = xdata[0] |
|---|
| 604 | bakPos[-1] = xdata[-1] |
|---|
| 605 | bakVals = np.zeros(nBak) |
|---|
| 606 | for i in range(nBak): |
|---|
| 607 | bakVals[i] = parmDict[pfx+'Back;'+str(i)] |
|---|
| 608 | bakInt = si.interp1d(bakPos,bakVals,'linear') |
|---|
| 609 | yb = bakInt(xdata) |
|---|
| 610 | sumBk[0] = np.sum(yb) |
|---|
| 611 | #Debye function |
|---|
| 612 | if pfx+'difC' in parmDict: |
|---|
| 613 | ff = 1. |
|---|
| 614 | else: |
|---|
| 615 | try: |
|---|
| 616 | wave = parmDict[pfx+'Lam'] |
|---|
| 617 | except KeyError: |
|---|
| 618 | wave = parmDict[pfx+'Lam1'] |
|---|
| 619 | SQ = (q/(4.*np.pi))**2 |
|---|
| 620 | FF = G2elem.GetFormFactorCoeff('Si')[0] |
|---|
| 621 | ff = np.array(G2elem.ScatFac(FF,SQ)[0])**2 |
|---|
| 622 | iD = 0 |
|---|
| 623 | while True: |
|---|
| 624 | try: |
|---|
| 625 | dbA = parmDict[pfx+'DebyeA;'+str(iD)] |
|---|
| 626 | dbR = parmDict[pfx+'DebyeR;'+str(iD)] |
|---|
| 627 | dbU = parmDict[pfx+'DebyeU;'+str(iD)] |
|---|
| 628 | ybi = ff*dbA*np.sin(q*dbR)*np.exp(-dbU*q**2)/(q*dbR) |
|---|
| 629 | yb += ybi |
|---|
| 630 | sumBk[1] += np.sum(ybi) |
|---|
| 631 | iD += 1 |
|---|
| 632 | except KeyError: |
|---|
| 633 | break |
|---|
| 634 | #peaks |
|---|
| 635 | iD = 0 |
|---|
| 636 | while True: |
|---|
| 637 | try: |
|---|
| 638 | pkP = parmDict[pfx+'BkPkpos;'+str(iD)] |
|---|
| 639 | pkI = parmDict[pfx+'BkPkint;'+str(iD)] |
|---|
| 640 | pkS = parmDict[pfx+'BkPksig;'+str(iD)] |
|---|
| 641 | pkG = parmDict[pfx+'BkPkgam;'+str(iD)] |
|---|
| 642 | if 'C' in dataType: |
|---|
| 643 | Wd,fmin,fmax = getWidthsCW(pkP,pkS,pkG,.002) |
|---|
| 644 | else: #'T'OF |
|---|
| 645 | Wd,fmin,fmax = getWidthsTOF(pkP,1.,1.,pkS,pkG) |
|---|
| 646 | iBeg = np.searchsorted(xdata,pkP-fmin) |
|---|
| 647 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 648 | lenX = len(xdata) |
|---|
| 649 | if not iBeg: |
|---|
| 650 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 651 | elif iBeg == lenX: |
|---|
| 652 | iFin = iBeg |
|---|
| 653 | else: |
|---|
| 654 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 655 | if 'C' in dataType: |
|---|
| 656 | ybi = pkI*getFCJVoigt3(pkP,pkS,pkG,0.002,xdata[iBeg:iFin]) |
|---|
| 657 | yb[iBeg:iFin] += ybi |
|---|
| 658 | else: #'T'OF |
|---|
| 659 | ybi = pkI*getEpsVoigt(pkP,1.,1.,pkS,pkG,xdata[iBeg:iFin]) |
|---|
| 660 | yb[iBeg:iFin] += ybi |
|---|
| 661 | sumBk[2] += np.sum(ybi) |
|---|
| 662 | iD += 1 |
|---|
| 663 | except KeyError: |
|---|
| 664 | break |
|---|
| 665 | except ValueError: |
|---|
| 666 | print '**** WARNING - backround peak '+str(iD)+' sigma is negative; fix & try again ****' |
|---|
| 667 | break |
|---|
| 668 | return yb,sumBk |
|---|
| 669 | |
|---|
| 670 | def getBackgroundDerv(hfx,parmDict,bakType,dataType,xdata): |
|---|
| 671 | 'needs a doc string' |
|---|
| 672 | if 'T' in dataType: |
|---|
| 673 | q = 2.*np.pi*parmDict[hfx+'difC']/xdata |
|---|
| 674 | elif 'C' in dataType: |
|---|
| 675 | wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0)) |
|---|
| 676 | q = 2.*np.pi*npsind(xdata/2.)/wave |
|---|
| 677 | nBak = 0 |
|---|
| 678 | while True: |
|---|
| 679 | key = hfx+'Back;'+str(nBak) |
|---|
| 680 | if key in parmDict: |
|---|
| 681 | nBak += 1 |
|---|
| 682 | else: |
|---|
| 683 | break |
|---|
| 684 | dydb = np.zeros(shape=(nBak,len(xdata))) |
|---|
| 685 | dyddb = np.zeros(shape=(3*parmDict[hfx+'nDebye'],len(xdata))) |
|---|
| 686 | dydpk = np.zeros(shape=(4*parmDict[hfx+'nPeaks'],len(xdata))) |
|---|
| 687 | cw = np.diff(xdata) |
|---|
| 688 | cw = np.append(cw,cw[-1]) |
|---|
| 689 | |
|---|
| 690 | if bakType in ['chebyschev','cosine']: |
|---|
| 691 | dt = xdata[-1]-xdata[0] |
|---|
| 692 | for iBak in range(nBak): |
|---|
| 693 | if bakType == 'chebyschev': |
|---|
| 694 | dydb[iBak] = (2.*(xdata-xdata[0])/dt-1.)**iBak |
|---|
| 695 | elif bakType == 'cosine': |
|---|
| 696 | dydb[iBak] = npcosd(xdata*iBak) |
|---|
| 697 | elif bakType in ['Q^2 power series','Q^-2 power series']: |
|---|
| 698 | QT = 1. |
|---|
| 699 | dydb[0] = np.ones_like(xdata) |
|---|
| 700 | for iBak in range(nBak-1): |
|---|
| 701 | if '-2' in bakType: |
|---|
| 702 | QT *= (iBak+1)*q**-2 |
|---|
| 703 | else: |
|---|
| 704 | QT *= q**2/(iBak+1) |
|---|
| 705 | dydb[iBak+1] = QT |
|---|
| 706 | elif bakType in ['lin interpolate','inv interpolate','log interpolate',]: |
|---|
| 707 | if nBak == 1: |
|---|
| 708 | dydb[0] = np.ones_like(xdata) |
|---|
| 709 | elif nBak == 2: |
|---|
| 710 | dX = xdata[-1]-xdata[0] |
|---|
| 711 | T2 = (xdata-xdata[0])/dX |
|---|
| 712 | T1 = 1.0-T2 |
|---|
| 713 | dydb = [T1,T2] |
|---|
| 714 | else: |
|---|
| 715 | if bakType == 'lin interpolate': |
|---|
| 716 | bakPos = np.linspace(xdata[0],xdata[-1],nBak,True) |
|---|
| 717 | elif bakType == 'inv interpolate': |
|---|
| 718 | bakPos = 1./np.linspace(1./xdata[-1],1./xdata[0],nBak,True) |
|---|
| 719 | elif bakType == 'log interpolate': |
|---|
| 720 | bakPos = np.exp(np.linspace(np.log(xdata[0]),np.log(xdata[-1]),nBak,True)) |
|---|
| 721 | bakPos[0] = xdata[0] |
|---|
| 722 | bakPos[-1] = xdata[-1] |
|---|
| 723 | for i,pos in enumerate(bakPos): |
|---|
| 724 | if i == 0: |
|---|
| 725 | dydb[0] = np.where(xdata<bakPos[1],(bakPos[1]-xdata)/(bakPos[1]-bakPos[0]),0.) |
|---|
| 726 | elif i == len(bakPos)-1: |
|---|
| 727 | dydb[i] = np.where(xdata>bakPos[-2],(bakPos[-1]-xdata)/(bakPos[-1]-bakPos[-2]),0.) |
|---|
| 728 | else: |
|---|
| 729 | dydb[i] = np.where(xdata>bakPos[i], |
|---|
| 730 | np.where(xdata<bakPos[i+1],(bakPos[i+1]-xdata)/(bakPos[i+1]-bakPos[i]),0.), |
|---|
| 731 | np.where(xdata>bakPos[i-1],(xdata-bakPos[i-1])/(bakPos[i]-bakPos[i-1]),0.)) |
|---|
| 732 | if hfx+'difC' in parmDict: |
|---|
| 733 | ff = 1. |
|---|
| 734 | else: |
|---|
| 735 | try: |
|---|
| 736 | wave = parmDict[hfx+'Lam'] |
|---|
| 737 | except KeyError: |
|---|
| 738 | wave = parmDict[hfx+'Lam1'] |
|---|
| 739 | q = 4.0*np.pi*npsind(xdata/2.0)/wave |
|---|
| 740 | SQ = (q/(4*np.pi))**2 |
|---|
| 741 | FF = G2elem.GetFormFactorCoeff('Si')[0] |
|---|
| 742 | ff = np.array(G2elem.ScatFac(FF,SQ)[0]) |
|---|
| 743 | iD = 0 |
|---|
| 744 | while True: |
|---|
| 745 | try: |
|---|
| 746 | if hfx+'difC' in parmDict: |
|---|
| 747 | q = 2*np.pi*parmDict[hfx+'difC']/xdata |
|---|
| 748 | dbA = parmDict[hfx+'DebyeA;'+str(iD)] |
|---|
| 749 | dbR = parmDict[hfx+'DebyeR;'+str(iD)] |
|---|
| 750 | dbU = parmDict[hfx+'DebyeU;'+str(iD)] |
|---|
| 751 | sqr = np.sin(q*dbR)/(q*dbR) |
|---|
| 752 | cqr = np.cos(q*dbR) |
|---|
| 753 | temp = np.exp(-dbU*q**2) |
|---|
| 754 | dyddb[3*iD] = ff*sqr*temp/(np.pi*cw) |
|---|
| 755 | dyddb[3*iD+1] = ff*dbA*temp*(cqr-sqr)/(np.pi*dbR*cw) |
|---|
| 756 | dyddb[3*iD+2] = -ff*dbA*sqr*temp*q**2/(np.pi*cw) |
|---|
| 757 | iD += 1 #ff*dbA*np.sin(q*dbR)*np.exp(-dbU*q**2)/(q*dbR) |
|---|
| 758 | except KeyError: |
|---|
| 759 | break |
|---|
| 760 | iD = 0 |
|---|
| 761 | while True: |
|---|
| 762 | try: |
|---|
| 763 | pkP = parmDict[hfx+'BkPkpos;'+str(iD)] |
|---|
| 764 | pkI = parmDict[hfx+'BkPkint;'+str(iD)] |
|---|
| 765 | pkS = parmDict[hfx+'BkPksig;'+str(iD)] |
|---|
| 766 | pkG = parmDict[hfx+'BkPkgam;'+str(iD)] |
|---|
| 767 | if 'C' in dataType: |
|---|
| 768 | Wd,fmin,fmax = getWidthsCW(pkP,pkS,pkG,.002) |
|---|
| 769 | else: #'T'OF |
|---|
| 770 | Wd,fmin,fmax = getWidthsTOF(pkP,1.,1.,pkS,pkG) |
|---|
| 771 | iBeg = np.searchsorted(xdata,pkP-fmin) |
|---|
| 772 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 773 | lenX = len(xdata) |
|---|
| 774 | if not iBeg: |
|---|
| 775 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 776 | elif iBeg == lenX: |
|---|
| 777 | iFin = iBeg |
|---|
| 778 | else: |
|---|
| 779 | iFin = np.searchsorted(xdata,pkP+fmax) |
|---|
| 780 | if 'C' in dataType: |
|---|
| 781 | Df,dFdp,dFds,dFdg,x = getdFCJVoigt3(pkP,pkS,pkG,.002,xdata[iBeg:iFin]) |
|---|
| 782 | dydpk[4*iD][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFdp |
|---|
| 783 | dydpk[4*iD+1][iBeg:iFin] += 100.*cw[iBeg:iFin]*Df |
|---|
| 784 | dydpk[4*iD+2][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFds |
|---|
| 785 | dydpk[4*iD+3][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFdg |
|---|
| 786 | else: #'T'OF |
|---|
| 787 | Df,dFdp,x,x,dFds,dFdg = getdEpsVoigt(pkP,1.,1.,pkS,pkG,xdata[iBeg:iFin]) |
|---|
| 788 | dydpk[4*iD][iBeg:iFin] += pkI*dFdp |
|---|
| 789 | dydpk[4*iD+1][iBeg:iFin] += Df |
|---|
| 790 | dydpk[4*iD+2][iBeg:iFin] += pkI*dFds |
|---|
| 791 | dydpk[4*iD+3][iBeg:iFin] += pkI*dFdg |
|---|
| 792 | iD += 1 |
|---|
| 793 | except KeyError: |
|---|
| 794 | break |
|---|
| 795 | except ValueError: |
|---|
| 796 | print '**** WARNING - backround peak '+str(iD)+' sigma is negative; fix & try again ****' |
|---|
| 797 | break |
|---|
| 798 | return dydb,dyddb,dydpk |
|---|
| 799 | |
|---|
| 800 | #use old fortran routine |
|---|
| 801 | def getFCJVoigt3(pos,sig,gam,shl,xdata): |
|---|
| 802 | 'needs a doc string' |
|---|
| 803 | |
|---|
| 804 | Df = pyd.pypsvfcj(len(xdata),xdata-pos,pos,sig,gam,shl) |
|---|
| 805 | # Df = pyd.pypsvfcjo(len(xdata),xdata-pos,pos,sig,gam,shl) |
|---|
| 806 | Df /= np.sum(Df) |
|---|
| 807 | return Df |
|---|
| 808 | |
|---|
| 809 | def getdFCJVoigt3(pos,sig,gam,shl,xdata): |
|---|
| 810 | 'needs a doc string' |
|---|
| 811 | |
|---|
| 812 | Df,dFdp,dFds,dFdg,dFdsh = pyd.pydpsvfcj(len(xdata),xdata-pos,pos,sig,gam,shl) |
|---|
| 813 | # Df,dFdp,dFds,dFdg,dFdsh = pyd.pydpsvfcjo(len(xdata),xdata-pos,pos,sig,gam,shl) |
|---|
| 814 | sumDf = np.sum(Df) |
|---|
| 815 | return Df,dFdp,dFds,dFdg,dFdsh |
|---|
| 816 | |
|---|
| 817 | def getPsVoigt(pos,sig,gam,xdata): |
|---|
| 818 | 'needs a doc string' |
|---|
| 819 | |
|---|
| 820 | Df = pyd.pypsvoigt(len(xdata),xdata-pos,sig,gam) |
|---|
| 821 | Df /= np.sum(Df) |
|---|
| 822 | return Df |
|---|
| 823 | |
|---|
| 824 | def getdPsVoigt(pos,sig,gam,xdata): |
|---|
| 825 | 'needs a doc string' |
|---|
| 826 | |
|---|
| 827 | Df,dFdp,dFds,dFdg = pyd.pydpsvoigt(len(xdata),xdata-pos,sig,gam) |
|---|
| 828 | sumDf = np.sum(Df) |
|---|
| 829 | return Df,dFdp,dFds,dFdg |
|---|
| 830 | |
|---|
| 831 | def getEpsVoigt(pos,alp,bet,sig,gam,xdata): |
|---|
| 832 | 'needs a doc string' |
|---|
| 833 | Df = pyd.pyepsvoigt(len(xdata),xdata-pos,alp,bet,sig,gam) |
|---|
| 834 | Df /= np.sum(Df) |
|---|
| 835 | return Df |
|---|
| 836 | |
|---|
| 837 | def getdEpsVoigt(pos,alp,bet,sig,gam,xdata): |
|---|
| 838 | 'needs a doc string' |
|---|
| 839 | Df,dFdp,dFda,dFdb,dFds,dFdg = pyd.pydepsvoigt(len(xdata),xdata-pos,alp,bet,sig,gam) |
|---|
| 840 | sumDf = np.sum(Df) |
|---|
| 841 | return Df,dFdp,dFda,dFdb,dFds,dFdg |
|---|
| 842 | |
|---|
| 843 | def ellipseSize(H,Sij,GB): |
|---|
| 844 | 'needs a doc string' |
|---|
| 845 | HX = np.inner(H.T,GB) |
|---|
| 846 | lenHX = np.sqrt(np.sum(HX**2)) |
|---|
| 847 | Esize,Rsize = nl.eigh(G2lat.U6toUij(Sij)) |
|---|
| 848 | R = np.inner(HX/lenHX,Rsize)*Esize #want column length for hkl in crystal |
|---|
| 849 | lenR = np.sqrt(np.sum(R**2)) |
|---|
| 850 | return lenR |
|---|
| 851 | |
|---|
| 852 | def ellipseSizeDerv(H,Sij,GB): |
|---|
| 853 | 'needs a doc string' |
|---|
| 854 | lenR = ellipseSize(H,Sij,GB) |
|---|
| 855 | delt = 0.001 |
|---|
| 856 | dRdS = np.zeros(6) |
|---|
| 857 | for i in range(6): |
|---|
| 858 | Sij[i] -= delt |
|---|
| 859 | lenM = ellipseSize(H,Sij,GB) |
|---|
| 860 | Sij[i] += 2.*delt |
|---|
| 861 | lenP = ellipseSize(H,Sij,GB) |
|---|
| 862 | Sij[i] -= delt |
|---|
| 863 | dRdS[i] = (lenP-lenM)/(2.*delt) |
|---|
| 864 | return lenR,dRdS |
|---|
| 865 | |
|---|
| 866 | def getHKLpeak(dmin,SGData,A,Inst=None): |
|---|
| 867 | 'needs a doc string' |
|---|
| 868 | HKL = G2lat.GenHLaue(dmin,SGData,A) |
|---|
| 869 | HKLs = [] |
|---|
| 870 | for h,k,l,d in HKL: |
|---|
| 871 | ext = G2spc.GenHKLf([h,k,l],SGData)[0] |
|---|
| 872 | if not ext: |
|---|
| 873 | if Inst == None: |
|---|
| 874 | HKLs.append([h,k,l,d,0,-1]) |
|---|
| 875 | else: |
|---|
| 876 | HKLs.append([h,k,l,d,G2lat.Dsp2pos(Inst,d),-1]) |
|---|
| 877 | return HKLs |
|---|
| 878 | |
|---|
| 879 | def getHKLMpeak(dmin,Inst,SGData,SSGData,Vec,maxH,A): |
|---|
| 880 | 'needs a doc string' |
|---|
| 881 | HKLs = [] |
|---|
| 882 | vec = np.array(Vec) |
|---|
| 883 | vstar = np.sqrt(G2lat.calc_rDsq(vec,A)) #find extra needed for -n SS reflections |
|---|
| 884 | dvec = 1./(maxH*vstar+1./dmin) |
|---|
| 885 | HKL = G2lat.GenHLaue(dvec,SGData,A) |
|---|
| 886 | SSdH = [vec*h for h in range(-maxH,maxH+1)] |
|---|
| 887 | SSdH = dict(zip(range(-maxH,maxH+1),SSdH)) |
|---|
| 888 | for h,k,l,d in HKL: |
|---|
| 889 | ext = G2spc.GenHKLf([h,k,l],SGData)[0] |
|---|
| 890 | if not ext and d >= dmin: |
|---|
| 891 | HKLs.append([h,k,l,0,d,G2lat.Dsp2pos(Inst,d),-1]) |
|---|
| 892 | for dH in SSdH: |
|---|
| 893 | if dH: |
|---|
| 894 | DH = SSdH[dH] |
|---|
| 895 | H = [h+DH[0],k+DH[1],l+DH[2]] |
|---|
| 896 | d = float(1/np.sqrt(G2lat.calc_rDsq(H,A))) |
|---|
| 897 | if d >= dmin: |
|---|
| 898 | HKLM = np.array([h,k,l,dH]) |
|---|
| 899 | if G2spc.checkSSextc(HKLM,SSGData): |
|---|
| 900 | HKLs.append([h,k,l,dH,d,G2lat.Dsp2pos(Inst,d),-1]) |
|---|
| 901 | # GSASIIpath.IPyBreak() |
|---|
| 902 | return G2lat.sortHKLd(HKLs,True,True,True) |
|---|
| 903 | |
|---|
| 904 | def getPeakProfile(dataType,parmDict,xdata,varyList,bakType): |
|---|
| 905 | 'needs a doc string' |
|---|
| 906 | |
|---|
| 907 | yb = getBackground('',parmDict,bakType,dataType,xdata)[0] |
|---|
| 908 | yc = np.zeros_like(yb) |
|---|
| 909 | cw = np.diff(xdata) |
|---|
| 910 | cw = np.append(cw,cw[-1]) |
|---|
| 911 | if 'C' in dataType: |
|---|
| 912 | shl = max(parmDict['SH/L'],0.002) |
|---|
| 913 | Ka2 = False |
|---|
| 914 | if 'Lam1' in parmDict.keys(): |
|---|
| 915 | Ka2 = True |
|---|
| 916 | lamRatio = 360*(parmDict['Lam2']-parmDict['Lam1'])/(np.pi*parmDict['Lam1']) |
|---|
| 917 | kRatio = parmDict['I(L2)/I(L1)'] |
|---|
| 918 | iPeak = 0 |
|---|
| 919 | while True: |
|---|
| 920 | try: |
|---|
| 921 | pos = parmDict['pos'+str(iPeak)] |
|---|
| 922 | tth = (pos-parmDict['Zero']) |
|---|
| 923 | intens = parmDict['int'+str(iPeak)] |
|---|
| 924 | sigName = 'sig'+str(iPeak) |
|---|
| 925 | if sigName in varyList: |
|---|
| 926 | sig = parmDict[sigName] |
|---|
| 927 | else: |
|---|
| 928 | sig = G2mth.getCWsig(parmDict,tth) |
|---|
| 929 | sig = max(sig,0.001) #avoid neg sigma^2 |
|---|
| 930 | gamName = 'gam'+str(iPeak) |
|---|
| 931 | if gamName in varyList: |
|---|
| 932 | gam = parmDict[gamName] |
|---|
| 933 | else: |
|---|
| 934 | gam = G2mth.getCWgam(parmDict,tth) |
|---|
| 935 | gam = max(gam,0.001) #avoid neg gamma |
|---|
| 936 | Wd,fmin,fmax = getWidthsCW(pos,sig,gam,shl) |
|---|
| 937 | iBeg = np.searchsorted(xdata,pos-fmin) |
|---|
| 938 | iFin = np.searchsorted(xdata,pos+fmin) |
|---|
| 939 | if not iBeg+iFin: #peak below low limit |
|---|
| 940 | iPeak += 1 |
|---|
| 941 | continue |
|---|
| 942 | elif not iBeg-iFin: #peak above high limit |
|---|
| 943 | return yb+yc |
|---|
| 944 | yc[iBeg:iFin] += intens*getFCJVoigt3(pos,sig,gam,shl,xdata[iBeg:iFin]) |
|---|
| 945 | if Ka2: |
|---|
| 946 | pos2 = pos+lamRatio*tand(pos/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 947 | iBeg = np.searchsorted(xdata,pos2-fmin) |
|---|
| 948 | iFin = np.searchsorted(xdata,pos2+fmin) |
|---|
| 949 | if iBeg-iFin: |
|---|
| 950 | yc[iBeg:iFin] += intens*kRatio*getFCJVoigt3(pos2,sig,gam,shl,xdata[iBeg:iFin]) |
|---|
| 951 | iPeak += 1 |
|---|
| 952 | except KeyError: #no more peaks to process |
|---|
| 953 | return yb+yc |
|---|
| 954 | else: |
|---|
| 955 | Pdabc = parmDict['Pdabc'] |
|---|
| 956 | difC = parmDict['difC'] |
|---|
| 957 | iPeak = 0 |
|---|
| 958 | while True: |
|---|
| 959 | try: |
|---|
| 960 | pos = parmDict['pos'+str(iPeak)] |
|---|
| 961 | tof = pos-parmDict['Zero'] |
|---|
| 962 | dsp = tof/difC |
|---|
| 963 | intens = parmDict['int'+str(iPeak)] |
|---|
| 964 | alpName = 'alp'+str(iPeak) |
|---|
| 965 | if alpName in varyList: |
|---|
| 966 | alp = parmDict[alpName] |
|---|
| 967 | else: |
|---|
| 968 | if len(Pdabc): |
|---|
| 969 | alp = np.interp(dsp,Pdabc[0],Pdabc[1]) |
|---|
| 970 | else: |
|---|
| 971 | alp = G2mth.getTOFalpha(parmDict,dsp) |
|---|
| 972 | alp = max(0.0001,alp) |
|---|
| 973 | betName = 'bet'+str(iPeak) |
|---|
| 974 | if betName in varyList: |
|---|
| 975 | bet = parmDict[betName] |
|---|
| 976 | else: |
|---|
| 977 | if len(Pdabc): |
|---|
| 978 | bet = np.interp(dsp,Pdabc[0],Pdabc[2]) |
|---|
| 979 | else: |
|---|
| 980 | bet = G2mth.getTOFbeta(parmDict,dsp) |
|---|
| 981 | bet = max(0.0001,bet) |
|---|
| 982 | sigName = 'sig'+str(iPeak) |
|---|
| 983 | if sigName in varyList: |
|---|
| 984 | sig = parmDict[sigName] |
|---|
| 985 | else: |
|---|
| 986 | sig = G2mth.getTOFsig(parmDict,dsp) |
|---|
| 987 | gamName = 'gam'+str(iPeak) |
|---|
| 988 | if gamName in varyList: |
|---|
| 989 | gam = parmDict[gamName] |
|---|
| 990 | else: |
|---|
| 991 | gam = G2mth.getTOFgamma(parmDict,dsp) |
|---|
| 992 | gam = max(gam,0.001) #avoid neg gamma |
|---|
| 993 | Wd,fmin,fmax = getWidthsTOF(pos,alp,bet,sig,gam) |
|---|
| 994 | iBeg = np.searchsorted(xdata,pos-fmin) |
|---|
| 995 | iFin = np.searchsorted(xdata,pos+fmax) |
|---|
| 996 | lenX = len(xdata) |
|---|
| 997 | if not iBeg: |
|---|
| 998 | iFin = np.searchsorted(xdata,pos+fmax) |
|---|
| 999 | elif iBeg == lenX: |
|---|
| 1000 | iFin = iBeg |
|---|
| 1001 | else: |
|---|
| 1002 | iFin = np.searchsorted(xdata,pos+fmax) |
|---|
| 1003 | if not iBeg+iFin: #peak below low limit |
|---|
| 1004 | iPeak += 1 |
|---|
| 1005 | continue |
|---|
| 1006 | elif not iBeg-iFin: #peak above high limit |
|---|
| 1007 | return yb+yc |
|---|
| 1008 | yc[iBeg:iFin] += intens*getEpsVoigt(pos,alp,bet,sig,gam,xdata[iBeg:iFin]) |
|---|
| 1009 | iPeak += 1 |
|---|
| 1010 | except KeyError: #no more peaks to process |
|---|
| 1011 | return yb+yc |
|---|
| 1012 | |
|---|
| 1013 | def getPeakProfileDerv(dataType,parmDict,xdata,varyList,bakType): |
|---|
| 1014 | 'needs a doc string' |
|---|
| 1015 | # needs to return np.array([dMdx1,dMdx2,...]) in same order as varylist = backVary,insVary,peakVary order |
|---|
| 1016 | dMdv = np.zeros(shape=(len(varyList),len(xdata))) |
|---|
| 1017 | dMdb,dMddb,dMdpk = getBackgroundDerv('',parmDict,bakType,dataType,xdata) |
|---|
| 1018 | if 'Back;0' in varyList: #background derivs are in front if present |
|---|
| 1019 | dMdv[0:len(dMdb)] = dMdb |
|---|
| 1020 | names = ['DebyeA','DebyeR','DebyeU'] |
|---|
| 1021 | for name in varyList: |
|---|
| 1022 | if 'Debye' in name: |
|---|
| 1023 | parm,id = name.split(';') |
|---|
| 1024 | ip = names.index(parm) |
|---|
| 1025 | dMdv[varyList.index(name)] = dMddb[3*int(id)+ip] |
|---|
| 1026 | names = ['BkPkpos','BkPkint','BkPksig','BkPkgam'] |
|---|
| 1027 | for name in varyList: |
|---|
| 1028 | if 'BkPk' in name: |
|---|
| 1029 | parm,id = name.split(';') |
|---|
| 1030 | ip = names.index(parm) |
|---|
| 1031 | dMdv[varyList.index(name)] = dMdpk[4*int(id)+ip] |
|---|
| 1032 | cw = np.diff(xdata) |
|---|
| 1033 | cw = np.append(cw,cw[-1]) |
|---|
| 1034 | if 'C' in dataType: |
|---|
| 1035 | shl = max(parmDict['SH/L'],0.002) |
|---|
| 1036 | Ka2 = False |
|---|
| 1037 | if 'Lam1' in parmDict.keys(): |
|---|
| 1038 | Ka2 = True |
|---|
| 1039 | lamRatio = 360*(parmDict['Lam2']-parmDict['Lam1'])/(np.pi*parmDict['Lam1']) |
|---|
| 1040 | kRatio = parmDict['I(L2)/I(L1)'] |
|---|
| 1041 | iPeak = 0 |
|---|
| 1042 | while True: |
|---|
| 1043 | try: |
|---|
| 1044 | pos = parmDict['pos'+str(iPeak)] |
|---|
| 1045 | tth = (pos-parmDict['Zero']) |
|---|
| 1046 | intens = parmDict['int'+str(iPeak)] |
|---|
| 1047 | sigName = 'sig'+str(iPeak) |
|---|
| 1048 | if sigName in varyList: |
|---|
| 1049 | sig = parmDict[sigName] |
|---|
| 1050 | dsdU = dsdV = dsdW = 0 |
|---|
| 1051 | else: |
|---|
| 1052 | sig = G2mth.getCWsig(parmDict,tth) |
|---|
| 1053 | dsdU,dsdV,dsdW = G2mth.getCWsigDeriv(tth) |
|---|
| 1054 | sig = max(sig,0.001) #avoid neg sigma |
|---|
| 1055 | gamName = 'gam'+str(iPeak) |
|---|
| 1056 | if gamName in varyList: |
|---|
| 1057 | gam = parmDict[gamName] |
|---|
| 1058 | dgdX = dgdY = 0 |
|---|
| 1059 | else: |
|---|
| 1060 | gam = G2mth.getCWgam(parmDict,tth) |
|---|
| 1061 | dgdX,dgdY = G2mth.getCWgamDeriv(tth) |
|---|
| 1062 | gam = max(gam,0.001) #avoid neg gamma |
|---|
| 1063 | Wd,fmin,fmax = getWidthsCW(pos,sig,gam,shl) |
|---|
| 1064 | iBeg = np.searchsorted(xdata,pos-fmin) |
|---|
| 1065 | iFin = np.searchsorted(xdata,pos+fmin) |
|---|
| 1066 | if not iBeg+iFin: #peak below low limit |
|---|
| 1067 | iPeak += 1 |
|---|
| 1068 | continue |
|---|
| 1069 | elif not iBeg-iFin: #peak above high limit |
|---|
| 1070 | break |
|---|
| 1071 | dMdpk = np.zeros(shape=(6,len(xdata))) |
|---|
| 1072 | dMdipk = getdFCJVoigt3(pos,sig,gam,shl,xdata[iBeg:iFin]) |
|---|
| 1073 | for i in range(1,5): |
|---|
| 1074 | dMdpk[i][iBeg:iFin] += 100.*cw[iBeg:iFin]*intens*dMdipk[i] |
|---|
| 1075 | dMdpk[0][iBeg:iFin] += 100.*cw[iBeg:iFin]*dMdipk[0] |
|---|
| 1076 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4]} |
|---|
| 1077 | if Ka2: |
|---|
| 1078 | pos2 = pos+lamRatio*tand(pos/2.0) # + 360/pi * Dlam/lam * tan(th) |
|---|
| 1079 | iBeg = np.searchsorted(xdata,pos2-fmin) |
|---|
| 1080 | iFin = np.searchsorted(xdata,pos2+fmin) |
|---|
| 1081 | if iBeg-iFin: |
|---|
| 1082 | dMdipk2 = getdFCJVoigt3(pos2,sig,gam,shl,xdata[iBeg:iFin]) |
|---|
| 1083 | for i in range(1,5): |
|---|
| 1084 | dMdpk[i][iBeg:iFin] += 100.*cw[iBeg:iFin]*intens*kRatio*dMdipk2[i] |
|---|
| 1085 | dMdpk[0][iBeg:iFin] += 100.*cw[iBeg:iFin]*kRatio*dMdipk2[0] |
|---|
| 1086 | dMdpk[5][iBeg:iFin] += 100.*cw[iBeg:iFin]*dMdipk2[0] |
|---|
| 1087 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4],'L1/L2':dMdpk[5]*intens} |
|---|
| 1088 | for parmName in ['pos','int','sig','gam']: |
|---|
| 1089 | try: |
|---|
| 1090 | idx = varyList.index(parmName+str(iPeak)) |
|---|
| 1091 | dMdv[idx] = dervDict[parmName] |
|---|
| 1092 | except ValueError: |
|---|
| 1093 | pass |
|---|
| 1094 | if 'U' in varyList: |
|---|
| 1095 | dMdv[varyList.index('U')] += dsdU*dervDict['sig'] |
|---|
| 1096 | if 'V' in varyList: |
|---|
| 1097 | dMdv[varyList.index('V')] += dsdV*dervDict['sig'] |
|---|
| 1098 | if 'W' in varyList: |
|---|
| 1099 | dMdv[varyList.index('W')] += dsdW*dervDict['sig'] |
|---|
| 1100 | if 'X' in varyList: |
|---|
| 1101 | dMdv[varyList.index('X')] += dgdX*dervDict['gam'] |
|---|
| 1102 | if 'Y' in varyList: |
|---|
| 1103 | dMdv[varyList.index('Y')] += dgdY*dervDict['gam'] |
|---|
| 1104 | if 'SH/L' in varyList: |
|---|
| 1105 | dMdv[varyList.index('SH/L')] += dervDict['shl'] #problem here |
|---|
| 1106 | if 'I(L2)/I(L1)' in varyList: |
|---|
| 1107 | dMdv[varyList.index('I(L2)/I(L1)')] += dervDict['L1/L2'] |
|---|
| 1108 | iPeak += 1 |
|---|
| 1109 | except KeyError: #no more peaks to process |
|---|
| 1110 | break |
|---|
| 1111 | else: |
|---|
| 1112 | Pdabc = parmDict['Pdabc'] |
|---|
| 1113 | difC = parmDict['difC'] |
|---|
| 1114 | iPeak = 0 |
|---|
| 1115 | while True: |
|---|
| 1116 | try: |
|---|
| 1117 | pos = parmDict['pos'+str(iPeak)] |
|---|
| 1118 | tof = pos-parmDict['Zero'] |
|---|
| 1119 | dsp = tof/difC |
|---|
| 1120 | intens = parmDict['int'+str(iPeak)] |
|---|
| 1121 | alpName = 'alp'+str(iPeak) |
|---|
| 1122 | if alpName in varyList: |
|---|
| 1123 | alp = parmDict[alpName] |
|---|
| 1124 | else: |
|---|
| 1125 | if len(Pdabc): |
|---|
| 1126 | alp = np.interp(dsp,Pdabc[0],Pdabc[1]) |
|---|
| 1127 | dad0 = 0 |
|---|
| 1128 | else: |
|---|
| 1129 | alp = G2mth.getTOFalpha(parmDict,dsp) |
|---|
| 1130 | dada0 = G2mth.getTOFalphaDeriv(dsp) |
|---|
| 1131 | betName = 'bet'+str(iPeak) |
|---|
| 1132 | if betName in varyList: |
|---|
| 1133 | bet = parmDict[betName] |
|---|
| 1134 | else: |
|---|
| 1135 | if len(Pdabc): |
|---|
| 1136 | bet = np.interp(dsp,Pdabc[0],Pdabc[2]) |
|---|
| 1137 | dbdb0 = dbdb1 = dbdb2 = 0 |
|---|
| 1138 | else: |
|---|
| 1139 | bet = G2mth.getTOFbeta(parmDict,dsp) |
|---|
| 1140 | dbdb0,dbdb1,dbdb2 = G2mth.getTOFbetaDeriv(dsp) |
|---|
| 1141 | sigName = 'sig'+str(iPeak) |
|---|
| 1142 | if sigName in varyList: |
|---|
| 1143 | sig = parmDict[sigName] |
|---|
| 1144 | dsds0 = dsds1 = dsds2 = dsds3 = 0 |
|---|
| 1145 | else: |
|---|
| 1146 | sig = G2mth.getTOFsig(parmDict,dsp) |
|---|
| 1147 | dsds0,dsds1,dsds2,dsds3 = G2mth.getTOFsigDeriv(dsp) |
|---|
| 1148 | gamName = 'gam'+str(iPeak) |
|---|
| 1149 | if gamName in varyList: |
|---|
| 1150 | gam = parmDict[gamName] |
|---|
| 1151 | dsdX = dsdY = 0 |
|---|
| 1152 | else: |
|---|
| 1153 | gam = G2mth.getTOFgamma(parmDict,dsp) |
|---|
| 1154 | dsdX,dsdY = G2mth.getTOFgammaDeriv(dsp) |
|---|
| 1155 | gam = max(gam,0.001) #avoid neg gamma |
|---|
| 1156 | Wd,fmin,fmax = getWidthsTOF(pos,alp,bet,sig,gam) |
|---|
| 1157 | iBeg = np.searchsorted(xdata,pos-fmin) |
|---|
| 1158 | lenX = len(xdata) |
|---|
| 1159 | if not iBeg: |
|---|
| 1160 | iFin = np.searchsorted(xdata,pos+fmax) |
|---|
| 1161 | elif iBeg == lenX: |
|---|
| 1162 | iFin = iBeg |
|---|
| 1163 | else: |
|---|
| 1164 | iFin = np.searchsorted(xdata,pos+fmax) |
|---|
| 1165 | if not iBeg+iFin: #peak below low limit |
|---|
| 1166 | iPeak += 1 |
|---|
| 1167 | continue |
|---|
| 1168 | elif not iBeg-iFin: #peak above high limit |
|---|
| 1169 | break |
|---|
| 1170 | dMdpk = np.zeros(shape=(7,len(xdata))) |
|---|
| 1171 | dMdipk = getdEpsVoigt(pos,alp,bet,sig,gam,xdata[iBeg:iFin]) |
|---|
| 1172 | for i in range(1,6): |
|---|
| 1173 | dMdpk[i][iBeg:iFin] += intens*cw[iBeg:iFin]*dMdipk[i] |
|---|
| 1174 | dMdpk[0][iBeg:iFin] += cw[iBeg:iFin]*dMdipk[0] |
|---|
| 1175 | dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'alp':dMdpk[2],'bet':dMdpk[3],'sig':dMdpk[4],'gam':dMdpk[5]} |
|---|
| 1176 | for parmName in ['pos','int','alp','bet','sig','gam']: |
|---|
| 1177 | try: |
|---|
| 1178 | idx = varyList.index(parmName+str(iPeak)) |
|---|
| 1179 | dMdv[idx] = dervDict[parmName] |
|---|
| 1180 | except ValueError: |
|---|
| 1181 | pass |
|---|
| 1182 | if 'alpha' in varyList: |
|---|
| 1183 | dMdv[varyList.index('alpha')] += dada0*dervDict['alp'] |
|---|
| 1184 | if 'beta-0' in varyList: |
|---|
| 1185 | dMdv[varyList.index('beta-0')] += dbdb0*dervDict['bet'] |
|---|
| 1186 | if 'beta-1' in varyList: |
|---|
| 1187 | dMdv[varyList.index('beta-1')] += dbdb1*dervDict['bet'] |
|---|
| 1188 | if 'beta-q' in varyList: |
|---|
| 1189 | dMdv[varyList.index('beta-q')] += dbdb2*dervDict['bet'] |
|---|
| 1190 | if 'sig-0' in varyList: |
|---|
| 1191 | dMdv[varyList.index('sig-0')] += dsds0*dervDict['sig'] |
|---|
| 1192 | if 'sig-1' in varyList: |
|---|
| 1193 | dMdv[varyList.index('sig-1')] += dsds1*dervDict['sig'] |
|---|
| 1194 | if 'sig-2' in varyList: |
|---|
| 1195 | dMdv[varyList.index('sig-2')] += dsds2*dervDict['sig'] |
|---|
| 1196 | if 'sig-q' in varyList: |
|---|
| 1197 | dMdv[varyList.index('sig-q')] += dsds3*dervDict['sig'] |
|---|
| 1198 | if 'X' in varyList: |
|---|
| 1199 | dMdv[varyList.index('X')] += dsdX*dervDict['gam'] |
|---|
| 1200 | if 'Y' in varyList: |
|---|
| 1201 | dMdv[varyList.index('Y')] += dsdY*dervDict['gam'] #problem here |
|---|
| 1202 | iPeak += 1 |
|---|
| 1203 | except KeyError: #no more peaks to process |
|---|
| 1204 | break |
|---|
| 1205 | return dMdv |
|---|
| 1206 | |
|---|
| 1207 | def Dict2Values(parmdict, varylist): |
|---|
| 1208 | '''Use before call to leastsq to setup list of values for the parameters |
|---|
| 1209 | in parmdict, as selected by key in varylist''' |
|---|
| 1210 | return [parmdict[key] for key in varylist] |
|---|
| 1211 | |
|---|
| 1212 | def Values2Dict(parmdict, varylist, values): |
|---|
| 1213 | ''' Use after call to leastsq to update the parameter dictionary with |
|---|
| 1214 | values corresponding to keys in varylist''' |
|---|
| 1215 | parmdict.update(zip(varylist,values)) |
|---|
| 1216 | |
|---|
| 1217 | def SetBackgroundParms(Background): |
|---|
| 1218 | 'needs a doc string' |
|---|
| 1219 | if len(Background) == 1: # fix up old backgrounds |
|---|
| 1220 | BackGround.append({'nDebye':0,'debyeTerms':[]}) |
|---|
| 1221 | bakType,bakFlag = Background[0][:2] |
|---|
| 1222 | backVals = Background[0][3:] |
|---|
| 1223 | backNames = ['Back;'+str(i) for i in range(len(backVals))] |
|---|
| 1224 | Debye = Background[1] #also has background peaks stuff |
|---|
| 1225 | backDict = dict(zip(backNames,backVals)) |
|---|
| 1226 | backVary = [] |
|---|
| 1227 | if bakFlag: |
|---|
| 1228 | backVary = backNames |
|---|
| 1229 | |
|---|
| 1230 | backDict['nDebye'] = Debye['nDebye'] |
|---|
| 1231 | debyeDict = {} |
|---|
| 1232 | debyeList = [] |
|---|
| 1233 | for i in range(Debye['nDebye']): |
|---|
| 1234 | debyeNames = ['DebyeA;'+str(i),'DebyeR;'+str(i),'DebyeU;'+str(i)] |
|---|
| 1235 | debyeDict.update(dict(zip(debyeNames,Debye['debyeTerms'][i][::2]))) |
|---|
| 1236 | debyeList += zip(debyeNames,Debye['debyeTerms'][i][1::2]) |
|---|
| 1237 | debyeVary = [] |
|---|
| 1238 | for item in debyeList: |
|---|
| 1239 | if item[1]: |
|---|
| 1240 | debyeVary.append(item[0]) |
|---|
| 1241 | backDict.update(debyeDict) |
|---|
| 1242 | backVary += debyeVary |
|---|
| 1243 | |
|---|
| 1244 | backDict['nPeaks'] = Debye['nPeaks'] |
|---|
| 1245 | peaksDict = {} |
|---|
| 1246 | peaksList = [] |
|---|
| 1247 | for i in range(Debye['nPeaks']): |
|---|
| 1248 | peaksNames = ['BkPkpos;'+str(i),'BkPkint;'+str(i),'BkPksig;'+str(i),'BkPkgam;'+str(i)] |
|---|
| 1249 | peaksDict.update(dict(zip(peaksNames,Debye['peaksList'][i][::2]))) |
|---|
| 1250 | peaksList += zip(peaksNames,Debye['peaksList'][i][1::2]) |
|---|
| 1251 | peaksVary = [] |
|---|
| 1252 | for item in peaksList: |
|---|
| 1253 | if item[1]: |
|---|
| 1254 | peaksVary.append(item[0]) |
|---|
| 1255 | backDict.update(peaksDict) |
|---|
| 1256 | backVary += peaksVary |
|---|
| 1257 | return bakType,backDict,backVary |
|---|
| 1258 | |
|---|
| 1259 | def DoCalibInst(IndexPeaks,Inst): |
|---|
| 1260 | |
|---|
| 1261 | def SetInstParms(): |
|---|
| 1262 | dataType = Inst['Type'][0] |
|---|
| 1263 | insVary = [] |
|---|
| 1264 | insNames = [] |
|---|
| 1265 | insVals = [] |
|---|
| 1266 | for parm in Inst: |
|---|
| 1267 | insNames.append(parm) |
|---|
| 1268 | insVals.append(Inst[parm][1]) |
|---|
| 1269 | if parm in ['Lam','difC','difA','difB','Zero',]: |
|---|
| 1270 | if Inst[parm][2]: |
|---|
| 1271 | insVary.append(parm) |
|---|
| 1272 | instDict = dict(zip(insNames,insVals)) |
|---|
| 1273 | return dataType,instDict,insVary |
|---|
| 1274 | |
|---|
| 1275 | def GetInstParms(parmDict,Inst,varyList): |
|---|
| 1276 | for name in Inst: |
|---|
| 1277 | Inst[name][1] = parmDict[name] |
|---|
| 1278 | |
|---|
| 1279 | def InstPrint(Inst,sigDict): |
|---|
| 1280 | print 'Instrument Parameters:' |
|---|
| 1281 | if 'C' in Inst['Type'][0]: |
|---|
| 1282 | ptfmt = "%12.6f" |
|---|
| 1283 | else: |
|---|
| 1284 | ptfmt = "%12.3f" |
|---|
| 1285 | ptlbls = 'names :' |
|---|
| 1286 | ptstr = 'values:' |
|---|
| 1287 | sigstr = 'esds :' |
|---|
| 1288 | for parm in Inst: |
|---|
| 1289 | if parm in ['Lam','difC','difA','difB','Zero',]: |
|---|
| 1290 | ptlbls += "%s" % (parm.center(12)) |
|---|
| 1291 | ptstr += ptfmt % (Inst[parm][1]) |
|---|
| 1292 | if parm in sigDict: |
|---|
| 1293 | sigstr += ptfmt % (sigDict[parm]) |
|---|
| 1294 | else: |
|---|
| 1295 | sigstr += 12*' ' |
|---|
| 1296 | print ptlbls |
|---|
| 1297 | print ptstr |
|---|
| 1298 | print sigstr |
|---|
| 1299 | |
|---|
| 1300 | def errPeakPos(values,peakDsp,peakPos,peakWt,dataType,parmDict,varyList): |
|---|
| 1301 | parmDict.update(zip(varyList,values)) |
|---|
| 1302 | return np.sqrt(peakWt)*(G2lat.getPeakPos(dataType,parmDict,peakDsp)-peakPos) |
|---|
| 1303 | |
|---|
| 1304 | peakPos = [] |
|---|
| 1305 | peakDsp = [] |
|---|
| 1306 | peakWt = [] |
|---|
| 1307 | for peak,sig in zip(IndexPeaks[0],IndexPeaks[1]): |
|---|
| 1308 | if peak[2] and peak[3] and sig > 0.: |
|---|
| 1309 | peakPos.append(peak[0]) |
|---|
| 1310 | peakDsp.append(peak[-1]) #d-calc |
|---|
| 1311 | peakWt.append(peak[-1]**2/sig**2) #weight by d**2 |
|---|
| 1312 | peakPos = np.array(peakPos) |
|---|
| 1313 | peakDsp = np.array(peakDsp) |
|---|
| 1314 | peakWt = np.array(peakWt) |
|---|
| 1315 | dataType,insDict,insVary = SetInstParms() |
|---|
| 1316 | parmDict = {} |
|---|
| 1317 | parmDict.update(insDict) |
|---|
| 1318 | varyList = insVary |
|---|
| 1319 | if not len(varyList): |
|---|
| 1320 | print '**** ERROR - nothing to refine! ****' |
|---|
| 1321 | return False |
|---|
| 1322 | while True: |
|---|
| 1323 | begin = time.time() |
|---|
| 1324 | values = np.array(Dict2Values(parmDict, varyList)) |
|---|
| 1325 | result = so.leastsq(errPeakPos,values,full_output=True,ftol=0.000001, |
|---|
| 1326 | args=(peakDsp,peakPos,peakWt,dataType,parmDict,varyList)) |
|---|
| 1327 | ncyc = int(result[2]['nfev']/2) |
|---|
| 1328 | runtime = time.time()-begin |
|---|
| 1329 | chisq = np.sum(result[2]['fvec']**2) |
|---|
| 1330 | Values2Dict(parmDict, varyList, result[0]) |
|---|
| 1331 | GOF = chisq/(len(peakPos)-len(varyList)) #reduced chi^2 |
|---|
| 1332 | print 'Number of function calls:',result[2]['nfev'],' Number of observations: ',len(peakPos),' Number of parameters: ',len(varyList) |
|---|
| 1333 | print 'calib time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc) |
|---|
| 1334 | print 'chi**2 = %12.6g, reduced chi**2 = %6.2f'%(chisq,GOF) |
|---|
| 1335 | try: |
|---|
| 1336 | sig = np.sqrt(np.diag(result[1])*GOF) |
|---|
| 1337 | if np.any(np.isnan(sig)): |
|---|
| 1338 | print '*** Least squares aborted - some invalid esds possible ***' |
|---|
| 1339 | break #refinement succeeded - finish up! |
|---|
| 1340 | except ValueError: #result[1] is None on singular matrix |
|---|
| 1341 | print '**** Refinement failed - singular matrix ****' |
|---|
| 1342 | |
|---|
| 1343 | sigDict = dict(zip(varyList,sig)) |
|---|
| 1344 | GetInstParms(parmDict,Inst,varyList) |
|---|
| 1345 | InstPrint(Inst,sigDict) |
|---|
| 1346 | return True |
|---|
| 1347 | |
|---|
| 1348 | def DoPeakFit(FitPgm,Peaks,Background,Limits,Inst,Inst2,data,prevVaryList=[],oneCycle=False,controls=None,dlg=None): |
|---|
| 1349 | '''Called to perform a peak fit, refining the selected items in the peak |
|---|
| 1350 | table as well as selected items in the background. |
|---|
| 1351 | |
|---|
| 1352 | :param str FitPgm: type of fit to perform. At present this is ignored. |
|---|
| 1353 | :param list Peaks: a list of peaks. Each peak entry is a list with 8 values: |
|---|
| 1354 | four values followed by a refine flag where the values are: position, intensity, |
|---|
| 1355 | sigma (Gaussian width) and gamma (Lorentzian width). From the Histogram/"Peak List" |
|---|
| 1356 | tree entry, dict item "peaks" |
|---|
| 1357 | :param list Background: describes the background. List with two items. |
|---|
| 1358 | Item 0 specifies a background model and coefficients. Item 1 is a dict. |
|---|
| 1359 | From the Histogram/Background tree entry. |
|---|
| 1360 | :param list Limits: min and max x-value to use |
|---|
| 1361 | :param dict Inst: Instrument parameters |
|---|
| 1362 | :param dict Inst2: more Instrument parameters |
|---|
| 1363 | :param numpy.array data: a 5xn array. data[0] is the x-values, |
|---|
| 1364 | data[1] is the y-values, data[2] are weight values, data[3], [4] and [5] are |
|---|
| 1365 | calc, background and difference intensities, respectively. |
|---|
| 1366 | :param list prevVaryList: Used in sequential refinements to override the |
|---|
| 1367 | variable list. Defaults as an empty list. |
|---|
| 1368 | :param bool oneCycle: True if only one cycle of fitting should be performed |
|---|
| 1369 | :param dict controls: a dict specifying two values, Ftol = controls['min dM/M'] |
|---|
| 1370 | and derivType = controls['deriv type']. If None default values are used. |
|---|
| 1371 | :param wx.Dialog dlg: A dialog box that is updated with progress from the fit. |
|---|
| 1372 | Defaults to None, which means no updates are done. |
|---|
| 1373 | ''' |
|---|
| 1374 | def GetBackgroundParms(parmList,Background): |
|---|
| 1375 | iBak = 0 |
|---|
| 1376 | while True: |
|---|
| 1377 | try: |
|---|
| 1378 | bakName = 'Back;'+str(iBak) |
|---|
| 1379 | Background[0][iBak+3] = parmList[bakName] |
|---|
| 1380 | iBak += 1 |
|---|
| 1381 | except KeyError: |
|---|
| 1382 | break |
|---|
| 1383 | iDb = 0 |
|---|
| 1384 | while True: |
|---|
| 1385 | names = ['DebyeA;','DebyeR;','DebyeU;'] |
|---|
| 1386 | try: |
|---|
| 1387 | for i,name in enumerate(names): |
|---|
| 1388 | val = parmList[name+str(iDb)] |
|---|
| 1389 | Background[1]['debyeTerms'][iDb][2*i] = val |
|---|
| 1390 | iDb += 1 |
|---|
| 1391 | except KeyError: |
|---|
| 1392 | break |
|---|
| 1393 | iDb = 0 |
|---|
| 1394 | while True: |
|---|
| 1395 | names = ['BkPkpos;','BkPkint;','BkPksig;','BkPkgam;'] |
|---|
| 1396 | try: |
|---|
| 1397 | for i,name in enumerate(names): |
|---|
| 1398 | val = parmList[name+str(iDb)] |
|---|
| 1399 | Background[1]['peaksList'][iDb][2*i] = val |
|---|
| 1400 | iDb += 1 |
|---|
| 1401 | except KeyError: |
|---|
| 1402 | break |
|---|
| 1403 | |
|---|
| 1404 | def BackgroundPrint(Background,sigDict): |
|---|
| 1405 | print 'Background coefficients for',Background[0][0],'function' |
|---|
| 1406 | ptfmt = "%12.5f" |
|---|
| 1407 | ptstr = 'value: ' |
|---|
| 1408 | sigstr = 'esd : ' |
|---|
| 1409 | for i,back in enumerate(Background[0][3:]): |
|---|
| 1410 | ptstr += ptfmt % (back) |
|---|
| 1411 | if Background[0][1]: |
|---|
| 1412 | sigstr += ptfmt % (sigDict['Back;'+str(i)]) |
|---|
| 1413 | if len(ptstr) > 75: |
|---|
| 1414 | print ptstr |
|---|
| 1415 | if Background[0][1]: print sigstr |
|---|
| 1416 | ptstr = 'value: ' |
|---|
| 1417 | sigstr = 'esd : ' |
|---|
| 1418 | if len(ptstr) > 8: |
|---|
| 1419 | print ptstr |
|---|
| 1420 | if Background[0][1]: print sigstr |
|---|
| 1421 | |
|---|
| 1422 | if Background[1]['nDebye']: |
|---|
| 1423 | parms = ['DebyeA;','DebyeR;','DebyeU;'] |
|---|
| 1424 | print 'Debye diffuse scattering coefficients' |
|---|
| 1425 | ptfmt = "%12.5f" |
|---|
| 1426 | print ' term DebyeA esd DebyeR esd DebyeU esd' |
|---|
| 1427 | for term in range(Background[1]['nDebye']): |
|---|
| 1428 | line = ' term %d'%(term) |
|---|
| 1429 | for ip,name in enumerate(parms): |
|---|
| 1430 | line += ptfmt%(Background[1]['debyeTerms'][term][2*ip]) |
|---|
| 1431 | if name+str(term) in sigDict: |
|---|
| 1432 | line += ptfmt%(sigDict[name+str(term)]) |
|---|
| 1433 | print line |
|---|
| 1434 | if Background[1]['nPeaks']: |
|---|
| 1435 | print 'Coefficients for Background Peaks' |
|---|
| 1436 | ptfmt = "%15.3f" |
|---|
| 1437 | for j,pl in enumerate(Background[1]['peaksList']): |
|---|
| 1438 | names = 'peak %3d:'%(j+1) |
|---|
| 1439 | ptstr = 'values :' |
|---|
| 1440 | sigstr = 'esds :' |
|---|
| 1441 | for i,lbl in enumerate(['BkPkpos','BkPkint','BkPksig','BkPkgam']): |
|---|
| 1442 | val = pl[2*i] |
|---|
| 1443 | prm = lbl+";"+str(j) |
|---|
| 1444 | names += '%15s'%(prm) |
|---|
| 1445 | ptstr += ptfmt%(val) |
|---|
| 1446 | if prm in sigDict: |
|---|
| 1447 | sigstr += ptfmt%(sigDict[prm]) |
|---|
| 1448 | else: |
|---|
| 1449 | sigstr += " "*15 |
|---|
| 1450 | print names |
|---|
| 1451 | print ptstr |
|---|
| 1452 | print sigstr |
|---|
| 1453 | |
|---|
| 1454 | def SetInstParms(Inst): |
|---|
| 1455 | dataType = Inst['Type'][0] |
|---|
| 1456 | insVary = [] |
|---|
| 1457 | insNames = [] |
|---|
| 1458 | insVals = [] |
|---|
| 1459 | for parm in Inst: |
|---|
| 1460 | insNames.append(parm) |
|---|
| 1461 | insVals.append(Inst[parm][1]) |
|---|
| 1462 | if parm in ['U','V','W','X','Y','SH/L','I(L2)/I(L1)','alpha', |
|---|
| 1463 | 'beta-0','beta-1','beta-q','sig-0','sig-1','sig-2','sig-q',] and Inst[parm][2]: |
|---|
| 1464 | insVary.append(parm) |
|---|
| 1465 | instDict = dict(zip(insNames,insVals)) |
|---|
| 1466 | instDict['X'] = max(instDict['X'],0.01) |
|---|
| 1467 | instDict['Y'] = max(instDict['Y'],0.01) |
|---|
| 1468 | if 'SH/L' in instDict: |
|---|
| 1469 | instDict['SH/L'] = max(instDict['SH/L'],0.002) |
|---|
| 1470 | return dataType,instDict,insVary |
|---|
| 1471 | |
|---|
| 1472 | def GetInstParms(parmDict,Inst,varyList,Peaks): |
|---|
| 1473 | for name in Inst: |
|---|
| 1474 | Inst[name][1] = parmDict[name] |
|---|
| 1475 | iPeak = 0 |
|---|
| 1476 | while True: |
|---|
| 1477 | try: |
|---|
| 1478 | sigName = 'sig'+str(iPeak) |
|---|
| 1479 | pos = parmDict['pos'+str(iPeak)] |
|---|
| 1480 | if sigName not in varyList: |
|---|
| 1481 | if 'C' in Inst['Type'][0]: |
|---|
| 1482 | parmDict[sigName] = G2mth.getCWsig(parmDict,pos) |
|---|
| 1483 | else: |
|---|
| 1484 | dsp = G2lat.Pos2dsp(Inst,pos) |
|---|
| 1485 | parmDict[sigName] = G2mth.getTOFsig(parmDict,dsp) |
|---|
| 1486 | gamName = 'gam'+str(iPeak) |
|---|
| 1487 | if gamName not in varyList: |
|---|
| 1488 | if 'C' in Inst['Type'][0]: |
|---|
| 1489 | parmDict[gamName] = G2mth.getCWgam(parmDict,pos) |
|---|
| 1490 | else: |
|---|
| 1491 | dsp = G2lat.Pos2dsp(Inst,pos) |
|---|
| 1492 | parmDict[gamName] = G2mth.getTOFgamma(parmDict,dsp) |
|---|
| 1493 | iPeak += 1 |
|---|
| 1494 | except KeyError: |
|---|
| 1495 | break |
|---|
| 1496 | |
|---|
| 1497 | def InstPrint(Inst,sigDict): |
|---|
| 1498 | print 'Instrument Parameters:' |
|---|
| 1499 | ptfmt = "%12.6f" |
|---|
| 1500 | ptlbls = 'names :' |
|---|
| 1501 | ptstr = 'values:' |
|---|
| 1502 | sigstr = 'esds :' |
|---|
| 1503 | for parm in Inst: |
|---|
| 1504 | if parm in ['U','V','W','X','Y','SH/L','I(L2)/I(L1)','alpha', |
|---|
| 1505 | 'beta-0','beta-1','beta-q','sig-0','sig-1','sig-2','sig-q',]: |
|---|
| 1506 | ptlbls += "%s" % (parm.center(12)) |
|---|
| 1507 | ptstr += ptfmt % (Inst[parm][1]) |
|---|
| 1508 | if parm in sigDict: |
|---|
| 1509 | sigstr += ptfmt % (sigDict[parm]) |
|---|
| 1510 | else: |
|---|
| 1511 | sigstr += 12*' ' |
|---|
| 1512 | print ptlbls |
|---|
| 1513 | print ptstr |
|---|
| 1514 | print sigstr |
|---|
| 1515 | |
|---|
| 1516 | def SetPeaksParms(dataType,Peaks): |
|---|
| 1517 | peakNames = [] |
|---|
| 1518 | peakVary = [] |
|---|
| 1519 | peakVals = [] |
|---|
| 1520 | if 'C' in dataType: |
|---|
| 1521 | names = ['pos','int','sig','gam'] |
|---|
| 1522 | else: |
|---|
| 1523 | names = ['pos','int','alp','bet','sig','gam'] |
|---|
| 1524 | for i,peak in enumerate(Peaks): |
|---|
| 1525 | for j,name in enumerate(names): |
|---|
| 1526 | peakVals.append(peak[2*j]) |
|---|
| 1527 | parName = name+str(i) |
|---|
| 1528 | peakNames.append(parName) |
|---|
| 1529 | if peak[2*j+1]: |
|---|
| 1530 | peakVary.append(parName) |
|---|
| 1531 | return dict(zip(peakNames,peakVals)),peakVary |
|---|
| 1532 | |
|---|
| 1533 | def GetPeaksParms(Inst,parmDict,Peaks,varyList): |
|---|
| 1534 | if 'C' in Inst['Type'][0]: |
|---|
| 1535 | names = ['pos','int','sig','gam'] |
|---|
| 1536 | else: #'T' |
|---|
| 1537 | names = ['pos','int','alp','bet','sig','gam'] |
|---|
| 1538 | for i,peak in enumerate(Peaks): |
|---|
| 1539 | pos = parmDict['pos'+str(i)] |
|---|
| 1540 | if 'difC' in Inst: |
|---|
| 1541 | dsp = pos/Inst['difC'][1] |
|---|
| 1542 | for j in range(len(names)): |
|---|
| 1543 | parName = names[j]+str(i) |
|---|
| 1544 | if parName in varyList: |
|---|
| 1545 | peak[2*j] = parmDict[parName] |
|---|
| 1546 | elif 'alpha' in parName: |
|---|
| 1547 | peak[2*j] = parmDict['alpha']/dsp |
|---|
| 1548 | elif 'beta' in parName: |
|---|
| 1549 | peak[2*j] = G2mth.getTOFbeta(parmDict,dsp) |
|---|
| 1550 | elif 'sig' in parName: |
|---|
| 1551 | if 'C' in Inst['Type'][0]: |
|---|
| 1552 | peak[2*j] = G2mth.getCWsig(parmDict,pos) |
|---|
| 1553 | else: |
|---|
| 1554 | peak[2*j] = G2mth.getTOFsig(parmDict,dsp) |
|---|
| 1555 | elif 'gam' in parName: |
|---|
| 1556 | if 'C' in Inst['Type'][0]: |
|---|
| 1557 | peak[2*j] = G2mth.getCWgam(parmDict,pos) |
|---|
| 1558 | else: |
|---|
| 1559 | peak[2*j] = G2mth.getTOFgamma(parmDict,dsp) |
|---|
| 1560 | |
|---|
| 1561 | def PeaksPrint(dataType,parmDict,sigDict,varyList): |
|---|
| 1562 | print 'Peak coefficients:' |
|---|
| 1563 | if 'C' in dataType: |
|---|
| 1564 | names = ['pos','int','sig','gam'] |
|---|
| 1565 | else: #'T' |
|---|
| 1566 | names = ['pos','int','alp','bet','sig','gam'] |
|---|
| 1567 | head = 13*' ' |
|---|
| 1568 | for name in names: |
|---|
| 1569 | if name in ['alp','bet']: |
|---|
| 1570 | head += name.center(8)+'esd'.center(8) |
|---|
| 1571 | else: |
|---|
| 1572 | head += name.center(10)+'esd'.center(10) |
|---|
| 1573 | print head |
|---|
| 1574 | if 'C' in dataType: |
|---|
| 1575 | ptfmt = {'pos':"%10.5f",'int':"%10.1f",'sig':"%10.3f",'gam':"%10.3f"} |
|---|
| 1576 | else: |
|---|
| 1577 | ptfmt = {'pos':"%10.2f",'int':"%10.4f",'alp':"%8.3f",'bet':"%8.5f",'sig':"%10.3f",'gam':"%10.3f"} |
|---|
| 1578 | for i,peak in enumerate(Peaks): |
|---|
| 1579 | ptstr = ':' |
|---|
| 1580 | for j in range(len(names)): |
|---|
| 1581 | name = names[j] |
|---|
| 1582 | parName = name+str(i) |
|---|
| 1583 | ptstr += ptfmt[name] % (parmDict[parName]) |
|---|
| 1584 | if parName in varyList: |
|---|
| 1585 | ptstr += ptfmt[name] % (sigDict[parName]) |
|---|
| 1586 | else: |
|---|
| 1587 | if name in ['alp','bet']: |
|---|
| 1588 | ptstr += 8*' ' |
|---|
| 1589 | else: |
|---|
| 1590 | ptstr += 10*' ' |
|---|
| 1591 | print '%s'%(('Peak'+str(i+1)).center(8)),ptstr |
|---|
| 1592 | |
|---|
| 1593 | def devPeakProfile(values,xdata,ydata, weights,dataType,parmdict,varylist,bakType,dlg): |
|---|
| 1594 | parmdict.update(zip(varylist,values)) |
|---|
| 1595 | return np.sqrt(weights)*getPeakProfileDerv(dataType,parmdict,xdata,varylist,bakType) |
|---|
| 1596 | |
|---|
| 1597 | def errPeakProfile(values,xdata,ydata,weights,dataType,parmdict,varylist,bakType,dlg): |
|---|
| 1598 | parmdict.update(zip(varylist,values)) |
|---|
| 1599 | M = np.sqrt(weights)*(getPeakProfile(dataType,parmdict,xdata,varylist,bakType)-ydata) |
|---|
| 1600 | Rwp = min(100.,np.sqrt(np.sum(M**2)/np.sum(weights*ydata**2))*100.) |
|---|
| 1601 | if dlg: |
|---|
| 1602 | GoOn = dlg.Update(Rwp,newmsg='%s%8.3f%s'%('Peak fit Rwp =',Rwp,'%'))[0] |
|---|
| 1603 | if not GoOn: |
|---|
| 1604 | return -M #abort!! |
|---|
| 1605 | return M |
|---|
| 1606 | |
|---|
| 1607 | if controls: |
|---|
| 1608 | Ftol = controls['min dM/M'] |
|---|
| 1609 | derivType = controls['deriv type'] |
|---|
| 1610 | else: |
|---|
| 1611 | Ftol = 0.0001 |
|---|
| 1612 | derivType = 'analytic' |
|---|
| 1613 | if oneCycle: |
|---|
| 1614 | Ftol = 1.0 |
|---|
| 1615 | x,y,w,yc,yb,yd = data #these are numpy arrays! |
|---|
| 1616 | yc *= 0. #set calcd ones to zero |
|---|
| 1617 | yb *= 0. |
|---|
| 1618 | yd *= 0. |
|---|
| 1619 | xBeg = np.searchsorted(x,Limits[0]) |
|---|
| 1620 | xFin = np.searchsorted(x,Limits[1]) |
|---|
| 1621 | bakType,bakDict,bakVary = SetBackgroundParms(Background) |
|---|
| 1622 | dataType,insDict,insVary = SetInstParms(Inst) |
|---|
| 1623 | peakDict,peakVary = SetPeaksParms(Inst['Type'][0],Peaks) |
|---|
| 1624 | parmDict = {} |
|---|
| 1625 | parmDict.update(bakDict) |
|---|
| 1626 | parmDict.update(insDict) |
|---|
| 1627 | parmDict.update(peakDict) |
|---|
| 1628 | parmDict['Pdabc'] = [] #dummy Pdabc |
|---|
| 1629 | parmDict.update(Inst2) #put in real one if there |
|---|
| 1630 | if prevVaryList: |
|---|
| 1631 | varyList = prevVaryList[:] |
|---|
| 1632 | else: |
|---|
| 1633 | varyList = bakVary+insVary+peakVary |
|---|
| 1634 | fullvaryList = varyList[:] |
|---|
| 1635 | while True: |
|---|
| 1636 | begin = time.time() |
|---|
| 1637 | values = np.array(Dict2Values(parmDict, varyList)) |
|---|
| 1638 | Rvals = {} |
|---|
| 1639 | badVary = [] |
|---|
| 1640 | result = so.leastsq(errPeakProfile,values,Dfun=devPeakProfile,full_output=True,ftol=Ftol,col_deriv=True, |
|---|
| 1641 | args=(x[xBeg:xFin],y[xBeg:xFin],w[xBeg:xFin],dataType,parmDict,varyList,bakType,dlg)) |
|---|
| 1642 | ncyc = int(result[2]['nfev']/2) |
|---|
| 1643 | runtime = time.time()-begin |
|---|
| 1644 | chisq = np.sum(result[2]['fvec']**2) |
|---|
| 1645 | Values2Dict(parmDict, varyList, result[0]) |
|---|
| 1646 | Rvals['Rwp'] = np.sqrt(chisq/np.sum(w[xBeg:xFin]*y[xBeg:xFin]**2))*100. #to % |
|---|
| 1647 | Rvals['GOF'] = chisq/(xFin-xBeg-len(varyList)) #reduced chi^2 |
|---|
| 1648 | print 'Number of function calls:',result[2]['nfev'],' Number of observations: ',xFin-xBeg,' Number of parameters: ',len(varyList) |
|---|
| 1649 | if ncyc: |
|---|
| 1650 | print 'fitpeak time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc) |
|---|
| 1651 | print 'Rwp = %7.2f%%, chi**2 = %12.6g, reduced chi**2 = %6.2f'%(Rvals['Rwp'],chisq,Rvals['GOF']) |
|---|
| 1652 | sig = [0]*len(varyList) |
|---|
| 1653 | if len(varyList) == 0: break # if nothing was refined |
|---|
| 1654 | try: |
|---|
| 1655 | sig = np.sqrt(np.diag(result[1])*Rvals['GOF']) |
|---|
| 1656 | if np.any(np.isnan(sig)): |
|---|
| 1657 | print '*** Least squares aborted - some invalid esds possible ***' |
|---|
| 1658 | break #refinement succeeded - finish up! |
|---|
| 1659 | except ValueError: #result[1] is None on singular matrix |
|---|
| 1660 | print '**** Refinement failed - singular matrix ****' |
|---|
| 1661 | Ipvt = result[2]['ipvt'] |
|---|
| 1662 | for i,ipvt in enumerate(Ipvt): |
|---|
| 1663 | if not np.sum(result[2]['fjac'],axis=1)[i]: |
|---|
| 1664 | print 'Removing parameter: ',varyList[ipvt-1] |
|---|
| 1665 | badVary.append(varyList[ipvt-1]) |
|---|
| 1666 | del(varyList[ipvt-1]) |
|---|
| 1667 | break |
|---|
| 1668 | else: # nothing removed |
|---|
| 1669 | break |
|---|
| 1670 | if dlg: dlg.Destroy() |
|---|
| 1671 | sigDict = dict(zip(varyList,sig)) |
|---|
| 1672 | yb[xBeg:xFin] = getBackground('',parmDict,bakType,dataType,x[xBeg:xFin])[0] |
|---|
| 1673 | yc[xBeg:xFin] = getPeakProfile(dataType,parmDict,x[xBeg:xFin],varyList,bakType) |
|---|
| 1674 | yd[xBeg:xFin] = y[xBeg:xFin]-yc[xBeg:xFin] |
|---|
| 1675 | GetBackgroundParms(parmDict,Background) |
|---|
| 1676 | if bakVary: BackgroundPrint(Background,sigDict) |
|---|
| 1677 | GetInstParms(parmDict,Inst,varyList,Peaks) |
|---|
| 1678 | if insVary: InstPrint(Inst,sigDict) |
|---|
| 1679 | GetPeaksParms(Inst,parmDict,Peaks,varyList) |
|---|
| 1680 | if peakVary: PeaksPrint(dataType,parmDict,sigDict,varyList) |
|---|
| 1681 | return sigDict,result,sig,Rvals,varyList,parmDict,fullvaryList,badVary |
|---|
| 1682 | |
|---|
| 1683 | def calcIncident(Iparm,xdata): |
|---|
| 1684 | 'needs a doc string' |
|---|
| 1685 | |
|---|
| 1686 | def IfunAdv(Iparm,xdata): |
|---|
| 1687 | Itype = Iparm['Itype'] |
|---|
| 1688 | Icoef = Iparm['Icoeff'] |
|---|
| 1689 | DYI = np.ones((12,xdata.shape[0])) |
|---|
| 1690 | YI = np.ones_like(xdata)*Icoef[0] |
|---|
| 1691 | |
|---|
| 1692 | x = xdata/1000. #expressions are in ms |
|---|
| 1693 | if Itype == 'Exponential': |
|---|
| 1694 | for i in [1,3,5,7,9]: |
|---|
| 1695 | Eterm = np.exp(-Icoef[i+1]*x**((i+1)/2)) |
|---|
| 1696 | YI += Icoef[i]*Eterm |
|---|
| 1697 | DYI[i] *= Eterm |
|---|
| 1698 | DYI[i+1] *= -Icoef[i]*Eterm*x**((i+1)/2) |
|---|
| 1699 | elif 'Maxwell'in Itype: |
|---|
| 1700 | Eterm = np.exp(-Icoef[2]/x**2) |
|---|
| 1701 | DYI[1] = Eterm/x**5 |
|---|
| 1702 | DYI[2] = -Icoef[1]*DYI[1]/x**2 |
|---|
| 1703 | YI += (Icoef[1]*Eterm/x**5) |
|---|
| 1704 | if 'Exponential' in Itype: |
|---|
| 1705 | for i in range(3,12,2): |
|---|
| 1706 | Eterm = np.exp(-Icoef[i+1]*x**((i+1)/2)) |
|---|
| 1707 | YI += Icoef[i]*Eterm |
|---|
| 1708 | DYI[i] *= Eterm |
|---|
| 1709 | DYI[i+1] *= -Icoef[i]*Eterm*x**((i+1)/2) |
|---|
| 1710 | else: #Chebyschev |
|---|
| 1711 | T = (2./x)-1. |
|---|
| 1712 | Ccof = np.ones((12,xdata.shape[0])) |
|---|
| 1713 | Ccof[1] = T |
|---|
| 1714 | for i in range(2,12): |
|---|
| 1715 | Ccof[i] = 2*T*Ccof[i-1]-Ccof[i-2] |
|---|
| 1716 | for i in range(1,10): |
|---|
| 1717 | YI += Ccof[i]*Icoef[i+2] |
|---|
| 1718 | DYI[i+2] =Ccof[i] |
|---|
| 1719 | return YI,DYI |
|---|
| 1720 | |
|---|
| 1721 | Iesd = np.array(Iparm['Iesd']) |
|---|
| 1722 | Icovar = Iparm['Icovar'] |
|---|
| 1723 | YI,DYI = IfunAdv(Iparm,xdata) |
|---|
| 1724 | YI = np.where(YI>0,YI,1.) |
|---|
| 1725 | WYI = np.zeros_like(xdata) |
|---|
| 1726 | vcov = np.zeros((12,12)) |
|---|
| 1727 | k = 0 |
|---|
| 1728 | for i in range(12): |
|---|
| 1729 | for j in range(i,12): |
|---|
| 1730 | vcov[i][j] = Icovar[k]*Iesd[i]*Iesd[j] |
|---|
| 1731 | vcov[j][i] = Icovar[k]*Iesd[i]*Iesd[j] |
|---|
| 1732 | k += 1 |
|---|
| 1733 | M = np.inner(vcov,DYI.T) |
|---|
| 1734 | WYI = np.sum(M*DYI,axis=0) |
|---|
| 1735 | WYI = np.where(WYI>0.,WYI,0.) |
|---|
| 1736 | return YI,WYI |
|---|
| 1737 | |
|---|
| 1738 | ################################################################################ |
|---|
| 1739 | # Stacking fault simulation codes |
|---|
| 1740 | ################################################################################ |
|---|
| 1741 | |
|---|
| 1742 | def GetStackParms(Layers): |
|---|
| 1743 | |
|---|
| 1744 | Parms = [] |
|---|
| 1745 | #cell parms |
|---|
| 1746 | cell = Layers['Cell'] |
|---|
| 1747 | if Layers['Laue'] in ['-3','-3m','4/m','4/mmm','6/m','6/mmm']: |
|---|
| 1748 | Parms.append('cellA') |
|---|
| 1749 | Parms.append('cellC') |
|---|
| 1750 | else: |
|---|
| 1751 | Parms.append('cellA') |
|---|
| 1752 | Parms.append('cellB') |
|---|
| 1753 | Parms.append('cellC') |
|---|
| 1754 | if Layers['Laue'] != 'mmm': |
|---|
| 1755 | Parms.append('cellG') |
|---|
| 1756 | #Transition parms |
|---|
| 1757 | Trans = Layers['Transitions'] |
|---|
| 1758 | for iY in range(len(Layers['Layers'])): |
|---|
| 1759 | for iX in range(len(Layers['Layers'])): |
|---|
| 1760 | Parms.append('TransP;%d;%d'%(iY,iX)) |
|---|
| 1761 | Parms.append('TransX;%d;%d'%(iY,iX)) |
|---|
| 1762 | Parms.append('TransY;%d;%d'%(iY,iX)) |
|---|
| 1763 | Parms.append('TransZ;%d;%d'%(iY,iX)) |
|---|
| 1764 | return Parms |
|---|
| 1765 | |
|---|
| 1766 | def StackSim(Layers,ctrls,HistName='',scale=0.,background={},limits=[],inst={},profile=[]): |
|---|
| 1767 | '''Simulate powder or selected area diffraction pattern from stacking faults using DIFFaX |
|---|
| 1768 | |
|---|
| 1769 | param: Layers dict: 'Laue':'-1','Cell':[False,1.,1.,1.,90.,90.,90,1.], |
|---|
| 1770 | 'Width':[[10.,10.],[False,False]],'Toler':0.01,'AtInfo':{}, |
|---|
| 1771 | 'Layers':[],'Stacking':[],'Transitions':[]} |
|---|
| 1772 | param: HistName str: histogram name to simulate 'PWDR...' |
|---|
| 1773 | param: scale float: scale factor |
|---|
| 1774 | param: background dict: background parameters |
|---|
| 1775 | param: limits list: min/max 2-theta to be calculated |
|---|
| 1776 | param: inst dict: instrument parameters dictionary |
|---|
| 1777 | param: profile list: powder pattern data |
|---|
| 1778 | |
|---|
| 1779 | all updated in place |
|---|
| 1780 | ''' |
|---|
| 1781 | import atmdata |
|---|
| 1782 | path = sys.path |
|---|
| 1783 | for name in path: |
|---|
| 1784 | if 'bin' in name: |
|---|
| 1785 | DIFFaX = name+'/DIFFaX.exe' |
|---|
| 1786 | print ' Execute ',DIFFaX |
|---|
| 1787 | break |
|---|
| 1788 | # make form factor file that DIFFaX wants - atom types are GSASII style |
|---|
| 1789 | sf = open('data.sfc','w') |
|---|
| 1790 | sf.write('GSASII special form factor file for DIFFaX\n\n') |
|---|
| 1791 | atTypes = Layers['AtInfo'].keys() |
|---|
| 1792 | if 'H' not in atTypes: |
|---|
| 1793 | atTypes.insert(0,'H') |
|---|
| 1794 | for atType in atTypes: |
|---|
| 1795 | if atType == 'H': |
|---|
| 1796 | blen = -.3741 |
|---|
| 1797 | else: |
|---|
| 1798 | blen = Layers['AtInfo'][atType]['Isotopes']['Nat. Abund.']['SL'][0] |
|---|
| 1799 | Adat = atmdata.XrayFF[atType] |
|---|
| 1800 | text = '%4s'%(atType.ljust(4)) |
|---|
| 1801 | for i in range(4): |
|---|
| 1802 | text += '%11.6f%11.6f'%(Adat['fa'][i],Adat['fb'][i]) |
|---|
| 1803 | text += '%11.6f%11.6f'%(Adat['fc'],blen) |
|---|
| 1804 | text += '%3d\n'%(Adat['Z']) |
|---|
| 1805 | sf.write(text) |
|---|
| 1806 | sf.close() |
|---|
| 1807 | #make DIFFaX control.dif file - future use GUI to set some of these flags |
|---|
| 1808 | cf = open('control.dif','w') |
|---|
| 1809 | if ctrls == '0\n0\n3\n': |
|---|
| 1810 | x0 = profile[0] |
|---|
| 1811 | iBeg = np.searchsorted(x0,limits[0]) |
|---|
| 1812 | iFin = np.searchsorted(x0,limits[1]) |
|---|
| 1813 | if iFin-iBeg > 20000: |
|---|
| 1814 | iFin = iBeg+20000 |
|---|
| 1815 | Dx = (x0[iFin]-x0[iBeg])/(iFin-iBeg) |
|---|
| 1816 | cf.write('GSASII-DIFFaX.dat\n'+ctrls) |
|---|
| 1817 | cf.write('%.6f %.6f %.6f\n1\n1\nend\n'%(x0[iBeg],x0[iFin],Dx)) |
|---|
| 1818 | else: |
|---|
| 1819 | cf.write('GSASII-DIFFaX.dat\n'+ctrls) |
|---|
| 1820 | inst = {'Type':['XSC','XSC',]} |
|---|
| 1821 | cf.close() |
|---|
| 1822 | #make DIFFaX data file |
|---|
| 1823 | df = open('GSASII-DIFFaX.dat','w') |
|---|
| 1824 | df.write('INSTRUMENTAL\n') |
|---|
| 1825 | if 'X' in inst['Type'][0]: |
|---|
| 1826 | df.write('X-RAY\n') |
|---|
| 1827 | elif 'N' in inst['Type'][0]: |
|---|
| 1828 | df.write('NEUTRON\n') |
|---|
| 1829 | if ctrls == '0\n0\n3\n': |
|---|
| 1830 | df.write('%.4f\n'%(G2mth.getMeanWave(inst))) |
|---|
| 1831 | U = forln2*inst['U'][1]/10000. |
|---|
| 1832 | V = forln2*inst['V'][1]/10000. |
|---|
| 1833 | W = forln2*inst['W'][1]/10000. |
|---|
| 1834 | HWHM = U*nptand(x0[iBeg:iFin]/2.)**2+V*nptand(x0[iBeg:iFin]/2.)+W |
|---|
| 1835 | HW = np.mean(HWHM) |
|---|
| 1836 | # df.write('PSEUDO-VOIGT 0.015 -0.0036 0.009 0.605 TRIM\n') |
|---|
| 1837 | # df.write('GAUSSIAN %.6f TRIM\n'%(HW)) #fast option - might not really matter |
|---|
| 1838 | df.write('GAUSSIAN %.6f %.6f %.6f TRIM\n'%(U,V,W)) #slow - make a GUI option? |
|---|
| 1839 | else: |
|---|
| 1840 | df.write('0.10\nNone\n') |
|---|
| 1841 | df.write('STRUCTURAL\n') |
|---|
| 1842 | a,b,c = Layers['Cell'][1:4] |
|---|
| 1843 | gam = Layers['Cell'][6] |
|---|
| 1844 | df.write('%.4f %.4f %.4f %.3f\n'%(a,b,c,gam)) |
|---|
| 1845 | laue = Layers['Laue'] |
|---|
| 1846 | if laue == '2/m(ab)': |
|---|
| 1847 | laue = '2/m(1)' |
|---|
| 1848 | elif laue == '2/m(c)': |
|---|
| 1849 | laue = '2/m(2)' |
|---|
| 1850 | if 'unknown' in Layers['Laue']: |
|---|
| 1851 | df.write('%s %.3f\n'%(laue,Layers['Toler'])) |
|---|
| 1852 | else: |
|---|
| 1853 | df.write('%s\n'%(laue)) |
|---|
| 1854 | df.write('%d\n'%(len(Layers['Layers']))) |
|---|
| 1855 | if Layers['Width'][0][0] < 1. or Layers['Width'][0][1] < 1.: |
|---|
| 1856 | df.write('%.1f %.1f\n'%(Layers['Width'][0][0]*10000.,Layers['Width'][0][0]*10000.)) #mum to A |
|---|
| 1857 | layerNames = [] |
|---|
| 1858 | for layer in Layers['Layers']: |
|---|
| 1859 | layerNames.append(layer['Name']) |
|---|
| 1860 | for il,layer in enumerate(Layers['Layers']): |
|---|
| 1861 | if layer['SameAs']: |
|---|
| 1862 | df.write('LAYER %d = %d\n'%(il+1,layerNames.index(layer['SameAs'])+1)) |
|---|
| 1863 | continue |
|---|
| 1864 | df.write('LAYER %d\n'%(il+1)) |
|---|
| 1865 | if '-1' in layer['Symm']: |
|---|
| 1866 | df.write('CENTROSYMMETRIC\n') |
|---|
| 1867 | else: |
|---|
| 1868 | df.write('NONE\n') |
|---|
| 1869 | for ia,atom in enumerate(layer['Atoms']): |
|---|
| 1870 | [name,atype,x,y,z,frac,Uiso] = atom |
|---|
| 1871 | if '-1' in layer['Symm'] and [x,y,z] == [0.,0.,0.]: |
|---|
| 1872 | frac /= 2. |
|---|
| 1873 | df.write('%4s %3d %.5f %.5f %.5f %.4f %.2f\n'%(atype.ljust(6),ia,x,y,z,78.9568*Uiso,frac)) |
|---|
| 1874 | df.write('STACKING\n') |
|---|
| 1875 | df.write('%s\n'%(Layers['Stacking'][0])) |
|---|
| 1876 | if 'recursive' in Layers['Stacking'][0]: |
|---|
| 1877 | df.write('%s\n'%Layers['Stacking'][1]) |
|---|
| 1878 | else: |
|---|
| 1879 | if 'list' in Layers['Stacking'][1]: |
|---|
| 1880 | Slen = len(Layers['Stacking'][2]) |
|---|
| 1881 | iB = 0 |
|---|
| 1882 | iF = 0 |
|---|
| 1883 | while True: |
|---|
| 1884 | iF += 68 |
|---|
| 1885 | if iF >= Slen: |
|---|
| 1886 | break |
|---|
| 1887 | iF = min(iF,Slen) |
|---|
| 1888 | df.write('%s\n'%(Layers['Stacking'][2][iB:iF])) |
|---|
| 1889 | iB = iF |
|---|
| 1890 | else: |
|---|
| 1891 | df.write('%s\n'%Layers['Stacking'][1]) |
|---|
| 1892 | df.write('TRANSITIONS\n') |
|---|
| 1893 | for iY in range(len(Layers['Layers'])): |
|---|
| 1894 | sumPx = 0. |
|---|
| 1895 | for iX in range(len(Layers['Layers'])): |
|---|
| 1896 | p,dx,dy,dz = Layers['Transitions'][iY][iX][:4] |
|---|
| 1897 | p = round(p,3) |
|---|
| 1898 | df.write('%.3f %.5f %.5f %.5f\n'%(p,dx,dy,dz)) |
|---|
| 1899 | sumPx += p |
|---|
| 1900 | if sumPx != 1.0: #this has to be picky since DIFFaX is. |
|---|
| 1901 | print 'ERROR - Layer probabilities sum to ',sumPx,' DIFFaX will insist it = 1.0' |
|---|
| 1902 | df.close() |
|---|
| 1903 | os.remove('data.sfc') |
|---|
| 1904 | os.remove('control.dif') |
|---|
| 1905 | os.remove('GSASII-DIFFaX.dat') |
|---|
| 1906 | return |
|---|
| 1907 | df.close() |
|---|
| 1908 | time0 = time.time() |
|---|
| 1909 | subp.call(DIFFaX) |
|---|
| 1910 | print 'DIFFaX time = %.2fs'%(time.time()-time0) |
|---|
| 1911 | if os.path.exists('GSASII-DIFFaX.spc'): |
|---|
| 1912 | Xpat = np.loadtxt('GSASII-DIFFaX.spc').T |
|---|
| 1913 | iFin = iBeg+Xpat.shape[1] |
|---|
| 1914 | bakType,backDict,backVary = SetBackgroundParms(background) |
|---|
| 1915 | backDict['Lam1'] = G2mth.getWave(inst) |
|---|
| 1916 | profile[4][iBeg:iFin] = getBackground('',backDict,bakType,inst['Type'][0],profile[0][iBeg:iFin])[0] |
|---|
| 1917 | profile[3][iBeg:iFin] = Xpat[2]*scale+profile[4][iBeg:iFin] |
|---|
| 1918 | if not np.any(profile[1]): #fill dummy data x,y,w,yc,yb,yd |
|---|
| 1919 | rv = st.poisson(profile[3][iBeg:iFin]) |
|---|
| 1920 | profile[1][iBeg:iFin] = rv.rvs() |
|---|
| 1921 | Z = np.ones_like(profile[3][iBeg:iFin]) |
|---|
| 1922 | Z[1::2] *= -1 |
|---|
| 1923 | profile[1][iBeg:iFin] = profile[3][iBeg:iFin]+np.abs(profile[1][iBeg:iFin]-profile[3][iBeg:iFin])*Z |
|---|
| 1924 | profile[2][iBeg:iFin] = np.where(profile[1][iBeg:iFin]>0.,1./profile[1][iBeg:iFin],1.0) |
|---|
| 1925 | profile[5][iBeg:iFin] = profile[1][iBeg:iFin]-profile[3][iBeg:iFin] |
|---|
| 1926 | #cleanup files.. |
|---|
| 1927 | os.remove('GSASII-DIFFaX.spc') |
|---|
| 1928 | elif os.path.exists('GSASII-DIFFaX.sadp'): |
|---|
| 1929 | Sadp = np.fromfile('GSASII-DIFFaX.sadp','>u2') |
|---|
| 1930 | Sadp = np.reshape(Sadp,(256,-1)) |
|---|
| 1931 | Layers['Sadp']['Img'] = Sadp |
|---|
| 1932 | os.remove('GSASII-DIFFaX.sadp') |
|---|
| 1933 | os.remove('data.sfc') |
|---|
| 1934 | os.remove('control.dif') |
|---|
| 1935 | os.remove('GSASII-DIFFaX.dat') |
|---|
| 1936 | |
|---|
| 1937 | def CalcStackingSADP(Layers): |
|---|
| 1938 | |
|---|
| 1939 | rand.seed() |
|---|
| 1940 | ranSeed = rand.randint(1,2**16-1) |
|---|
| 1941 | # Scattering factors |
|---|
| 1942 | import atmdata |
|---|
| 1943 | atTypes = Layers['AtInfo'].keys() |
|---|
| 1944 | aTypes = [] |
|---|
| 1945 | for atype in atTypes: |
|---|
| 1946 | aTypes.append('%4s'%(atype.ljust(4))) |
|---|
| 1947 | SFdat = [] |
|---|
| 1948 | for atType in atTypes: |
|---|
| 1949 | if atType == 'H': |
|---|
| 1950 | blen = -.3741 |
|---|
| 1951 | else: |
|---|
| 1952 | blen = Layers['AtInfo'][atType]['Isotopes']['Nat. Abund.']['SL'][0] |
|---|
| 1953 | Adat = atmdata.XrayFF[atType] |
|---|
| 1954 | SF = np.zeros(9) |
|---|
| 1955 | SF[:8:2] = Adat['fa'] |
|---|
| 1956 | SF[1:8:2] = Adat['fb'] |
|---|
| 1957 | SF[8] = Adat['fc'] |
|---|
| 1958 | SFdat.append(SF) |
|---|
| 1959 | SFdat = np.array(SFdat) |
|---|
| 1960 | pyx.pyloadscf(len(atTypes),aTypes,SFdat.T) |
|---|
| 1961 | # Controls |
|---|
| 1962 | try: |
|---|
| 1963 | laueId = ['-1','2/m(ab)','2/m(c)','mmm','-3','-3m','4/m','4/mmm', |
|---|
| 1964 | '6/m','6/mmm'].index(Layers['Laue'])+1 |
|---|
| 1965 | except ValueError: |
|---|
| 1966 | laueId = -1 |
|---|
| 1967 | planeId = ['h0l','0kl','hhl','h-hl'].index(Layers['Sadp']['Plane'])+1 |
|---|
| 1968 | lmax = int(Layers['Sadp']['Lmax']) |
|---|
| 1969 | mult = int(Layers['Sadp']['Mult']) |
|---|
| 1970 | # Sequences |
|---|
| 1971 | StkType = ['recursive','explicit'].index(Layers['Stacking'][0]) |
|---|
| 1972 | try: |
|---|
| 1973 | StkParm = ['infinite','random','list'].index(Layers['Stacking'][1]) |
|---|
| 1974 | except ValueError: |
|---|
| 1975 | StkParm = -1 |
|---|
| 1976 | if StkParm == 2: #list |
|---|
| 1977 | StkSeq = [int(val) for val in Layers['Stacking'][2].split()] |
|---|
| 1978 | Nstk = len(StkSeq) |
|---|
| 1979 | else: |
|---|
| 1980 | Nstk = 1 |
|---|
| 1981 | StkSeq = [0,] |
|---|
| 1982 | if StkParm == -1: |
|---|
| 1983 | StkParm = int(Layers['Stacking'][1]) |
|---|
| 1984 | Wdth = Layers['Width'][0] |
|---|
| 1985 | controls = [laueId,planeId,lmax,mult,StkType,StkParm,ranSeed] |
|---|
| 1986 | LaueSym = Layers['Laue'].ljust(12) |
|---|
| 1987 | pyx.pygetclay(controls,LaueSym,Wdth,Nstk,StkSeq) |
|---|
| 1988 | |
|---|
| 1989 | Cell = Layers['Cell'][1:4]+Layers['Cell'][6:7] |
|---|
| 1990 | # atoms in layers |
|---|
| 1991 | AtomXOU = [] |
|---|
| 1992 | AtomTp = [] |
|---|
| 1993 | LayerSymm = [] |
|---|
| 1994 | LayerNum = [] |
|---|
| 1995 | layerNames = [] |
|---|
| 1996 | Natm = 0 |
|---|
| 1997 | Nuniq = 0 |
|---|
| 1998 | for layer in Layers['Layers']: |
|---|
| 1999 | layerNames.append(layer['Name']) |
|---|
| 2000 | for il,layer in enumerate(Layers['Layers']): |
|---|
| 2001 | if layer['SameAs']: |
|---|
| 2002 | LayerNum.append(layerNames.index(layer['SameAs'])+1) |
|---|
| 2003 | continue |
|---|
| 2004 | else: |
|---|
| 2005 | LayerNum.append(il+1) |
|---|
| 2006 | Nuniq += 1 |
|---|
| 2007 | if '-1' in layer['Symm']: |
|---|
| 2008 | LayerSymm.append(1) |
|---|
| 2009 | else: |
|---|
| 2010 | LayerSymm.append(0) |
|---|
| 2011 | for ia,atom in enumerate(layer['Atoms']): |
|---|
| 2012 | [name,atype,x,y,z,frac,Uiso] = atom |
|---|
| 2013 | Natm += 1 |
|---|
| 2014 | AtomTp.append('%4s'%(atype.ljust(4))) |
|---|
| 2015 | Ta = atTypes.index(atype)+1 |
|---|
| 2016 | AtomXOU.append([float(Nuniq),float(ia+1),float(Ta),x,y,z,frac,Uiso*78.9568]) |
|---|
| 2017 | AtomXOU = np.array(AtomXOU) |
|---|
| 2018 | Nlayers = len(layerNames) |
|---|
| 2019 | pyx.pycellayer(Cell,Natm,AtomTp,AtomXOU.T,Nuniq,LayerSymm,Nlayers,LayerNum) |
|---|
| 2020 | # Transitions |
|---|
| 2021 | TransX = [] |
|---|
| 2022 | TransP = [] |
|---|
| 2023 | for Ytrans in Layers['Transitions']: |
|---|
| 2024 | TransP.append([trans[0] for trans in Ytrans]) #get just the numbers |
|---|
| 2025 | TransX.append([trans[1:4] for trans in Ytrans]) #get just the numbers |
|---|
| 2026 | TransP = np.array(TransP,dtype='float') |
|---|
| 2027 | TransX = np.array(TransX,dtype='float') |
|---|
| 2028 | pyx.pygettrans(Nlayers,TransP,TransX) |
|---|
| 2029 | # result as Sadp |
|---|
| 2030 | mirror = laueId in [2,3,4,7,8,9,10] |
|---|
| 2031 | Nspec = 20001 |
|---|
| 2032 | spec = np.zeros(Nspec,dtype='double') |
|---|
| 2033 | time0 = time.time() |
|---|
| 2034 | hkLim,Incr = pyx.pygetsadp(controls,Nspec,spec) |
|---|
| 2035 | # GSASIIpath.IPyBreak() |
|---|
| 2036 | Sapd = np.zeros((256,256)) |
|---|
| 2037 | maxInt = np.max(spec[1:]) |
|---|
| 2038 | Scale = mult*32767./maxInt |
|---|
| 2039 | iB = 0 |
|---|
| 2040 | for i in range(hkLim): |
|---|
| 2041 | iF = iB+128 |
|---|
| 2042 | p1 = 128+int(i*Incr) |
|---|
| 2043 | Sapd[:128,p1] = spec[iB:iF] |
|---|
| 2044 | Sapd[128:,p1] = spec[iF:iB:-1] |
|---|
| 2045 | if mirror: |
|---|
| 2046 | p2 = 128-int(i*Incr) |
|---|
| 2047 | Sapd[:128,p2] = spec[iB:iF] |
|---|
| 2048 | Sapd[128:,p2] = spec[iF:iB:-1] |
|---|
| 2049 | iB += 128 |
|---|
| 2050 | Sapd *= Scale |
|---|
| 2051 | Sapd = np.where(Sapd<32767.,Sapd,32767.) |
|---|
| 2052 | Layers['Sadp']['Img'] = Sapd |
|---|
| 2053 | print 'GETSAD time = %.2fs'%(time.time()-time0) |
|---|
| 2054 | |
|---|
| 2055 | #testing data |
|---|
| 2056 | NeedTestData = True |
|---|
| 2057 | def TestData(): |
|---|
| 2058 | 'needs a doc string' |
|---|
| 2059 | # global NeedTestData |
|---|
| 2060 | NeedTestData = False |
|---|
| 2061 | global bakType |
|---|
| 2062 | bakType = 'chebyschev' |
|---|
| 2063 | global xdata |
|---|
| 2064 | xdata = np.linspace(4.0,40.0,36000) |
|---|
| 2065 | global parmDict0 |
|---|
| 2066 | parmDict0 = { |
|---|
| 2067 | 'pos0':5.6964,'int0':8835.8,'sig0':1.0,'gam0':1.0, |
|---|
| 2068 | 'pos1':11.4074,'int1':3922.3,'sig1':1.0,'gam1':1.0, |
|---|
| 2069 | 'pos2':20.6426,'int2':1573.7,'sig2':1.0,'gam2':1.0, |
|---|
| 2070 | 'pos3':26.9568,'int3':925.1,'sig3':1.0,'gam3':1.0, |
|---|
| 2071 | 'U':1.163,'V':-0.605,'W':0.093,'X':0.0,'Y':2.183,'SH/L':0.002, |
|---|
| 2072 | 'Back0':5.384,'Back1':-0.015,'Back2':.004, |
|---|
| 2073 | } |
|---|
| 2074 | global parmDict1 |
|---|
| 2075 | parmDict1 = { |
|---|
| 2076 | 'pos0':13.4924,'int0':48697.6,'sig0':1.0,'gam0':1.0, |
|---|
| 2077 | 'pos1':23.4360,'int1':43685.5,'sig1':1.0,'gam1':1.0, |
|---|
| 2078 | 'pos2':27.1152,'int2':123712.6,'sig2':1.0,'gam2':1.0, |
|---|
| 2079 | 'pos3':33.7196,'int3':65349.4,'sig3':1.0,'gam3':1.0, |
|---|
| 2080 | 'pos4':36.1119,'int4':115829.8,'sig4':1.0,'gam4':1.0, |
|---|
| 2081 | 'pos5':39.0122,'int5':6916.9,'sig5':1.0,'gam5':1.0, |
|---|
| 2082 | 'U':22.75,'V':-17.596,'W':10.594,'X':1.577,'Y':5.778,'SH/L':0.002, |
|---|
| 2083 | 'Back0':36.897,'Back1':-0.508,'Back2':.006, |
|---|
| 2084 | 'Lam1':1.540500,'Lam2':1.544300,'I(L2)/I(L1)':0.5, |
|---|
| 2085 | } |
|---|
| 2086 | global parmDict2 |
|---|
| 2087 | parmDict2 = { |
|---|
| 2088 | 'pos0':5.7,'int0':1000.0,'sig0':0.5,'gam0':0.5, |
|---|
| 2089 | 'U':2.,'V':-2.,'W':5.,'X':0.5,'Y':0.5,'SH/L':0.02, |
|---|
| 2090 | 'Back0':5.,'Back1':-0.02,'Back2':.004, |
|---|
| 2091 | # 'Lam1':1.540500,'Lam2':1.544300,'I(L2)/I(L1)':0.5, |
|---|
| 2092 | } |
|---|
| 2093 | global varyList |
|---|
| 2094 | varyList = [] |
|---|
| 2095 | |
|---|
| 2096 | def test0(): |
|---|
| 2097 | if NeedTestData: TestData() |
|---|
| 2098 | msg = 'test ' |
|---|
| 2099 | gplot = plotter.add('FCJ-Voigt, 11BM').gca() |
|---|
| 2100 | gplot.plot(xdata,getBackground('',parmDict0,bakType,'PXC',xdata)[0]) |
|---|
| 2101 | gplot.plot(xdata,getPeakProfile(parmDict0,xdata,varyList,bakType)) |
|---|
| 2102 | fplot = plotter.add('FCJ-Voigt, Ka1+2').gca() |
|---|
| 2103 | fplot.plot(xdata,getBackground('',parmDict1,bakType,'PXC',xdata)[0]) |
|---|
| 2104 | fplot.plot(xdata,getPeakProfile(parmDict1,xdata,varyList,bakType)) |
|---|
| 2105 | |
|---|
| 2106 | def test1(): |
|---|
| 2107 | if NeedTestData: TestData() |
|---|
| 2108 | time0 = time.time() |
|---|
| 2109 | for i in range(100): |
|---|
| 2110 | y = getPeakProfile(parmDict1,xdata,varyList,bakType) |
|---|
| 2111 | print '100+6*Ka1-2 peaks=1200 peaks',time.time()-time0 |
|---|
| 2112 | |
|---|
| 2113 | def test2(name,delt): |
|---|
| 2114 | if NeedTestData: TestData() |
|---|
| 2115 | varyList = [name,] |
|---|
| 2116 | xdata = np.linspace(5.6,5.8,400) |
|---|
| 2117 | hplot = plotter.add('derivatives test for '+name).gca() |
|---|
| 2118 | hplot.plot(xdata,getPeakProfileDerv(parmDict2,xdata,varyList,bakType)[0]) |
|---|
| 2119 | y0 = getPeakProfile(parmDict2,xdata,varyList,bakType) |
|---|
| 2120 | parmDict2[name] += delt |
|---|
| 2121 | y1 = getPeakProfile(parmDict2,xdata,varyList,bakType) |
|---|
| 2122 | hplot.plot(xdata,(y1-y0)/delt,'r+') |
|---|
| 2123 | |
|---|
| 2124 | def test3(name,delt): |
|---|
| 2125 | if NeedTestData: TestData() |
|---|
| 2126 | names = ['pos','sig','gam','shl'] |
|---|
| 2127 | idx = names.index(name) |
|---|
| 2128 | myDict = {'pos':parmDict2['pos0'],'sig':parmDict2['sig0'],'gam':parmDict2['gam0'],'shl':parmDict2['SH/L']} |
|---|
| 2129 | xdata = np.linspace(5.6,5.8,800) |
|---|
| 2130 | dx = xdata[1]-xdata[0] |
|---|
| 2131 | hplot = plotter.add('derivatives test for '+name).gca() |
|---|
| 2132 | hplot.plot(xdata,100.*dx*getdFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata)[idx+1]) |
|---|
| 2133 | y0 = getFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata) |
|---|
| 2134 | myDict[name] += delt |
|---|
| 2135 | y1 = getFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata) |
|---|
| 2136 | hplot.plot(xdata,(y1-y0)/delt,'r+') |
|---|
| 2137 | |
|---|
| 2138 | if __name__ == '__main__': |
|---|
| 2139 | import GSASIItestplot as plot |
|---|
| 2140 | global plotter |
|---|
| 2141 | plotter = plot.PlotNotebook() |
|---|
| 2142 | # test0() |
|---|
| 2143 | # for name in ['int0','pos0','sig0','gam0','U','V','W','X','Y','SH/L','I(L2)/I(L1)']: |
|---|
| 2144 | for name,shft in [['int0',0.1],['pos0',0.0001],['sig0',0.01],['gam0',0.00001], |
|---|
| 2145 | ['U',0.1],['V',0.01],['W',0.01],['X',0.0001],['Y',0.0001],['SH/L',0.00005]]: |
|---|
| 2146 | test2(name,shft) |
|---|
| 2147 | for name,shft in [['pos',0.0001],['sig',0.01],['gam',0.0001],['shl',0.00005]]: |
|---|
| 2148 | test3(name,shft) |
|---|
| 2149 | print "OK" |
|---|
| 2150 | plotter.StartEventLoop() |
|---|
