| 1 | #!/usr/bin/env python |
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| 2 | """ |
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| 3 | Application to explore the difference between sasview 3.x orientation |
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| 4 | dispersity and possible replacement algorithms. |
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| 5 | """ |
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| 6 | from __future__ import division, print_function |
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| 7 | |
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| 8 | import sys, os |
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| 9 | sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.realpath(__file__)))) |
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| 10 | |
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| 11 | import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot |
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| 12 | import matplotlib.pyplot as plt |
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| 13 | from matplotlib.widgets import Slider, CheckButtons |
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| 14 | from matplotlib import cm |
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| 15 | import numpy as np |
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| 16 | from numpy import pi, cos, sin, sqrt, exp, degrees, radians |
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| 17 | |
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| 18 | def draw_beam(ax, view=(0, 0)): |
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| 19 | """ |
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| 20 | Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1) |
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| 21 | """ |
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| 22 | #ax.plot([0,0],[0,0],[1,-1]) |
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| 23 | #ax.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=0.8) |
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| 24 | |
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| 25 | steps = 25 |
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| 26 | u = np.linspace(0, 2 * np.pi, steps) |
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| 27 | v = np.linspace(-1, 1, steps) |
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| 28 | |
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| 29 | r = 0.02 |
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| 30 | x = r*np.outer(np.cos(u), np.ones_like(v)) |
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| 31 | y = r*np.outer(np.sin(u), np.ones_like(v)) |
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| 32 | z = 1.3*np.outer(np.ones_like(u), v) |
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| 33 | |
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| 34 | theta, phi = view |
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| 35 | shape = x.shape |
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| 36 | points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) |
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| 37 | points = Rz(phi)*Ry(theta)*points |
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| 38 | x, y, z = [v.reshape(shape) for v in points] |
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| 39 | |
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| 40 | ax.plot_surface(x, y, z, rstride=4, cstride=4, color='y', alpha=0.5) |
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| 41 | |
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| 42 | def draw_jitter(ax, view, jitter, dist='gaussian', size=(0.1, 0.4, 1.0)): |
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| 43 | """ |
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| 44 | Represent jitter as a set of shapes at different orientations. |
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| 45 | """ |
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| 46 | # set max diagonal to 0.95 |
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| 47 | scale = 0.95/sqrt(sum(v**2 for v in size)) |
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| 48 | size = tuple(scale*v for v in size) |
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| 49 | draw_shape = draw_parallelepiped |
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| 50 | #draw_shape = draw_ellipsoid |
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| 51 | |
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| 52 | #np.random.seed(10) |
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| 53 | #cloud = np.random.randn(10,3) |
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| 54 | cloud = [ |
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| 55 | [-1, -1, -1], |
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| 56 | [-1, -1, 0], |
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| 57 | [-1, -1, 1], |
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| 58 | [-1, 0, -1], |
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| 59 | [-1, 0, 0], |
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| 60 | [-1, 0, 1], |
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| 61 | [-1, 1, -1], |
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| 62 | [-1, 1, 0], |
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| 63 | [-1, 1, 1], |
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| 64 | [ 0, -1, -1], |
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| 65 | [ 0, -1, 0], |
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| 66 | [ 0, -1, 1], |
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| 67 | [ 0, 0, -1], |
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| 68 | [ 0, 0, 0], |
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| 69 | [ 0, 0, 1], |
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| 70 | [ 0, 1, -1], |
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| 71 | [ 0, 1, 0], |
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| 72 | [ 0, 1, 1], |
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| 73 | [ 1, -1, -1], |
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| 74 | [ 1, -1, 0], |
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| 75 | [ 1, -1, 1], |
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| 76 | [ 1, 0, -1], |
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| 77 | [ 1, 0, 0], |
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| 78 | [ 1, 0, 1], |
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| 79 | [ 1, 1, -1], |
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| 80 | [ 1, 1, 0], |
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| 81 | [ 1, 1, 1], |
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| 82 | ] |
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| 83 | dtheta, dphi, dpsi = jitter |
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| 84 | if dtheta == 0: |
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| 85 | cloud = [v for v in cloud if v[0] == 0] |
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| 86 | if dphi == 0: |
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| 87 | cloud = [v for v in cloud if v[1] == 0] |
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| 88 | if dpsi == 0: |
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| 89 | cloud = [v for v in cloud if v[2] == 0] |
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| 90 | draw_shape(ax, size, view, [0, 0, 0], steps=100, alpha=0.8) |
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| 91 | scale = 1/sqrt(3) if dist == 'rectangle' else 1 |
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| 92 | for point in cloud: |
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| 93 | delta = [scale*dtheta*point[0], scale*dphi*point[1], scale*dpsi*point[2]] |
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| 94 | draw_shape(ax, size, view, delta, alpha=0.8) |
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| 95 | for v in 'xyz': |
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| 96 | a, b, c = size |
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| 97 | lim = np.sqrt(a**2+b**2+c**2) |
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| 98 | getattr(ax, 'set_'+v+'lim')([-lim, lim]) |
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| 99 | getattr(ax, v+'axis').label.set_text(v) |
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| 100 | |
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| 101 | def draw_ellipsoid(ax, size, view, jitter, steps=25, alpha=1): |
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| 102 | """Draw an ellipsoid.""" |
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| 103 | a,b,c = size |
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| 104 | u = np.linspace(0, 2 * np.pi, steps) |
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| 105 | v = np.linspace(0, np.pi, steps) |
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| 106 | x = a*np.outer(np.cos(u), np.sin(v)) |
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| 107 | y = b*np.outer(np.sin(u), np.sin(v)) |
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| 108 | z = c*np.outer(np.ones_like(u), np.cos(v)) |
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| 109 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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| 110 | |
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| 111 | ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w', alpha=alpha) |
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| 112 | |
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| 113 | draw_labels(ax, view, jitter, [ |
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| 114 | ('c+', [ 0, 0, c], [ 1, 0, 0]), |
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| 115 | ('c-', [ 0, 0,-c], [ 0, 0,-1]), |
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| 116 | ('a+', [ a, 0, 0], [ 0, 0, 1]), |
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| 117 | ('a-', [-a, 0, 0], [ 0, 0,-1]), |
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| 118 | ('b+', [ 0, b, 0], [-1, 0, 0]), |
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| 119 | ('b-', [ 0,-b, 0], [-1, 0, 0]), |
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| 120 | ]) |
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| 121 | |
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| 122 | def draw_parallelepiped(ax, size, view, jitter, steps=None, alpha=1): |
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| 123 | """Draw a parallelepiped.""" |
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| 124 | a,b,c = size |
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| 125 | x = a*np.array([ 1,-1, 1,-1, 1,-1, 1,-1]) |
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| 126 | y = b*np.array([ 1, 1,-1,-1, 1, 1,-1,-1]) |
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| 127 | z = c*np.array([ 1, 1, 1, 1,-1,-1,-1,-1]) |
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| 128 | tri = np.array([ |
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| 129 | # counter clockwise triangles |
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| 130 | # z: up/down, x: right/left, y: front/back |
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| 131 | [0,1,2], [3,2,1], # top face |
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| 132 | [6,5,4], [5,6,7], # bottom face |
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| 133 | [0,2,6], [6,4,0], # right face |
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| 134 | [1,5,7], [7,3,1], # left face |
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| 135 | [2,3,6], [7,6,3], # front face |
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| 136 | [4,1,0], [5,1,4], # back face |
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| 137 | ]) |
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| 138 | |
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| 139 | x, y, z = transform_xyz(view, jitter, x, y, z) |
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| 140 | ax.plot_trisurf(x, y, triangles=tri, Z=z, color='w', alpha=alpha) |
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| 141 | |
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| 142 | draw_labels(ax, view, jitter, [ |
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| 143 | ('c+', [ 0, 0, c], [ 1, 0, 0]), |
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| 144 | ('c-', [ 0, 0,-c], [ 0, 0,-1]), |
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| 145 | ('a+', [ a, 0, 0], [ 0, 0, 1]), |
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| 146 | ('a-', [-a, 0, 0], [ 0, 0,-1]), |
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| 147 | ('b+', [ 0, b, 0], [-1, 0, 0]), |
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| 148 | ('b-', [ 0,-b, 0], [-1, 0, 0]), |
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| 149 | ]) |
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| 150 | |
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| 151 | def draw_sphere(ax, radius=10., steps=100): |
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| 152 | """Draw a sphere""" |
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| 153 | u = np.linspace(0, 2 * np.pi, steps) |
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| 154 | v = np.linspace(0, np.pi, steps) |
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| 155 | |
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| 156 | x = radius * np.outer(np.cos(u), np.sin(v)) |
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| 157 | y = radius * np.outer(np.sin(u), np.sin(v)) |
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| 158 | z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) |
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| 159 | ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w') |
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| 160 | |
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| 161 | def draw_mesh(ax, view, jitter, radius=1.2, n=11, dist='gaussian'): |
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| 162 | """ |
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| 163 | Draw the dispersion mesh showing the theta-phi orientations at which |
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| 164 | the model will be evaluated. |
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| 165 | """ |
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| 166 | theta, phi, psi = view |
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| 167 | dtheta, dphi, dpsi = jitter |
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| 168 | |
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| 169 | if dist == 'gaussian': |
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| 170 | t = np.linspace(-3, 3, n) |
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| 171 | weights = exp(-0.5*t**2) |
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| 172 | elif dist == 'rectangle': |
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| 173 | # Note: uses sasmodels ridiculous definition of rectangle width |
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| 174 | t = np.linspace(-1, 1, n)*sqrt(3) |
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| 175 | weights = np.ones_like(t) |
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| 176 | else: |
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| 177 | raise ValueError("expected dist to be 'gaussian' or 'rectangle'") |
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| 178 | |
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| 179 | #PROJECTION = 'stretched_phi' |
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| 180 | PROJECTION = 'azimuthal_equidistance' |
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| 181 | #PROJECTION = 'azimuthal_equal_area' |
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| 182 | if PROJECTION == 'stretced_phi': |
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| 183 | def rotate(theta_i, phi_j): |
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| 184 | if theta_i != 90: |
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| 185 | phi_j /= cos(radians(theta_i)) |
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| 186 | return Rx(phi_j)*Ry(theta_i) |
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| 187 | def weight(theta_i, phi_j, wi, wj): |
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| 188 | if theta_i != 90: |
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| 189 | phi_j /= cos(radians(theta_i)) |
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| 190 | return wi*wj if abs(phi_j) < 180 else 0 |
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| 191 | elif PROJECTION == 'azimuthal_equidistance': |
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| 192 | # https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection |
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| 193 | def rotate(theta_i, phi_j): |
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| 194 | latitude = sqrt(theta_i**2 + phi_j**2) |
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| 195 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
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| 196 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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| 197 | return Rz(longitude)*Ry(latitude) |
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| 198 | def weight(theta_i, phi_j, wi, wj): |
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| 199 | # Weighting for each point comes from the integral: |
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| 200 | # \int\int I(q, lat, log) sin(lat) dlat dlog |
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| 201 | # We are doing a conformal mapping from disk to sphere, so we need |
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| 202 | # a change of variables g(theta, phi) -> (lat, long): |
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| 203 | # lat, long = sqrt(theta^2 + phi^2), arctan(phi/theta) |
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| 204 | # giving: |
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| 205 | # dtheta dphi = det(J) dlat dlong |
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| 206 | # where J is the jacobian from the partials of g. Using |
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| 207 | # R = sqrt(theta^2 + phi^2), |
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| 208 | # then |
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| 209 | # J = [[x/R, Y/R], -y/R^2, x/R^2]] |
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| 210 | # and |
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| 211 | # det(J) = 1/R |
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| 212 | # with the final integral being: |
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| 213 | # \int\int I(q, theta, phi) sin(R)/R dtheta dphi |
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| 214 | # |
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| 215 | # This does approximately the right thing, decreasing the weight |
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| 216 | # of each point as you go farther out on the disk, but it hasn't |
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| 217 | # yet been checked against the 1D integral results. Prior |
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| 218 | # to declaring this "good enough" and checking that integrals |
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| 219 | # work in practice, we will examine alternative mappings. |
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| 220 | # |
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| 221 | # The issue is that the mapping does not support the case of free |
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| 222 | # rotation about a single axis correctly, with a small deviation |
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| 223 | # in the orthogonal axis independent of the first axis. Like the |
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| 224 | # usual polar coordiates integration, the integrated sections |
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| 225 | # form wedges, though at least in this case the wedge cuts through |
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| 226 | # the entire sphere, and treats theta and phi identically. |
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| 227 | latitude = sqrt(theta_i**2 + phi_j**2) |
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| 228 | w = sin(radians(latitude))/latitude if latitude != 0 else 1 |
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| 229 | return w*wi*wj if latitude < 180 else 0 |
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| 230 | elif PROJECTION == 'azimuthal_equal_area': |
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| 231 | # https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection |
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| 232 | def rotate(theta_i, phi_j): |
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| 233 | R = min(1, sqrt(theta_i**2 + phi_j**2)/180) |
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| 234 | latitude = 180-degrees(2*np.arccos(R)) |
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| 235 | longitude = degrees(np.arctan2(phi_j, theta_i)) |
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| 236 | #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) |
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| 237 | return Rz(longitude)*Ry(latitude) |
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| 238 | def weight(theta_i, phi_j, wi, wj): |
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| 239 | latitude = sqrt(theta_i**2 + phi_j**2) |
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| 240 | w = sin(radians(latitude))/latitude if latitude != 0 else 1 |
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| 241 | return w*wi*wj if latitude < 180 else 0 |
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| 242 | elif SCALED_PHI == 10: # random thrashing |
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| 243 | def rotate(theta_i, phi_j): |
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| 244 | theta_i, phi_j = 2*theta_i/abs(cos(radians(phi_j))), 2*phi_j/cos(radians(theta_i)) |
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| 245 | return Rx(phi_j)*Ry(theta_i) |
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| 246 | def weight(theta_i, phi_j, wi, wj): |
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| 247 | theta_i, phi_j = 2*theta_i/abs(cos(radians(phi_j))), 2*phi_j/cos(radians(theta_i)) |
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| 248 | return wi*wj if abs(phi_j) < 180 else 0 |
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| 249 | else: |
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| 250 | def rotate(theta_i, phi_j): |
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| 251 | return Rx(phi_j)*Ry(theta_i) |
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| 252 | def weight(theta_i, phi_j, wi, wj): |
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| 253 | return wi*wj*cos(radians(theta_i)) |
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| 254 | |
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| 255 | # mesh in theta, phi formed by rotating z |
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| 256 | z = np.matrix([[0], [0], [radius]]) |
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| 257 | points = np.hstack([rotate(theta_i, phi_j)*z |
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| 258 | for theta_i in dtheta*t |
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| 259 | for phi_j in dphi*t]) |
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| 260 | # select just the active points (i.e., those with phi < 180 |
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| 261 | w = np.array([weight(theta_i, phi_j, wi, wj) |
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| 262 | for wi, theta_i in zip(weights, dtheta*t) |
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| 263 | for wj, phi_j in zip(weights, dphi*t)]) |
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| 264 | #print(max(w), min(w), min(w[w>0])) |
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| 265 | points = points[:, w>0] |
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| 266 | w = w[w>0] |
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| 267 | w /= max(w) |
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| 268 | |
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| 269 | if 0: # Kent distribution |
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| 270 | points = np.hstack([Rx(phi_j)*Ry(theta_i)*z for theta_i in 30*t for phi_j in 60*t]) |
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| 271 | xp, yp, zp = [np.array(v).flatten() for v in points] |
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| 272 | kappa = max(1e6, radians(dtheta)/(2*pi)) |
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| 273 | beta = 1/max(1e-6, radians(dphi)/(2*pi))/kappa |
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| 274 | w = exp(kappa*zp) #+ beta*(xp**2 + yp**2) |
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| 275 | print(kappa, dtheta, radians(dtheta), min(w), max(w), sum(w)) |
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| 276 | #w /= abs(cos(radians( |
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| 277 | #w /= sum(w) |
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| 278 | |
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| 279 | # rotate relative to beam |
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| 280 | points = orient_relative_to_beam(view, points) |
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| 281 | |
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| 282 | x, y, z = [np.array(v).flatten() for v in points] |
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| 283 | #plt.figure(2); plt.clf(); plt.hist(z, bins=np.linspace(-1, 1, 51)) |
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| 284 | ax.scatter(x, y, z, c=w, marker='o', vmin=0., vmax=1.) |
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| 285 | |
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| 286 | def draw_labels(ax, view, jitter, text): |
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| 287 | """ |
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| 288 | Draw text at a particular location. |
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| 289 | """ |
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| 290 | labels, locations, orientations = zip(*text) |
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| 291 | px, py, pz = zip(*locations) |
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| 292 | dx, dy, dz = zip(*orientations) |
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| 293 | |
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| 294 | px, py, pz = transform_xyz(view, jitter, px, py, pz) |
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| 295 | dx, dy, dz = transform_xyz(view, jitter, dx, dy, dz) |
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| 296 | |
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| 297 | # TODO: zdir for labels is broken, and labels aren't appearing. |
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| 298 | for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)): |
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| 299 | zdir = np.asarray(zdir).flatten() |
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| 300 | ax.text(p[0], p[1], p[2], label, zdir=zdir) |
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| 301 | |
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| 302 | # Definition of rotation matrices comes from wikipedia: |
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| 303 | # https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations |
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| 304 | def Rx(angle): |
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| 305 | """Construct a matrix to rotate points about *x* by *angle* degrees.""" |
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| 306 | a = radians(angle) |
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| 307 | R = [[1, 0, 0], |
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| 308 | [0, +cos(a), -sin(a)], |
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| 309 | [0, +sin(a), +cos(a)]] |
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| 310 | return np.matrix(R) |
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| 311 | |
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| 312 | def Ry(angle): |
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| 313 | """Construct a matrix to rotate points about *y* by *angle* degrees.""" |
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| 314 | a = radians(angle) |
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| 315 | R = [[+cos(a), 0, +sin(a)], |
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| 316 | [0, 1, 0], |
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| 317 | [-sin(a), 0, +cos(a)]] |
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| 318 | return np.matrix(R) |
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| 319 | |
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| 320 | def Rz(angle): |
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| 321 | """Construct a matrix to rotate points about *z* by *angle* degrees.""" |
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| 322 | a = radians(angle) |
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| 323 | R = [[+cos(a), -sin(a), 0], |
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| 324 | [+sin(a), +cos(a), 0], |
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| 325 | [0, 0, 1]] |
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| 326 | return np.matrix(R) |
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| 327 | |
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| 328 | def transform_xyz(view, jitter, x, y, z): |
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| 329 | """ |
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| 330 | Send a set of (x,y,z) points through the jitter and view transforms. |
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| 331 | """ |
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| 332 | x, y, z = [np.asarray(v) for v in (x, y, z)] |
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| 333 | shape = x.shape |
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| 334 | points = np.matrix([x.flatten(),y.flatten(),z.flatten()]) |
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| 335 | points = apply_jitter(jitter, points) |
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| 336 | points = orient_relative_to_beam(view, points) |
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| 337 | x, y, z = [np.array(v).reshape(shape) for v in points] |
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| 338 | return x, y, z |
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| 339 | |
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| 340 | def apply_jitter(jitter, points): |
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| 341 | """ |
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| 342 | Apply the jitter transform to a set of points. |
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| 343 | |
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| 344 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
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| 345 | """ |
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| 346 | dtheta, dphi, dpsi = jitter |
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| 347 | points = Rx(dphi)*Ry(dtheta)*Rz(dpsi)*points |
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| 348 | return points |
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| 349 | |
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| 350 | def orient_relative_to_beam(view, points): |
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| 351 | """ |
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| 352 | Apply the view transform to a set of points. |
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| 353 | |
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| 354 | Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. |
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| 355 | """ |
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| 356 | theta, phi, psi = view |
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| 357 | points = Rz(phi)*Ry(theta)*Rz(psi)*points |
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| 358 | return points |
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| 359 | |
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| 360 | # translate between number of dimension of dispersity and the number of |
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| 361 | # points along each dimension. |
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| 362 | PD_N_TABLE = { |
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| 363 | (0, 0, 0): (0, 0, 0), # 0 |
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| 364 | (1, 0, 0): (100, 0, 0), # 100 |
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| 365 | (0, 1, 0): (0, 100, 0), |
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| 366 | (0, 0, 1): (0, 0, 100), |
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| 367 | (1, 1, 0): (30, 30, 0), # 900 |
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| 368 | (1, 0, 1): (30, 0, 30), |
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| 369 | (0, 1, 1): (0, 30, 30), |
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| 370 | (1, 1, 1): (15, 15, 15), # 3375 |
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| 371 | } |
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| 372 | |
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| 373 | def clipped_range(data, portion=1.0, mode='central'): |
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| 374 | """ |
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| 375 | Determine range from data. |
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| 376 | |
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| 377 | If *portion* is 1, use full range, otherwise use the center of the range |
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| 378 | or the top of the range, depending on whether *mode* is 'central' or 'top'. |
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| 379 | """ |
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| 380 | if portion == 1.0: |
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| 381 | return data.min(), data.max() |
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| 382 | elif mode == 'central': |
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| 383 | data = np.sort(data.flatten()) |
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| 384 | offset = int(portion*len(data)/2 + 0.5) |
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| 385 | return data[offset], data[-offset] |
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| 386 | elif mode == 'top': |
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| 387 | data = np.sort(data.flatten()) |
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| 388 | offset = int(portion*len(data) + 0.5) |
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| 389 | return data[offset], data[-1] |
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| 390 | |
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| 391 | def draw_scattering(calculator, ax, view, jitter, dist='gaussian'): |
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| 392 | """ |
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| 393 | Plot the scattering for the particular view. |
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| 394 | |
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| 395 | *calculator* is returned from :func:`build_model`. *ax* are the 3D axes |
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| 396 | on which the data will be plotted. *view* and *jitter* are the current |
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| 397 | orientation and orientation dispersity. *dist* is one of the sasmodels |
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| 398 | weight distributions. |
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| 399 | """ |
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| 400 | ## Sasmodels use sqrt(3)*width for the rectangle range; scale to the |
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| 401 | ## proper width for comparison. Commented out since now using the |
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| 402 | ## sasmodels definition of width for rectangle. |
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| 403 | #scale = 1/sqrt(3) if dist == 'rectangle' else 1 |
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| 404 | scale = 1 |
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| 405 | |
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| 406 | # add the orientation parameters to the model parameters |
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| 407 | theta, phi, psi = view |
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| 408 | theta_pd, phi_pd, psi_pd = [scale*v for v in jitter] |
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| 409 | theta_pd_n, phi_pd_n, psi_pd_n = PD_N_TABLE[(theta_pd>0, phi_pd>0, psi_pd>0)] |
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| 410 | ## increase pd_n for testing jitter integration rather than simple viz |
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| 411 | #theta_pd_n, phi_pd_n, psi_pd_n = [5*v for v in (theta_pd_n, phi_pd_n, psi_pd_n)] |
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| 412 | |
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| 413 | pars = dict( |
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| 414 | theta=theta, theta_pd=theta_pd, theta_pd_type=dist, theta_pd_n=theta_pd_n, |
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| 415 | phi=phi, phi_pd=phi_pd, phi_pd_type=dist, phi_pd_n=phi_pd_n, |
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| 416 | psi=psi, psi_pd=psi_pd, psi_pd_type=dist, psi_pd_n=psi_pd_n, |
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| 417 | ) |
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| 418 | pars.update(calculator.pars) |
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| 419 | |
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| 420 | # compute the pattern |
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| 421 | qx, qy = calculator._data.x_bins, calculator._data.y_bins |
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| 422 | Iqxy = calculator(**pars).reshape(len(qx), len(qy)) |
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| 423 | |
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| 424 | # scale it and draw it |
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| 425 | Iqxy = np.log(Iqxy) |
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| 426 | if calculator.limits: |
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| 427 | # use limits from orientation (0,0,0) |
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| 428 | vmin, vmax = calculator.limits |
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| 429 | else: |
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| 430 | vmin, vmax = clipped_range(Iqxy, portion=0.95, mode='top') |
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| 431 | #print("range",(vmin,vmax)) |
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| 432 | #qx, qy = np.meshgrid(qx, qy) |
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| 433 | if 0: |
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| 434 | level = np.asarray(255*(Iqxy - vmin)/(vmax - vmin), 'i') |
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| 435 | level[level<0] = 0 |
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| 436 | colors = plt.get_cmap()(level) |
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| 437 | ax.plot_surface(qx, qy, -1.1, rstride=1, cstride=1, facecolors=colors) |
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| 438 | elif 1: |
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| 439 | ax.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1, |
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| 440 | levels=np.linspace(vmin, vmax, 24)) |
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| 441 | else: |
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| 442 | ax.pcolormesh(qx, qy, Iqxy) |
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| 443 | |
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| 444 | def build_model(model_name, n=150, qmax=0.5, **pars): |
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| 445 | """ |
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| 446 | Build a calculator for the given shape. |
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| 447 | |
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| 448 | *model_name* is any sasmodels model. *n* and *qmax* define an n x n mesh |
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| 449 | on which to evaluate the model. The remaining parameters are stored in |
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| 450 | the returned calculator as *calculator.pars*. They are used by |
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| 451 | :func:`draw_scattering` to set the non-orientation parameters in the |
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| 452 | calculation. |
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| 453 | |
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| 454 | Returns a *calculator* function which takes a dictionary or parameters and |
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| 455 | produces Iqxy. The Iqxy value needs to be reshaped to an n x n matrix |
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| 456 | for plotting. See the :class:`sasmodels.direct_model.DirectModel` class |
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| 457 | for details. |
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| 458 | """ |
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| 459 | from sasmodels.core import load_model_info, build_model |
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| 460 | from sasmodels.data import empty_data2D |
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| 461 | from sasmodels.direct_model import DirectModel |
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| 462 | |
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| 463 | model_info = load_model_info(model_name) |
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| 464 | model = build_model(model_info) #, dtype='double!') |
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| 465 | q = np.linspace(-qmax, qmax, n) |
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| 466 | data = empty_data2D(q, q) |
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| 467 | calculator = DirectModel(data, model) |
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| 468 | |
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| 469 | # stuff the values for non-orientation parameters into the calculator |
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| 470 | calculator.pars = pars.copy() |
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| 471 | calculator.pars.setdefault('backgound', 1e-3) |
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| 472 | |
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| 473 | # fix the data limits so that we can see if the pattern fades |
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| 474 | # under rotation or angular dispersion |
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| 475 | Iqxy = calculator(theta=0, phi=0, psi=0, **calculator.pars) |
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| 476 | Iqxy = np.log(Iqxy) |
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| 477 | vmin, vmax = clipped_range(Iqxy, 0.95, mode='top') |
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| 478 | calculator.limits = vmin, vmax+1 |
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| 479 | |
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| 480 | return calculator |
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| 481 | |
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| 482 | def select_calculator(model_name, n=150, size=(10,40,100)): |
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| 483 | """ |
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| 484 | Create a model calculator for the given shape. |
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| 485 | |
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| 486 | *model_name* is one of sphere, cylinder, ellipsoid, triaxial_ellipsoid, |
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| 487 | parallelepiped or bcc_paracrystal. *n* is the number of points to use |
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| 488 | in the q range. *qmax* is chosen based on model parameters for the |
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| 489 | given model to show something intersting. |
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| 490 | |
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| 491 | Returns *calculator* and tuple *size* (a,b,c) giving minor and major |
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| 492 | equitorial axes and polar axis respectively. See :func:`build_model` |
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| 493 | for details on the returned calculator. |
|---|
| 494 | """ |
|---|
| 495 | a, b, c = size |
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| 496 | if model_name == 'sphere': |
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| 497 | calculator = build_model('sphere', n=n, radius=c) |
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| 498 | a = b = c |
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| 499 | elif model_name == 'bcc_paracrystal': |
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| 500 | calculator = build_model('bcc_paracrystal', n=n, dnn=c, |
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| 501 | d_factor=0.06, radius=40) |
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| 502 | a = b = c |
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| 503 | elif model_name == 'cylinder': |
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| 504 | calculator = build_model('cylinder', n=n, qmax=0.3, radius=b, length=c) |
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| 505 | a = b |
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| 506 | elif model_name == 'ellipsoid': |
|---|
| 507 | calculator = build_model('ellipsoid', n=n, qmax=1.0, |
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| 508 | radius_polar=c, radius_equatorial=b) |
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| 509 | a = b |
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| 510 | elif model_name == 'triaxial_ellipsoid': |
|---|
| 511 | calculator = build_model('triaxial_ellipsoid', n=n, qmax=0.5, |
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| 512 | radius_equat_minor=a, |
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| 513 | radius_equat_major=b, |
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| 514 | radius_polar=c) |
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| 515 | elif model_name == 'parallelepiped': |
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| 516 | calculator = build_model('parallelepiped', n=n, a=a, b=b, c=c) |
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| 517 | else: |
|---|
| 518 | raise ValueError("unknown model %s"%model_name) |
|---|
| 519 | |
|---|
| 520 | return calculator, (a, b, c) |
|---|
| 521 | |
|---|
| 522 | def main(model_name='parallelepiped', size=(10, 40, 100)): |
|---|
| 523 | """ |
|---|
| 524 | Show an interactive orientation and jitter demo. |
|---|
| 525 | |
|---|
| 526 | *model_name* is one of the models available in :func:`select_model`. |
|---|
| 527 | """ |
|---|
| 528 | # set up calculator |
|---|
| 529 | calculator, size = select_calculator(model_name, n=150, size=size) |
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| 530 | |
|---|
| 531 | ## uncomment to set an independent the colour range for every view |
|---|
| 532 | ## If left commented, the colour range is fixed for all views |
|---|
| 533 | calculator.limits = None |
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| 534 | |
|---|
| 535 | ## use gaussian distribution unless testing integration |
|---|
| 536 | dist = 'rectangle' |
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| 537 | #dist = 'gaussian' |
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| 538 | |
|---|
| 539 | ## initial view |
|---|
| 540 | #theta, dtheta = 70., 10. |
|---|
| 541 | #phi, dphi = -45., 3. |
|---|
| 542 | #psi, dpsi = -45., 3. |
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| 543 | theta, phi, psi = 0, 0, 0 |
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| 544 | dtheta, dphi, dpsi = 0, 0, 0 |
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| 545 | |
|---|
| 546 | ## create the plot window |
|---|
| 547 | #plt.hold(True) |
|---|
| 548 | plt.set_cmap('gist_earth') |
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| 549 | plt.clf() |
|---|
| 550 | #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) |
|---|
| 551 | #ax = plt.subplot(gs[0], projection='3d') |
|---|
| 552 | ax = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') |
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| 553 | try: # CRUFT: not all versions of matplotlib accept 'square' 3d projection |
|---|
| 554 | ax.axis('square') |
|---|
| 555 | except Exception: |
|---|
| 556 | pass |
|---|
| 557 | |
|---|
| 558 | axcolor = 'lightgoldenrodyellow' |
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| 559 | |
|---|
| 560 | ## add control widgets to plot |
|---|
| 561 | axtheta = plt.axes([0.1, 0.15, 0.45, 0.04], axisbg=axcolor) |
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| 562 | axphi = plt.axes([0.1, 0.1, 0.45, 0.04], axisbg=axcolor) |
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| 563 | axpsi = plt.axes([0.1, 0.05, 0.45, 0.04], axisbg=axcolor) |
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| 564 | stheta = Slider(axtheta, 'Theta', -90, 90, valinit=theta) |
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| 565 | sphi = Slider(axphi, 'Phi', -180, 180, valinit=phi) |
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| 566 | spsi = Slider(axpsi, 'Psi', -180, 180, valinit=psi) |
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| 567 | |
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| 568 | axdtheta = plt.axes([0.75, 0.15, 0.15, 0.04], axisbg=axcolor) |
|---|
| 569 | axdphi = plt.axes([0.75, 0.1, 0.15, 0.04], axisbg=axcolor) |
|---|
| 570 | axdpsi= plt.axes([0.75, 0.05, 0.15, 0.04], axisbg=axcolor) |
|---|
| 571 | # Note: using ridiculous definition of rectangle distribution, whose width |
|---|
| 572 | # in sasmodels is sqrt(3) times the given width. Divide by sqrt(3) to keep |
|---|
| 573 | # the maximum width to 90. |
|---|
| 574 | dlimit = 30 if dist == 'gaussian' else 90/sqrt(3) |
|---|
| 575 | sdtheta = Slider(axdtheta, 'dTheta', 0, 2*dlimit, valinit=dtheta) |
|---|
| 576 | sdphi = Slider(axdphi, 'dPhi', 0, 2*dlimit, valinit=dphi) |
|---|
| 577 | sdpsi = Slider(axdpsi, 'dPsi', 0, 2*dlimit, valinit=dpsi) |
|---|
| 578 | |
|---|
| 579 | ## callback to draw the new view |
|---|
| 580 | def update(val, axis=None): |
|---|
| 581 | view = stheta.val, sphi.val, spsi.val |
|---|
| 582 | jitter = sdtheta.val, sdphi.val, sdpsi.val |
|---|
| 583 | # set small jitter as 0 if multiple pd dims |
|---|
| 584 | dims = sum(v > 0 for v in jitter) |
|---|
| 585 | limit = [0, 0, 2, 5][dims] |
|---|
| 586 | jitter = [0 if v < limit else v for v in jitter] |
|---|
| 587 | ax.cla() |
|---|
| 588 | draw_beam(ax, (0, 0)) |
|---|
| 589 | draw_jitter(ax, view, jitter, dist=dist, size=size) |
|---|
| 590 | #draw_jitter(ax, view, (0,0,0)) |
|---|
| 591 | draw_mesh(ax, view, jitter, dist=dist, n=30) |
|---|
| 592 | draw_scattering(calculator, ax, view, jitter, dist=dist) |
|---|
| 593 | plt.gcf().canvas.draw() |
|---|
| 594 | |
|---|
| 595 | ## bind control widgets to view updater |
|---|
| 596 | stheta.on_changed(lambda v: update(v,'theta')) |
|---|
| 597 | sphi.on_changed(lambda v: update(v, 'phi')) |
|---|
| 598 | spsi.on_changed(lambda v: update(v, 'psi')) |
|---|
| 599 | sdtheta.on_changed(lambda v: update(v, 'dtheta')) |
|---|
| 600 | sdphi.on_changed(lambda v: update(v, 'dphi')) |
|---|
| 601 | sdpsi.on_changed(lambda v: update(v, 'dpsi')) |
|---|
| 602 | |
|---|
| 603 | ## initialize view |
|---|
| 604 | update(None, 'phi') |
|---|
| 605 | |
|---|
| 606 | ## go interactive |
|---|
| 607 | plt.show() |
|---|
| 608 | |
|---|
| 609 | if __name__ == "__main__": |
|---|
| 610 | model_name = sys.argv[1] if len(sys.argv) > 1 else 'parallelepiped' |
|---|
| 611 | size = tuple(int(v) for v in sys.argv[2].split(',')) if len(sys.argv) > 2 else (10, 40, 100) |
|---|
| 612 | main(model_name, size) |
|---|
