Source code for sasmodels.jitter

#!/usr/bin/env python
"""
Jitter Explorer
===============

Application to explore orientation angle and angular dispersity.
"""
from __future__ import division, print_function

import argparse

try: # CRUFT: travis-ci does not support mpl_toolkits.mplot3d
    import mpl_toolkits.mplot3d  # Adds projection='3d' option to subplot
except ImportError:
    pass

import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
import numpy as np
from numpy import pi, cos, sin, sqrt, exp, degrees, radians

[docs]def draw_beam(axes, view=(0, 0)): """ Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1) """ #axes.plot([0,0],[0,0],[1,-1]) #axes.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=0.8) steps = 25 u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(-1, 1, steps) r = 0.02 x = r*np.outer(np.cos(u), np.ones_like(v)) y = r*np.outer(np.sin(u), np.ones_like(v)) z = 1.3*np.outer(np.ones_like(u), v) theta, phi = view shape = x.shape points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) points = Rz(phi)*Ry(theta)*points x, y, z = [v.reshape(shape) for v in points] axes.plot_surface(x, y, z, rstride=4, cstride=4, color='y', alpha=0.5)
[docs]def draw_ellipsoid(axes, size, view, jitter, steps=25, alpha=1): """Draw an ellipsoid.""" a, b, c = size u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(0, np.pi, steps) x = a*np.outer(np.cos(u), np.sin(v)) y = b*np.outer(np.sin(u), np.sin(v)) z = c*np.outer(np.ones_like(u), np.cos(v)) x, y, z = transform_xyz(view, jitter, x, y, z) axes.plot_surface(x, y, z, rstride=4, cstride=4, color='w', alpha=alpha) draw_labels(axes, view, jitter, [ ('c+', [+0, +0, +c], [+1, +0, +0]), ('c-', [+0, +0, -c], [+0, +0, -1]), ('a+', [+a, +0, +0], [+0, +0, +1]), ('a-', [-a, +0, +0], [+0, +0, -1]), ('b+', [+0, +b, +0], [-1, +0, +0]), ('b-', [+0, -b, +0], [-1, +0, +0]), ])
[docs]def draw_sc(axes, size, view, jitter, steps=None, alpha=1): """Draw points for simple cubic paracrystal""" atoms = _build_sc() _draw_crystal(axes, size, view, jitter, atoms=atoms)
[docs]def draw_fcc(axes, size, view, jitter, steps=None, alpha=1): """Draw points for face-centered cubic paracrystal""" # Build the simple cubic crystal atoms = _build_sc() # Define the centers for each face # x planes at -1, 0, 1 have four centers per plane, at +/- 0.5 in y and z x, y, z = ( [-1]*4 + [0]*4 + [1]*4, ([-0.5]*2 + [0.5]*2)*3, [-0.5, 0.5]*12, ) # y and z planes can be generated by substituting x for y and z respectively atoms.extend(zip(x+y+z, y+z+x, z+x+y)) _draw_crystal(axes, size, view, jitter, atoms=atoms)
[docs]def draw_bcc(axes, size, view, jitter, steps=None, alpha=1): """Draw points for body-centered cubic paracrystal""" # Build the simple cubic crystal atoms = _build_sc() # Define the centers for each octant # x plane at +/- 0.5 have four centers per plane at +/- 0.5 in y and z x, y, z = ( [-0.5]*4 + [0.5]*4, ([-0.5]*2 + [0.5]*2)*2, [-0.5, 0.5]*8, ) atoms.extend(zip(x, y, z)) _draw_crystal(axes, size, view, jitter, atoms=atoms)
def _draw_crystal(axes, size, view, jitter, atoms=None): atoms, size = np.asarray(atoms, 'd').T, np.asarray(size, 'd') x, y, z = atoms*size[:, None] x, y, z = transform_xyz(view, jitter, x, y, z) axes.scatter([x[0]], [y[0]], [z[0]], c='yellow', marker='o') axes.scatter(x[1:], y[1:], z[1:], c='r', marker='o') def _build_sc(): # three planes of 9 dots for x at -1, 0 and 1 x, y, z = ( [-1]*9 + [0]*9 + [1]*9, ([-1]*3 + [0]*3 + [1]*3)*3, [-1, 0, 1]*9, ) atoms = list(zip(x, y, z)) #print(list(enumerate(atoms))) # Pull the dot at (0, 0, 1) to the front of the list # It will be highlighted in the view index = 14 highlight = atoms[index] del atoms[index] atoms.insert(0, highlight) return atoms
[docs]def draw_parallelepiped(axes, size, view, jitter, steps=None, alpha=1): """Draw a parallelepiped.""" a, b, c = size x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) tri = np.array([ # counter clockwise triangles # z: up/down, x: right/left, y: front/back [0, 1, 2], [3, 2, 1], # top face [6, 5, 4], [5, 6, 7], # bottom face [0, 2, 6], [6, 4, 0], # right face [1, 5, 7], [7, 3, 1], # left face [2, 3, 6], [7, 6, 3], # front face [4, 1, 0], [5, 1, 4], # back face ]) x, y, z = transform_xyz(view, jitter, x, y, z) axes.plot_trisurf(x, y, triangles=tri, Z=z, color='w', alpha=alpha) # Draw pink face on box. # Since I can't control face color, instead draw a thin box situated just # in front of the "c+" face. Use the c face so that rotations about psi # rotate that face. if 1: x = a*np.array([+1, -1, +1, -1, +1, -1, +1, -1]) y = b*np.array([+1, +1, -1, -1, +1, +1, -1, -1]) z = c*np.array([+1, +1, +1, +1, -1, -1, -1, -1]) x, y, z = transform_xyz(view, jitter, x, y, abs(z)+0.001) axes.plot_trisurf(x, y, triangles=tri, Z=z, color=[1, 0.6, 0.6], alpha=alpha) draw_labels(axes, view, jitter, [ ('c+', [+0, +0, +c], [+1, +0, +0]), ('c-', [+0, +0, -c], [+0, +0, -1]), ('a+', [+a, +0, +0], [+0, +0, +1]), ('a-', [-a, +0, +0], [+0, +0, -1]), ('b+', [+0, +b, +0], [-1, +0, +0]), ('b-', [+0, -b, +0], [-1, +0, +0]), ])
[docs]def draw_sphere(axes, radius=10., steps=100): """Draw a sphere""" u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(0, np.pi, steps) x = radius * np.outer(np.cos(u), np.sin(v)) y = radius * np.outer(np.sin(u), np.sin(v)) z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) axes.plot_surface(x, y, z, rstride=4, cstride=4, color='w')
[docs]def draw_jitter(axes, view, jitter, dist='gaussian', size=(0.1, 0.4, 1.0), draw_shape=draw_parallelepiped): """ Represent jitter as a set of shapes at different orientations. """ # set max diagonal to 0.95 scale = 0.95/sqrt(sum(v**2 for v in size)) size = tuple(scale*v for v in size) #np.random.seed(10) #cloud = np.random.randn(10,3) cloud = [ [-1, -1, -1], [-1, -1, +0], [-1, -1, +1], [-1, +0, -1], [-1, +0, +0], [-1, +0, +1], [-1, +1, -1], [-1, +1, +0], [-1, +1, +1], [+0, -1, -1], [+0, -1, +0], [+0, -1, +1], [+0, +0, -1], [+0, +0, +0], [+0, +0, +1], [+0, +1, -1], [+0, +1, +0], [+0, +1, +1], [+1, -1, -1], [+1, -1, +0], [+1, -1, +1], [+1, +0, -1], [+1, +0, +0], [+1, +0, +1], [+1, +1, -1], [+1, +1, +0], [+1, +1, +1], ] dtheta, dphi, dpsi = jitter if dtheta == 0: cloud = [v for v in cloud if v[0] == 0] if dphi == 0: cloud = [v for v in cloud if v[1] == 0] if dpsi == 0: cloud = [v for v in cloud if v[2] == 0] draw_shape(axes, size, view, [0, 0, 0], steps=100, alpha=0.8) scale = {'gaussian':1, 'rectangle':1/sqrt(3), 'uniform':1/3}[dist] for point in cloud: delta = [scale*dtheta*point[0], scale*dphi*point[1], scale*dpsi*point[2]] draw_shape(axes, size, view, delta, alpha=0.8) for v in 'xyz': a, b, c = size lim = np.sqrt(a**2 + b**2 + c**2) getattr(axes, 'set_'+v+'lim')([-lim, lim]) getattr(axes, v+'axis').label.set_text(v)
PROJECTIONS = [ # in order of PROJECTION number; do not change without updating the # constants in kernel_iq.c 'equirectangular', 'sinusoidal', 'guyou', 'azimuthal_equidistance', 'azimuthal_equal_area', ]
[docs]def draw_mesh(axes, view, jitter, radius=1.2, n=11, dist='gaussian', projection='equirectangular'): """ Draw the dispersion mesh showing the theta-phi orientations at which the model will be evaluated. jitter projections <https://en.wikipedia.org/wiki/List_of_map_projections> equirectangular (standard latitude-longitude mesh) <https://en.wikipedia.org/wiki/Equirectangular_projection> Allows free movement in phi (around the equator), but theta is limited to +/- 90, and points are cos-weighted. Jitter in phi is uniform in weight along a line of latitude. With small theta and phi ranging over +/- 180 this forms a wobbling disk. With small phi and theta ranging over +/- 90 this forms a wedge like a slice of an orange. azimuthal_equidistance (Postel) <https://en.wikipedia.org/wiki/Azimuthal_equidistant_projection> Preserves distance from center, and so is an excellent map for representing a bivariate gaussian on the surface. Theta and phi operate identically, cutting wegdes from the antipode of the viewing angle. This unfortunately does not allow free movement in either theta or phi since the orthogonal wobble decreases to 0 as the body rotates through 180 degrees. sinusoidal (Sanson-Flamsteed, Mercator equal-area) <https://en.wikipedia.org/wiki/Sinusoidal_projection> Preserves arc length with latitude, giving bad behaviour at theta near +/- 90. Theta and phi operate somewhat differently, so a system with a-b-c dtheta-dphi-dpsi will not give the same value as one with b-a-c dphi-dtheta-dpsi, as would be the case for azimuthal equidistance. Free movement using theta or phi uniform over +/- 180 will work, but not as well as equirectangular phi, with theta being slightly worse. Computationally it is much cheaper for wide theta-phi meshes since it excludes points which lie outside the sinusoid near theta +/- 90 rather than packing them close together as in equirectangle. Note that the poles will be slightly overweighted for theta > 90 with the circle from theta at 90+dt winding backwards around the pole, overlapping the circle from theta at 90-dt. Guyou (hemisphere-in-a-square) **not weighted** <https://en.wikipedia.org/wiki/Guyou_hemisphere-in-a-square_projection> With tiling, allows rotation in phi or theta through +/- 180, with uniform spacing. Both theta and phi allow free rotation, with wobble in the orthogonal direction reasonably well behaved (though not as good as equirectangular phi). The forward/reverse transformations relies on elliptic integrals that are somewhat expensive, so the behaviour has to be very good to justify the cost and complexity. The weighting function for each point has not yet been computed. Note: run the module *guyou.py* directly and it will show the forward and reverse mappings. azimuthal_equal_area **incomplete** <https://en.wikipedia.org/wiki/Lambert_azimuthal_equal-area_projection> Preserves the relative density of the surface patches. Not that useful and not completely implemented Gauss-Kreuger **not implemented** <https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Ellipsoidal_transverse_Mercator> Should allow free movement in theta, but phi is distorted. """ # TODO: try Kent distribution instead of a gaussian warped by projection dist_x = np.linspace(-1, 1, n) weights = np.ones_like(dist_x) if dist == 'gaussian': dist_x *= 3 weights = exp(-0.5*dist_x**2) elif dist == 'rectangle': # Note: uses sasmodels ridiculous definition of rectangle width dist_x *= sqrt(3) elif dist == 'uniform': pass else: raise ValueError("expected dist to be gaussian, rectangle or uniform") if projection == 'equirectangular': #define PROJECTION 1 def _rotate(theta_i, phi_j): return Rx(phi_j)*Ry(theta_i) def _weight(theta_i, phi_j, w_i, w_j): return w_i*w_j*abs(cos(radians(theta_i))) elif projection == 'sinusoidal': #define PROJECTION 2 def _rotate(theta_i, phi_j): latitude = theta_i scale = cos(radians(latitude)) longitude = phi_j/scale if abs(phi_j) < abs(scale)*180 else 0 #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) return Rx(longitude)*Ry(latitude) def _weight(theta_i, phi_j, w_i, w_j): latitude = theta_i scale = cos(radians(latitude)) active = 1 if abs(phi_j) < abs(scale)*180 else 0 return active*w_i*w_j elif projection == 'guyou': #define PROJECTION 3 (eventually?) def _rotate(theta_i, phi_j): from .guyou import guyou_invert #latitude, longitude = guyou_invert([theta_i], [phi_j]) longitude, latitude = guyou_invert([phi_j], [theta_i]) return Rx(longitude[0])*Ry(latitude[0]) def _weight(theta_i, phi_j, w_i, w_j): return w_i*w_j elif projection == 'azimuthal_equidistance': # Note: Rz Ry, not Rx Ry def _rotate(theta_i, phi_j): latitude = sqrt(theta_i**2 + phi_j**2) longitude = degrees(np.arctan2(phi_j, theta_i)) #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) return Rz(longitude)*Ry(latitude) def _weight(theta_i, phi_j, w_i, w_j): # Weighting for each point comes from the integral: # \int\int I(q, lat, log) sin(lat) dlat dlog # We are doing a conformal mapping from disk to sphere, so we need # a change of variables g(theta, phi) -> (lat, long): # lat, long = sqrt(theta^2 + phi^2), arctan(phi/theta) # giving: # dtheta dphi = det(J) dlat dlong # where J is the jacobian from the partials of g. Using # R = sqrt(theta^2 + phi^2), # then # J = [[x/R, Y/R], -y/R^2, x/R^2]] # and # det(J) = 1/R # with the final integral being: # \int\int I(q, theta, phi) sin(R)/R dtheta dphi # # This does approximately the right thing, decreasing the weight # of each point as you go farther out on the disk, but it hasn't # yet been checked against the 1D integral results. Prior # to declaring this "good enough" and checking that integrals # work in practice, we will examine alternative mappings. # # The issue is that the mapping does not support the case of free # rotation about a single axis correctly, with a small deviation # in the orthogonal axis independent of the first axis. Like the # usual polar coordiates integration, the integrated sections # form wedges, though at least in this case the wedge cuts through # the entire sphere, and treats theta and phi identically. latitude = sqrt(theta_i**2 + phi_j**2) weight = sin(radians(latitude))/latitude if latitude != 0 else 1 return weight*w_i*w_j if latitude < 180 else 0 elif projection == 'azimuthal_equal_area': def _rotate(theta_i, phi_j): radius = min(1, sqrt(theta_i**2 + phi_j**2)/180) latitude = 180-degrees(2*np.arccos(radius)) longitude = degrees(np.arctan2(phi_j, theta_i)) #print("(%+7.2f, %+7.2f) => (%+7.2f, %+7.2f)"%(theta_i, phi_j, latitude, longitude)) return Rz(longitude)*Ry(latitude) def _weight(theta_i, phi_j, w_i, w_j): latitude = sqrt(theta_i**2 + phi_j**2) weight = sin(radians(latitude))/latitude if latitude != 0 else 1 return weight*w_i*w_j if latitude < 180 else 0 else: raise ValueError("unknown projection %r"%projection) # mesh in theta, phi formed by rotating z dtheta, dphi, dpsi = jitter z = np.matrix([[0], [0], [radius]]) points = np.hstack([_rotate(theta_i, phi_j)*z for theta_i in dtheta*dist_x for phi_j in dphi*dist_x]) dist_w = np.array([_weight(theta_i, phi_j, w_i, w_j) for w_i, theta_i in zip(weights, dtheta*dist_x) for w_j, phi_j in zip(weights, dphi*dist_x)]) #print(max(dist_w), min(dist_w), min(dist_w[dist_w > 0])) points = points[:, dist_w > 0] dist_w = dist_w[dist_w > 0] dist_w /= max(dist_w) # rotate relative to beam points = orient_relative_to_beam(view, points) x, y, z = [np.array(v).flatten() for v in points] #plt.figure(2); plt.clf(); plt.hist(z, bins=np.linspace(-1, 1, 51)) axes.scatter(x, y, z, c=dist_w, marker='o', vmin=0., vmax=1.)
[docs]def draw_labels(axes, view, jitter, text): """ Draw text at a particular location. """ labels, locations, orientations = zip(*text) px, py, pz = zip(*locations) dx, dy, dz = zip(*orientations) px, py, pz = transform_xyz(view, jitter, px, py, pz) dx, dy, dz = transform_xyz(view, jitter, dx, dy, dz) # TODO: zdir for labels is broken, and labels aren't appearing. for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)): zdir = np.asarray(zdir).flatten() axes.text(p[0], p[1], p[2], label, zdir=zdir)
# Definition of rotation matrices comes from wikipedia: # https://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
[docs]def Rx(angle): """Construct a matrix to rotate points about *x* by *angle* degrees.""" angle = radians(angle) rot = [[1, 0, 0], [0, +cos(angle), -sin(angle)], [0, +sin(angle), +cos(angle)]] return np.matrix(rot)
[docs]def Ry(angle): """Construct a matrix to rotate points about *y* by *angle* degrees.""" angle = radians(angle) rot = [[+cos(angle), 0, +sin(angle)], [0, 1, 0], [-sin(angle), 0, +cos(angle)]] return np.matrix(rot)
[docs]def Rz(angle): """Construct a matrix to rotate points about *z* by *angle* degrees.""" angle = radians(angle) rot = [[+cos(angle), -sin(angle), 0], [+sin(angle), +cos(angle), 0], [0, 0, 1]] return np.matrix(rot)
[docs]def transform_xyz(view, jitter, x, y, z): """ Send a set of (x,y,z) points through the jitter and view transforms. """ x, y, z = [np.asarray(v) for v in (x, y, z)] shape = x.shape points = np.matrix([x.flatten(), y.flatten(), z.flatten()]) points = apply_jitter(jitter, points) points = orient_relative_to_beam(view, points) x, y, z = [np.array(v).reshape(shape) for v in points] return x, y, z
[docs]def apply_jitter(jitter, points): """ Apply the jitter transform to a set of points. Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. """ dtheta, dphi, dpsi = jitter points = Rx(dphi)*Ry(dtheta)*Rz(dpsi)*points return points
[docs]def orient_relative_to_beam(view, points): """ Apply the view transform to a set of points. Points are stored in a 3 x n numpy matrix, not a numpy array or tuple. """ theta, phi, psi = view points = Rz(phi)*Ry(theta)*Rz(psi)*points return points
# translate between number of dimension of dispersity and the number of # points along each dimension. PD_N_TABLE = { (0, 0, 0): (0, 0, 0), # 0 (1, 0, 0): (100, 0, 0), # 100 (0, 1, 0): (0, 100, 0), (0, 0, 1): (0, 0, 100), (1, 1, 0): (30, 30, 0), # 900 (1, 0, 1): (30, 0, 30), (0, 1, 1): (0, 30, 30), (1, 1, 1): (15, 15, 15), # 3375 }
[docs]def clipped_range(data, portion=1.0, mode='central'): """ Determine range from data. If *portion* is 1, use full range, otherwise use the center of the range or the top of the range, depending on whether *mode* is 'central' or 'top'. """ if portion == 1.0: return data.min(), data.max() elif mode == 'central': data = np.sort(data.flatten()) offset = int(portion*len(data)/2 + 0.5) return data[offset], data[-offset] elif mode == 'top': data = np.sort(data.flatten()) offset = int(portion*len(data) + 0.5) return data[offset], data[-1]
[docs]def draw_scattering(calculator, axes, view, jitter, dist='gaussian'): """ Plot the scattering for the particular view. *calculator* is returned from :func:`build_model`. *axes* are the 3D axes on which the data will be plotted. *view* and *jitter* are the current orientation and orientation dispersity. *dist* is one of the sasmodels weight distributions. """ if dist == 'uniform': # uniform is not yet in this branch dist, scale = 'rectangle', 1/sqrt(3) else: scale = 1 # add the orientation parameters to the model parameters theta, phi, psi = view theta_pd, phi_pd, psi_pd = [scale*v for v in jitter] theta_pd_n, phi_pd_n, psi_pd_n = PD_N_TABLE[(theta_pd > 0, phi_pd > 0, psi_pd > 0)] ## increase pd_n for testing jitter integration rather than simple viz #theta_pd_n, phi_pd_n, psi_pd_n = [5*v for v in (theta_pd_n, phi_pd_n, psi_pd_n)] pars = dict( theta=theta, theta_pd=theta_pd, theta_pd_type=dist, theta_pd_n=theta_pd_n, phi=phi, phi_pd=phi_pd, phi_pd_type=dist, phi_pd_n=phi_pd_n, psi=psi, psi_pd=psi_pd, psi_pd_type=dist, psi_pd_n=psi_pd_n, ) pars.update(calculator.pars) # compute the pattern qx, qy = calculator._data.x_bins, calculator._data.y_bins Iqxy = calculator(**pars).reshape(len(qx), len(qy)) # scale it and draw it Iqxy = np.log(Iqxy) if calculator.limits: # use limits from orientation (0,0,0) vmin, vmax = calculator.limits else: vmax = Iqxy.max() vmin = vmax*10**-7 #vmin, vmax = clipped_range(Iqxy, portion=portion, mode='top') #print("range",(vmin,vmax)) #qx, qy = np.meshgrid(qx, qy) if 0: level = np.asarray(255*(Iqxy - vmin)/(vmax - vmin), 'i') level[level < 0] = 0 colors = plt.get_cmap()(level) axes.plot_surface(qx, qy, -1.1, rstride=1, cstride=1, facecolors=colors) elif 1: axes.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1, levels=np.linspace(vmin, vmax, 24)) else: axes.pcolormesh(qx, qy, Iqxy)
[docs]def build_model(model_name, n=150, qmax=0.5, **pars): """ Build a calculator for the given shape. *model_name* is any sasmodels model. *n* and *qmax* define an n x n mesh on which to evaluate the model. The remaining parameters are stored in the returned calculator as *calculator.pars*. They are used by :func:`draw_scattering` to set the non-orientation parameters in the calculation. Returns a *calculator* function which takes a dictionary or parameters and produces Iqxy. The Iqxy value needs to be reshaped to an n x n matrix for plotting. See the :class:`sasmodels.direct_model.DirectModel` class for details. """ from sasmodels.core import load_model_info, build_model as build_sasmodel from sasmodels.data import empty_data2D from sasmodels.direct_model import DirectModel model_info = load_model_info(model_name) model = build_sasmodel(model_info) #, dtype='double!') q = np.linspace(-qmax, qmax, n) data = empty_data2D(q, q) calculator = DirectModel(data, model) # stuff the values for non-orientation parameters into the calculator calculator.pars = pars.copy() calculator.pars.setdefault('backgound', 1e-3) # fix the data limits so that we can see if the pattern fades # under rotation or angular dispersion Iqxy = calculator(theta=0, phi=0, psi=0, **calculator.pars) Iqxy = np.log(Iqxy) vmin, vmax = clipped_range(Iqxy, 0.95, mode='top') calculator.limits = vmin, vmax+1 return calculator
[docs]def select_calculator(model_name, n=150, size=(10, 40, 100)): """ Create a model calculator for the given shape. *model_name* is one of sphere, cylinder, ellipsoid, triaxial_ellipsoid, parallelepiped or bcc_paracrystal. *n* is the number of points to use in the q range. *qmax* is chosen based on model parameters for the given model to show something intersting. Returns *calculator* and tuple *size* (a,b,c) giving minor and major equitorial axes and polar axis respectively. See :func:`build_model` for details on the returned calculator. """ a, b, c = size d_factor = 0.06 # for paracrystal models if model_name == 'sphere': calculator = build_model('sphere', n=n, radius=c) a = b = c elif model_name == 'sc_paracrystal': a = b = c dnn = c radius = 0.5*c calculator = build_model('sc_paracrystal', n=n, dnn=dnn, d_factor=d_factor, radius=(1-d_factor)*radius, background=0) elif model_name == 'fcc_paracrystal': a = b = c # nearest neigbour distance dnn should be 2 radius, but I think the # model uses lattice spacing rather than dnn in its calculations dnn = 0.5*c radius = sqrt(2)/4 * c calculator = build_model('fcc_paracrystal', n=n, dnn=dnn, d_factor=d_factor, radius=(1-d_factor)*radius, background=0) elif model_name == 'bcc_paracrystal': a = b = c # nearest neigbour distance dnn should be 2 radius, but I think the # model uses lattice spacing rather than dnn in its calculations dnn = 0.5*c radius = sqrt(3)/2 * c calculator = build_model('bcc_paracrystal', n=n, dnn=dnn, d_factor=d_factor, radius=(1-d_factor)*radius, background=0) elif model_name == 'cylinder': calculator = build_model('cylinder', n=n, qmax=0.3, radius=b, length=c) a = b elif model_name == 'ellipsoid': calculator = build_model('ellipsoid', n=n, qmax=1.0, radius_polar=c, radius_equatorial=b) a = b elif model_name == 'triaxial_ellipsoid': calculator = build_model('triaxial_ellipsoid', n=n, qmax=0.5, radius_equat_minor=a, radius_equat_major=b, radius_polar=c) elif model_name == 'parallelepiped': calculator = build_model('parallelepiped', n=n, a=a, b=b, c=c) else: raise ValueError("unknown model %s"%model_name) return calculator, (a, b, c)
SHAPES = [ 'parallelepiped', 'sphere', 'ellipsoid', 'triaxial_ellipsoid', 'cylinder', 'fcc_paracrystal', 'bcc_paracrystal', 'sc_paracrystal', ] DRAW_SHAPES = { 'fcc_paracrystal': draw_fcc, 'bcc_paracrystal': draw_bcc, 'sc_paracrystal': draw_sc, 'parallelepiped': draw_parallelepiped, } DISTRIBUTIONS = [ 'gaussian', 'rectangle', 'uniform', ] DIST_LIMITS = { 'gaussian': 30, 'rectangle': 90/sqrt(3), 'uniform': 90, }
[docs]def run(model_name='parallelepiped', size=(10, 40, 100), dist='gaussian', mesh=30, projection='equirectangular'): """ Show an interactive orientation and jitter demo. *model_name* is one of: sphere, ellipsoid, triaxial_ellipsoid, parallelepiped, cylinder, or sc/fcc/bcc_paracrystal *size* gives the dimensions (a, b, c) of the shape. *dist* is the type of dispersition: gaussian, rectangle, or uniform. *mesh* is the number of points in the dispersion mesh. *projection* is the map projection to use for the mesh: equirectangular, sinusoidal, guyou, azimuthal_equidistance, or azimuthal_equal_area. """ # projection number according to 1-order position in list, but # only 1 and 2 are implemented so far. from sasmodels import generate generate.PROJECTION = PROJECTIONS.index(projection) + 1 if generate.PROJECTION > 2: print("*** PROJECTION %s not implemented in scattering function ***"%projection) generate.PROJECTION = 2 # set up calculator calculator, size = select_calculator(model_name, n=150, size=size) draw_shape = DRAW_SHAPES.get(model_name, draw_parallelepiped) ## uncomment to set an independent the colour range for every view ## If left commented, the colour range is fixed for all views calculator.limits = None ## initial view #theta, dtheta = 70., 10. #phi, dphi = -45., 3. #psi, dpsi = -45., 3. theta, phi, psi = 0, 0, 0 dtheta, dphi, dpsi = 0, 0, 0 ## create the plot window #plt.hold(True) plt.subplots(num=None, figsize=(5.5, 5.5)) plt.set_cmap('gist_earth') plt.clf() plt.gcf().canvas.set_window_title(projection) #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) #axes = plt.subplot(gs[0], projection='3d') axes = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') try: # CRUFT: not all versions of matplotlib accept 'square' 3d projection axes.axis('square') except Exception: pass axcolor = 'lightgoldenrodyellow' ## add control widgets to plot axes_theta = plt.axes([0.1, 0.15, 0.45, 0.04], axisbg=axcolor) axes_phi = plt.axes([0.1, 0.1, 0.45, 0.04], axisbg=axcolor) axes_psi = plt.axes([0.1, 0.05, 0.45, 0.04], axisbg=axcolor) stheta = Slider(axes_theta, 'Theta', -90, 90, valinit=theta) sphi = Slider(axes_phi, 'Phi', -180, 180, valinit=phi) spsi = Slider(axes_psi, 'Psi', -180, 180, valinit=psi) axes_dtheta = plt.axes([0.75, 0.15, 0.15, 0.04], axisbg=axcolor) axes_dphi = plt.axes([0.75, 0.1, 0.15, 0.04], axisbg=axcolor) axes_dpsi = plt.axes([0.75, 0.05, 0.15, 0.04], axisbg=axcolor) # Note: using ridiculous definition of rectangle distribution, whose width # in sasmodels is sqrt(3) times the given width. Divide by sqrt(3) to keep # the maximum width to 90. dlimit = DIST_LIMITS[dist] sdtheta = Slider(axes_dtheta, 'dTheta', 0, 2*dlimit, valinit=dtheta) sdphi = Slider(axes_dphi, 'dPhi', 0, 2*dlimit, valinit=dphi) sdpsi = Slider(axes_dpsi, 'dPsi', 0, 2*dlimit, valinit=dpsi) ## callback to draw the new view def update(val, axis=None): view = stheta.val, sphi.val, spsi.val jitter = sdtheta.val, sdphi.val, sdpsi.val # set small jitter as 0 if multiple pd dims dims = sum(v > 0 for v in jitter) limit = [0, 0.5, 5][dims] jitter = [0 if v < limit else v for v in jitter] axes.cla() draw_beam(axes, (0, 0)) draw_jitter(axes, view, jitter, dist=dist, size=size, draw_shape=draw_shape) #draw_jitter(axes, view, (0,0,0)) draw_mesh(axes, view, jitter, dist=dist, n=mesh, projection=projection) draw_scattering(calculator, axes, view, jitter, dist=dist) plt.gcf().canvas.draw() ## bind control widgets to view updater stheta.on_changed(lambda v: update(v, 'theta')) sphi.on_changed(lambda v: update(v, 'phi')) spsi.on_changed(lambda v: update(v, 'psi')) sdtheta.on_changed(lambda v: update(v, 'dtheta')) sdphi.on_changed(lambda v: update(v, 'dphi')) sdpsi.on_changed(lambda v: update(v, 'dpsi')) ## initialize view update(None, 'phi') ## go interactive plt.show()
[docs]def main(): parser = argparse.ArgumentParser( description="Display jitter", formatter_class=argparse.ArgumentDefaultsHelpFormatter, ) parser.add_argument('-p', '--projection', choices=PROJECTIONS, default=PROJECTIONS[0], help='coordinate projection') parser.add_argument('-s', '--size', type=str, default='10,40,100', help='a,b,c lengths') parser.add_argument('-d', '--distribution', choices=DISTRIBUTIONS, default=DISTRIBUTIONS[0], help='jitter distribution') parser.add_argument('-m', '--mesh', type=int, default=30, help='#points in theta-phi mesh') parser.add_argument('shape', choices=SHAPES, nargs='?', default=SHAPES[0], help='oriented shape') opts = parser.parse_args() size = tuple(int(v) for v in opts.size.split(',')) run(opts.shape, size=size, mesh=opts.mesh, dist=opts.distribution, projection=opts.projection)
if __name__ == "__main__": main()