-                      rd4c33d6
+                      raa6989b
+#!/usr/bin/env python
 """
 Application to explore the difference between sasview 3.x orientation
 dispersity and possible replacement algorithms.
 """
+import sys
+from __future__ import division, print_function
+import sys, os
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.realpath(__file__))))
 import mpl_toolkits.mplot3d   # Adds projection='3d' option to subplot
 …
 def draw_beam(ax, view=(0, 0)):
+    """
+    Draw the beam going from source at (0, 0, 1) to detector at (0, 0, -1)
+    """
     #ax.plot([0,0],[0,0],[1,-1])
     #ax.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=0.8)
 …
     ax.plot_surface(x, y, z, rstride=4, cstride=4, color='y', alpha=0.5)
+def draw_jitter(ax, view, jitter):
+    size = [0.1, 0.4, 1.0]
+def draw_jitter(ax, view, jitter, dist='gaussian', size=(0.1, 0.4, 1.0)):
+    """
+    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)
     draw_shape = draw_parallelepiped
     #draw_shape = draw_ellipsoid
 …
         cloud = [v for v in cloud if v[2] == 0]
     draw_shape(ax, size, view, [0, 0, 0], steps=100, alpha=0.8)
+    scale = 1/sqrt(3) if dist == 'rectangle' else 1
     for point in cloud:
         delta = [dtheta*point[0], dphi*point[1], dpsi*point[2]]
+        delta = [scale*dtheta*point[0], scale*dphi*point[1], scale*dpsi*point[2]]
         draw_shape(ax, size, view, delta, alpha=0.8)
     for v in 'xyz':
 …
 def draw_ellipsoid(ax, size, view, jitter, steps=25, alpha=1):
+    """Draw an ellipsoid."""
     a,b,c = size
     u = np.linspace(0, 2 * np.pi, steps)
 …
 def draw_parallelepiped(ax, 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])
 …
     ])
+def draw_mesh(ax, view, jitter, radius=1.2, n=11, dist='gauss'):
+def draw_sphere(ax, 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))
+    ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w')
+def draw_mesh(ax, view, jitter, radius=1.2, n=11, dist='gaussian'):
+    """
+    Draw the dispersion mesh showing the theta-phi orientations at which
+    the model will be evaluated.
+    """
     theta, phi, psi = view
     dtheta, dphi, dpsi = jitter
+    if dist == 'gauss':
+    if dist == 'gaussian':
         t = np.linspace(-3, 3, n)
         weights = exp(-0.5*t**2)
+    elif dist == 'rect':
+        t = np.linspace(0, 1, n)
+    elif dist == 'rectangle':
+        # Note: uses sasmodels ridiculous definition of rectangle width
+        t = np.linspace(-1, 1, n)*sqrt(3)
         weights = np.ones_like(t)
     else:
         raise ValueError("expected dist to be 'gauss' or 'rect'")
+        raise ValueError("expected dist to be 'gaussian' or 'rectangle'")
     # mesh in theta, phi formed by rotating z
 …
     points = orient_relative_to_beam(view, points)
     w = np.outer(weights, weights)
+    w = np.outer(weights*cos(radians(dtheta*t)), weights)
     x, y, z = [np.array(v).flatten() for v in points]
     ax.scatter(x, y, z, c=w.flatten(), marker='o', vmin=0., vmax=1.)
+def draw_labels(ax, 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()
+        ax.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
 def Rx(angle):
+    """Construct a matrix to rotate points about *x* by *angle* degrees."""
     a = radians(angle)
     R = [[1., 0., 0.],
          [0.,  cos(a), sin(a)],
          [0., -sin(a), cos(a)]]
+    R = [[1, 0, 0],
+         [0, +cos(a), -sin(a)],
+         [0, +sin(a), +cos(a)]]
     return np.matrix(R)
 def Ry(angle):
+    """Construct a matrix to rotate points about *y* by *angle* degrees."""
     a = radians(angle)
     R = [[cos(a), 0., -sin(a)],
          [0., 1., 0.],
          [sin(a), 0.,  cos(a)]]
+    R = [[+cos(a), 0, +sin(a)],
+         [0, 1, 0],
+         [-sin(a), 0, +cos(a)]]
     return np.matrix(R)
 def Rz(angle):
+    """Construct a matrix to rotate points about *z* by *angle* degrees."""
     a = radians(angle)
     R = [[cos(a), -sin(a), 0.],
          [sin(a),  cos(a), 0.],
          [0., 0., 1.]]
+    R = [[+cos(a), -sin(a), 0],
+         [+sin(a), +cos(a), 0],
+         [0, 0, 1]]
     return np.matrix(R)
 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
 …
 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
 …
 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
+def draw_labels(ax, view, jitter, text):
+    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)
+    for label, p, zdir in zip(labels, zip(px, py, pz), zip(dx, dy, dz)):
+        zdir = np.asarray(zdir).flatten()
+        ax.text(p[0], p[1], p[2], label, zdir=zdir)
+def draw_sphere(ax, radius=10., steps=100):
+    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))
+    ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w')
+def main():
+# 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
+}
+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]
+def draw_scattering(calculator, ax, view, jitter, dist='gaussian'):
+    """
+    Plot the scattering for the particular view.
+    *calculator* is returned from :func:`build_model`.  *ax* 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.
+    """
+    ## Sasmodels use sqrt(3)*width for the rectangle range; scale to the
+    ## proper width for comparison. Commented out since now using the
+    ## sasmodels definition of width for rectangle.
+    #scale = 1/sqrt(3) if dist == 'rectangle' else 1
+    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:
+        vmin, vmax = clipped_range(Iqxy, portion=0.95, 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)
+        ax.plot_surface(qx, qy, -1.1, rstride=1, cstride=1, facecolors=colors)
+    elif 1:
+        ax.contourf(qx/qx.max(), qy/qy.max(), Iqxy, zdir='z', offset=-1.1,
+                    levels=np.linspace(vmin, vmax, 24))
+    else:
+        ax.pcolormesh(qx, qy, Iqxy)
+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
+    from sasmodels.data import empty_data2D
+    from sasmodels.direct_model import DirectModel
+    model_info = load_model_info(model_name)
+    model = build_model(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
+def select_calculator(model_name, n=150):
+    """
+    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 = 10, 40, 100
+    if model_name == 'sphere':
+        calculator = build_model('sphere', n=n, radius=c)
+        a = b = c
+    elif model_name == 'bcc_paracrystal':
+        calculator = build_model('bcc_paracrystal', n=n, dnn=c,
+                                  d_factor=0.06, radius=40)
+        a = b = c
+    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)
+def main(model_name='parallelepiped'):
+    """
+    Show an interactive orientation and jitter demo.
+    *model_name* is one of the models available in :func:`select_model`.
+    """
+    # set up calculator
+    calculator, size = select_calculator(model_name, n=150)
+    ## 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
+    ## use gaussian distribution unless testing integration
+    #dist = 'rectangle'
+    dist = 'gaussian'
+    ## 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.set_cmap('gist_earth')
 …
     #ax = plt.subplot(gs[0], projection='3d')
     ax = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d')
+    theta, dtheta = 70., 10.
+    phi, dphi = -45., 3.
+    psi, dpsi = -45., 3.
+    theta, phi, psi = 0, 0, 0
+    dtheta, dphi, dpsi = 0, 0, 0
+    #dist = 'rect'
+    dist = 'gauss'
+    ax.axis('square')
     axcolor = 'lightgoldenrodyellow'
+    ## add control widgets to plot
     axtheta  = plt.axes([0.1, 0.15, 0.45, 0.04], axisbg=axcolor)
     axphi = plt.axes([0.1, 0.1, 0.45, 0.04], axisbg=axcolor)
 …
     axdphi = plt.axes([0.75, 0.1, 0.15, 0.04], axisbg=axcolor)
     axdpsi= plt.axes([0.75, 0.05, 0.15, 0.04], axisbg=axcolor)
+    sdtheta = Slider(axdtheta, 'dTheta', 0, 30, valinit=dtheta)
+    sdphi = Slider(axdphi, 'dPhi', 0, 30, valinit=dphi)
+    sdpsi = Slider(axdpsi, 'dPsi', 0, 30, valinit=dpsi)
+    # 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 = 30 if dist == 'gaussian' else 90/sqrt(3)
+    sdtheta = Slider(axdtheta, 'dTheta', 0, dlimit, valinit=dtheta)
+    sdphi = Slider(axdphi, 'dPhi', 0, 2*dlimit, valinit=dphi)
+    sdpsi = Slider(axdpsi, '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, 2, 5][dims]
+        jitter = [0 if v < limit else v for v in jitter]
         ax.cla()
         draw_beam(ax, (0, 0))
         draw_jitter(ax, view, jitter)
+        draw_jitter(ax, view, jitter, dist=dist, size=size)
         #draw_jitter(ax, view, (0,0,0))
+        draw_mesh(ax, view, jitter)
+        draw_mesh(ax, view, jitter, dist=dist)
+        draw_scattering(calculator, ax, 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'))
 …
     sdpsi.on_changed(lambda v: update(v, 'dpsi'))
+    ## initialize view
     update(None, 'phi')
+    ## go interactive
     plt.show()
 if __name__ == "__main__":
+    main()
+    model_name = sys.argv[1] if len(sys.argv) > 1 else 'parallelepiped'
+    main(model_name)

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SasView

Changeset aa6989b in sasmodels for explore/jitter.py

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explore/jitter.py

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