Initial data added.

1 files changed, 118 insertions, 0 deletions

diff --git a/day2/demo.py b/day2/demo.py
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+import numpy as np
+import pylab as P
+from enthought.mayavi import mlab
+from scipy.integrate import odeint
+
+
+######################################################################
+def lorenz(x, y, z, s=10.,r=28., b=8./3.):
+    """The Lorenz system."""
+    u = s*(y-x)
+    v = r*x -y - x*z
+    w = x*y - b*z
+    return u, v, w
+
+def lorenz_ode(r, t):
+    x, y, z = r
+    u, v, w = lorenz(x, y, z)
+    return np.array([u, v, w])
+
+def show_lorenz(new_fig=True):
+    x, y, z = np.mgrid[-50:50:100j,-50:50:100j,-10:60:70j]
+    u, v, w = lorenz(x, y, z)
+
+    if new_fig:
+        fig = mlab.figure(size=(600,600), bgcolor=(0, 0, 0))
+
+    # Plot the flow of trajectories with suitable parameters.
+    f = mlab.flow(x, y, z, u, v, w, line_width=3, colormap='Paired')
+    f.module_manager.scalar_lut_manager.reverse_lut = True
+    f.stream_tracer.integration_direction = 'both'
+    f.stream_tracer.maximum_propagation = 200
+
+def show_lorenz_traj(start=(0.,0.,0.)):
+    t = np.linspace(0., 50., 2000)
+    ret = lorenz_traj(t, np.asarray(start))
+    x, y, z = ret[:,0], ret[:,1], ret[:,2]
+    mlab.plot3d(x, y, z, t, tube_radius=None)
+
+
+def lorenz_traj(t, start=(0.,0.,0.)):
+    return odeint(lorenz_ode, start, t)
+    
+
+######################################################################
+
+def convection_cell(x, y, z):
+    """velocity field of a multi-axis convection cell [1], in
+    hydrodynamics, as defined by its components sampled on a grid. 
+    """
+    u =  np.sin(np.pi*x) * np.cos(np.pi*z)
+    v = -2*np.sin(np.pi*y) * np.cos(2*np.pi*z)
+    w = np.cos(np.pi*x)*np.sin(np.pi*z) + np.cos(np.pi*y)*np.sin(2*np.pi*z)
+    return u, v, w
+
+def show_convection1(new_fig=True):
+    x, y, z = np.mgrid[0:1:20j, 0:1:20j, 0:1:20j]
+    u, v, w = convection_cell(x, y, z)
+    if new_fig:
+        mlab.figure(size=(600,600))
+
+    mlab.quiver3d(u, v, w)
+    mlab.outline()
+
+def show_convection2(new_fig=True):
+    x, y, z = np.mgrid[0:1:20j, 0:1:20j, 0:1:20j]
+    u, v, w = convection_cell(x, y, z)
+    if new_fig:
+        mlab.figure(size=(600,600))
+
+    src = mlab.pipeline.vector_field(u, v, w)
+    mlab.pipeline.vectors(src, mask_points=20, scale_factor=3.)
+    mlab.outline()
+
+def show_convection3(new_fig=True):
+    x, y, z = np.mgrid[0:1:20j, 0:1:20j, 0:1:20j]
+    u, v, w = convection_cell(x, y, z)
+
+    if new_fig:
+        mlab.figure(fgcolor=(0., 0., 0.), bgcolor=(0.5, 0.5, 0.5),
+                    size=(600,600))
+    src = mlab.pipeline.vector_field(u, v, w)
+    magnitude = mlab.pipeline.extract_vector_norm(src)
+    mlab.outline()
+
+    # We apply the following modules on the magnitude object, in order to
+    # be able to display the norm of the vectors, eg as the color.
+    iso = mlab.pipeline.iso_surface(magnitude, contours=[1.9, ], 
+                                    opacity=0.3)
+
+    vec = mlab.pipeline.vectors(magnitude, 
+                                mask_points=40,
+                                line_width=1,
+                                color=(1, 1, 1),
+                                scale_factor=4.)
+
+    flow = mlab.pipeline.streamline(magnitude, 
+                                    seedtype='plane',
+                                    seed_visible=True,
+                                    seed_scale=0.5,
+                                    seed_resolution=1,
+                                    linetype='ribbon',)
+
+    vcp = mlab.pipeline.vector_cut_plane(magnitude, mask_points=2,
+                                         scale_factor=4,
+                                         colormap='jet',
+                                         plane_orientation='x_axes')
+
+
+def test():
+    show_lorenz()
+    show_lorenz_traj((10, 50, 50))
+    show_convection1()
+    show_convection2()
+    show_convection3()
+
+if __name__ == '__main__':
+    test()
+