adds interpolation plot

documentation/figs/interpolation.py

 import matplotlib.pyplot as plt
 import matplotlib.patches as mpatches
 import math
+import numpy as np
 
-def main():
+def main1():
+    slab = 2
+    nproc = 6
+    f = plt.figure(figsize = (4., 4.))
+    a = f.add_subplot(111)
+    for p in range(nproc):
+        for y in range((nproc)*slab):
+            a.plot([y, y],
+                   range(p*slab, (p+1)*slab),
+                   marker = '.',
+                   linestyle = 'none',
+                   color = 'brown')
+    a.set_ylim(bottom = -1, top = 12)
+    a.set_xlim(left = -1)
+    a.set_xlabel('$z$')
+    a.set_ylabel('$x,y$')
+    a.set_aspect('equal')
+    f.tight_layout(pad = 0.5)
+    f.savefig('interp_problem_0.pdf')
+    for p in range(nproc):
+        color = plt.get_cmap('plasma')(p*1./nproc)
+        a.add_patch(
+                mpatches.Rectangle(
+                        [p*slab, 0],
+                        1, slab*(nproc)-1,
+                        color = color,
+                        alpha = .2))
+        a.text(p*slab+.5, -.6, '$p_{0}$'.format(p),
+               verticalalignment = 'center')
+    f.savefig('interp_problem_1.pdf')
+    for X, Y in [(8.9, 8.3),
+                 (3.3, 2.7)]:
+        a.plot([X], [Y],
+               color = 'black',
+               marker = 'x',
+               markersize = 10,
+               markeredgewidth=3)
+    f.savefig('interp_problem_2.pdf')
+    for X, Y in [(8.9, 8.3),
+                 (3.3, 2.7)]:
+        for n in [1, 2]:
+            a.add_patch(
+                    mpatches.Rectangle(
+                            [math.floor(X-n), math.floor(Y-n)],
+                            2*n+1, 2*n+1,
+                            color = 'green',
+                            alpha = .2))
+            a.text(math.floor(X)+.5, math.floor(Y - n)+.3,
+                   '$I = {0}$'.format(2*n+2),
+                   horizontalalignment = 'center')
+    f.savefig('interp_problem.pdf')
+    f.savefig('interp_problem_3.pdf')
+    return None
+
+def main0():
     slab = 2
     nproc = 6
     f = plt.figure(figsize = (4., 4.))
@@ -56,6 +111,105 @@ def main():
     f.savefig('interp_problem_3.pdf')
     return None
 
+def main_method():
+    N = 5
+    # field is on grid
+    f = plt.figure(figsize = (4., 4.))
+    a = f.add_subplot(111)
+    x = np.array(range(N))
+    xx = np.zeros((x.shape[0], x.shape[0], 2), dtype = np.float64)
+    xx[:, :, 0] = x[None, :]
+    xx[:, :, 1] = x[:, None]
+    a.plot(xx[..., 0], xx[..., 1],
+           marker = '.',
+           linestyle = 'none',
+           color = 'brown')
+    a.set_ylim(bottom = -0.5, top = N-0.5)
+    a.set_xlim(left = -0.5, right = N-0.5)
+    a.set_xlabel('$z$')
+    a.set_ylabel('$x,y$')
+    a.set_aspect('equal')
+    f.tight_layout(pad = 0.5)
+    f.savefig('interp_problem_0.pdf')
+    # add point
+    X = np.array([1.2, 2.6])
+    cell = np.floor([1.2, 2.6])
+    xbar = X - cell
+    a.plot([X[0]], [X[1]],
+            color = 'black',
+            marker = 'x',
+            markersize = 10,
+            markeredgewidth=3)
+    f.savefig('interp_problem_1.pdf')
+    # add cell, position within cell
+    a.add_patch(
+        mpatches.Rectangle(
+                [cell[0], cell[1]],
+                1, 1,
+                color = 'red',
+                alpha = .2))
+    a.plot([cell[0], X[0]],
+           [0.75, 0.75],
+           color = 'black',
+           linewidth = 2,
+           marker = '|'
+           )
+    a.text((cell[0] + X[0])/2, 0.5, '$\\bar{z}$',
+           verticalalignment = 'center',
+           horizontalalignment = 'center')
+    a.plot([3.25, 3.25],
+           [cell[1], X[1]],
+           color = 'black',
+           linewidth = 2,
+           marker = '_'
+           )
+    a.text(3.7, (cell[1] + X[1])/2, '$\\bar{x}, \\bar{y}$',
+           verticalalignment = 'center',
+           horizontalalignment = 'center')
+    f.savefig('interp_problem_2.pdf')
+    a.add_patch(
+        mpatches.Rectangle(
+                [cell[0]-1, cell[1]-1],
+                3, 3,
+                color = 'green',
+                alpha = .2))
+    f.savefig('interp_problem_3.pdf')
+    # add interpolation kernel
+    #for p in range(nproc):
+    #    color = plt.get_cmap('plasma')(p*1./nproc)
+    #    a.add_patch(
+    #            mpatches.Rectangle(
+    #                    [p*slab, 0],
+    #                    1, slab*(nproc)-1,
+    #                    color = color,
+    #                    alpha = .2))
+    #    a.text(p*slab+.5, -.6, '$p_{0}$'.format(p),
+    #           verticalalignment = 'center')
+    #f.savefig('interp_problem_1.pdf')
+    #for X, Y in [(8.9, 8.3),
+    #             (3.3, 2.7)]:
+    #    a.plot([X], [Y],
+    #           color = 'black',
+    #           marker = 'x',
+    #           markersize = 10,
+    #           markeredgewidth=3)
+    #f.savefig('interp_problem_2.pdf')
+    #for X, Y in [(8.9, 8.3),
+    #             (3.3, 2.7)]:
+    #    for n in [1, 2]:
+    #        a.add_patch(
+    #                mpatches.Rectangle(
+    #                        [math.floor(X-n), math.floor(Y-n)],
+    #                        2*n+1, 2*n+1,
+    #                        color = 'green',
+    #                        alpha = .2))
+    #        a.text(math.floor(X)+.5, math.floor(Y - n)+.3,
+    #               '$I = {0}$'.format(2*n+2),
+    #               horizontalalignment = 'center')
+    #f.savefig('interp_problem.pdf')
+    #f.savefig('interp_problem_3.pdf')
+    return None
+
 if __name__ == '__main__':
-    main()
+    main_method()