Include the Python code needed in exercise

interface/c/heat.py

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+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+
+# Set the colormap
+plt.rcParams['image.cmap'] = 'BrBG'
+
+def evolve(u, u_previous, a, dt, dx2, dy2):
+    """Explicit time evolution.
+       u:            new temperature field
+       u_previous:   previous field
+       a:            diffusion constant
+       dt:           time step. """
+
+    n, m = u.shape
+
+    for i in range(1, n-1):
+        for j in range(1, m-1):
+            u[i, j] = u_previous[i, j] + a * dt * ( \
+             (u_previous[i+1, j] - 2*u_previous[i, j] + \
+              u_previous[i-1, j]) / dx2 + \
+             (u_previous[i, j+1] - 2*u_previous[i, j] + \
+                 u_previous[i, j-1]) / dy2 )
+    u_previous[:] = u[:]
+
+def iterate(field, field0, a, dx, dy, timesteps, image_interval):
+    """Run fixed number of time steps of heat equation"""
+
+    dx2 = dx**2
+    dy2 = dy**2
+
+    # For stability, this is the largest interval possible
+    # for the size of the time-step:
+    dt = dx2*dy2 / ( 2*a*(dx2+dy2) )    
+
+    for m in range(1, timesteps+1):
+        evolve(field, field0, a, dt, dx2, dy2)
+        if m % image_interval == 0:
+            write_field(field, m)
+
+def init_fields(filename):
+    # Read the initial temperature field from file
+    field = np.loadtxt(filename)
+    field0 = field.copy() # Array for field of previous time step
+    return field, field0
+
+def write_field(field, step):
+    plt.gca().clear()
+    plt.imshow(field)
+    plt.axis('off')
+    plt.savefig('heat_{0:03d}.png'.format(step))
+
+

interface/c/heat_main.py

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+from __future__ import print_function
+import time
+import argparse
+
+from heat import init_fields, write_field, iterate
+
+
+def main(input_file='bottle.dat', a=0.5, dx=0.1, dy=0.1, 
+         timesteps=200, image_interval=4000):
+
+    # Initialise the temperature field
+    field, field0 = init_fields(input_file)
+
+    print("Heat equation solver")
+    print("Diffusion constant: {}".format(a))
+    print("Input file: {}".format(input_file))
+    print("Parameters")
+    print("----------")
+    print("  nx={} ny={} dx={} dy={}".format(field.shape[0], field.shape[1],
+                                             dx, dy))
+    print("  time steps={}  image interval={}".format(timesteps,
+                                                         image_interval))
+
+    # Plot/save initial field
+    write_field(field, 0)
+    # Iterate
+    t0 = time.time()
+    iterate(field, field0, a, dx, dy, timesteps, image_interval)
+    t1 = time.time()
+    # Plot/save final field
+    write_field(field, timesteps)
+
+    print("Simulation finished in {0} s".format(t1-t0))
+
+if __name__ == '__main__':
+
+    # Process command line arguments
+    parser = argparse.ArgumentParser(description='Heat equation')
+    parser.add_argument('-dx', type=float, default=0.01,
+                        help='grid spacing in x-direction')
+    parser.add_argument('-dy', type=float, default=0.01,
+                        help='grid spacing in y-direction')
+    parser.add_argument('-a', type=float, default=0.5,
+                        help='diffusion constant')
+    parser.add_argument('-n', type=int, default=200,
+                        help='number of time steps')
+    parser.add_argument('-i', type=int, default=4000,
+                        help='image interval')
+    parser.add_argument('-f', type=str, default='bottle.dat', 
+                        help='input file')
+
+    args = parser.parse_args()
+
+    main(args.f, args.a, args.dx, args.dy, args.n, args.i)
+