def viz(I, V, f, c, L, dt, C, T, umin, umax, animate=True):
"""Run solver and visualize u at each time level."""
import scitools.std as plt
import time, glob, os
def plot_u(u, x, t, n):
"""user_action function for solver."""
u_e = u_exact(x,t,n)
plt.plot(x, u, 'r-', x, u_e, 'bo',
xlabel='x', ylabel='u',
axis=[0, L, umin, umax],
title='t=%f' % t[n], legend=['numerical sol.', 'Exact sol.'],
show=True)
# Let the initial condition stay on the screen for 2
# seconds, else insert a pause of 0.2 s between each plot
time.sleep(2) if t[n] == 0 else time.sleep(0.2)
plt.savefig('frame_%04d.png' % n) # for movie making
def write_error(u,x,t,n):
u_e = u_exact(x,t,n)
max_diff = ((u-u_e)).max()
err_list.append(max_diff)
print "At t= %.2f, maximum error: %.4E" %(t[n],max_diff)
axis_max = 0.00073*len(t) # Experimentally found (max_err scales ~linearly)
plt.plot(x, u-u_e, 'r-',
xlabel='x', ylabel='u_{num}-u_{exact}',
axis=[0, (len(x)-1)/2.0, -axis_max, axis_max],
title='t=%f' % t[n], legend='Absolute error',
show=True)
def plot_both(u,x,t,n):
u_e = u_exact(x,t,n)
max_diff = ((u-u_e)).max()
err_list.append(max_diff)
print "At t= %.2f, maximum error: %.4E" %(t[n],max_diff)
axis_max = 0.00073*len(t) # Experimentally found (max_err scales ~linearly)
plt.subplot(211)
plt.plot(x, u, 'r-', x, u_e, 'bo',
xlabel='x', ylabel='u',
axis=[0, L, umin, umax],
title='t=%f' % t[n], legend=['numerical sol.', 'Exact sol.'])
plt.subplot(212)
plt.plot(x, u-u_e, 'r-',
xlabel='x', ylabel='u_{num}-u_{exact}',
axis=[0, (len(x)-1)/2.0, -axis_max, axis_max],
legend='Absolute error',
show=True)
# Clean up old movie frames
for filename in glob.glob('frame_*.png'):
os.remove(filename)
# Choose user_action
if animate == None:
user_action = plot_both
else:
user_action = plot_u if animate else write_error
# Let the magic happen
u, x, t, cpu = solver(I, V, f, c, L, dt, C, T, user_action)
def viz(
I,
V,
f,
c,
L,
dt,
C,
T,
ymax, # y axis: [-ymax, ymax]
u_exact, # u_exact(x, t)
animate='u and u_exact', # or 'error'
movie_filename='movie',
):
"""Run solver and visualize u at each time level."""
import scitools.std as plt
import time, glob, os
class Plot:
def __init__(self, ymax, frame_name='frame'):
self.max_error = [] # hold max amplitude errors
self.max_error_t = [] # time points corresp. to max_error
self.frame_name = frame_name
self.ymax = ymax
def __call__(self, u, x, t, n):
"""user_action function for solver."""
if animate == 'u and u_exact':
plt.plot(x,
u,
'r-',
x,
u_exact(x, t[n]),
'b--',
xlabel='x',
ylabel='u',
axis=[0, L, -self.ymax, self.ymax],
title='t=%f' % t[n],
show=True)
else:
error = u_exact(x, t[n]) - u
local_max_error = np.abs(error).max()
# self.max_error holds the increasing amplitude error
if self.max_error == [] or \
local_max_error > max(self.max_error):
self.max_error.append(local_max_error)
self.max_error_t.append(t[n])
# Use user's ymax until the error exceeds that value.
# This gives a growing max value of the yaxis (but
# never shrinking)
self.ymax = max(self.ymax, max(self.max_error))
plt.plot(x,
error,
'r-',
xlabel='x',
ylabel='error',
axis=[0, L, -self.ymax, self.ymax],
title='t=%f' % t[n],
show=True)
plt.savefig('%s_%04d.png' % (self.frame_name, n))
# Clean up old movie frames
for filename in glob.glob('frame_*.png'):
os.remove(filename)
plot = Plot(ymax)
u, x, t, cpu = solver(I, V, f, c, L, dt, C, T, plot)
# Make plot of max error versus time
plt.figure()
plt.plot(plot.max_error_t, plot.max_error)
plt.xlabel('time')
plt.ylabel('max abs(error)')
plt.savefig('error.png')
plt.savefig('error.pdf')
# Make .flv movie file
fps = 4 # Frames per second
codec2ext = dict(flv='flv') #, libx64='mp4',
#libvpx='webm', libtheora='ogg')
filespec = 'frame_%04d.png'
movie_program = 'avconv' # or 'ffmpeg'
for codec in codec2ext:
ext = codec2ext[codec]
cmd = '%(movie_program)s -r %(fps)d -i %(filespec)s '\
'-vcodec %(codec)s %(movie_filename)s.%(ext)s' % vars()
os.system(cmd)
def viz(I, V, f, c, L, Nx, C, T,
ymax, # y axis: [-ymax, ymax]
u_exact, # u_exact(x, t)
animate='u and u_exact', # or 'error'
movie_filename='movie',
):
"""Run solver and visualize u at each time level."""
import scitools.std as plt
import time, glob, os
class Plot:
def __init__(self, ymax, frame_name='frame'):
self.max_error = [] # hold max amplitude errors
self.max_error_t = [] # time points corresponding to max_error
self.frame_name = frame_name
self.ymax = ymax
def __call__(self, u, x, t, n):
"""user_action function for solver."""
if animate == 'u and u_exact':
plt.plot(x, u, 'r-',
x, u_exact(x, t[n]), 'b--',
xlabel='x', ylabel='u',
axis=[0, L, -self.ymax, self.ymax],
title='t=%f' % t[n], show=True)
else:
error = u_exact(x, t[n]) - u
local_max_error = np.abs(error).max()
# self.max_error holds the increasing amplitude error
if self.max_error == [] or \
local_max_error > max(self.max_error):
self.max_error.append(local_max_error)
self.max_error_t.append(t[n])
# Use user's ymax until the error exceeds that value.
# This gives a growing max value of the yaxis (but
# never shrinking)
self.ymax = max(self.ymax, max(self.max_error))
plt.plot(x, error, 'r-',
xlabel='x', ylabel='error',
axis=[0, L, -self.ymax, self.ymax],
title='t=%f' % t[n], show=True)
plt.savefig('%s_%04d.png' % (self.frame_name, n))
# Clean up old movie frames
for filename in glob.glob('frame_*.png'):
os.remove(filename)
plot = Plot(ymax)
u, x, t, cpu = solver(I, V, f, c, L, Nx, C, T, plot)
# Make plot of max error versus time
plt.figure()
plt.plot(plot.max_error_t, plot.max_error)
plt.xlabel('time'); plt.ylabel('max abs(error)')
plt.savefig('error.png')
plt.savefig('error.pdf')
# Make .flv movie file
fps = 4 # Frames per second
codec2ext = dict(flv='flv') #, libx64='mp4', libvpx='webm', libtheora='ogg')
filespec = 'frame_%04d.png'
movie_program = 'avconv' # or 'ffmpeg'
for codec in codec2ext:
ext = codec2ext[codec]
cmd = '%(movie_program)s -r %(fps)d -i %(filespec)s '\
'-vcodec %(codec)s %(movie_filename)s.%(ext)s' % vars()
os.system(cmd)
