def non_physical_behavior(I, a, T, dt, theta):
"""
Given lists/arrays a and dt, and numbers I, dt, and theta,
make a two-dimensional contour line B=0.5, where B=1>0.5
means oscillatory (unstable) solution, and B=0<0.5 means
monotone solution of u'=-au.
"""
a = np.asarray(a); dt = np.asarray(dt) # must be arrays
B = np.zeros((len(a), len(dt))) # results
for i in range(len(a)):
for j in range(len(dt)):
u, t = solver(I, a[i], T, dt[j], theta)
# Does u have the right monotone decay properties?
correct_qualitative_behavior = True
for n in range(1, len(u)):
if u[n] > u[n-1]: # Not decaying?
correct_qualitative_behavior = False
break # Jump out of loop
B[i,j] = float(correct_qualitative_behavior)
a_, dt_ = st.ndgrid(a, dt) # make mesh of a and dt values
st.contour(a_, dt_, B, 1)
st.grid('on')
st.title('theta=%g' % theta)
st.xlabel('a'); st.ylabel('dt')
st.savefig('osc_region_theta_%s.png' % theta)
st.savefig('osc_region_theta_%s.pdf' % theta)
def non_physical_behavior(I, a, T, dt, theta):
"""
Given lists/arrays a and dt, and numbers I, dt, and theta,
make a two-dimensional contour line B=0.5, where B=1>0.5
means oscillatory (unstable) solution, and B=0<0.5 means
monotone solution of u'=-au.
"""
a = np.asarray(a)
dt = np.asarray(dt) # must be arrays
B = np.zeros((len(a), len(dt))) # results
for i in range(len(a)):
for j in range(len(dt)):
u, t = solver(I, a[i], T, dt[j], theta)
# Does u have the right monotone decay properties?
correct_qualitative_behavior = True
for n in range(1, len(u)):
if u[n] > u[n - 1]: # Not decaying?
correct_qualitative_behavior = False
break # Jump out of loop
B[i, j] = float(correct_qualitative_behavior)
a_, dt_ = st.ndgrid(a, dt) # make mesh of a and dt values
st.contour(a_, dt_, B, 1)
st.grid('on')
st.title('theta=%g' % theta)
st.xlabel('a')
st.ylabel('dt')
st.savefig('osc_region_theta_%s.png' % theta)
st.savefig('osc_region_theta_%s.eps' % theta)
def amplification_factor(names):
# Use SciTools since it adds markers to colored lines
from scitools.std import (
plot, title, xlabel, ylabel, hold, savefig,
axis, legend, grid, show, figure)
figure()
curves = {}
p = linspace(0, 3, 99)
curves['exact'] = A_exact(p)
plot(p, curves['exact'])
hold('on')
name2theta = dict(FE=0, BE=1, CN=0.5)
for name in names:
curves[name] = A(p, name2theta[name])
plot(p, curves[name])
axis([p[0], p[-1], -20, 20])
#semilogy(p, curves[name])
plot([p[0], p[-1]], [0, 0], '--') # A=0 line
title('Amplification factors')
grid('on')
legend(['exact'] + names, loc='lower left', fancybox=True)
xlabel(r'$p=-a\cdot dt$')
ylabel('Amplification factor')
savefig('A_growth.png'); savefig('A_growth.pdf')
def amplification_factor(names):
# Use SciTools since it adds markers to colored lines
from scitools.std import (plot, title, xlabel, ylabel, hold, savefig,
axis, legend, grid, show, figure)
figure()
curves = {}
p = linspace(0, 3, 99)
curves['exact'] = A_exact(p)
plot(p, curves['exact'])
hold('on')
name2theta = dict(FE=0, BE=1, CN=0.5)
for name in names:
curves[name] = A(p, name2theta[name])
plot(p, curves[name])
axis([p[0], p[-1], -20, 20])
#semilogy(p, curves[name])
plot([p[0], p[-1]], [0, 0], '--') # A=0 line
title('Amplification factors')
grid('on')
legend(['exact'] + names, loc='lower left', fancybox=True)
xlabel(r'$p=-a\cdot dt$')
ylabel('Amplification factor')
savefig('A_growth.png')
savefig('A_growth.pdf')
