def comparison_plot(f, u, Omega, plotfile='tmp'):
"""Compare f(x,y) and u(x,y) for x,y in Omega in a plot."""
x, y = sm.symbols('x y')
f = sm.lambdify([x,y], f, modules="numpy")
u = sm.lambdify([x,y], u, modules="numpy")
# When doing symbolics, Omega can easily contain symbolic expressions,
# assume .evalf() will work in that case to obtain numerical
# expressions, which then must be converted to float before calling
# linspace below
for r in range(2):
for s in range(2):
if not isinstance(Omega[r][s], (int,float)):
Omega[r][s] = float(Omega[r][s].evalf())
resolution = 41 # no of points in plot
xcoor = linspace(Omega[0][0], Omega[0][1], resolution)
ycoor = linspace(Omega[1][0], Omega[1][1], resolution)
xv, yv = ndgrid(xcoor, ycoor)
# Vectorized functions expressions does not work with
# lambdify'ed functions without the modules="numpy"
exact = f(xv, yv)
approx = u(xv, yv)
figure()
surfc(xv, yv, exact, title='f(x,y)',
colorbar=True, colormap=hot(), shading='flat')
if plotfile:
savefig('%s_f.pdf' % plotfile, color=True)
savefig('%s_f.png' % plotfile)
figure()
surfc(xv, yv, approx, title='f(x,y)',
colorbar=True, colormap=hot(), shading='flat')
if plotfile:
savefig('%s_u.pdf' % plotfile, color=True)
savefig('%s_u.png' % plotfile)
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 test_easyviz():
from scitools.std import linspace, ndgrid, plot, contour, peaks, \
quiver, surfc, backend, get_backend
n = 21
x = linspace(-3, 3, n)
xx, yy = ndgrid(x, x, sparse=False)
# a basic plot
plot(x, x**2, 'bx:')
wait()
if backend in ['gnuplot', 'vtk', 'matlab', 'dx', 'visit', 'veusz']:
# a contour plot
contour(peaks(n), title="contour plot")
wait()
# a vector plot
uu = yy
vv = xx
quiver(xx, yy, uu, vv)
wait()
# a surface plot with contours
zz = peaks(xx, yy)
surfc(xx, yy, zz, colorbar=True)
wait()
if backend == 'grace':
g = get_backend()
g('exit')
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 test_easyviz():
from scitools.std import linspace, ndgrid, plot, contour, peaks, \
quiver, surfc, backend, get_backend
n = 21
x = linspace(-3, 3, n)
xx, yy = ndgrid(x, x, sparse=False)
# a basic plot
plot(x, x**2, 'bx:')
wait()
if backend in ['gnuplot', 'vtk', 'matlab', 'dx', 'visit', 'veusz']:
# a contour plot
contour(peaks(n), title="contour plot")
wait()
# a vector plot
uu = yy
vv = xx
quiver(xx, yy, uu, vv)
wait()
# a surface plot with contours
zz = peaks(xx, yy)
surfc(xx, yy, zz, colorbar=True)
wait()
if backend == 'grace':
g = get_backend()
g('exit')
