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 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 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 plot_u(u, x, xv, y, yv, t, n):
"""User action function for plotting."""
if t[n] == 0:
time.sleep(2)
if plot_method == 1:
# Works well with Gnuplot backend, not with Matplotlib
st.mesh(x, y, u, title='t=%g' % t[n], zlim=[-1,1],
caxis=[-1,1])
elif plot_method == 2:
# Works well with Gnuplot backend, not with Matplotlib
st.surfc(xv, yv, u, title='t=%g' % t[n], zlim=[-1, 1],
colorbar=True, colormap=st.hot(), caxis=[-1,1],
shading='flat')
elif plot_method == 3:
print 'Experimental 3D matplotlib...under development...'
# Probably too slow
#plt.clf()
ax = fig.add_subplot(111, projection='3d')
u_surf = ax.plot_surface(xv, yv, u, alpha=0.3)
#ax.contourf(xv, yv, u, zdir='z', offset=-100, cmap=cm.coolwarm)
#ax.set_zlim(-1, 1)
# Remove old surface before drawing
if u_surf is not None:
ax.collections.remove(u_surf)
plt.draw()
time.sleep(1)
elif plot_method == 4:
# Mayavi visualization
mlab.clf()
extent1 = (0, 20, 0, 20,-2, 2)
s = mlab.surf(x , y, u,
colormap='Blues',
warp_scale=5,extent=extent1)
mlab.axes(s, color=(.7, .7, .7), extent=extent1,
ranges=(0, 10, 0, 10, -1, 1),
xlabel='', ylabel='', zlabel='',
x_axis_visibility=False,
z_axis_visibility=False)
mlab.outline(s, color=(0.7, .7, .7), extent=extent1)
mlab.text(6, -2.5, '', z=-4, width=0.14)
mlab.colorbar(object=None, title=None,
orientation='horizontal',
nb_labels=None, nb_colors=None,
label_fmt=None)
mlab.title('Gaussian t=%g' % t[n])
mlab.view(142, -72, 50)
f = mlab.gcf()
camera = f.scene.camera
camera.yaw(0)
if plot_method > 0:
time.sleep(0) # pause between frames
if save_plot:
filename = 'tmp_%04d.png' % n
if plot_method == 4:
mlab.savefig(filename) # time consuming!
elif plot_method in (1,2):
st.savefig(filename) # time consuming!
def surf(self, N, component=0):
"""surf plot of scalar or one component of tensor"""
if comm.Get_size() > 1:
print "No surf for multiple processors"
return
if len(self.dims) == 3:
print "No surf for 3D cube"
return
z = self.array(N=N, component=component).reshape(*self.dims[::-1])
x = self.create_dense_grid()
surfc(x[:, 0].reshape(*self.dims[::-1]), x[:, 1].reshape(*self.dims[::-1]), z, indexing='xy')
def surf(self, N, component=0):
"""surf plot of scalar or one component of tensor"""
if comm.Get_size() > 1:
print("No surf for multiple processors")
return
if len(self.dims) == 3:
print("No surf for 3D cube")
return
z = self.array(N=N, component=component).reshape(*self.dims[::-1])
x = self.create_dense_grid()
surfc(x[:, 0].reshape(*self.dims[::-1]), x[:, 1].reshape(*self.dims[::-1]), z, indexing='xy')
def plot_u(u, x, xv, y, yv, t, n):
"""User action function for plotting."""
if t[n] == 0:
time.sleep(2)
if plot_method == 1:
# Works well with Gnuplot backend, not with Matplotlib
st.mesh(x, y, u, title='t=%g' % t[n], zlim=[-1, 1], caxis=[-1, 1])
elif plot_method == 2:
# Works well with Gnuplot backend, not with Matplotlib
st.surfc(xv,
yv,
u,
title='t=%g' % t[n],
zlim=[-1, 1],
colorbar=True,
colormap=st.hot(),
caxis=[-1, 1],
shading='flat')
elif plot_method == 3:
print 'Experimental 3D matplotlib...under development...'
# Probably too slow
#plt.clf()
ax = fig.add_subplot(111, projection='3d')
u_surf = ax.plot_surface(xv, yv, u, alpha=0.3)
#ax.contourf(xv, yv, u, zdir='z', offset=-100, cmap=cm.coolwarm)
#ax.set_zlim(-1, 1)
# Remove old surface before drawing
if u_surf is not None:
ax.collections.remove(u_surf)
plt.draw()
time.sleep(1)
elif plot_method == 4:
# Mayavi visualization
mlab.clf()
extent1 = (0, 20, 0, 20, -2, 2)
s = mlab.surf(x,
y,
u,
colormap='Blues',
warp_scale=5,
extent=extent1)
mlab.axes(s,
color=(.7, .7, .7),
extent=extent1,
ranges=(0, 10, 0, 10, -1, 1),
xlabel='',
ylabel='',
zlabel='',
x_axis_visibility=False,
z_axis_visibility=False)
mlab.outline(s, color=(0.7, .7, .7), extent=extent1)
mlab.text(6, -2.5, '', z=-4, width=0.14)
mlab.colorbar(object=None,
title=None,
orientation='horizontal',
nb_labels=None,
nb_colors=None,
label_fmt=None)
mlab.title('Gaussian t=%g' % t[n])
mlab.view(142, -72, 50)
f = mlab.gcf()
camera = f.scene.camera
camera.yaw(0)
if plot_method > 0:
time.sleep(0) # pause between frames
if save_plot:
filename = 'tmp_%04d.png' % n
if plot_method == 4:
mlab.savefig(filename) # time consuming!
elif plot_method in (1, 2):
st.savefig(filename) # time consuming!
def project5f(self):
'''2D surface plots '''
dxValues = [0.1] #, 0.01]
safetyFacors = [1.04] #[0.8]
movieCounter = 0
dimension = "2D"
threadNumber = 8
FontSizeUniversal = 22
showMovie = True
for dx in dxValues:
nx = int(round(1. / dx + 1))
x = np.linspace(0, 1, nx)
y = x
X, Y = np.meshgrid(x, y)
for safetyFactor in safetyFacors:
movieCounter += 1
dt = dx**2 / 4.0 * (1 / safetyFactor)
alpha = dt / dx**2
theta = 0.5
T = .15
nT = int(round(T / dt + 1))
outfileName = 'out5f'
outfileName2 = os.getcwd() + '/results/' + outfileName
saveEveryNSolution = 10
self.runCpp(outfileName2, dt, dx, theta, T, dimension,
threadNumber)
# Read data
scenerios = ['Explicit', 'Analytical']
xv = x.reshape((x.size, 1))
yv = y.reshape((1, y.size))
fileCounter = 1
st.setp(interactive=False)
if showMovie:
for fileCounter in xrange(1, nT):
data = pd.read_csv(
outfileName2 +
'ImplicitSolutionMatrixUTime%d.txt' % fileCounter,
delim_whitespace=True,
header=None)
st.surfc(xv,
yv,
data,
title='Implicit Time = %.4f' %
((fileCounter - 1) * dt),
zlim=[-0.1, 1.1],
colorbar=True,
colormap=st.hot(),
caxis=[-0.1, 1.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpImplicit_%04d' % fileCounter +
outfileName + '.png')
data2 = pd.read_csv(
outfileName2 +
'ExplicitSolutionMatrixUTime%d.txt' % fileCounter,
delim_whitespace=True,
header=None)
st.surfc(xv,
yv,
data2,
title='Explicit Time = %.4f' %
((fileCounter - 1) * dt),
zlim=[-0.1, 1.1],
colorbar=True,
colormap=st.hot(),
caxis=[-0.1, 1.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpExplicit_%04d' % fileCounter +
outfileName + '.png')
data3 = pd.read_csv(
outfileName2 +
'AnalyticalSolutionMatrixU2D%d.txt' % fileCounter,
delim_whitespace=True,
header=None)
st.surfc(xv,
yv,
data3,
title='Analytical Time = %.4f' %
((fileCounter - 1) * dt),
fontsize=30,
zlim=[-0.1, 1.1],
colorbar=True,
colormap=st.hot(),
caxis=[-0.1, 1.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpAnalytic_%04d' % fileCounter +
outfileName + '.png')
data4 = pd.read_csv(
outfileName2 +
'GaussSeidelSolutionMatrixUTime%d.txt' %
fileCounter,
delim_whitespace=True,
header=None)
st.surfc(xv,
yv,
data4,
title='Gauss-Seidel Time = %.4f' %
((fileCounter - 1) * dt),
fontsize=30,
zlim=[-0.1, 1.1],
colorbar=True,
colormap=st.hot(),
caxis=[-0.1, 1.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpGaussSeidel_%04d' % fileCounter +
outfileName + '.png')
st.surfc(xv,
yv, (data / data3 - 1) * 100,
title='Implicit-Analytical time = %.4f' %
((fileCounter - 1) * dt),
zlim=[-100.1, 100.1],
colorbar=True,
colormap=st.hot(),
caxis=[-100.1, 100.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpErrorImplicit_%04d' %
fileCounter + outfileName + '.png')
st.surfc(xv,
yv, (data2 / data3 - 1) * 100,
title='Explicit-Analytical time = %.4f' %
((fileCounter - 1) * dt),
zlim=[-100.1, 100.1],
colorbar=True,
colormap=st.hot(),
caxis=[-100.1, 100.1],
shading='flat',
xlabel='x',
ylabel='y',
zlabel='u') #
st.savefig('movie/tmpErrorExplicit_%04d' %
fileCounter + outfileName + '.png')
data = pd.read_csv(outfileName2 + 'Timing.txt', delimiter=',')
width = 0.35
fig, ax = plt.subplots()
rects1 = ax.bar(np.arange(3), [
np.asscalar(data.implicit.values),
np.asscalar(data.analytic.values),
np.asscalar(data.analytic.values) /
np.asscalar(data.implicit.values)
], width) #, color='r')
fontSizes = 20
ax.set_title('Timing Numerical and analytical', fontsize=fontSizes)
ax.set_xticks(np.arange(3) + width / 10)
ax.set_xticklabels(
('Implicit', 'Analytical', r'$\frac{Analytical}{Numerical}$'))
#plt.show()
fig.tight_layout()
plt.savefig(outfileName2 + 'Timing.png')
return data