def plot(x, y, f, title, plt=None):
if plt is None:
#import matplotlib.pylab as plt
import scitools.easyviz as plt
plt.figure()
plt.plot(x, y, x, f)
plt.legend(["approximation", "exact"])
plt.title(title)
return plt
def plot(x, y, f, title, plt=None):
if plt is None:
# import matplotlib.pylab as plt
import scitools.easyviz as plt
plt.figure()
plt.plot(x, y, x, f)
plt.legend(["approximation", "exact"])
plt.title(title)
return plt
def plotConvergence(cls, scale, error4scale, title, legend, regression = False):
p.figure()
p.loglog(scale, error4scale, "k-d", xlabel = "samples", ylabel = "error",) # semilogy
p.title(title)
p.legend(legend)
if regression and len(error4scale) > 1:
p.hold('on')
lineSpace = np.array((scale[0], scale[-1]))
slope, intercept, r_value, p_value, std_err = stats.linregress(scale, np.log10(error4scale))
line = np.power(10, slope * lineSpace + intercept)
p.plot(lineSpace, line, "k:", legend = "{slope:.2}x + c" \
.format(slope = slope))
p.hardcopy(cls.folder + title + " " + t.strftime('%Y-%m-%d_%H-%M') + ".pdf")
def plotConvergenceMean(cls, approx, exact, regression = False):
nApprox = approx.shape[0]
errorMean = np.empty(nApprox)
for curSampleN in range(0, nApprox):
errorMean[curSampleN] = cls.computeError(np.mean(approx[:curSampleN + 1], 0), exact)
p.figure()
# lSpace = p.linspace(0, errorMean.size, errorMean.size)
lSpace = list(i * (len(exact) ** 2) for i in range(nApprox))
p.loglog(lSpace, errorMean, "k-", xlabel = "samples", ylabel = "error",
legend = "E[(Q_M - E[Q])^2]^{1/2}")
print("CompCost: {compCost:5.2e}\t Error: {error:5.4e}"
.format(compCost = lSpace[-1], error = errorMean[-1]))
if regression:
p.hold('on')
lineSpace = np.array((lSpace[0], lSpace[-1]))
slope, intercept, r_value, p_value, std_err = stats.linregress(lSpace, np.log10(errorMean))
line = np.power(10, slope * lineSpace + intercept)
p.plot(lineSpace, line, "k:", legend = "{slope:.2}x + c" \
.format(slope = slope))
# visual_mesh = plot(mesh,title = "Mesh")
# visual_mesh.write_png("Image/mesh_%gx%g.png"%(nx,ny))
# Plot solution
X = 0; Y = 1;
u1,u2 = u0.split(deepcopy = True)
us = u1 if u1.ufl_element().degree() == 1 else \
interpolate(u1, FunctionSpace(mesh, 'Lagrange', 1))
u_box = scitools.BoxField.dolfin_function2BoxField(us, mesh, (nx,ny), uniform_mesh=True)
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, 20,
savefig='Image/Contour of u1_P%g(mesh:%g-%g).png'% (nz,nx,ny), title='Contour plot of u1', colorbar='on')
ev.figure()
ev.surf(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, shading='interp', colorbar='on', title='surf plot of u1', savefig='Image/Surf of u1_P%g(mesh:%g-%g).png'% (nz,nx,ny))
#ev.figure()
#ev.mesh(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values,colorbar='on',shading='interp', title='mesh plot of u1', savefig='Image/Mesh of u1_P%g(mesh:%g-%g).png'% (nz,nx,ny))
# Plot exact solution
u1_ex,u2_ex = u_ex.split(deepcopy = True)
u1_ex = u1_ex if u1_ex.ufl_element().degree() == 1 else \
interpolate(u1_ex, FunctionSpace(mesh, 'Lagrange', 1))
u_box = scitools.BoxField.dolfin_function2BoxField(u1_ex, mesh, (nx,ny), uniform_mesh=True)
ev.figure()
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, 20,
savefig='Image/Contour of exact solution u1_P%g(mesh:%g-%g).png'% (nz,nx,ny), title='Contour plot of exact u1',colorbar='on')
mesh, (nx, ny),
uniform_mesh=True)
# Write out u at mesh point (i,j)
i = nx
j = ny
print 'u(%g,%g)=%g' % (u_box.grid.coor[X][i], u_box.grid.coor[Y][j],
u_box.values[i, j])
ev.contour(u_box.grid.coorv[X],
u_box.grid.coorv[Y],
u_box.values,
14,
savefig='tmp0.eps',
title='Contour plot of u',
clabels='on')
ev.figure()
ev.surf(u_box.grid.coorv[X],
u_box.grid.coorv[Y],
u_box.values,
shading='interp',
colorbar='on',
title='surf plot of u',
savefig='tmp3.eps')
ev.figure()
ev.mesh(u_box.grid.coorv[X],
u_box.grid.coorv[Y],
u_box.values,
title='mesh plot of u',
savefig='tmp4.eps')
# Extract and plot u along the line y=0.5
#from scitools.easyviz.gnuplot_ import *
h0 = 2277. # Height of the top of the mountain (m)
R = 4. # The radius of the mountain (km)
x = y = np.linspace(-10., 10., 41)
xv, yv = plt.ndgrid(x, y) # Grid for x, y values (km)
hv = h0 / (1 + (xv**2 + yv**2) / (R**2)) # Compute height (m)
x = y = np.linspace(-10., 10., 11)
x2v, y2v = plt.ndgrid(x, y) # Define a coarser grid for the vector field
h2v = h0 / (1 + (x2v**2 + y2v**2) / (R**2)) # Compute height for new grid
dhdx, dhdy = np.gradient(h2v) # Compute the gradient vector (dh/dx,dh/dy)
# Draw contours and gradient field of h
plt.figure(9)
plt.quiver(x2v, y2v, dhdx, dhdy, 0, 'r')
plt.hold('on')
plt.contour(xv, yv, hv)
plt.axis('equal')
# end draw contours and gradient field of h
x = y = np.linspace(-5, 5, 11)
xv, yv = plt.ndgrid(x, y)
u = xv**2 + 2 * yv - .5 * xv * yv
v = -3 * yv
# Draw 2D-field
plt.figure(10)
plt.quiver(xv, yv, u, v, 200, 'b')
plt.axis('equal')
import scitools.easyviz as plt
h0 = 2277. # Height of the top of the mountain (m)
R = 4. # The radius of the mountain (km)
x = y = np.linspace(-10., 10., 41)
xv, yv = plt.ndgrid(x, y)
hv = h0/(1+(xv**2+yv**2)/(R**2))
s = np.linspace(0, 2*np.pi, 100)
curve_x = 10*(1 - s/(2*np.pi))*np.cos(s)
curve_y = 10*(1 - s/(2*np.pi))*np.sin(s)
curve_z = h0/(1 + 100*(1 - s/(2*np.pi))**2/(R**2))
# Simple plot of mountain
plt.figure(1)
plt.mesh(xv, yv, hv)
# Simple plot of mountain and parametric curve
plt.figure(2)
plt.surf(xv, yv, hv)
plt.hold('on')
# add the parametric curve. Last parameter controls color of the curve
plt.plot3(curve_x, curve_y, curve_z, 'b-')
# endsimpleplots
# Default two-dimensional contour plot
plt.figure(3)
plt.contour(xv, yv, hv)
"""
# Define a higher-order approximation to the exact solution
t3 = time.time()
Ue=VectorFunctionSpace(mesh,"Lagrange",degree= 3)
u_ex = interpolate(u_exact,Ue)
t4 = time.time()
# Plot exact solution
visual_ue1 = plot(u_ex[0],wireframe = False,title="the exact solution of u1",rescale = True , axes = True, basename = "deflection" ,legend ="u1")
visual_ue2 = plot(u_ex[1],wireframe = False,title="the exact solution of u2",rescale = True , axes = True, basename = "deflection" ,legend ="u2")
visual_ue1.elevate(-65) #tilt camera -65 degree(latitude dir)
visual_ue2.elevate(-65) #tilt camera -65 degree(latitude dir)
visual_ue1.write_png("Image/P%gu1_exact_%gx%g.png"%(num,nx,ny))
visual_ue2.write_png("Image/P%gu2_exact_%gx%g.png"%(num,nx,ny))
interactive()
"""
u1_ex,u2_ex = u_ex.split(deepcopy = True)
u1_ex = u1_ex if u1_ex.ufl_element().degree() == 1 else \
interpolate(u1_ex, FunctionSpace(mesh, 'Lagrange', 1))
u_box = scitools.BoxField.dolfin_function2BoxField(u1_ex, mesh, (nx,ny), uniform_mesh=True)
ev.figure()
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, 20,
savefig='Image/Contour of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny), title='Contour plot of exact u1',colorbar='on')
ev.figure()
ev.surf(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, shading='interp', colorbar='on',
title='surf plot of exact u1', savefig='Image/Surf of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny))
ev.figure()
ev.mesh(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, colorbar="on",
title='mesh plot of exact u1', savefig='Image/Mesh of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny))
"""
h0 = 2277. # Height of the top of the mountain (m)
R = 4. # The radius of the mountain (km)
x = y = np.linspace(-10., 10., 41)
xv, yv = plt.ndgrid(x, y) # Grid for x, y values (km)
hv = h0/(1+(xv**2+yv**2)/(R**2)) # Compute height (m)
x = y = np.linspace(-10.,10.,11)
x2v, y2v = plt.ndgrid(x, y) # Define a coarser grid for the vector field
h2v = h0/(1+(x2v**2+y2v**2)/(R**2)) # Compute height for new grid
dhdx, dhdy = np.gradient(h2v) # Compute the gradient vector (dh/dx,dh/dy)
# Draw contours and gradient field of h
plt.figure(9)
plt.quiver(x2v, y2v, dhdx, dhdy, 0, 'r')
plt.hold('on')
plt.contour(xv, yv, hv)
plt.axis('equal')
# end draw contours and gradient field of h
x = y = np.linspace(-5, 5, 11)
xv, yv = plt.ndgrid(x, y)
u = xv**2 + 2*yv - .5*xv*yv
v = -3*yv
# Draw 2D-field
plt.figure(10)
plt.quiver(xv, yv, u, v, 200, 'b')
plt.axis('equal')
axes=True,
basename="deflection",
legend="u1")
visual_ue2 = plot(u_ex[1],
wireframe=False,
title="the exact solution of u2",
rescale=True,
axes=True,
basename="deflection",
legend="u2")
visual_ue1.elevate(-65) #tilt camera -65 degree(latitude dir)
visual_ue2.elevate(-65) #tilt camera -65 degree(latitude dir)
visual_ue1.write_png("Image/P%gu1_exact_%gx%g.png" % (num, nx, ny))
visual_ue2.write_png("Image/P%gu2_exact_%gx%g.png" % (num, nx, ny))
interactive()
"""
u1_ex,u2_ex = u_ex.split(deepcopy = True)
u1_ex = u1_ex if u1_ex.ufl_element().degree() == 1 else \
interpolate(u1_ex, FunctionSpace(mesh, 'Lagrange', 1))
u_box = scitools.BoxField.dolfin_function2BoxField(u1_ex, mesh, (nx,ny), uniform_mesh=True)
ev.figure()
ev.contour(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, 20,
savefig='Image/Contour of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny), title='Contour plot of exact u1',colorbar='on')
ev.figure()
ev.surf(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, shading='interp', colorbar='on',
title='surf plot of exact u1', savefig='Image/Surf of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny))
ev.figure()
ev.mesh(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values, colorbar="on",
title='mesh plot of exact u1', savefig='Image/Mesh of exact solution u1_P%g(mesh:%g-%g).png'% (num,nx,ny))
"""
import scitools.easyviz as plt
h0 = 2277. # Height of the top of the mountain (m)
R = 4. # The radius of the mountain (km)
x = y = np.linspace(-10., 10., 41)
xv, yv = plt.ndgrid(x, y)
hv = h0 / (1 + (xv**2 + yv**2) / (R**2))
s = np.linspace(0, 2 * np.pi, 100)
curve_x = 10 * (1 - s / (2 * np.pi)) * np.cos(s)
curve_y = 10 * (1 - s / (2 * np.pi)) * np.sin(s)
curve_z = h0 / (1 + 100 * (1 - s / (2 * np.pi))**2 / (R**2))
# Simple plot of mountain
plt.figure(1)
plt.mesh(xv, yv, hv)
# Simple plot of mountain and parametric curve
plt.figure(2)
plt.surf(xv, yv, hv)
plt.hold('on')
# add the parametric curve. Last parameter controls color of the curve
plt.plot3(curve_x, curve_y, curve_z, 'b-')
# endsimpleplots
# Default two-dimensional contour plot
plt.figure(3)
plt.contour(xv, yv, hv)