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))
n = 0
while n<N and T[n]>=temp_after_death-0.0001 :
T[n+1] = (T[n] - k*dt*((1-theta)*T[n] - T_s))/(1.0 + theta*dt*k)
n = n + 1
t = linspace(0,t_end,N+1)
return T,t
def exact_sol(T0,k,T_s,t_end,dt):
N = int(round(t_end/float(dt)))
t = linspace(0,t_end,N+1)
exact = (T0-T_s)*exp(-t*k) + T_s
return exact,t
if __name__ == "__main__":
T,t = cooling(37.5, 0.1, 14.0, 60.0, 5, 0.5)
plot(t,T,"r--o")
T_exact,t = exact_sol(37.5, 0.1, 14.0, 60.0, 5)
#figure()
hold("on")
plot(t,T_exact)
legend(["discrete sol","exact sol"])
print "maximum error :" ,max(abs(T-T_exact))
raw_input("press enter")
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')
# end draw 2D-field
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)
# Default three-dimensional contour plot
plt.figure(4)
plt.contour3(xv, yv, hv, 10)
# 10 contour lines (equally spaced contour levels)
plt.figure(5)