def compute4web(I, a, T, dt, theta=0.5):
"""
Run a case with the solver, compute error measure,
and plot the numerical and exact solutions in a PNG
plot whose data are embedded in an HTML image tag.
"""
u, t = solver(I, a, T, dt, theta)
u_e = u_exact(t, I, a)
e = u_e - u
E = np.sqrt(dt * np.sum(e**2))
plt.figure()
t_e = np.linspace(0, T, 1001) # fine mesh for u_e
u_e = u_exact(t_e, I, a)
plt.plot(t, u, 'r--o')
plt.plot(t_e, u_e, 'b-')
plt.legend(['numerical', 'exact'])
plt.xlabel('t')
plt.ylabel('u')
plt.title('theta=%g, dt=%g' % (theta, dt))
# Save plot to HTML img tag with PNG code as embedded data
from parampool.utils import save_png_to_str
html_text = save_png_to_str(plt, plotwidth=400)
return E, html_text
def compute4web(I, a, T, dt, theta=0.5):
"""
Run a case with the solver, compute error measure,
and plot the numerical and exact solutions in a PNG
plot whose data are embedded in an HTML image tag.
"""
u, t = solver(I, a, T, dt, theta)
u_e = u_exact(t, I, a)
e = u_e - u
E = np.sqrt(dt * np.sum(e ** 2))
plt.figure()
t_e = np.linspace(0, T, 1001) # fine mesh for u_e
u_e = u_exact(t_e, I, a)
plt.plot(t, u, "r--o")
plt.plot(t_e, u_e, "b-")
plt.legend(["numerical", "exact"])
plt.xlabel("t")
plt.ylabel("u")
plt.title("theta=%g, dt=%g" % (theta, dt))
# Save plot to HTML img tag with PNG code as embedded data
from parampool.utils import save_png_to_str
html_text = save_png_to_str(plt, plotwidth=400)
return E, html_text
def compute4web(I, a, T, dt, theta=0.5):
"""
Run a case with the solver, compute error measure,
and plot the numerical and exact solutions in a PNG
plot whose data are embedded in an HTML image tag.
"""
u, t = solver(I, a, T, dt, theta)
u_e = exact_solution(t, I, a)
e = u_e - u
E = np.sqrt(dt*np.sum(e**2))
plt.figure()
t_e = np.linspace(0, T, 1001) # fine mesh for u_e
u_e = exact_solution(t_e, I, a)
plt.plot(t, u, 'r--o') # red dashes w/circles
plt.plot(t_e, u_e, 'b-') # blue line for exact sol.
plt.legend(['numerical', 'exact'])
plt.xlabel('t')
plt.ylabel('u')
plt.title('theta=%g, dt=%g' % (theta, dt))
# Save plot to HTML img tag with PNG code as embedded data
from parampool.utils import save_png_to_str
html_text = save_png_to_str(plt, plotwidth=400)
return E, html_text
def explore(I, a, T, dt, theta=0.5, makeplot=True):
"""
Run a case with the solver, compute error measure,
and plot the numerical and exact solutions (if makeplot=True).
"""
u, t = solver(I, a, T, dt, theta) # Numerical solution
u_e = exact_solution(t, I, a)
e = u_e - u
E = sqrt(dt * sum(e**2))
if makeplot:
plt.figure() # create new plot
t_e = linspace(0, T, 1001) # fine mesh for u_e
u_e = exact_solution(t_e, I, a)
plt.plot(t, u, 'r--o') # red dashes w/circles
plt.plot(t_e, u_e, 'b-') # blue line for exact sol.
plt.legend(['numerical', 'exact'])
plt.xlabel('t')
plt.ylabel('u')
plt.title('theta=%g, dt=%g' % (theta, dt))
from parampool.utils import save_png_to_str
html_text = save_png_to_str(plt, plotwidth=400)
return E, html_text
def explore(I, a, T, dt, theta=0.5, makeplot=True):
"""
Run a case with the solver, compute error measure,
and plot the numerical and exact solutions (if makeplot=True).
"""
u, t = solver(I, a, T, dt, theta) # Numerical solution
u_e = exact_solution(t, I, a)
e = u_e - u
E = sqrt(dt*sum(e**2))
if makeplot:
plt.figure() # create new plot
t_e = linspace(0, T, 1001) # fine mesh for u_e
u_e = exact_solution(t_e, I, a)
plt.plot(t, u, 'r--o') # red dashes w/circles
plt.plot(t_e, u_e, 'b-') # blue line for exact sol.
plt.legend(['numerical', 'exact'])
plt.xlabel('t')
plt.ylabel('u')
plt.title('theta=%g, dt=%g' % (theta, dt))
from parampool.utils import save_png_to_str
html_text = save_png_to_str(plt, plotwidth=400)
return E, html_text