def run_solvers_and_check_amplitudes(solvers,
timesteps_per_period=20,
num_periods=1,
I=1,
w=2 * np.pi):
P = 2 * np.pi / w # duration of one period
dt = P / timesteps_per_period
Nt = num_periods * timesteps_per_period
T = Nt * dt
t_mesh = np.linspace(0, T, Nt + 1)
file_name = 'Amplitudes' # initialize filename for plot
for solver in solvers:
solver.set(f_kwargs={'w': w})
solver.set_initial_condition([0, I])
u, t = solver.solve(t_mesh)
solver_name = \
'CrankNicolson' if solver.__class__.__name__ == \
'MidpointImplicit' else solver.__class__.__name__
file_name = file_name + '_' + solver_name
minima, maxima = minmax(t, u[:, 0])
a = amplitudes(minima, maxima)
plt.plot(range(len(a)), a, '-', label=solver_name)
plt.hold('on')
plt.xlabel('Number of periods')
plt.ylabel('Amplitude (absolute value)')
plt.legend(loc='upper left')
plt.savefig(file_name + '.png')
plt.savefig(file_name + '.pdf')
plt.show()
def run_solvers_and_check_amplitudes(solvers, timesteps_per_period=20,
num_periods=1, I=1, w=2*np.pi):
P = 2*np.pi/w # duration of one period
dt = P/timesteps_per_period
Nt = num_periods*timesteps_per_period
T = Nt*dt
t_mesh = np.linspace(0, T, Nt+1)
file_name = 'Amplitudes' # initialize filename for plot
for solver in solvers:
solver.set(f_kwargs={'w': w})
solver.set_initial_condition([0, I])
u, t = solver.solve(t_mesh)
solver_name = \
'CrankNicolson' if solver.__class__.__name__ == \
'MidpointImplicit' else solver.__class__.__name__
file_name = file_name + '_' + solver_name
minima, maxima = minmax(t, u[:,0])
a = amplitudes(minima, maxima)
plt.plot(range(len(a)), a, '-', label=solver_name)
plt.hold('on')
plt.xlabel('Number of periods')
plt.ylabel('Amplitude (absolute value)')
plt.legend(loc='upper left')
plt.savefig(file_name + '.png')
plt.savefig(file_name + '.pdf')
plt.show()
def u_P1():
"""
Plot P1 basis functions and a resulting u to
illustrate what it means to use finite elements.
"""
import matplotlib.pyplot as plt
x = [0, 1.5, 2.5, 3.5, 4]
phi = [np.zeros(len(x)) for i in range(len(x)-2)]
for i in range(len(phi)):
phi[i][i+1] = 1
#u = 5*x*np.exp(-0.25*x**2)*(4-x)
u = [0, 8, 5, 4, 0]
for i in range(len(phi)):
plt.plot(x, phi[i], 'r-') #, label=r'$\varphi_%d$' % i)
plt.text(x[i+1], 1.2, r'$\varphi_%d$' % i)
plt.plot(x, u, 'b-', label='$u$')
plt.legend(loc='upper left')
plt.axis([0, x[-1], 0, 9])
plt.savefig('u_example_P1.png')
plt.savefig('u_example_P1.pdf')
# Mark elements
for xi in x[1:-1]:
plt.plot([xi, xi], [0, 9], 'm--')
# Mark nodes
#plt.plot(x, np.zeros(len(x)), 'ro', markersize=4)
plt.savefig('u_example_P1_welms.png')
plt.savefig('u_example_P1_welms.pdf')
plt.show()
def demo1(f=f1, nx=4, ny=3, viewx=58, viewy=345, plain_gnuplot=True):
vertices, cells = mesh(nx, ny, x=[0, 1], y=[0, 1], diagonal='right')
if f == 'basis':
# basis function
zvalues = np.zeros(vertices.shape[0])
zvalues[int(round(len(zvalues) / 2.)) + int(round(nx / 2.))] = 1
else:
zvalues = fill(f1, vertices)
if plain_gnuplot:
plt = Gnuplotter()
else:
import scitools.std as plt
"""
if plt.backend == 'gnuplot':
gpl = plt.get_backend()
gpl('unset border; unset xtics; unset ytics; unset ztics')
#gpl('replot')
"""
draw_mesh(vertices, cells, plt)
draw_surface(zvalues, vertices, cells, plt)
plt.axis([0, 1, 0, 1, 0, zvalues.max()])
plt.view(viewx, viewy)
if plain_gnuplot:
plt.savefig('tmp')
else:
plt.savefig('tmp.pdf')
plt.savefig('tmp.eps')
plt.savefig('tmp.png')
plt.show()
def slides_waves():
L = 10.
a = 0.5
B0 = 1.
A = B0/5
t0 = 3.
v = 1.
x0 = lambda t: L/4 + v*t if t < t0 else L/4 + v*t0
sigma = 1.0
def bottom(x, t):
return (B(x, a, L, B0) + S(x, A, x0(t), sigma))
def depth(x, t):
return -bottom(x, t)
import scitools.std as plt
x = np.linspace(0, L, 101)
plt.plot(x, bottom(x, 0), x, depth(x, 0), legend=['bottom', 'depth'])
plt.show()
raw_input()
plt.figure()
dt_b = 0.01
solver(I=0, V=0,
f=lambda x, t: -(depth(x, t-dt_b) - 2*depth(x, t) + depth(x, t+dt_b))/dt_b**2,
c=lambda x, t: np.sqrt(np.abs(depth(x, t))),
U_0=None,
U_L=None,
L=L,
dt=0.1,
C=0.9,
T=20,
user_action=PlotSurfaceAndBottom(B, S, a, L, B0, A, x0, sigma, umin=-2, umax=2),
stability_safety_factor=0.9)
def u_P1():
"""
Plot P1 basis functions and a resulting u to
illustrate what it means to use finite elements.
"""
import matplotlib.pyplot as plt
x = [0, 1.5, 2.5, 3.5, 4]
phi = [np.zeros(len(x)) for i in range(len(x)-2)]
for i in range(len(phi)):
phi[i][i+1] = 1
#u = 5*x*np.exp(-0.25*x**2)*(4-x)
u = [0, 8, 5, 4, 0]
for i in range(len(phi)):
plt.plot(x, phi[i], 'r-') #, label=r'$\varphi_%d$' % i)
plt.text(x[i+1], 1.2, r'$\varphi_%d$' % i)
plt.plot(x, u, 'b-', label='$u$')
plt.legend(loc='upper left')
plt.axis([0, x[-1], 0, 9])
plt.savefig('tmp_u_P1.png')
plt.savefig('tmp_u_P1.pdf')
# Mark elements
for xi in x[1:-1]:
plt.plot([xi, xi], [0, 9], 'm--')
# Mark nodes
#plt.plot(x, np.zeros(len(x)), 'ro', markersize=4)
plt.savefig('tmp_u_P1_welms.png')
plt.savefig('tmp_u_P1_welms.pdf')
plt.show()
def demo_two_stars(animate=True):
# Initial condition
ic = [0.6, 0, 0, 1, # star A: velocity (0,1)
0, 0, 0, -0.5] # star B: velocity (0,-0.5)
# Solve ODEs
x_A, x_B, y_A, y_B, t = solver(
alpha=0.5, ic=ic, T=4*np.pi, dt=0.05)
if animate:
# Animate motion and draw the objects' paths in time
for i in range(len(x_A)):
plt.plot(x_A[:i+1], x_B[:i+1], 'r-',
y_A[:i+1], y_B[:i+1], 'b-',
[x_A[0], x_A[i]], [x_B[0], x_B[i]], 'r2o',
[y_A[0], y_A[i]], [y_B[0], y_B[i]], 'b4o',
daspectmode='equal', # axes aspect
legend=['A', 'B', 'A', 'B'],
axis=[-1, 1, -1, 1],
savefig='tmp_%04d.png' % i,
title='t=%.2f' % t[i])
else:
# Make a simple static plot of the solution
plt.plot(x_A, x_B, 'r-', y_A, y_B, 'b-',
daspectmode='equal', legend=['A', 'B'],
axis=[-1, 1, -1, 1], savefig='tmp_two_stars.png')
#plt.axes().set_aspect('equal') # mpl
plt.show()
def demo1(f=f1, nx=4, ny=3, viewx=58, viewy=345, plain_gnuplot=True):
vertices, cells = mesh(nx, ny, x=[0,1], y=[0,1], diagonal='right')
if f == 'basis':
# basis function
zvalues = np.zeros(vertices.shape[0])
zvalues[int(round(len(zvalues)/2.)) + int(round(nx/2.))] = 1
else:
zvalues = fill(f1, vertices)
if plain_gnuplot:
plt = Gnuplotter()
else:
import scitools.std as plt
"""
if plt.backend == 'gnuplot':
gpl = plt.get_backend()
gpl('unset border; unset xtics; unset ytics; unset ztics')
#gpl('replot')
"""
draw_mesh(vertices, cells, plt)
draw_surface(zvalues, vertices, cells, plt)
plt.axis([0, 1, 0, 1, 0, zvalues.max()])
plt.view(viewx, viewy)
if plain_gnuplot:
plt.savefig('tmp')
else:
plt.savefig('tmp.pdf')
plt.savefig('tmp.eps')
plt.savefig('tmp.png')
plt.show()
def visualize(self):
u = self.solver.u; t = self.solver.t # short forms
num_periods = vib_plot_empirical_freq_and_amplitude(u, t)
if num_periods <= 40:
plt.figure()
vib_visualize(u, t)
else:
vib_visualize_front(u, t, self.window_width, self.savefig)
vib_visualize_front_ascii(u, t)
plt.show()
def visualize(self):
u = self.solver.u; t = self.solver.t # short forms
num_periods = vib_plot_empirical_freq_and_amplitude(u, t)
if num_periods <= 40:
plt.figure()
vib_visualize(u, t)
else:
vib_visualize_front(u, t, self.window_width, self.savefig)
vib_visualize_front_ascii(u, t)
plt.show()
def visualize(u, t, title='', filename='tmp'):
plt.plot(t, u, 'b-')
plt.xlabel('t')
plt.ylabel('u')
dt = t[1] - t[0]
plt.title('dt=%g' % dt)
umin = 1.2*u.min(); umax = 1.2*u.max()
plt.axis([t[0], t[-1], umin, umax])
plt.title(title)
plt.savefig(filename + '.png')
plt.savefig(filename + '.pdf')
plt.show()
def visualize(list_of_curves, legends, title='', filename='tmp'):
"""Plot list of curves: (u, t)."""
for u, t in list_of_curves:
plt.plot(t, u)
plt.hold('on')
plt.legend(legends)
plt.xlabel('t')
plt.ylabel('u')
plt.title(title)
plt.savefig(filename + '.png')
plt.savefig(filename + '.pdf')
plt.show()
def visualize(list_of_curves, legends, title='', filename='tmp'):
"""Plot list of curves: (u, t)."""
for u, t in list_of_curves:
plt.plot(t, u)
plt.hold('on')
plt.legend(legends)
plt.xlabel('t')
plt.ylabel('u')
plt.title(title)
plt.savefig(filename + '.png')
plt.savefig(filename + '.pdf')
plt.show()
def demo_circular():
# Mass B is at rest at the origin,
# mass A is at (1, 0) with vel. (0, 1)
ic = [1, 0, 0, 1, 0, 0, 0, 0]
x_A, x_B, y_A, y_B, t = solver(
alpha=0.001, ic=ic, T=2*np.pi, dt=0.01)
plt.plot(x_A, x_B, 'r2-', y_A, y_B, 'b2-',
legend=['A', 'B'],
daspectmode='equal') # x and y axis have same scaling
plt.savefig('tmp_circular.png')
plt.savefig('tmp_circular.pdf')
plt.show()
def visualize(u, t, title='', filename='tmp'):
plt.plot(t, u, 'b-')
plt.xlabel('t')
plt.ylabel('u')
dt = t[1] - t[0]
plt.title('dt=%g' % dt)
umin = 1.2*u.min(); umax = 1.2*u.max()
plt.axis([t[0], t[-1], umin, umax])
plt.title(title)
plt.savefig(filename + '.png')
plt.savefig(filename + '.pdf')
plt.show()
def visualize(u, t, title="", filename="tmp"):
plt.plot(t, u, "b-")
plt.xlabel("t")
plt.ylabel("u")
dt = t[1] - t[0]
plt.title("dt=%g" % dt)
umin = 1.2 * u.min()
umax = 1.2 * u.max()
plt.axis([t[0], t[-1], umin, umax])
plt.title(title)
plt.savefig(filename + ".png")
plt.savefig(filename + ".pdf")
plt.show()
def demo_two_stars(animate=True):
# Initial condition
ic = [
0.6,
0,
0,
1, # star A: velocity (0,1)
0,
0,
0,
-0.5
] # star B: velocity (0,-0.5)
# Solve ODEs
x_A, x_B, y_A, y_B, t = solver(alpha=0.5, ic=ic, T=4 * np.pi, dt=0.05)
if animate:
# Animate motion and draw the objects' paths in time
for i in range(len(x_A)):
plt.plot(
x_A[:i + 1],
x_B[:i + 1],
'r-',
y_A[:i + 1],
y_B[:i + 1],
'b-',
[x_A[0], x_A[i]],
[x_B[0], x_B[i]],
'r2o',
[y_A[0], y_A[i]],
[y_B[0], y_B[i]],
'b4o',
daspectmode='equal', # axes aspect
legend=['A', 'B', 'A', 'B'],
axis=[-1, 1, -1, 1],
savefig='tmp_%04d.png' % i,
title='t=%.2f' % t[i])
else:
# Make a simple static plot of the solution
plt.plot(x_A,
x_B,
'r-',
y_A,
y_B,
'b-',
daspectmode='equal',
legend=['A', 'B'],
axis=[-1, 1, -1, 1],
savefig='tmp_two_stars.png')
#plt.axes().set_aspect('equal') # mpl
plt.show()
def main():
problem = Problem()
solver = Solver(problem)
viz = Visualizer(problem, solver)
parser = problem.define_command_line_options()
parser = solver.define_command_line_options(parser)
args = parser.parse_args()
problem.init_from_command_line(args)
solver.init_from_command_line(args)
solver.solve()
import matplotlib.pyplot as plt
plt = viz.plot(plt=plt)
plt.show()
def main(): problem = Problem() solver = Solver(problem) viz = Visualizer(problem, solver) parser = problem.define_command_line_options() parser = solver.define_command_line_options(parser) args = parser.parse_args() problem.init_from_command_line(args) solver.init_from_command_line(args) solver.solve() import matplotlib.pyplot as plt plt = viz.plot(plt = plt) plt.show()
def demo_circular():
# Mass B is at rest at the origin,
# mass A is at (1, 0) with vel. (0, 1)
ic = [1, 0, 0, 1, 0, 0, 0, 0]
x_A, x_B, y_A, y_B, t = solver(alpha=0.001, ic=ic, T=2 * np.pi, dt=0.01)
plt.plot(x_A,
x_B,
'r2-',
y_A,
y_B,
'b2-',
legend=['A', 'B'],
daspectmode='equal') # x and y axis have same scaling
plt.savefig('tmp_circular.png')
plt.savefig('tmp_circular.pdf')
plt.show()
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument("--I", type=float, default=1.0)
parser.add_argument("--V", type=float, default=0.0)
parser.add_argument("--m", type=float, default=1.0)
parser.add_argument("--b", type=float, default=0.0)
parser.add_argument("--s", type=str, default="u")
parser.add_argument("--F", type=str, default="0")
parser.add_argument("--dt", type=float, default=0.05)
# parser.add_argument('--T', type=float, default=10)
parser.add_argument("--T", type=float, default=20)
parser.add_argument("--window_width", type=float, default=30.0, help="Number of periods in a window")
parser.add_argument("--damping", type=str, default="linear")
parser.add_argument("--savefig", action="store_true")
# Hack to allow --SCITOOLS options (scitools.std reads this argument
# at import)
parser.add_argument("--SCITOOLS_easyviz_backend", default="matplotlib")
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable="u")
F = StringFunction(a.F, independent_variable="t")
I, V, m, b, dt, T, window_width, savefig, damping = (
a.I,
a.V,
a.m,
a.b,
a.dt,
a.T,
a.window_width,
a.savefig,
a.damping,
)
u, t = solver(I, V, m, b, s, F, dt, T, damping)
num_periods = plot_empirical_freq_and_amplitude(u, t)
if num_periods <= 40:
plt.figure()
visualize(u, t)
else:
visualize_front(u, t, window_width, savefig)
visualize_front_ascii(u, t)
plt.show()
def slides_waves():
L = 10.
a = 0.5
B0 = 1.
A = B0 / 5
t0 = 3.
v = 1.
x0 = lambda t: L / 4 + v * t if t < t0 else L / 4 + v * t0
sigma = 1.0
def bottom(x, t):
return (B(x, a, L, B0) + S(x, A, x0(t), sigma))
def depth(x, t):
return -bottom(x, t)
import scitools.std as plt
x = np.linspace(0, L, 101)
plt.plot(x, bottom(x, 0), x, depth(x, 0), legend=['bottom', 'depth'])
plt.show()
raw_input()
plt.figure()
dt_b = 0.01
solver(I=0,
V=0,
f=lambda x, t: -(depth(x, t - dt_b) - 2 * depth(x, t) + depth(
x, t + dt_b)) / dt_b**2,
c=lambda x, t: np.sqrt(np.abs(depth(x, t))),
U_0=None,
U_L=None,
L=L,
dt=0.1,
C=0.9,
T=20,
user_action=PlotSurfaceAndBottom(B,
S,
a,
L,
B0,
A,
x0,
sigma,
umin=-2,
umax=2),
stability_safety_factor=0.9)
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='4*pi**2*u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width',
type=float,
default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options
# (scitools.std reads this argument at import)
parser.add_argument('--SCITOOLS_easyviz_backend', default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
# compute u by both methods and then visualize the difference
u, t = solver2(I, V, m, b, s, F, dt, T, damping)
u_bw, _ = solver_bwdamping(I, V, m, b, s, F, dt, T, damping)
u_diff = u - u_bw
num_periods = plot_empirical_freq_and_amplitude(u_diff, t)
if num_periods <= 40:
plt.figure()
legends = [
'1st-2nd order method', '2nd order method', '1st order method'
]
visualize([(u_diff, t), (u, t), (u_bw, t)], legends)
else:
visualize_front(u_diff, t, window_width, savefig)
#visualize_front_ascii(u_diff, t)
plt.show()
def draw_sparsity_pattern(elements, num_nodes):
"""Illustrate the matrix sparsity pattern."""
import matplotlib.pyplot as plt
sparsity_pattern = {}
for e in elements:
for i in range(len(e)):
for j in range(len(e)):
sparsity_pattern[(e[i],e[j])] = 1
y = [i for i, j in sorted(sparsity_pattern)]
x = [j for i, j in sorted(sparsity_pattern)]
y.reverse()
plt.plot(x, y, 'bo')
ax = plt.gca()
ax.set_aspect('equal')
plt.axis('off')
plt.plot([-1, num_nodes, num_nodes, -1, -1], [-1, -1, num_nodes, num_nodes, -1], 'k-')
plt.savefig('tmp_sparsity_pattern.pdf')
plt.savefig('tmp_sparsity_pattern.png')
plt.show()
def u_sines():
"""
Plot sine basis functions and a resulting u to
illustrate what it means to use global basis functions.
"""
import matplotlib.pyplot as plt
x = np.linspace(0, 4, 1001)
psi0 = np.sin(2*np.pi/4*x)
psi1 = np.sin(2*np.pi*x)
psi2 = np.sin(2*np.pi*4*x)
u = 4*psi0 - 0.5*psi1 - 0*psi2
plt.plot(x, psi0, 'r-', label=r"$\psi_0$")
plt.plot(x, psi1, 'g-', label=r"$\psi_1$")
#plt.plot(x, psi2, label=r"$\psi_2$")
plt.plot(x, u, 'b-', label=r"u")
plt.legend()
plt.savefig('tmp_u_sines.pdf')
plt.savefig('tmp_u_sines.png')
plt.show()
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='4*pi**2*u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width', type=float, default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options
# (scitools.std reads this argument at import)
parser.add_argument('--SCITOOLS_easyviz_backend',
default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
# compute u by both methods and then visualize the difference
u, t = solver2(I, V, m, b, s, F, dt, T, damping)
u_bw, _ = solver_bwdamping(I, V, m, b, s, F, dt, T, damping)
u_diff = u - u_bw
num_periods = plot_empirical_freq_and_amplitude(u_diff, t)
if num_periods <= 40:
plt.figure()
legends = ['1st-2nd order method',
'2nd order method',
'1st order method']
visualize([(u_diff, t), (u, t), (u_bw, t)], legends)
else:
visualize_front(u_diff, t, window_width, savefig)
#visualize_front_ascii(u_diff, t)
plt.show()
def draw_sparsity_pattern(elements, num_nodes):
"""Illustrate the matrix sparsity pattern."""
import matplotlib.pyplot as plt
sparsity_pattern = {}
for e in elements:
for i in range(len(e)):
for j in range(len(e)):
sparsity_pattern[(e[i],e[j])] = 1
y = [i for i, j in sorted(sparsity_pattern)]
x = [j for i, j in sorted(sparsity_pattern)]
y.reverse()
plt.plot(x, y, 'bo')
ax = plt.gca()
ax.set_aspect('equal')
plt.axis('off')
plt.plot([-1, num_nodes, num_nodes, -1, -1], [-1, -1, num_nodes, num_nodes, -1], 'k-')
plt.savefig('tmp_sparsity_pattern.pdf')
plt.savefig('tmp_sparsity_pattern.png')
plt.show()
def u_sines():
"""
Plot sine basis functions and a resulting u to
illustrate what it means to use global basis functions.
"""
import matplotlib.pyplot as plt
x = np.linspace(0, 4, 1001)
psi0 = np.sin(2*np.pi/4*x)
psi1 = np.sin(2*np.pi*x)
psi2 = np.sin(2*np.pi*4*x)
#u = 4*psi0 - 0.5*psi1 - 0*psi2
u = 4*psi0 - 0.5*psi1
plt.plot(x, psi0, 'r-', label=r"$\psi_0$")
plt.plot(x, psi1, 'g-', label=r"$\psi_1$")
#plt.plot(x, psi2, label=r"$\psi_2$")
plt.plot(x, u, 'b-', label=r"$u=4\psi_0 - \frac{1}{2}\psi_1$")
plt.legend()
plt.savefig('u_example_sin.pdf')
plt.savefig('u_example_sin.png')
plt.show()
def main():
problem = Problem()
solver = Solver(problem)
viz = Visualizer(problem, solver)
# Read input from the command line
parser = problem.define_command_line_options()
parser = solver. define_command_line_options(parser)
args = parser.parse_args()
problem.init_from_command_line(args)
solver. init_from_command_line(args)
# Solve and plot
solver.solve()
import matplotlib.pyplot as plt
#import scitools.std as plt
plt = viz.plot(plt=plt)
E = solver.error()
if E is not None:
print 'Error: %.4E' % E
plt.show()
def main():
problem = Problem()
solver = Solver(problem)
viz = Visualizer(problem, solver)
# Read input from the command line
parser = problem.define_command_line_options()
parser = solver. define_command_line_options(parser)
args = parser.parse_args()
problem.init_from_command_line(args)
solver. init_from_command_line(args)
# Solve and plot
solver.solve()
import matplotlib.pyplot as plt
#import scitools.std as plt
plt = viz.plot(plt=plt)
E = solver.error()
if E is not None:
print 'Error: %.4E' % E
plt.show()
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
#parser.add_argument('--T', type=float, default=10)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width',
type=float,
default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options (scitools.std reads this argument
# at import)
parser.add_argument('--SCITOOLS_easyviz_backend', default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
u, t = solver(I, V, m, b, s, F, dt, T, damping)
num_periods = plot_empirical_freq_and_amplitude(u, t)
if num_periods <= 40:
plt.figure()
visualize(u, t)
else:
visualize_front(u, t, window_width, savefig)
visualize_front_ascii(u, t)
plt.show()
def main():
import argparse
parser = argparse.ArgumentParser()
parser.add_argument('--I', type=float, default=1.0)
parser.add_argument('--V', type=float, default=0.0)
parser.add_argument('--m', type=float, default=1.0)
parser.add_argument('--b', type=float, default=0.0)
parser.add_argument('--s', type=str, default='u')
parser.add_argument('--F', type=str, default='0')
parser.add_argument('--dt', type=float, default=0.05)
#parser.add_argument('--T', type=float, default=10)
parser.add_argument('--T', type=float, default=20)
parser.add_argument('--window_width', type=float, default=30.,
help='Number of periods in a window')
parser.add_argument('--damping', type=str, default='linear')
parser.add_argument('--savefig', action='store_true')
# Hack to allow --SCITOOLS options (scitools.std reads this argument
# at import)
parser.add_argument('--SCITOOLS_easyviz_backend', default='matplotlib')
a = parser.parse_args()
from scitools.std import StringFunction
s = StringFunction(a.s, independent_variable='u')
F = StringFunction(a.F, independent_variable='t')
I, V, m, b, dt, T, window_width, savefig, damping = \
a.I, a.V, a.m, a.b, a.dt, a.T, a.window_width, a.savefig, \
a.damping
u, t = solver(I, V, m, b, s, F, dt, T, damping)
num_periods = plot_empirical_freq_and_amplitude(u, t)
if num_periods <= 40:
plt.figure()
visualize(u, t)
else:
visualize_front(u, t, window_width, savefig)
visualize_front_ascii(u, t)
plt.show()
b = 1
w = 1
delta_t = (2 * pi) / (w * n)
counter = 0
X = []
Y = []
for k in range(n + 1):
tk = k * delta_t #each time through we need to add a new k value
x = a * cos(w * tk)
y = b * sin(w * tk)
X.append(x)
Y.append(y)
XP = array(X)
YP = array(Y)
XF = array([x])
YF = array([y])
velo = w * sqrt(a**2 * sin(w * tk)**2 + b**2 * cos(w * tk)**2)
plot(XP,
YP,
'-r',
XF,
YF,
'bo',
axis=[-1.2, 1.2, -1.2, 1.2],
title='Planetary orbit',
legend=(['Instaneous velocity=%6f' % velo, 'present location']),
savefig='pix/planet%4d.png' % counter)
counter += 1
show()
D = 500
dt = dx**2*D
dt = 1.25
D = dt/dx**2
T = 2.5
umin = u_R
umax = u_L
a_consts = [[0, 1]]
a_consts = [[0, 1], [0.5, 8]]
a_consts = [[0, 1], [0.5, 8], [0.75, 0.1]]
a = fill_a(a_consts, L, Nx)
#a = random.uniform(0, 10, Nx+1)
from scitools.std import plot, hold, subplot, figure, show
figure()
subplot(2,1,1)
u, x, cpu = viz(I, a, L, Nx, D, T, umin, umax, theta, u_L, u_R)
v = u_exact_stationary(x, a, u_L, u_R)
print 'v', v
print 'u', u
hold('on')
symbol = 'bo' if Nx < 32 else 'b-'
plot(x, v, symbol, legend='exact stationary')
subplot(2,1,2)
plot(x, a, legend='a')
show()
def plot(self):
filename = 'logistic_' + str(self.problem) + '.pdf'
plot(self.t, self.u)
title(str(self.problem) + ', dt=%g' % self.dt)
savefig(filename)
show()
# -*- coding: utf-8 -*- """ Created on Thu Jun 25 00:23:08 2015 @author: shiftehs """ import numpy as np import matplotlib.pyplot as plt import scitools.std as sci x = np.linspace(1,10,100) y = np.cos(x) sci.plot(x,y) sci.xaxis = [0,3] sci.show()
def plot(self):
filename = 'logistic_' + str(self.problem) + '.pdf'
plot(self.t, self.u)
title(str(self.problem) + ', dt=%g' % self.dt)
savefig(filename)
show()
solvers_theta = [
odespy.ForwardEuler(f),
# Implicit methods must use Newton solver to converge
odespy.BackwardEuler(f, nonlinear_solver='Newton'),
odespy.CrankNicolson(f, nonlinear_solver='Newton'),
]
solvers_RK = [odespy.RK2(f), odespy.RK4(f)]
solvers_accurate = [
odespy.RK4(f),
odespy.CrankNicolson(f, nonlinear_solver='Newton'),
odespy.DormandPrince(f, atol=0.001, rtol=0.02)
]
solvers_CN = [odespy.CrankNicolson(f, nonlinear_solver='Newton')]
if __name__ == '__main__':
timesteps_per_period = 20
solver_collection = 'theta'
num_periods = 1
try:
# Example: python vib_odespy.py 30 accurate 50
timesteps_per_period = int(sys.argv[1])
solver_collection = sys.argv[2]
num_periods = int(sys.argv[3])
except IndexError:
pass # default values are ok
solvers = eval('solvers_' + solver_collection) # list of solvers
run_solvers_and_plot(solvers, timesteps_per_period, num_periods)
plt.show()
raw_input()
def visualize(t):
plot(range(len(t)), log(abs(t)), ’ro’)
# or just plot(log(abs(t)), ’ro’)
show()
T = num_periods * P
t = np.linspace(0, T, time_steps_per_period * num_periods + 1)
import odespy
def f(u, t, alpha):
# Note the sequence of unknowns: v, u (v=du/dt)
v, u = u
return [-alpha * np.sign(v) - u, v]
solver = odespy.RK4(f, f_args=[alpha])
solver.set_initial_condition([beta, 1]) # sequence must match f
uv, t = solver.solve(t)
u = uv[:, 1] # recall sequence in f: v, u
v = uv[:, 0]
return u, t
if __name__ == "__main__":
alpha_values = [0, 0.05, 0.1]
for alpha in alpha_values:
u, t = simulate(alpha, 0, 6, 60)
plt.plot(t, u)
plt.hold("on")
plt.legend([r"$\alpha=%g$" % alpha for alpha in alpha_values])
plt.xlabel(r"$\bar t$")
plt.ylabel(r"$\bar u$")
plt.savefig("tmp.png")
plt.savefig("tmp.pdf")
plt.show()
raw_input() # for scitools' matplotlib engine