def test():
from scipy.linalg import inv
from time import perf_counter
from ppp.Plots import plot_setup
import matplotlib.pyplot as pt
M = 100
times = np.empty((2, M))
for i in range(M):
A = np.random.randint(10, size=(i + 2, i + 2))
b = np.random.randint(10, size=(i + 2, 1))
start = perf_counter()
inv(A) @ b
times[0, i] = perf_counter() - start
start = perf_counter()
LU = alu(A)
LU.solve(b)
times[1, i] = perf_counter() - start
fig, ax = plot_setup('Matrix Size', 'Time [s]')
lineObjects = ax.plot(np.arange(M) + 2, times.T)
ax.legend(iter(lineObjects), ['LARPACK', 'LU Decomposition'], fontsize=16)
pt.show()
def show_mesh2D(self):
import matplotlib.pyplot as pt
from ppp.Plots import plot_setup
fig, ax = plot_setup('$x$', '$y$')
ax.triplot(self.P[:self.Np, 0], self.P[:self.Np, 1], self.T[:, :3])
ax.plot(self.P[:, 0], self.P[:, 1], 'o')
ax.plot(self.B[:, 0], self.B[:, 1], 'bx')
self.draw_boundary(ax)
pt.show()
def show_mesh2D(self):
import matplotlib.pyplot as pt
print('hi there')
from ppp.Plots import plot_setup
fig, ax = plot_setup('$x$', '$y$')
ax.triplot(self.P[:, 0], self.P[:, 1], self.T)
ax.plot(self.P[:, 0], self.P[:, 1], 'o')
ax.plot(self.B[:, 0], self.B[:, 1], 'bx')
pt.show()
def test(func, exact, t0, tN, y0):
from ppp.Plots import plot_setup
import matplotlib.pyplot as pt
from time import perf_counter
methods = [
'Forward Euler', 'Heun', 'Ralston', 'RK3', 'Heun3', 'Ralston3',
'SSPRK3', 'RK4', '3/8 Rule', 'RK5'
]
N_vals = 10**np.linspace(0, 5, 11)
average_errs = np.empty((len(methods), len(N_vals)))
times = np.copy(average_errs)
for i, method_input in enumerate(methods):
print(method_input)
for j, N_input in enumerate(N_vals.astype(int)):
start = perf_counter()
ode = explicit(function,
y_0,
t_0,
t_N,
N=N_input,
method=method_input)
times[i, j] = perf_counter() - start
err = np.abs((exact(t_N) - ode.y_vals[-1]))
if type(err) == float:
average_errs[i,
j] = err #np.abs((exact(t_N) - ode.y_vals[-1]))
else:
average_errs[i, j] = np.mean(err)
fig, ax = plot_setup('$N$', 'Time [s]', x_log=True, y_log=True)
lineObjects = ax.plot(N_vals, times.T, 'x-')
ax.legend(iter(lineObjects), methods, fontsize=16)
pt.show()
fig, ax = plot_setup('$N$', 'Absolute Error', x_log=True, y_log=True)
lineObjects = ax.plot(N_vals, average_errs.T, 'x-')
ax.legend(iter(lineObjects), methods, fontsize=16)
pt.show()
def test(f, g, exact, t0, tN, y0):
from ppp.Plots import plot_setup
import matplotlib.pyplot as pt
from time import perf_counter
u0, v0 = y0
methods = ['Euler', 'Stromer--Verlet', 'Ruth3']
N_vals = 10**np.linspace(0, 5, 11)
average_errs = np.empty((len(methods), len(N_vals)))
times = np.copy(average_errs)
for i, method_input in enumerate(methods):
print(method_input)
for j, N_input in enumerate(N_vals.astype(int)):
start = perf_counter()
ode = symplectic(f, g, u_0, v_0, t_0, t_N, N=N_input, method=method_input)
times[i, j] = perf_counter() - start
u_exact, v_exact = exact(t_N)
u_approx, v_approx = ode.u_vals[-1], ode.v_vals[-1]
err = np.array([
np.abs(u_exact - u_approx), np.abs(v_exact - v_approx)
])
if type(err) == float:
average_errs[i, j] = err#np.abs((exact(t_N) - ode.y_vals[-1]))
else:
average_errs[i, j] = np.mean(err)
fig, ax = plot_setup('$N$', 'Time [s]', x_log=True, y_log=True)
lineObjects = ax.plot(N_vals, times.T, 'x-')
ax.legend(iter(lineObjects), methods, fontsize=16)
pt.show()
fig, ax = plot_setup('$N$', 'Absolute Error', x_log=True, y_log=True)
lineObjects = ax.plot(N_vals, average_errs.T, 'x-')
ax.legend(iter(lineObjects), methods, fontsize=16)
pt.show()
def plot_grid(P, T, seedings=None):
from ppp.Plots import plot_setup
fig, ax = plot_setup('$x$', '$y$')
cells = P[T]
for cell in cells:
ax.plot(cell[[0, 1], 0], cell[[0, 1], 1], 'k-')
ax.plot(cell[[1, 2], 0], cell[[1, 2], 1], 'k-')
ax.plot(cell[[2, 0], 0], cell[[2, 0], 1], 'k-')
ax.plot(P[:, 0], P[:, 1], 'ro', markersize=3)
if seedings is not None:
ax.plot(seedings[:, 0], seedings[:, 1], 'bx', markersize=4)
return fig, ax