def plot_solution(series_type, N, func):
print "series_type ", series_type, " N ", N, " func ", func
psi = series(series_type, N)
print psi
u, c = least_squares(func, psi, Omega, False)
u = sym.lambdify([x], u)
U = [u(xi) for xi in X]
pylab.plot(X, U)
def plot_solution(series_type, N, func): print "series_type ", series_type, " N ", N, " func ", func psi = series(series_type, N) print psi u, c = least_squares(func, psi, Omega, False) u = sym.lambdify([x], u) U = [u(xi) for xi in X] pylab.plot(X, U)
import sys, os
sys.path.insert(0, os.path.join(os.pardir, 'src-approx'))
from approx1D import least_squares, comparison_plot
import matplotlib.pyplot as plt
import sympy as sym
from math import factorial
import numpy as np
x = sym.Symbol('x')
f = sym.exp(-x)
Omega = [0, 8]
for N in 2,4,6:
psi = [x**i for i in range(N+1)]
u, c = least_squares(f,psi,Omega)
print N, u
plt.figure()
comparison_plot(f, u, Omega, filename='tmp_exp_%d' % N,
plot_title='N=%d' % N)
[x**i for i in range(0, N + 1)]
] # V_2
symbolic = False
for V, psi in enumerate(psi_bases):
for domain_no in range(1, 3):
for k in range(2, 6):
if symbolic:
Omega = [0, k*sym.pi] if domain_no == 1 else \
[-k*sym.pi/2, k*sym.pi/2]
else:
# cannot use sym.pi with numerical sympy computing
Omega = [0, k*pi] if domain_no == 1 else \
[-k*pi/2, k*pi/2]
u, c = least_squares(f, psi, Omega, symbolic=symbolic)
comparison_plot(f,
u,
Omega,
ymin=-2,
ymax=2,
filename='tmp_N%d_V%dOmega%dk%d' %
(N, V, k, domain_no),
plot_title='sin(x) on [0,%d*pi/2] by %s' %
(k, ','.join([str(p) for p in psi])))
# Need to kill the plot to proceed!
for ext in 'png', 'pdf':
cmd = 'doconce combine_images -2 ' + \
' '.join(['tmp_N%d_V%dOmega%dk%d.' %
(N, V, k, domain_no) + ext
psi_bases = [[x**i for i in range(1, N+1, 2)], # V_1
[x**i for i in range(0, N+1)]] # V_2
symbolic = False
for V, psi in enumerate(psi_bases):
for domain_no in range(1, 3):
for k in range(2, 6):
if symbolic:
Omega = [0, k*sym.pi] if domain_no == 1 else \
[-k*sym.pi/2, k*sym.pi/2]
else:
# cannot use sym.pi with numerical sympy computing
Omega = [0, k*pi] if domain_no == 1 else \
[-k*pi/2, k*pi/2]
u, c = least_squares(f, psi, Omega, symbolic=symbolic)
comparison_plot(
f, u, Omega,
ymin=-2, ymax=2,
filename='tmp_N%d_V%dOmega%dk%d' %
(N, V, k, domain_no),
plot_title='sin(x) on [0,%d*pi/2] by %s' %
(k, ','.join([str(p) for p in psi])))
# Need to kill the plot to proceed!
for ext in 'png', 'pdf':
cmd = 'doconce combine_images -2 ' + \
' '.join(['tmp_N%d_V%dOmega%dk%d.' %
(N, V, k, domain_no) + ext
for k in range(2, 6)]) + \
' sin_powers_N%d_V%d_Omega%d.' % (N, V, domain_no) + ext
