def a(N):
def psi(x, i):
#return sin((i+1)*x)
return sin((2 * i + 1) * x)
#return sin((2*(i+1))*x)
u, c = least_squares_numerical(
f,
psi,
N,
x,
#integration_method='trapezoidal',
integration_method='scipy',
orthogonal_basis=True)
os.system('rm -f *.png')
u_sum = 0
print 'XXX c', c
for i in range(N + 1):
u_sum = u_sum + c[i] * psi(x, i)
plt.plot(x,
f(x),
'-',
x,
u_sum,
'-',
legend=['exact', 'approx'],
title='Highest frequency component: sin(%d*x)' % (2 * i + 1),
axis=[x[0], x[-1], -1.5, 1.5])
plt.savefig('tmp_frame%04d.png' % i)
time.sleep(0.3)
cmd = 'avconv -r 2 -i tmp_frame%04d.png -vcodec libtheora movie.ogg'
def a(N):
def psi(x, i):
#return sin((i+1)*x)
return sin((2*i+1)*x)
#return sin((2*(i+1))*x)
u, c = least_squares_numerical(f, psi, N, x,
#integration_method='trapezoidal',
integration_method='scipy',
orthogonal_basis=True)
os.system('rm -f *.png')
u_sum = 0
print 'XXX c', c
for i in range(N+1):
u_sum = u_sum + c[i]*psi(x, i)
plt.plot(x, f(x), '-', x, u_sum, '-',
legend=['exact', 'approx'],
title='Highest frequency component: sin(%d*x)' % (2*i+1),
axis=[x[0], x[-1], -1.5, 1.5])
plt.savefig('tmp_frame%04d.png' % i)
time.sleep(0.3)
cmd = 'avconv -r 2 -i tmp_frame%04d.png -vcodec libtheora movie.ogg'