def test_uneven(self):
# Use uniform weight, should just get the lagendre polynomials.
# Get lots of polynomials to test the numerical stability.
m = 300
n = 10
x = sp.log(sp.arange(m, dtype=float) / 2 + 0.5)
window = sp.sin(x)**2
polys = utils.ortho_poly(x, n, window)
self.check_ortho_norm(polys, window)
def test_uneven(self):
# Use uniform weight, should just get the lagendre polynomials.
# Get lots of polynomials to test the numerical stability.
m = 300
n = 10
x = sp.log(sp.arange(m, dtype=float)/2 + 0.5)
window = sp.sin(x)**2
polys = utils.ortho_poly(x, n, window)
self.check_ortho_norm(polys, window)
def test_multiD2(self):
# Use uniform weight, should just get the lagendre polynomials.
m = 40
n = 10
x = sp.log(sp.arange(m, dtype=float) / 2 + 0.5)
window = sp.empty((2, m), dtype=float)
window[0, :] = sp.sin(x)**2
window[1, :] = sp.cos(x)**2
x.shape = (1, m)
polys = utils.ortho_poly(x, n, window, axis=1)
self.check_ortho_norm(polys, window, axis=1)
def test_multiD2(self):
# Use uniform weight, should just get the lagendre polynomials.
m = 40
n = 10
x = sp.log(sp.arange(m, dtype=float)/2 + 0.5)
window = sp.empty((2, m), dtype=float)
window[0,:] = sp.sin(x)**2
window[1,:] = sp.cos(x)**2
x.shape = (1, m)
polys = utils.ortho_poly(x, n, window, axis=1)
self.check_ortho_norm(polys, window, axis=1)
def test_flat_even_spaced(self):
# Use uniform weight, should just get the lagendre polynomials.
m = 20
n = 10
x = sp.arange(m, dtype=float)
window = 1.
polys = utils.ortho_poly(x, n, window)
# The first one should just be the mean.
self.assertTrue(sp.allclose(polys[0, :], 1. / sp.sqrt(m)))
# The second one should be a slope.
expected = x - sp.mean(x)
expected = expected / sp.sqrt(sp.sum(expected**2))
self.assertTrue(sp.allclose(polys[1, :], expected))
# Check that they are all orthonormal.
self.check_ortho_norm(polys, 1.)
def test_flat_even_spaced(self):
# Use uniform weight, should just get the lagendre polynomials.
m = 20
n = 10
x = sp.arange(m, dtype=float)
window = 1.
polys = utils.ortho_poly(x, n, window)
# The first one should just be the mean.
self.assertTrue(sp.allclose(polys[0,:], 1./sp.sqrt(m)))
# The second one should be a slope.
expected = x - sp.mean(x)
expected = expected / sp.sqrt(sp.sum(expected**2))
self.assertTrue(sp.allclose(polys[1,:], expected))
# Check that they are all orthonormal.
self.check_ortho_norm(polys, 1.)