def test_legendre_table():
"""Test Legendre table calculation."""
# double-check our table generation
n = 10
for ch_type in ['eeg', 'meg']:
lut1, n_fact1 = _get_legen_table(ch_type, n_coeff=25, force_calc=True)
lut1 = lut1[:, :n - 1].copy()
n_fact1 = n_fact1[:n - 1].copy()
lut2, n_fact2 = _get_legen_table(ch_type, n_coeff=n, force_calc=True)
assert_allclose(lut1, lut2)
assert_allclose(n_fact1, n_fact2)
def test_legendre_table():
"""Test Legendre table calculation."""
# double-check our table generation
n = 10
for ch_type in ['eeg', 'meg']:
lut1, n_fact1 = _get_legen_table(ch_type, n_coeff=25, force_calc=True)
lut1 = lut1[:, :n - 1].copy()
n_fact1 = n_fact1[:n - 1].copy()
lut2, n_fact2 = _get_legen_table(ch_type, n_coeff=n, force_calc=True)
assert_allclose(lut1, lut2)
assert_allclose(n_fact1, n_fact2)
def test_legendre_val():
"""Test Legendre polynomial (derivative) equivalence."""
rng = np.random.RandomState(0)
# check table equiv
xs = np.linspace(-1., 1., 1000)
n_terms = 100
# True, numpy
vals_np = legendre.legvander(xs, n_terms - 1)
# Table approximation
for nc, interp in zip([100, 50], ['nearest', 'linear']):
lut, n_fact = _get_legen_table('eeg', n_coeff=nc, force_calc=True)
lut_fun = interp1d(np.linspace(-1, 1, lut.shape[0]),
lut,
interp,
axis=0)
vals_i = lut_fun(xs)
# Need a "1:" here because we omit the first coefficient in our table!
assert_allclose(vals_np[:, 1:vals_i.shape[1] + 1],
vals_i,
rtol=1e-2,
atol=5e-3)
# Now let's look at our sums
ctheta = rng.rand(20, 30) * 2.0 - 1.0
beta = rng.rand(20, 30) * 0.8
c1 = _comp_sum_eeg(beta.flatten(), ctheta.flatten(), lut_fun, n_fact)
c1.shape = beta.shape
# compare to numpy
n = np.arange(1, n_terms, dtype=float)[:, np.newaxis, np.newaxis]
coeffs = np.zeros((n_terms, ) + beta.shape)
coeffs[1:] = (np.cumprod([beta] * (n_terms - 1), axis=0) *
(2.0 * n + 1.0) * (2.0 * n + 1.0) / n)
# can't use tensor=False here b/c it isn't in old numpy
c2 = np.empty((20, 30))
for ci1 in range(20):
for ci2 in range(30):
c2[ci1, ci2] = legendre.legval(ctheta[ci1, ci2], coeffs[:, ci1,
ci2])
assert_allclose(c1, c2, 1e-2, 1e-3) # close enough...
# compare fast and slow for MEG
ctheta = rng.rand(20 * 30) * 2.0 - 1.0
beta = rng.rand(20 * 30) * 0.8
lut, n_fact = _get_legen_table('meg', n_coeff=10, force_calc=True)
fun = interp1d(np.linspace(-1, 1, lut.shape[0]), lut, 'nearest', axis=0)
coeffs = _comp_sums_meg(beta, ctheta, fun, n_fact, False)
lut, n_fact = _get_legen_table('meg', n_coeff=20, force_calc=True)
fun = interp1d(np.linspace(-1, 1, lut.shape[0]), lut, 'linear', axis=0)
coeffs = _comp_sums_meg(beta, ctheta, fun, n_fact, False)
def test_legendre_val():
"""Test Legendre polynomial (derivative) equivalence
"""
rng = np.random.RandomState(0)
# check table equiv
xs = np.linspace(-1., 1., 1000)
n_terms = 100
# True, numpy
vals_np = legendre.legvander(xs, n_terms - 1)
# Table approximation
for fun, nc in zip([_get_legen_lut_fast, _get_legen_lut_accurate],
[100, 50]):
lut, n_fact = _get_legen_table('eeg', n_coeff=nc, force_calc=True)
vals_i = fun(xs, lut)
# Need a "1:" here because we omit the first coefficient in our table!
assert_allclose(vals_np[:, 1:vals_i.shape[1] + 1], vals_i,
rtol=1e-2, atol=5e-3)
# Now let's look at our sums
ctheta = rng.rand(20, 30) * 2.0 - 1.0
beta = rng.rand(20, 30) * 0.8
lut_fun = partial(fun, lut=lut)
c1 = _comp_sum_eeg(beta.flatten(), ctheta.flatten(), lut_fun, n_fact)
c1.shape = beta.shape
# compare to numpy
n = np.arange(1, n_terms, dtype=float)[:, np.newaxis, np.newaxis]
coeffs = np.zeros((n_terms,) + beta.shape)
coeffs[1:] = (np.cumprod([beta] * (n_terms - 1), axis=0) *
(2.0 * n + 1.0) * (2.0 * n + 1.0) / n)
# can't use tensor=False here b/c it isn't in old numpy
c2 = np.empty((20, 30))
for ci1 in range(20):
for ci2 in range(30):
c2[ci1, ci2] = legendre.legval(ctheta[ci1, ci2],
coeffs[:, ci1, ci2])
assert_allclose(c1, c2, 1e-2, 1e-3) # close enough...
# compare fast and slow for MEG
ctheta = rng.rand(20 * 30) * 2.0 - 1.0
beta = rng.rand(20 * 30) * 0.8
lut, n_fact = _get_legen_table('meg', n_coeff=10, force_calc=True)
fun = partial(_get_legen_lut_fast, lut=lut)
coeffs = _comp_sums_meg(beta, ctheta, fun, n_fact, False)
lut, n_fact = _get_legen_table('meg', n_coeff=20, force_calc=True)
fun = partial(_get_legen_lut_accurate, lut=lut)
coeffs = _comp_sums_meg(beta, ctheta, fun, n_fact, False)
