def test_w1d_2d_fit():
x = numpy.linspace(-1, 1, 1000)
c = numpy.array([[3, 0.2, 1, -1], [4, 0.4, 0.8, -0.8]])
y = numpy.sum(
[_c[:, None] * numpy.power(x, i)[None, :] for i, _c in enumerate(c.T)],
axis=0)
# Add noise
y += numpy.random.normal(scale=0.01, size=y.size).reshape(y.shape)
# Add in deviates
indx = numpy.unique(numpy.random.randint(1000, size=10))
y[0, indx] += numpy.random.normal(scale=10, size=len(indx))
y[1, indx] += numpy.random.normal(scale=10, size=len(indx))
# Weight all y vectors the same
w = numpy.ones(x.shape, dtype=float)
w[indx] = 0.
c_nw = numpy.polynomial.legendre.legfit(x, y.T, 4)
c = numpy.polynomial.legendre.legfit(x, y.T, 4, w=w)
leg = Legendre1D(x, 4)
_c_nw = leg.fit(y)
_c = leg.fit(y, w=w)
assert numpy.allclose(c_nw, _c_nw.T), 'Legendre1D fits should match numpy.'
assert numpy.allclose(c,
_c.T), 'Weighted Legendre1D fits should match numpy.'
def test_locrej_2d_fit():
x = numpy.linspace(-1, 1, 1000)
c = numpy.array([[3, 0.2, 1, -1], [4, 0.4, 0.8, -0.8]])
y = numpy.sum(
[_c[:, None] * numpy.power(x, i)[None, :] for i, _c in enumerate(c.T)],
axis=0)
# Add noise
sigma = 0.01
y += numpy.random.normal(scale=sigma, size=y.size).reshape(y.shape) \
* numpy.absolute(x)[None,:] * 5
# Add in deviates
outlier = numpy.unravel_index(
numpy.unique(numpy.random.randint(y.size, size=20)), y.shape)
offset = numpy.random.normal(scale=10, size=len(outlier[0]))
indx = numpy.absolute(offset) > 10 * sigma
outlier = (outlier[0][indx], outlier[1][indx])
y[outlier] += offset[indx]
leg = Legendre1D(x, 4)
c, rej = leg.fit(y, rej_iter=-1, rej_win=51)
# Rejected all the outliers?
assert numpy.all(rej[outlier]), 'Should have rejected all the outliers'
# Don't use a local sigma
_c, _rej = leg.fit(y, rej_iter=-1)
# Should reject more when not considering local sigma
assert numpy.sum(_rej) > numpy.sum(
rej), 'Should have rejected more when using global sigma'
def test_ew_glbrej_1d_fit():
x = numpy.linspace(-1, 1, 1000)
y = 3 + 0.2 * x + x * x - x * x * x
# Add noise
sigma = 0.01
noise = numpy.random.normal(scale=sigma, size=x.size)
err = numpy.full(y.shape, sigma, dtype=float)
outlier = numpy.unique(numpy.random.randint(1000, size=10))
offset = numpy.random.normal(scale=10., size=len(outlier))
noise[outlier] = offset
err[outlier] = 10.
# Add noise including larger error
y += noise
leg = Legendre1D(x, 4)
c, rej = leg.fit(y, err=err, rej_iter=-1)
_c, _rej = leg.fit(y, rej_iter=-1)
# Fewer points should be rejected when accounting for errors
assert numpy.sum(_rej) > numpy.sum(rej), \
'Should not have rejected as many points when accounting for error'
def test_locrej_1d_fit():
x = numpy.linspace(-1, 1, 1000)
y = 3 + 0.2 * x + x * x - x * x * x
# Add noise
sigma = 0.01
y += numpy.random.normal(scale=sigma, size=x.size) * numpy.absolute(x) * 5
# Add in deviates
outlier = numpy.unique(numpy.random.randint(1000, size=10))
offset = numpy.random.normal(scale=10, size=len(outlier))
indx = numpy.absolute(offset) > 10 * sigma
outlier = outlier[indx]
y[outlier] += offset[indx]
leg = Legendre1D(x, 4)
c, rej = leg.fit(y, rej_iter=-1, rej_win=51)
# Rejected all the outliers?
assert numpy.all(rej[outlier]), 'Should have rejected all the outliers'
# Don't use a local sigma
_c, _rej = leg.fit(y, rej_iter=-1)
# Should reject more when not considering local sigma
assert numpy.sum(_rej) > numpy.sum(
rej), 'Should have rejected more when using global sigma'
# Don't use a local sigma and only one iteration
_c, __rej = leg.fit(y, rej_iter=1)
# Should reject more when allowed to continue until no more rejections
assert numpy.sum(_rej) > numpy.sum(
__rej), 'Should have rejected fewer in one iteration'
def test_w2d_2d_fit():
x = numpy.linspace(-1, 1, 1000)
c = numpy.array([[3, 0.2, 1, -1], [4, 0.4, 0.8, -0.8]])
y = numpy.sum(
[_c[:, None] * numpy.power(x, i)[None, :] for i, _c in enumerate(c.T)],
axis=0)
# Add noise
y += numpy.random.normal(scale=0.01, size=y.size).reshape(y.shape)
# Add in deviates
indx = numpy.unravel_index(
numpy.unique(numpy.random.randint(y.size, size=20)), y.shape)
y[indx] += numpy.random.normal(scale=10, size=len(indx[0]))
# Weight y vectors independently
w = numpy.ones(y.shape, dtype=float)
w[indx] = 0.
c = numpy.zeros((y.shape[0], 5), dtype=float)
for i in range(y.shape[0]):
c[i] = numpy.polynomial.legendre.legfit(x, y[i], 4, w=w[i])
leg = Legendre1D(x, 4)
_c = leg.fit(y, w=w)
assert numpy.allclose(c,
_c), 'Weighted Legendre1D fits should match numpy.'
# Tests both the construction of the model and that the residuals
# are close to the expectation from the noise added to the data
# (i.e. is the fit good).
resid = numpy.ma.std(
numpy.ma.MaskedArray(y, mask=numpy.logical_not(w > 0)) - leg.model(_c))
assert numpy.isclose(numpy.round(resid, decimals=2),
0.01), 'Residuals too large'
def test_glbrej_2d_fit():
rng = numpy.random.default_rng(seed=8001)
x = numpy.linspace(-1, 1, 1000)
c = numpy.array([[3, 0.2, 1, -1], [4, 0.4, 0.8, -0.8]])
y = numpy.sum(
[_c[:, None] * numpy.power(x, i)[None, :] for i, _c in enumerate(c.T)],
axis=0)
# Add noise
sigma = 0.01
y += rng.normal(scale=sigma, size=y.size).reshape(y.shape)
# Add in deviates
outlier = numpy.unravel_index(numpy.unique(rng.integers(y.size, size=20)),
y.shape)
offset = rng.normal(scale=10, size=len(outlier[0]))
indx = numpy.absolute(offset) > 10 * sigma
outlier = (outlier[0][indx], outlier[1][indx])
y[outlier] += offset[indx]
leg = Legendre1D(x, 4)
c, rej = leg.fit(y, rej_iter=-1)
# Rejected all the outliers?
assert numpy.all(rej[outlier]), 'Should have rejected all the outliers'
def test_1d_fit():
x = numpy.linspace(-1, 1, 1000)
y = 3 + 0.2 * x + x * x - x * x * x
y += numpy.random.normal(scale=0.01, size=x.size)
c = numpy.polynomial.legendre.legfit(x, y, 4)
leg = Legendre1D(x, 4)
_c = leg.fit(y)
assert numpy.allclose(c, _c), 'Legendre1D should match numpy.'
def test_2d_fit():
x = numpy.linspace(-1, 1, 1000)
c = numpy.array([[3, 0.2, 1, -1], [4, 0.4, 0.8, -0.8]])
y = numpy.sum(
[_c[:, None] * numpy.power(x, i)[None, :] for i, _c in enumerate(c.T)],
axis=0)
y += numpy.random.normal(scale=0.01, size=y.size).reshape(y.shape)
c = numpy.polynomial.legendre.legfit(x, y.T, 4)
leg = Legendre1D(x, 4)
_c = leg.fit(y)
assert numpy.allclose(c, _c.T), 'Legendre1D should match numpy.'
def test_glbrej_1d_fit():
x = numpy.linspace(-1, 1, 1000)
y = 3 + 0.2 * x + x * x - x * x * x
# Add noise
sigma = 0.01
y += numpy.random.normal(scale=sigma, size=x.size)
# Add in deviates
outlier = numpy.unique(numpy.random.randint(1000, size=10))
offset = numpy.random.normal(scale=10, size=len(outlier))
indx = numpy.absolute(offset) > 10 * sigma
outlier = outlier[indx]
y[outlier] += offset[indx]
leg = Legendre1D(x, 4)
c, rej = leg.fit(y, rej_iter=-1)
# Rejected all the outliers?
assert numpy.all(rej[outlier]), 'Should have rejected all the outliers'
def test_w1d_1d_fit():
x = numpy.linspace(-1, 1, 1000)
y = 3 + 0.2 * x + x * x - x * x * x
# Add noise
y += numpy.random.normal(scale=0.01, size=x.size)
# Add in deviates
indx = numpy.unique(numpy.random.randint(1000, size=10))
y[indx] += numpy.random.normal(scale=10, size=len(indx))
w = numpy.ones(y.shape, dtype=float)
w[indx] = 0.
c_nw = numpy.polynomial.legendre.legfit(x, y, 4)
c = numpy.polynomial.legendre.legfit(x, y, 4, w=w)
leg = Legendre1D(x, 4)
_c_nw = leg.fit(y)
_c = leg.fit(y, w=w)
assert numpy.allclose(c_nw, _c_nw), 'Legendre1D fits should match numpy.'
assert numpy.allclose(c,
_c), 'Weighted Legendre1D fits should match numpy.'