def test_nd_array(shape: tuple):
xdata = [np.arange(s) for s in shape]
ydata = np.arange(0, np.prod(shape)).reshape(shape)
sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata, smooth=1.0)
ydata_s = sp(xdata)
assert ydata_s == pytest.approx(ydata)
def test_invalid_evaluate_data(x, xi):
np.random.seed(1234)
y = np.random.randn(*tuple(len(xx) for xx in x))
s = csaps.NdGridCubicSmoothingSpline(x, y)
with pytest.raises((ValueError, TypeError)):
s(xi)
def test_ndgrid_2d_integrate(ndgrid_2d_data):
xy = ndgrid_2d_data.xy
z = ndgrid_2d_data.z
integral_expected = ndgrid_2d_data.integral
spline = csaps.NdGridCubicSmoothingSpline(xy, z, smooth=None).spline
integral = spline.integrate(((xy[0][0], xy[0][-1]), (xy[1][0], xy[1][-1])))
assert integral == pytest.approx(integral_expected)
def test_surface(surface_data):
xdata, ydata = surface_data
sp = csaps.NdGridCubicSmoothingSpline(xdata, ydata)
noisy_s = sp(xdata)
assert isinstance(sp.smooth, tuple)
assert len(sp.smooth) == 2
assert isinstance(sp.spline, csaps.NdGridSplinePPForm)
assert noisy_s.shape == ydata.shape
def test_auto_smooth_2d(ndgrid_2d_data):
xy = ndgrid_2d_data.xy
z = ndgrid_2d_data.z
zi_expected = ndgrid_2d_data.zi
smooth_expected = ndgrid_2d_data.smooth
s = csaps.NdGridCubicSmoothingSpline(xy, z, smooth=None)
zi = s(xy)
assert s.smooth == pytest.approx(smooth_expected)
assert zi == pytest.approx(zi_expected)
def test_smooth_factor(shape, smooth):
x = [np.arange(s) for s in shape]
y = np.arange(0, np.prod(shape)).reshape(shape)
sp = csaps.NdGridCubicSmoothingSpline(x, y, smooth=smooth)
if isinstance(smooth, tuple):
expected_smooth = smooth
else:
expected_smooth = tuple([smooth] * len(shape))
assert sp.smooth == pytest.approx(expected_smooth)
def test_ndsplineppform(shape, coeffs_shape, order, pieces, ndim):
x = tuple(np.arange(s) for s in shape)
y = np.arange(float(np.prod(shape))).reshape(shape)
ss = csaps.NdGridCubicSmoothingSpline(x, y).spline
assert all(np.allclose(bi, xi) for bi, xi in zip(ss.breaks, x))
assert ss.coeffs.shape == coeffs_shape
assert ss.order == order
assert ss.pieces == pieces
assert ss.ndim == ndim
assert ss.shape == shape
def test_ndgrid_2d_antiderivative(ndgrid_2d_data):
xy = ndgrid_2d_data.xy
z = ndgrid_2d_data.z
zi_ad1_expected = ndgrid_2d_data.zi_ad1
spline = csaps.NdGridCubicSmoothingSpline(xy, z, smooth=None).spline
spline_ad1: csaps.NdGridSplinePPForm = spline.antiderivative(nu=(1, 1))
zi_ad1 = spline_ad1(xy)
assert spline_ad1.order == (5, 5)
assert zi_ad1 == pytest.approx(zi_ad1_expected)
def test_surface_smoothing():
xdata = [np.linspace(-3, 3, 61), np.linspace(-3.5, 3.5, 51)]
i, j = np.meshgrid(*xdata, indexing='ij')
ydata = (3 * (1 - j)**2. * np.exp(-(j**2) - (i + 1)**2) - 10 *
(j / 5 - j**3 - i**5) * np.exp(-j**2 - i**2) -
1 / 3 * np.exp(-(j + 1)**2 - i**2))
np.random.seed(12345)
noisy = ydata + (np.random.randn(*ydata.shape) * 0.75)
sp = csaps.NdGridCubicSmoothingSpline(xdata, noisy)
_ = sp(xdata)
def test_evaluate_nu_extrapolate(nu: tuple, extrapolate: bool):
x = ([1, 2, 3, 4], [1, 2, 3, 4])
xi = ([0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5])
y = np.arange(4 * 4).reshape((4, 4))
ss = csaps.NdGridCubicSmoothingSpline(x, y, smooth=1.0)
y_ss = ss(xi, nu=nu, extrapolate=extrapolate)
pp = NdPPoly(ss.spline.c, x)
xx = tuple(np.meshgrid(*xi, indexing='ij'))
y_pp = pp(xx, nu=nu, extrapolate=extrapolate)
np.testing.assert_allclose(y_ss,
y_pp,
rtol=1e-05,
atol=1e-08,
equal_nan=True)
def test_surface():
xdata = [np.linspace(-3, 3, 61), np.linspace(-3.5, 3.5, 51)]
i, j = np.meshgrid(*xdata, indexing='ij')
ydata = (3 * (1 - j)**2. * np.exp(-(j**2) - (i + 1)**2) - 10 *
(j / 5 - j**3 - i**5) * np.exp(-j**2 - i**2) -
1 / 3 * np.exp(-(j + 1)**2 - i**2))
np.random.seed(12345)
noisy = ydata + (np.random.randn(*ydata.shape) * 0.75)
sp = csaps.NdGridCubicSmoothingSpline(xdata, noisy)
noisy_s = sp(xdata)
assert isinstance(sp.smooth, tuple)
assert len(sp.smooth) == 2
assert isinstance(sp.spline, csaps.NdGridSplinePPForm)
assert noisy_s.shape == noisy.shape
def test_ndgrid_2d_derivative(ndgrid_2d_data):
xy = ndgrid_2d_data.xy
z = ndgrid_2d_data.z
zi_d1_expected = ndgrid_2d_data.zi_d1
zi_d2_expected = ndgrid_2d_data.zi_d2
spline = csaps.NdGridCubicSmoothingSpline(xy, z, smooth=None).spline
spline_d1: csaps.NdGridSplinePPForm = spline.derivative(nu=(1, 1))
spline_d2: csaps.NdGridSplinePPForm = spline.derivative(nu=(2, 2))
zi_d1 = spline_d1(xy)
zi_d2 = spline_d2(xy)
assert spline_d1.order == (3, 3)
assert spline_d2.order == (2, 2)
assert zi_d1 == pytest.approx(zi_d1_expected)
assert zi_d2 == pytest.approx(zi_d2_expected)
def test_grid_invalid_data(x, y, w, p):
with pytest.raises((ValueError, TypeError)):
csaps.NdGridCubicSmoothingSpline(x, y, w, p)