1348 lines
57 KiB
Python
1348 lines
57 KiB
Python
# Created by Pearu Peterson, June 2003
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import itertools
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import numpy as np
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from numpy.testing import (assert_equal, assert_almost_equal, assert_array_equal,
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assert_array_almost_equal, assert_allclose, suppress_warnings)
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from pytest import raises as assert_raises
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from numpy import array, diff, linspace, meshgrid, ones, pi, shape
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from scipy.interpolate._fitpack_py import bisplrep, bisplev, splrep, spalde
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from scipy.interpolate._fitpack2 import (UnivariateSpline,
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LSQUnivariateSpline, InterpolatedUnivariateSpline,
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LSQBivariateSpline, SmoothBivariateSpline, RectBivariateSpline,
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LSQSphereBivariateSpline, SmoothSphereBivariateSpline,
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RectSphereBivariateSpline)
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class TestUnivariateSpline:
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def test_linear_constant(self):
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x = [1,2,3]
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y = [3,3,3]
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lut = UnivariateSpline(x,y,k=1)
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assert_array_almost_equal(lut.get_knots(),[1,3])
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assert_array_almost_equal(lut.get_coeffs(),[3,3])
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assert_almost_equal(lut.get_residual(),0.0)
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assert_array_almost_equal(lut([1,1.5,2]),[3,3,3])
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def test_preserve_shape(self):
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x = [1, 2, 3]
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y = [0, 2, 4]
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lut = UnivariateSpline(x, y, k=1)
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arg = 2
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assert_equal(shape(arg), shape(lut(arg)))
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assert_equal(shape(arg), shape(lut(arg, nu=1)))
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arg = [1.5, 2, 2.5]
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assert_equal(shape(arg), shape(lut(arg)))
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assert_equal(shape(arg), shape(lut(arg, nu=1)))
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def test_linear_1d(self):
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x = [1,2,3]
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y = [0,2,4]
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lut = UnivariateSpline(x,y,k=1)
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assert_array_almost_equal(lut.get_knots(),[1,3])
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assert_array_almost_equal(lut.get_coeffs(),[0,4])
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assert_almost_equal(lut.get_residual(),0.0)
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assert_array_almost_equal(lut([1,1.5,2]),[0,1,2])
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def test_subclassing(self):
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# See #731
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class ZeroSpline(UnivariateSpline):
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def __call__(self, x):
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return 0*array(x)
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sp = ZeroSpline([1,2,3,4,5], [3,2,3,2,3], k=2)
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assert_array_equal(sp([1.5, 2.5]), [0., 0.])
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def test_empty_input(self):
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# Test whether empty input returns an empty output. Ticket 1014
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x = [1,3,5,7,9]
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y = [0,4,9,12,21]
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spl = UnivariateSpline(x, y, k=3)
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assert_array_equal(spl([]), array([]))
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def test_roots(self):
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x = [1, 3, 5, 7, 9]
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y = [0, 4, 9, 12, 21]
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spl = UnivariateSpline(x, y, k=3)
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assert_almost_equal(spl.roots()[0], 1.050290639101332)
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def test_derivatives(self):
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x = [1, 3, 5, 7, 9]
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y = [0, 4, 9, 12, 21]
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spl = UnivariateSpline(x, y, k=3)
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assert_almost_equal(spl.derivatives(3.5),
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[5.5152902, 1.7146577, -0.1830357, 0.3125])
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def test_derivatives_2(self):
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x = np.arange(8)
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y = x**3 + 2.*x**2
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tck = splrep(x, y, s=0)
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ders = spalde(3, tck)
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assert_allclose(ders, [45., # 3**3 + 2*(3)**2
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39., # 3*(3)**2 + 4*(3)
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22., # 6*(3) + 4
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6.], # 6*3**0
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atol=1e-15)
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spl = UnivariateSpline(x, y, s=0, k=3)
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assert_allclose(spl.derivatives(3),
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ders,
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atol=1e-15)
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def test_resize_regression(self):
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"""Regression test for #1375."""
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x = [-1., -0.65016502, -0.58856235, -0.26903553, -0.17370892,
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-0.10011001, 0., 0.10011001, 0.17370892, 0.26903553, 0.58856235,
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0.65016502, 1.]
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y = [1.,0.62928599, 0.5797223, 0.39965815, 0.36322694, 0.3508061,
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0.35214793, 0.3508061, 0.36322694, 0.39965815, 0.5797223,
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0.62928599, 1.]
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w = [1.00000000e+12, 6.88875973e+02, 4.89314737e+02, 4.26864807e+02,
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6.07746770e+02, 4.51341444e+02, 3.17480210e+02, 4.51341444e+02,
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6.07746770e+02, 4.26864807e+02, 4.89314737e+02, 6.88875973e+02,
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1.00000000e+12]
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spl = UnivariateSpline(x=x, y=y, w=w, s=None)
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desired = array([0.35100374, 0.51715855, 0.87789547, 0.98719344])
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assert_allclose(spl([0.1, 0.5, 0.9, 0.99]), desired, atol=5e-4)
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def test_out_of_range_regression(self):
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# Test different extrapolation modes. See ticket 3557
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x = np.arange(5, dtype=float)
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y = x**3
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xp = linspace(-8, 13, 100)
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xp_zeros = xp.copy()
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xp_zeros[np.logical_or(xp_zeros < 0., xp_zeros > 4.)] = 0
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xp_clip = xp.copy()
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xp_clip[xp_clip < x[0]] = x[0]
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xp_clip[xp_clip > x[-1]] = x[-1]
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for cls in [UnivariateSpline, InterpolatedUnivariateSpline]:
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spl = cls(x=x, y=y)
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for ext in [0, 'extrapolate']:
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assert_allclose(spl(xp, ext=ext), xp**3, atol=1e-16)
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assert_allclose(cls(x, y, ext=ext)(xp), xp**3, atol=1e-16)
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for ext in [1, 'zeros']:
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assert_allclose(spl(xp, ext=ext), xp_zeros**3, atol=1e-16)
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assert_allclose(cls(x, y, ext=ext)(xp), xp_zeros**3, atol=1e-16)
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for ext in [2, 'raise']:
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assert_raises(ValueError, spl, xp, **dict(ext=ext))
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for ext in [3, 'const']:
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assert_allclose(spl(xp, ext=ext), xp_clip**3, atol=1e-16)
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assert_allclose(cls(x, y, ext=ext)(xp), xp_clip**3, atol=1e-16)
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# also test LSQUnivariateSpline [which needs explicit knots]
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t = spl.get_knots()[3:4] # interior knots w/ default k=3
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spl = LSQUnivariateSpline(x, y, t)
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assert_allclose(spl(xp, ext=0), xp**3, atol=1e-16)
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assert_allclose(spl(xp, ext=1), xp_zeros**3, atol=1e-16)
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assert_raises(ValueError, spl, xp, **dict(ext=2))
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assert_allclose(spl(xp, ext=3), xp_clip**3, atol=1e-16)
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# also make sure that unknown values for `ext` are caught early
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for ext in [-1, 'unknown']:
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spl = UnivariateSpline(x, y)
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assert_raises(ValueError, spl, xp, **dict(ext=ext))
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assert_raises(ValueError, UnivariateSpline,
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**dict(x=x, y=y, ext=ext))
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def test_lsq_fpchec(self):
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xs = np.arange(100) * 1.
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ys = np.arange(100) * 1.
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knots = np.linspace(0, 99, 10)
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bbox = (-1, 101)
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assert_raises(ValueError, LSQUnivariateSpline, xs, ys, knots,
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bbox=bbox)
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def test_derivative_and_antiderivative(self):
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# Thin wrappers to splder/splantider, so light smoke test only.
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x = np.linspace(0, 1, 70)**3
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y = np.cos(x)
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spl = UnivariateSpline(x, y, s=0)
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spl2 = spl.antiderivative(2).derivative(2)
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assert_allclose(spl(0.3), spl2(0.3))
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spl2 = spl.antiderivative(1)
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assert_allclose(spl2(0.6) - spl2(0.2),
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spl.integral(0.2, 0.6))
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def test_derivative_extrapolation(self):
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# Regression test for gh-10195: for a const-extrapolation spline
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# its derivative evaluates to zero for extrapolation
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5, 5]
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f = UnivariateSpline(x_values, y_values, ext='const', k=3)
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x = [-1, 0, -0.5, 9, 9.5, 10]
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assert_allclose(f.derivative()(x), 0, atol=1e-15)
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def test_integral_out_of_bounds(self):
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# Regression test for gh-7906: .integral(a, b) is wrong if both
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# a and b are out-of-bounds
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x = np.linspace(0., 1., 7)
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for ext in range(4):
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f = UnivariateSpline(x, x, s=0, ext=ext)
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for (a, b) in [(1, 1), (1, 5), (2, 5),
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(0, 0), (-2, 0), (-2, -1)]:
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assert_allclose(f.integral(a, b), 0, atol=1e-15)
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def test_nan(self):
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# bail out early if the input data contains nans
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x = np.arange(10, dtype=float)
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y = x**3
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w = np.ones_like(x)
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# also test LSQUnivariateSpline [which needs explicit knots]
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spl = UnivariateSpline(x, y, check_finite=True)
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t = spl.get_knots()[3:4] # interior knots w/ default k=3
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y_end = y[-1]
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for z in [np.nan, np.inf, -np.inf]:
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y[-1] = z
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assert_raises(ValueError, UnivariateSpline,
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**dict(x=x, y=y, check_finite=True))
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assert_raises(ValueError, InterpolatedUnivariateSpline,
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**dict(x=x, y=y, check_finite=True))
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assert_raises(ValueError, LSQUnivariateSpline,
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**dict(x=x, y=y, t=t, check_finite=True))
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y[-1] = y_end # check valid y but invalid w
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w[-1] = z
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assert_raises(ValueError, UnivariateSpline,
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**dict(x=x, y=y, w=w, check_finite=True))
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assert_raises(ValueError, InterpolatedUnivariateSpline,
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**dict(x=x, y=y, w=w, check_finite=True))
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assert_raises(ValueError, LSQUnivariateSpline,
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**dict(x=x, y=y, t=t, w=w, check_finite=True))
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def test_strictly_increasing_x(self):
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# Test the x is required to be strictly increasing for
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# UnivariateSpline if s=0 and for InterpolatedUnivariateSpline,
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# but merely increasing for UnivariateSpline if s>0
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# and for LSQUnivariateSpline; see gh-8535
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xx = np.arange(10, dtype=float)
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yy = xx**3
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x = np.arange(10, dtype=float)
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x[1] = x[0]
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y = x**3
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w = np.ones_like(x)
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# also test LSQUnivariateSpline [which needs explicit knots]
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spl = UnivariateSpline(xx, yy, check_finite=True)
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t = spl.get_knots()[3:4] # interior knots w/ default k=3
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UnivariateSpline(x=x, y=y, w=w, s=1, check_finite=True)
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LSQUnivariateSpline(x=x, y=y, t=t, w=w, check_finite=True)
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assert_raises(ValueError, UnivariateSpline,
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**dict(x=x, y=y, s=0, check_finite=True))
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assert_raises(ValueError, InterpolatedUnivariateSpline,
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**dict(x=x, y=y, check_finite=True))
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def test_increasing_x(self):
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# Test that x is required to be increasing, see gh-8535
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xx = np.arange(10, dtype=float)
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yy = xx**3
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x = np.arange(10, dtype=float)
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x[1] = x[0] - 1.0
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y = x**3
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w = np.ones_like(x)
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# also test LSQUnivariateSpline [which needs explicit knots]
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spl = UnivariateSpline(xx, yy, check_finite=True)
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t = spl.get_knots()[3:4] # interior knots w/ default k=3
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assert_raises(ValueError, UnivariateSpline,
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**dict(x=x, y=y, check_finite=True))
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assert_raises(ValueError, InterpolatedUnivariateSpline,
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**dict(x=x, y=y, check_finite=True))
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assert_raises(ValueError, LSQUnivariateSpline,
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**dict(x=x, y=y, t=t, w=w, check_finite=True))
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def test_invalid_input_for_univariate_spline(self):
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5]
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UnivariateSpline(x_values, y_values)
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assert "x and y should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5, 2.8]
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w_values = [-1.0, 1.0, 1.0, 1.0]
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UnivariateSpline(x_values, y_values, w=w_values)
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assert "x, y, and w should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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bbox = (-1)
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UnivariateSpline(x_values, y_values, bbox=bbox)
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assert "bbox shape should be (2,)" in str(info.value)
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with assert_raises(ValueError) as info:
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UnivariateSpline(x_values, y_values, k=6)
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assert "k should be 1 <= k <= 5" in str(info.value)
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with assert_raises(ValueError) as info:
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UnivariateSpline(x_values, y_values, s=-1.0)
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assert "s should be s >= 0.0" in str(info.value)
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def test_invalid_input_for_interpolated_univariate_spline(self):
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5]
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InterpolatedUnivariateSpline(x_values, y_values)
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assert "x and y should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5, 2.8]
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w_values = [-1.0, 1.0, 1.0, 1.0]
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InterpolatedUnivariateSpline(x_values, y_values, w=w_values)
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assert "x, y, and w should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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bbox = (-1)
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InterpolatedUnivariateSpline(x_values, y_values, bbox=bbox)
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assert "bbox shape should be (2,)" in str(info.value)
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with assert_raises(ValueError) as info:
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InterpolatedUnivariateSpline(x_values, y_values, k=6)
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assert "k should be 1 <= k <= 5" in str(info.value)
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def test_invalid_input_for_lsq_univariate_spline(self):
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5, 2.8]
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spl = UnivariateSpline(x_values, y_values, check_finite=True)
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t_values = spl.get_knots()[3:4] # interior knots w/ default k=3
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5]
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LSQUnivariateSpline(x_values, y_values, t_values)
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assert "x and y should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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x_values = [1, 2, 4, 6, 8.5]
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y_values = [0.5, 0.8, 1.3, 2.5, 2.8]
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w_values = [1.0, 1.0, 1.0, 1.0]
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LSQUnivariateSpline(x_values, y_values, t_values, w=w_values)
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assert "x, y, and w should have a same length" in str(info.value)
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with assert_raises(ValueError) as info:
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bbox = (100, -100)
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LSQUnivariateSpline(x_values, y_values, t_values, bbox=bbox)
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assert "Interior knots t must satisfy Schoenberg-Whitney conditions" in str(info.value)
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with assert_raises(ValueError) as info:
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bbox = (-1)
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LSQUnivariateSpline(x_values, y_values, t_values, bbox=bbox)
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assert "bbox shape should be (2,)" in str(info.value)
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with assert_raises(ValueError) as info:
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LSQUnivariateSpline(x_values, y_values, t_values, k=6)
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assert "k should be 1 <= k <= 5" in str(info.value)
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def test_array_like_input(self):
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x_values = np.array([1, 2, 4, 6, 8.5])
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y_values = np.array([0.5, 0.8, 1.3, 2.5, 2.8])
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w_values = np.array([1.0, 1.0, 1.0, 1.0, 1.0])
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bbox = np.array([-100, 100])
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# np.array input
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spl1 = UnivariateSpline(x=x_values, y=y_values, w=w_values,
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bbox=bbox)
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# list input
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spl2 = UnivariateSpline(x=x_values.tolist(), y=y_values.tolist(),
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w=w_values.tolist(), bbox=bbox.tolist())
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assert_allclose(spl1([0.1, 0.5, 0.9, 0.99]),
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spl2([0.1, 0.5, 0.9, 0.99]))
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def test_fpknot_oob_crash(self):
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# https://github.com/scipy/scipy/issues/3691
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x = range(109)
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y = [0., 0., 0., 0., 0., 10.9, 0., 11., 0.,
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0., 0., 10.9, 0., 0., 0., 0., 0., 0.,
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10.9, 0., 0., 0., 11., 0., 0., 0., 10.9,
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0., 0., 0., 10.5, 0., 0., 0., 10.7, 0.,
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0., 0., 11., 0., 0., 0., 0., 0., 0.,
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10.9, 0., 0., 10.7, 0., 0., 0., 10.6, 0.,
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0., 0., 10.5, 0., 0., 10.7, 0., 0., 10.5,
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0., 0., 11.5, 0., 0., 0., 10.7, 0., 0.,
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10.7, 0., 0., 10.9, 0., 0., 10.8, 0., 0.,
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0., 10.7, 0., 0., 10.6, 0., 0., 0., 10.4,
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0., 0., 10.6, 0., 0., 10.5, 0., 0., 0.,
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10.7, 0., 0., 0., 10.4, 0., 0., 0., 10.8, 0.]
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with suppress_warnings() as sup:
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r = sup.record(
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UserWarning,
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|
r"""
|
|
The maximal number of iterations maxit \(set to 20 by the program\)
|
|
allowed for finding a smoothing spline with fp=s has been reached: s
|
|
too small.
|
|
There is an approximation returned but the corresponding weighted sum
|
|
of squared residuals does not satisfy the condition abs\(fp-s\)/s < tol.""")
|
|
UnivariateSpline(x, y, k=1)
|
|
assert_equal(len(r), 1)
|
|
|
|
|
|
class TestLSQBivariateSpline:
|
|
# NOTE: The systems in this test class are rank-deficient
|
|
def test_linear_constant(self):
|
|
x = [1,1,1,2,2,2,3,3,3]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = [3,3,3,3,3,3,3,3,3]
|
|
s = 0.1
|
|
tx = [1+s,3-s]
|
|
ty = [1+s,3-s]
|
|
with suppress_warnings() as sup:
|
|
r = sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
|
|
assert_equal(len(r), 1)
|
|
|
|
assert_almost_equal(lut(2,2), 3.)
|
|
|
|
def test_bilinearity(self):
|
|
x = [1,1,1,2,2,2,3,3,3]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = [0,7,8,3,4,7,1,3,4]
|
|
s = 0.1
|
|
tx = [1+s,3-s]
|
|
ty = [1+s,3-s]
|
|
with suppress_warnings() as sup:
|
|
# This seems to fail (ier=1, see ticket 1642).
|
|
sup.filter(UserWarning, "\nThe coefficients of the spline")
|
|
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
|
|
|
|
tx, ty = lut.get_knots()
|
|
for xa, xb in zip(tx[:-1], tx[1:]):
|
|
for ya, yb in zip(ty[:-1], ty[1:]):
|
|
for t in [0.1, 0.5, 0.9]:
|
|
for s in [0.3, 0.4, 0.7]:
|
|
xp = xa*(1-t) + xb*t
|
|
yp = ya*(1-s) + yb*s
|
|
zp = (+ lut(xa, ya)*(1-t)*(1-s)
|
|
+ lut(xb, ya)*t*(1-s)
|
|
+ lut(xa, yb)*(1-t)*s
|
|
+ lut(xb, yb)*t*s)
|
|
assert_almost_equal(lut(xp,yp), zp)
|
|
|
|
def test_integral(self):
|
|
x = [1,1,1,2,2,2,8,8,8]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = array([0,7,8,3,4,7,1,3,4])
|
|
|
|
s = 0.1
|
|
tx = [1+s,3-s]
|
|
ty = [1+s,3-s]
|
|
with suppress_warnings() as sup:
|
|
r = sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
|
|
assert_equal(len(r), 1)
|
|
tx, ty = lut.get_knots()
|
|
tz = lut(tx, ty)
|
|
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
|
|
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
|
|
|
|
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]),
|
|
trpz)
|
|
|
|
def test_empty_input(self):
|
|
# Test whether empty inputs returns an empty output. Ticket 1014
|
|
x = [1,1,1,2,2,2,3,3,3]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = [3,3,3,3,3,3,3,3,3]
|
|
s = 0.1
|
|
tx = [1+s,3-s]
|
|
ty = [1+s,3-s]
|
|
with suppress_warnings() as sup:
|
|
r = sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
|
|
assert_equal(len(r), 1)
|
|
|
|
assert_array_equal(lut([], []), np.zeros((0,0)))
|
|
assert_array_equal(lut([], [], grid=False), np.zeros((0,)))
|
|
|
|
def test_invalid_input(self):
|
|
s = 0.1
|
|
tx = [1 + s, 3 - s]
|
|
ty = [1 + s, 3 - s]
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = np.linspace(1.0, 10.0)
|
|
y = np.linspace(1.0, 10.0)
|
|
z = np.linspace(1.0, 10.0, num=10)
|
|
LSQBivariateSpline(x, y, z, tx, ty)
|
|
assert "x, y, and z should have a same length" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = np.linspace(1.0, 10.0)
|
|
y = np.linspace(1.0, 10.0)
|
|
z = np.linspace(1.0, 10.0)
|
|
w = np.linspace(1.0, 10.0, num=20)
|
|
LSQBivariateSpline(x, y, z, tx, ty, w=w)
|
|
assert "x, y, z, and w should have a same length" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
w = np.linspace(-1.0, 10.0)
|
|
LSQBivariateSpline(x, y, z, tx, ty, w=w)
|
|
assert "w should be positive" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
bbox = (-100, 100, -100)
|
|
LSQBivariateSpline(x, y, z, tx, ty, bbox=bbox)
|
|
assert "bbox shape should be (4,)" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
LSQBivariateSpline(x, y, z, tx, ty, kx=10, ky=10)
|
|
assert "The length of x, y and z should be at least (kx+1) * (ky+1)" in \
|
|
str(info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
LSQBivariateSpline(x, y, z, tx, ty, eps=0.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
LSQBivariateSpline(x, y, z, tx, ty, eps=1.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
def test_array_like_input(self):
|
|
s = 0.1
|
|
tx = np.array([1 + s, 3 - s])
|
|
ty = np.array([1 + s, 3 - s])
|
|
x = np.linspace(1.0, 10.0)
|
|
y = np.linspace(1.0, 10.0)
|
|
z = np.linspace(1.0, 10.0)
|
|
w = np.linspace(1.0, 10.0)
|
|
bbox = np.array([1.0, 10.0, 1.0, 10.0])
|
|
|
|
with suppress_warnings() as sup:
|
|
r = sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
# np.array input
|
|
spl1 = LSQBivariateSpline(x, y, z, tx, ty, w=w, bbox=bbox)
|
|
# list input
|
|
spl2 = LSQBivariateSpline(x.tolist(), y.tolist(), z.tolist(),
|
|
tx.tolist(), ty.tolist(), w=w.tolist(),
|
|
bbox=bbox)
|
|
assert_allclose(spl1(2.0, 2.0), spl2(2.0, 2.0))
|
|
assert_equal(len(r), 2)
|
|
|
|
def test_unequal_length_of_knots(self):
|
|
"""Test for the case when the input knot-location arrays in x and y are
|
|
of different lengths.
|
|
"""
|
|
x, y = np.mgrid[0:100, 0:100]
|
|
x = x.ravel()
|
|
y = y.ravel()
|
|
z = 3.0 * np.ones_like(x)
|
|
tx = np.linspace(0.1, 98.0, 29)
|
|
ty = np.linspace(0.1, 98.0, 33)
|
|
with suppress_warnings() as sup:
|
|
r = sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
lut = LSQBivariateSpline(x,y,z,tx,ty)
|
|
assert_equal(len(r), 1)
|
|
|
|
assert_almost_equal(lut(x, y, grid=False), z)
|
|
|
|
|
|
class TestSmoothBivariateSpline:
|
|
def test_linear_constant(self):
|
|
x = [1,1,1,2,2,2,3,3,3]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = [3,3,3,3,3,3,3,3,3]
|
|
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
|
|
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
|
|
assert_array_almost_equal(lut.get_coeffs(),[3,3,3,3])
|
|
assert_almost_equal(lut.get_residual(),0.0)
|
|
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[3,3],[3,3],[3,3]])
|
|
|
|
def test_linear_1d(self):
|
|
x = [1,1,1,2,2,2,3,3,3]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = [0,0,0,2,2,2,4,4,4]
|
|
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
|
|
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
|
|
assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
|
|
assert_almost_equal(lut.get_residual(),0.0)
|
|
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]])
|
|
|
|
def test_integral(self):
|
|
x = [1,1,1,2,2,2,4,4,4]
|
|
y = [1,2,3,1,2,3,1,2,3]
|
|
z = array([0,7,8,3,4,7,1,3,4])
|
|
|
|
with suppress_warnings() as sup:
|
|
# This seems to fail (ier=1, see ticket 1642).
|
|
sup.filter(UserWarning, "\nThe required storage space")
|
|
lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
|
|
|
|
tx = [1,2,4]
|
|
ty = [1,2,3]
|
|
|
|
tz = lut(tx, ty)
|
|
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
|
|
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
|
|
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
|
|
|
|
lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
|
|
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
|
|
decimal=0) # the quadratures give 23.75 and 23.85
|
|
|
|
tz = lut(tx[:-1], ty[:-1])
|
|
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
|
|
* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
|
|
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
|
|
|
|
def test_rerun_lwrk2_too_small(self):
|
|
# in this setting, lwrk2 is too small in the default run. Here we
|
|
# check for equality with the bisplrep/bisplev output because there,
|
|
# an automatic re-run of the spline representation is done if ier>10.
|
|
x = np.linspace(-2, 2, 80)
|
|
y = np.linspace(-2, 2, 80)
|
|
z = x + y
|
|
xi = np.linspace(-1, 1, 100)
|
|
yi = np.linspace(-2, 2, 100)
|
|
tck = bisplrep(x, y, z)
|
|
res1 = bisplev(xi, yi, tck)
|
|
interp_ = SmoothBivariateSpline(x, y, z)
|
|
res2 = interp_(xi, yi)
|
|
assert_almost_equal(res1, res2)
|
|
|
|
def test_invalid_input(self):
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = np.linspace(1.0, 10.0)
|
|
y = np.linspace(1.0, 10.0)
|
|
z = np.linspace(1.0, 10.0, num=10)
|
|
SmoothBivariateSpline(x, y, z)
|
|
assert "x, y, and z should have a same length" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = np.linspace(1.0, 10.0)
|
|
y = np.linspace(1.0, 10.0)
|
|
z = np.linspace(1.0, 10.0)
|
|
w = np.linspace(1.0, 10.0, num=20)
|
|
SmoothBivariateSpline(x, y, z, w=w)
|
|
assert "x, y, z, and w should have a same length" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
w = np.linspace(-1.0, 10.0)
|
|
SmoothBivariateSpline(x, y, z, w=w)
|
|
assert "w should be positive" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
bbox = (-100, 100, -100)
|
|
SmoothBivariateSpline(x, y, z, bbox=bbox)
|
|
assert "bbox shape should be (4,)" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
SmoothBivariateSpline(x, y, z, kx=10, ky=10)
|
|
assert "The length of x, y and z should be at least (kx+1) * (ky+1)" in\
|
|
str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
SmoothBivariateSpline(x, y, z, s=-1.0)
|
|
assert "s should be s >= 0.0" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
SmoothBivariateSpline(x, y, z, eps=0.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
SmoothBivariateSpline(x, y, z, eps=1.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
def test_array_like_input(self):
|
|
x = np.array([1, 1, 1, 2, 2, 2, 3, 3, 3])
|
|
y = np.array([1, 2, 3, 1, 2, 3, 1, 2, 3])
|
|
z = np.array([3, 3, 3, 3, 3, 3, 3, 3, 3])
|
|
w = np.array([1, 1, 1, 1, 1, 1, 1, 1, 1])
|
|
bbox = np.array([1.0, 3.0, 1.0, 3.0])
|
|
# np.array input
|
|
spl1 = SmoothBivariateSpline(x, y, z, w=w, bbox=bbox, kx=1, ky=1)
|
|
# list input
|
|
spl2 = SmoothBivariateSpline(x.tolist(), y.tolist(), z.tolist(),
|
|
bbox=bbox.tolist(), w=w.tolist(),
|
|
kx=1, ky=1)
|
|
assert_allclose(spl1(0.1, 0.5), spl2(0.1, 0.5))
|
|
|
|
|
|
class TestLSQSphereBivariateSpline:
|
|
def setup_method(self):
|
|
# define the input data and coordinates
|
|
ntheta, nphi = 70, 90
|
|
theta = linspace(0.5/(ntheta - 1), 1 - 0.5/(ntheta - 1), ntheta) * pi
|
|
phi = linspace(0.5/(nphi - 1), 1 - 0.5/(nphi - 1), nphi) * 2. * pi
|
|
data = ones((theta.shape[0], phi.shape[0]))
|
|
# define knots and extract data values at the knots
|
|
knotst = theta[::5]
|
|
knotsp = phi[::5]
|
|
knotdata = data[::5, ::5]
|
|
# calculate spline coefficients
|
|
lats, lons = meshgrid(theta, phi)
|
|
lut_lsq = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp)
|
|
self.lut_lsq = lut_lsq
|
|
self.data = knotdata
|
|
self.new_lons, self.new_lats = knotsp, knotst
|
|
|
|
def test_linear_constant(self):
|
|
assert_almost_equal(self.lut_lsq.get_residual(), 0.0)
|
|
assert_array_almost_equal(self.lut_lsq(self.new_lats, self.new_lons),
|
|
self.data)
|
|
|
|
def test_empty_input(self):
|
|
assert_array_almost_equal(self.lut_lsq([], []), np.zeros((0,0)))
|
|
assert_array_almost_equal(self.lut_lsq([], [], grid=False), np.zeros((0,)))
|
|
|
|
def test_invalid_input(self):
|
|
ntheta, nphi = 70, 90
|
|
theta = linspace(0.5 / (ntheta - 1), 1 - 0.5 / (ntheta - 1),
|
|
ntheta) * pi
|
|
phi = linspace(0.5 / (nphi - 1), 1 - 0.5 / (nphi - 1), nphi) * 2. * pi
|
|
data = ones((theta.shape[0], phi.shape[0]))
|
|
# define knots and extract data values at the knots
|
|
knotst = theta[::5]
|
|
knotsp = phi[::5]
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_theta = linspace(-0.1, 1.0, num=ntheta) * pi
|
|
invalid_lats, lons = meshgrid(invalid_theta, phi)
|
|
LSQSphereBivariateSpline(invalid_lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp)
|
|
assert "theta should be between [0, pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_theta = linspace(0.1, 1.1, num=ntheta) * pi
|
|
invalid_lats, lons = meshgrid(invalid_theta, phi)
|
|
LSQSphereBivariateSpline(invalid_lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp)
|
|
assert "theta should be between [0, pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_phi = linspace(-0.1, 1.0, num=ntheta) * 2.0 * pi
|
|
lats, invalid_lons = meshgrid(theta, invalid_phi)
|
|
LSQSphereBivariateSpline(lats.ravel(), invalid_lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp)
|
|
assert "phi should be between [0, 2pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_phi = linspace(0.0, 1.1, num=ntheta) * 2.0 * pi
|
|
lats, invalid_lons = meshgrid(theta, invalid_phi)
|
|
LSQSphereBivariateSpline(lats.ravel(), invalid_lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp)
|
|
assert "phi should be between [0, 2pi]" in str(exc_info.value)
|
|
|
|
lats, lons = meshgrid(theta, phi)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_knotst = np.copy(knotst)
|
|
invalid_knotst[0] = -0.1
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), invalid_knotst, knotsp)
|
|
assert "tt should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_knotst = np.copy(knotst)
|
|
invalid_knotst[0] = pi
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), invalid_knotst, knotsp)
|
|
assert "tt should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_knotsp = np.copy(knotsp)
|
|
invalid_knotsp[0] = -0.1
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, invalid_knotsp)
|
|
assert "tp should be between (0, 2pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_knotsp = np.copy(knotsp)
|
|
invalid_knotsp[0] = 2 * pi
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, invalid_knotsp)
|
|
assert "tp should be between (0, 2pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_w = array([-1.0, 1.0, 1.5, 0.5, 1.0, 1.5, 0.5, 1.0, 1.0])
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(),
|
|
knotst, knotsp, w=invalid_w)
|
|
assert "w should be positive" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(),
|
|
knotst, knotsp, eps=0.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
LSQSphereBivariateSpline(lats.ravel(), lons.ravel(), data.T.ravel(),
|
|
knotst, knotsp, eps=1.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
def test_array_like_input(self):
|
|
ntheta, nphi = 70, 90
|
|
theta = linspace(0.5 / (ntheta - 1), 1 - 0.5 / (ntheta - 1),
|
|
ntheta) * pi
|
|
phi = linspace(0.5 / (nphi - 1), 1 - 0.5 / (nphi - 1),
|
|
nphi) * 2. * pi
|
|
lats, lons = meshgrid(theta, phi)
|
|
data = ones((theta.shape[0], phi.shape[0]))
|
|
# define knots and extract data values at the knots
|
|
knotst = theta[::5]
|
|
knotsp = phi[::5]
|
|
w = ones((lats.ravel().shape[0]))
|
|
|
|
# np.array input
|
|
spl1 = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
|
|
data.T.ravel(), knotst, knotsp, w=w)
|
|
# list input
|
|
spl2 = LSQSphereBivariateSpline(lats.ravel().tolist(),
|
|
lons.ravel().tolist(),
|
|
data.T.ravel().tolist(),
|
|
knotst.tolist(),
|
|
knotsp.tolist(), w=w.tolist())
|
|
assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0))
|
|
|
|
|
|
class TestSmoothSphereBivariateSpline:
|
|
def setup_method(self):
|
|
theta = array([.25*pi, .25*pi, .25*pi, .5*pi, .5*pi, .5*pi, .75*pi,
|
|
.75*pi, .75*pi])
|
|
phi = array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, pi,
|
|
1.5 * pi])
|
|
r = array([3, 3, 3, 3, 3, 3, 3, 3, 3])
|
|
self.lut = SmoothSphereBivariateSpline(theta, phi, r, s=1E10)
|
|
|
|
def test_linear_constant(self):
|
|
assert_almost_equal(self.lut.get_residual(), 0.)
|
|
assert_array_almost_equal(self.lut([1, 1.5, 2],[1, 1.5]),
|
|
[[3, 3], [3, 3], [3, 3]])
|
|
|
|
def test_empty_input(self):
|
|
assert_array_almost_equal(self.lut([], []), np.zeros((0,0)))
|
|
assert_array_almost_equal(self.lut([], [], grid=False), np.zeros((0,)))
|
|
|
|
def test_invalid_input(self):
|
|
theta = array([.25 * pi, .25 * pi, .25 * pi, .5 * pi, .5 * pi, .5 * pi,
|
|
.75 * pi, .75 * pi, .75 * pi])
|
|
phi = array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, pi,
|
|
1.5 * pi])
|
|
r = array([3, 3, 3, 3, 3, 3, 3, 3, 3])
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_theta = array([-0.1 * pi, .25 * pi, .25 * pi, .5 * pi,
|
|
.5 * pi, .5 * pi, .75 * pi, .75 * pi,
|
|
.75 * pi])
|
|
SmoothSphereBivariateSpline(invalid_theta, phi, r, s=1E10)
|
|
assert "theta should be between [0, pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_theta = array([.25 * pi, .25 * pi, .25 * pi, .5 * pi,
|
|
.5 * pi, .5 * pi, .75 * pi, .75 * pi,
|
|
1.1 * pi])
|
|
SmoothSphereBivariateSpline(invalid_theta, phi, r, s=1E10)
|
|
assert "theta should be between [0, pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_phi = array([-.1 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi,
|
|
.5 * pi, pi, 1.5 * pi])
|
|
SmoothSphereBivariateSpline(theta, invalid_phi, r, s=1E10)
|
|
assert "phi should be between [0, 2pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_phi = array([1.0 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi,
|
|
.5 * pi, pi, 2.1 * pi])
|
|
SmoothSphereBivariateSpline(theta, invalid_phi, r, s=1E10)
|
|
assert "phi should be between [0, 2pi]" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
invalid_w = array([-1.0, 1.0, 1.5, 0.5, 1.0, 1.5, 0.5, 1.0, 1.0])
|
|
SmoothSphereBivariateSpline(theta, phi, r, w=invalid_w, s=1E10)
|
|
assert "w should be positive" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
SmoothSphereBivariateSpline(theta, phi, r, s=-1.0)
|
|
assert "s should be positive" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
SmoothSphereBivariateSpline(theta, phi, r, eps=-1.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
SmoothSphereBivariateSpline(theta, phi, r, eps=1.0)
|
|
assert "eps should be between (0, 1)" in str(exc_info.value)
|
|
|
|
def test_array_like_input(self):
|
|
theta = np.array([.25 * pi, .25 * pi, .25 * pi, .5 * pi, .5 * pi,
|
|
.5 * pi, .75 * pi, .75 * pi, .75 * pi])
|
|
phi = np.array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi,
|
|
pi, 1.5 * pi])
|
|
r = np.array([3, 3, 3, 3, 3, 3, 3, 3, 3])
|
|
w = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0])
|
|
|
|
# np.array input
|
|
spl1 = SmoothSphereBivariateSpline(theta, phi, r, w=w, s=1E10)
|
|
|
|
# list input
|
|
spl2 = SmoothSphereBivariateSpline(theta.tolist(), phi.tolist(),
|
|
r.tolist(), w=w.tolist(), s=1E10)
|
|
assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0))
|
|
|
|
|
|
class TestRectBivariateSpline:
|
|
def test_defaults(self):
|
|
x = array([1,2,3,4,5])
|
|
y = array([1,2,3,4,5])
|
|
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
|
|
lut = RectBivariateSpline(x,y,z)
|
|
assert_array_almost_equal(lut(x,y),z)
|
|
|
|
def test_evaluate(self):
|
|
x = array([1,2,3,4,5])
|
|
y = array([1,2,3,4,5])
|
|
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
|
|
lut = RectBivariateSpline(x,y,z)
|
|
|
|
xi = [1, 2.3, 5.3, 0.5, 3.3, 1.2, 3]
|
|
yi = [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]
|
|
zi = lut.ev(xi, yi)
|
|
zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)])
|
|
|
|
assert_almost_equal(zi, zi2)
|
|
|
|
def test_derivatives_grid(self):
|
|
x = array([1,2,3,4,5])
|
|
y = array([1,2,3,4,5])
|
|
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
|
|
dx = array([[0,0,-20,0,0],[0,0,13,0,0],[0,0,4,0,0],
|
|
[0,0,-11,0,0],[0,0,4,0,0]])/6.
|
|
dy = array([[4,-1,0,1,-4],[4,-1,0,1,-4],[0,1.5,0,-1.5,0],
|
|
[2,.25,0,-.25,-2],[4,-1,0,1,-4]])
|
|
dxdy = array([[40,-25,0,25,-40],[-26,16.25,0,-16.25,26],
|
|
[-8,5,0,-5,8],[22,-13.75,0,13.75,-22],[-8,5,0,-5,8]])/6.
|
|
lut = RectBivariateSpline(x,y,z)
|
|
assert_array_almost_equal(lut(x,y,dx=1),dx)
|
|
assert_array_almost_equal(lut(x,y,dy=1),dy)
|
|
assert_array_almost_equal(lut(x,y,dx=1,dy=1),dxdy)
|
|
|
|
def test_derivatives(self):
|
|
x = array([1,2,3,4,5])
|
|
y = array([1,2,3,4,5])
|
|
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
|
|
dx = array([0,0,2./3,0,0])
|
|
dy = array([4,-1,0,-.25,-4])
|
|
dxdy = array([160,65,0,55,32])/24.
|
|
lut = RectBivariateSpline(x,y,z)
|
|
assert_array_almost_equal(lut(x,y,dx=1,grid=False),dx)
|
|
assert_array_almost_equal(lut(x,y,dy=1,grid=False),dy)
|
|
assert_array_almost_equal(lut(x,y,dx=1,dy=1,grid=False),dxdy)
|
|
|
|
def test_partial_derivative_method_grid(self):
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1],
|
|
[1, 2, 1, 2, 1],
|
|
[1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1],
|
|
[1, 2, 1, 2, 1]])
|
|
dx = array([[0, 0, -20, 0, 0],
|
|
[0, 0, 13, 0, 0],
|
|
[0, 0, 4, 0, 0],
|
|
[0, 0, -11, 0, 0],
|
|
[0, 0, 4, 0, 0]]) / 6.
|
|
dy = array([[4, -1, 0, 1, -4],
|
|
[4, -1, 0, 1, -4],
|
|
[0, 1.5, 0, -1.5, 0],
|
|
[2, .25, 0, -.25, -2],
|
|
[4, -1, 0, 1, -4]])
|
|
dxdy = array([[40, -25, 0, 25, -40],
|
|
[-26, 16.25, 0, -16.25, 26],
|
|
[-8, 5, 0, -5, 8],
|
|
[22, -13.75, 0, 13.75, -22],
|
|
[-8, 5, 0, -5, 8]]) / 6.
|
|
lut = RectBivariateSpline(x, y, z)
|
|
assert_array_almost_equal(lut.partial_derivative(1, 0)(x, y), dx)
|
|
assert_array_almost_equal(lut.partial_derivative(0, 1)(x, y), dy)
|
|
assert_array_almost_equal(lut.partial_derivative(1, 1)(x, y), dxdy)
|
|
|
|
def test_partial_derivative_method(self):
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1],
|
|
[1, 2, 1, 2, 1],
|
|
[1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1],
|
|
[1, 2, 1, 2, 1]])
|
|
dx = array([0, 0, 2./3, 0, 0])
|
|
dy = array([4, -1, 0, -.25, -4])
|
|
dxdy = array([160, 65, 0, 55, 32]) / 24.
|
|
lut = RectBivariateSpline(x, y, z)
|
|
assert_array_almost_equal(lut.partial_derivative(1, 0)(x, y,
|
|
grid=False),
|
|
dx)
|
|
assert_array_almost_equal(lut.partial_derivative(0, 1)(x, y,
|
|
grid=False),
|
|
dy)
|
|
assert_array_almost_equal(lut.partial_derivative(1, 1)(x, y,
|
|
grid=False),
|
|
dxdy)
|
|
|
|
def test_partial_derivative_order_too_large(self):
|
|
x = array([0, 1, 2, 3, 4], dtype=float)
|
|
y = x.copy()
|
|
z = ones((x.size, y.size))
|
|
lut = RectBivariateSpline(x, y, z)
|
|
with assert_raises(ValueError):
|
|
lut.partial_derivative(4, 1)
|
|
|
|
def test_broadcast(self):
|
|
x = array([1,2,3,4,5])
|
|
y = array([1,2,3,4,5])
|
|
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
|
|
lut = RectBivariateSpline(x,y,z)
|
|
assert_allclose(lut(x, y), lut(x[:,None], y[None,:], grid=False))
|
|
|
|
def test_invalid_input(self):
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = array([6, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
|
|
RectBivariateSpline(x, y, z)
|
|
assert "x must be strictly increasing" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([2, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
|
|
RectBivariateSpline(x, y, z)
|
|
assert "y must be strictly increasing" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1]])
|
|
RectBivariateSpline(x, y, z)
|
|
assert "x dimension of z must have same number of elements as x"\
|
|
in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2], [1, 2, 1, 2], [1, 2, 3, 2],
|
|
[1, 2, 2, 2], [1, 2, 1, 2]])
|
|
RectBivariateSpline(x, y, z)
|
|
assert "y dimension of z must have same number of elements as y"\
|
|
in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
|
|
bbox = (-100, 100, -100)
|
|
RectBivariateSpline(x, y, z, bbox=bbox)
|
|
assert "bbox shape should be (4,)" in str(info.value)
|
|
|
|
with assert_raises(ValueError) as info:
|
|
RectBivariateSpline(x, y, z, s=-1.0)
|
|
assert "s should be s >= 0.0" in str(info.value)
|
|
|
|
def test_array_like_input(self):
|
|
x = array([1, 2, 3, 4, 5])
|
|
y = array([1, 2, 3, 4, 5])
|
|
z = array([[1, 2, 1, 2, 1], [1, 2, 1, 2, 1], [1, 2, 3, 2, 1],
|
|
[1, 2, 2, 2, 1], [1, 2, 1, 2, 1]])
|
|
bbox = array([1, 5, 1, 5])
|
|
|
|
spl1 = RectBivariateSpline(x, y, z, bbox=bbox)
|
|
spl2 = RectBivariateSpline(x.tolist(), y.tolist(), z.tolist(),
|
|
bbox=bbox.tolist())
|
|
assert_array_almost_equal(spl1(1.0, 1.0), spl2(1.0, 1.0))
|
|
|
|
def test_not_increasing_input(self):
|
|
# gh-8565
|
|
NSamp = 20
|
|
Theta = np.random.uniform(0, np.pi, NSamp)
|
|
Phi = np.random.uniform(0, 2 * np.pi, NSamp)
|
|
Data = np.ones(NSamp)
|
|
|
|
Interpolator = SmoothSphereBivariateSpline(Theta, Phi, Data, s=3.5)
|
|
|
|
NLon = 6
|
|
NLat = 3
|
|
GridPosLats = np.arange(NLat) / NLat * np.pi
|
|
GridPosLons = np.arange(NLon) / NLon * 2 * np.pi
|
|
|
|
# No error
|
|
Interpolator(GridPosLats, GridPosLons)
|
|
|
|
nonGridPosLats = GridPosLats.copy()
|
|
nonGridPosLats[2] = 0.001
|
|
with assert_raises(ValueError) as exc_info:
|
|
Interpolator(nonGridPosLats, GridPosLons)
|
|
assert "x must be strictly increasing" in str(exc_info.value)
|
|
|
|
nonGridPosLons = GridPosLons.copy()
|
|
nonGridPosLons[2] = 0.001
|
|
with assert_raises(ValueError) as exc_info:
|
|
Interpolator(GridPosLats, nonGridPosLons)
|
|
assert "y must be strictly increasing" in str(exc_info.value)
|
|
|
|
|
|
class TestRectSphereBivariateSpline:
|
|
def test_defaults(self):
|
|
y = linspace(0.01, 2*pi-0.01, 7)
|
|
x = linspace(0.01, pi-0.01, 7)
|
|
z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
|
|
[1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
|
|
[1,2,1,2,1,2,1]])
|
|
lut = RectSphereBivariateSpline(x,y,z)
|
|
assert_array_almost_equal(lut(x,y),z)
|
|
|
|
def test_evaluate(self):
|
|
y = linspace(0.01, 2*pi-0.01, 7)
|
|
x = linspace(0.01, pi-0.01, 7)
|
|
z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
|
|
[1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
|
|
[1,2,1,2,1,2,1]])
|
|
lut = RectSphereBivariateSpline(x,y,z)
|
|
yi = [0.2, 1, 2.3, 2.35, 3.0, 3.99, 5.25]
|
|
xi = [1.5, 0.4, 1.1, 0.45, 0.2345, 1., 0.0001]
|
|
zi = lut.ev(xi, yi)
|
|
zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)])
|
|
assert_almost_equal(zi, zi2)
|
|
|
|
def test_invalid_input(self):
|
|
data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T,
|
|
np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(-1, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(0, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "u should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 181, 9) * np.pi / 180.
|
|
lons = np.linspace(0, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "u should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(-181, 10, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "v[0] should be between [-pi, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(-10, 360, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "v[-1] should be v[0] + 2pi or less" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(10, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data, s=-1)
|
|
assert "s should be positive" in str(exc_info.value)
|
|
|
|
def test_derivatives_grid(self):
|
|
y = linspace(0.01, 2*pi-0.01, 7)
|
|
x = linspace(0.01, pi-0.01, 7)
|
|
z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
|
|
[1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
|
|
[1,2,1,2,1,2,1]])
|
|
|
|
lut = RectSphereBivariateSpline(x,y,z)
|
|
|
|
y = linspace(0.02, 2*pi-0.02, 7)
|
|
x = linspace(0.02, pi-0.02, 7)
|
|
|
|
assert_allclose(lut(x, y, dtheta=1), _numdiff_2d(lut, x, y, dx=1),
|
|
rtol=1e-4, atol=1e-4)
|
|
assert_allclose(lut(x, y, dphi=1), _numdiff_2d(lut, x, y, dy=1),
|
|
rtol=1e-4, atol=1e-4)
|
|
assert_allclose(lut(x, y, dtheta=1, dphi=1), _numdiff_2d(lut, x, y, dx=1, dy=1, eps=1e-6),
|
|
rtol=1e-3, atol=1e-3)
|
|
|
|
assert_array_equal(lut(x, y, dtheta=1),
|
|
lut.partial_derivative(1, 0)(x, y))
|
|
assert_array_equal(lut(x, y, dphi=1),
|
|
lut.partial_derivative(0, 1)(x, y))
|
|
assert_array_equal(lut(x, y, dtheta=1, dphi=1),
|
|
lut.partial_derivative(1, 1)(x, y))
|
|
|
|
assert_array_equal(lut(x, y, dtheta=1, grid=False),
|
|
lut.partial_derivative(1, 0)(x, y, grid=False))
|
|
assert_array_equal(lut(x, y, dphi=1, grid=False),
|
|
lut.partial_derivative(0, 1)(x, y, grid=False))
|
|
assert_array_equal(lut(x, y, dtheta=1, dphi=1, grid=False),
|
|
lut.partial_derivative(1, 1)(x, y, grid=False))
|
|
|
|
def test_derivatives(self):
|
|
y = linspace(0.01, 2*pi-0.01, 7)
|
|
x = linspace(0.01, pi-0.01, 7)
|
|
z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
|
|
[1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
|
|
[1,2,1,2,1,2,1]])
|
|
|
|
lut = RectSphereBivariateSpline(x,y,z)
|
|
|
|
y = linspace(0.02, 2*pi-0.02, 7)
|
|
x = linspace(0.02, pi-0.02, 7)
|
|
|
|
assert_equal(lut(x, y, dtheta=1, grid=False).shape, x.shape)
|
|
assert_allclose(lut(x, y, dtheta=1, grid=False),
|
|
_numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dx=1),
|
|
rtol=1e-4, atol=1e-4)
|
|
assert_allclose(lut(x, y, dphi=1, grid=False),
|
|
_numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dy=1),
|
|
rtol=1e-4, atol=1e-4)
|
|
assert_allclose(lut(x, y, dtheta=1, dphi=1, grid=False),
|
|
_numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dx=1, dy=1, eps=1e-6),
|
|
rtol=1e-3, atol=1e-3)
|
|
|
|
def test_invalid_input_2(self):
|
|
data = np.dot(np.atleast_2d(90. - np.linspace(-80., 80., 18)).T,
|
|
np.atleast_2d(180. - np.abs(np.linspace(0., 350., 9)))).T
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(0, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(0, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "u should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 180, 9) * np.pi / 180.
|
|
lons = np.linspace(0, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "u should be between (0, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(-181, 10, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "v[0] should be between [-pi, pi)" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(-10, 360, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data)
|
|
assert "v[-1] should be v[0] + 2pi or less" in str(exc_info.value)
|
|
|
|
with assert_raises(ValueError) as exc_info:
|
|
lats = np.linspace(10, 170, 9) * np.pi / 180.
|
|
lons = np.linspace(10, 350, 18) * np.pi / 180.
|
|
RectSphereBivariateSpline(lats, lons, data, s=-1)
|
|
assert "s should be positive" in str(exc_info.value)
|
|
|
|
def test_array_like_input(self):
|
|
y = linspace(0.01, 2 * pi - 0.01, 7)
|
|
x = linspace(0.01, pi - 0.01, 7)
|
|
z = array([[1, 2, 1, 2, 1, 2, 1], [1, 2, 1, 2, 1, 2, 1],
|
|
[1, 2, 3, 2, 1, 2, 1],
|
|
[1, 2, 2, 2, 1, 2, 1], [1, 2, 1, 2, 1, 2, 1],
|
|
[1, 2, 2, 2, 1, 2, 1],
|
|
[1, 2, 1, 2, 1, 2, 1]])
|
|
# np.array input
|
|
spl1 = RectSphereBivariateSpline(x, y, z)
|
|
# list input
|
|
spl2 = RectSphereBivariateSpline(x.tolist(), y.tolist(), z.tolist())
|
|
assert_array_almost_equal(spl1(x, y), spl2(x, y))
|
|
|
|
def test_negative_evaluation(self):
|
|
lats = np.array([25, 30, 35, 40, 45])
|
|
lons = np.array([-90, -85, -80, -75, 70])
|
|
mesh = np.meshgrid(lats, lons)
|
|
data = mesh[0] + mesh[1] # lon + lat value
|
|
lat_r = np.radians(lats)
|
|
lon_r = np.radians(lons)
|
|
interpolator = RectSphereBivariateSpline(lat_r, lon_r, data)
|
|
query_lat = np.radians(np.array([35, 37.5]))
|
|
query_lon = np.radians(np.array([-80, -77.5]))
|
|
data_interp = interpolator(query_lat, query_lon)
|
|
ans = np.array([[-45.0, -42.480862],
|
|
[-49.0625, -46.54315]])
|
|
assert_array_almost_equal(data_interp, ans)
|
|
|
|
def test_pole_continuity_gh_14591(self):
|
|
# regression test for https://github.com/scipy/scipy/issues/14591
|
|
# with pole_continuty=(True, True), the internal work array size
|
|
# was too small, leading to a FITPACK data validation error.
|
|
|
|
# The reproducer in gh-14591 was using a NetCDF4 file with
|
|
# 361x507 arrays, so here we trivialize array sizes to a minimum
|
|
# which still demonstrates the issue.
|
|
u = np.arange(1, 10) * np.pi / 10
|
|
v = np.arange(1, 10) * np.pi / 10
|
|
r = np.zeros((9, 9))
|
|
for p in [(True, True), (True, False), (False, False)]:
|
|
RectSphereBivariateSpline(u, v, r, s=0, pole_continuity=p)
|
|
|
|
|
|
def _numdiff_2d(func, x, y, dx=0, dy=0, eps=1e-8):
|
|
if dx == 0 and dy == 0:
|
|
return func(x, y)
|
|
elif dx == 1 and dy == 0:
|
|
return (func(x + eps, y) - func(x - eps, y)) / (2*eps)
|
|
elif dx == 0 and dy == 1:
|
|
return (func(x, y + eps) - func(x, y - eps)) / (2*eps)
|
|
elif dx == 1 and dy == 1:
|
|
return (func(x + eps, y + eps) - func(x - eps, y + eps)
|
|
- func(x + eps, y - eps) + func(x - eps, y - eps)) / (2*eps)**2
|
|
else:
|
|
raise ValueError("invalid derivative order")
|
|
|
|
|
|
class Test_DerivedBivariateSpline(object):
|
|
"""Test the creation, usage, and attribute access of the (private)
|
|
_DerivedBivariateSpline class.
|
|
"""
|
|
def setup_method(self):
|
|
x = np.concatenate(list(zip(range(10), range(10))))
|
|
y = np.concatenate(list(zip(range(10), range(1, 11))))
|
|
z = np.concatenate((np.linspace(3, 1, 10), np.linspace(1, 3, 10)))
|
|
with suppress_warnings() as sup:
|
|
sup.record(UserWarning, "\nThe coefficients of the spline")
|
|
self.lut_lsq = LSQBivariateSpline(x, y, z,
|
|
linspace(0.5, 19.5, 4),
|
|
linspace(1.5, 20.5, 4),
|
|
eps=1e-2)
|
|
self.lut_smooth = SmoothBivariateSpline(x, y, z)
|
|
xx = linspace(0, 1, 20)
|
|
yy = xx + 1.0
|
|
zz = array([np.roll(z, i) for i in range(z.size)])
|
|
self.lut_rect = RectBivariateSpline(xx, yy, zz)
|
|
self.orders = list(itertools.product(range(3), range(3)))
|
|
|
|
def test_creation_from_LSQ(self):
|
|
for nux, nuy in self.orders:
|
|
lut_der = self.lut_lsq.partial_derivative(nux, nuy)
|
|
a = lut_der(3.5, 3.5, grid=False)
|
|
b = self.lut_lsq(3.5, 3.5, dx=nux, dy=nuy, grid=False)
|
|
assert_equal(a, b)
|
|
|
|
def test_creation_from_Smooth(self):
|
|
for nux, nuy in self.orders:
|
|
lut_der = self.lut_smooth.partial_derivative(nux, nuy)
|
|
a = lut_der(5.5, 5.5, grid=False)
|
|
b = self.lut_smooth(5.5, 5.5, dx=nux, dy=nuy, grid=False)
|
|
assert_equal(a, b)
|
|
|
|
def test_creation_from_Rect(self):
|
|
for nux, nuy in self.orders:
|
|
lut_der = self.lut_rect.partial_derivative(nux, nuy)
|
|
a = lut_der(0.5, 1.5, grid=False)
|
|
b = self.lut_rect(0.5, 1.5, dx=nux, dy=nuy, grid=False)
|
|
assert_equal(a, b)
|
|
|
|
def test_invalid_attribute_fp(self):
|
|
der = self.lut_rect.partial_derivative(1, 1)
|
|
with assert_raises(AttributeError):
|
|
der.fp
|
|
|
|
def test_invalid_attribute_get_residual(self):
|
|
der = self.lut_smooth.partial_derivative(1, 1)
|
|
with assert_raises(AttributeError):
|
|
der.get_residual()
|