512 lines
21 KiB
Python
512 lines
21 KiB
Python
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# Created by Pearu Peterson, June 2003
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from __future__ import division, print_function, absolute_import
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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)
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from scipy._lib._numpy_compat import 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 import bisplrep, bisplev
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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(object):
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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_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_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_increasing_x(self):
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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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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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class TestLSQBivariateSpline(object):
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# NOTE: The systems in this test class are rank-deficient
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def test_linear_constant(self):
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x = [1,1,1,2,2,2,3,3,3]
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y = [1,2,3,1,2,3,1,2,3]
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z = [3,3,3,3,3,3,3,3,3]
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s = 0.1
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tx = [1+s,3-s]
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ty = [1+s,3-s]
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with suppress_warnings() as sup:
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r = sup.record(UserWarning, "\nThe coefficients of the spline")
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lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
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assert_equal(len(r), 1)
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assert_almost_equal(lut(2,2), 3.)
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def test_bilinearity(self):
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x = [1,1,1,2,2,2,3,3,3]
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y = [1,2,3,1,2,3,1,2,3]
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z = [0,7,8,3,4,7,1,3,4]
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s = 0.1
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tx = [1+s,3-s]
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ty = [1+s,3-s]
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with suppress_warnings() as sup:
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# This seems to fail (ier=1, see ticket 1642).
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sup.filter(UserWarning, "\nThe coefficients of the spline")
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lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
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tx, ty = lut.get_knots()
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for xa, xb in zip(tx[:-1], tx[1:]):
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for ya, yb in zip(ty[:-1], ty[1:]):
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for t in [0.1, 0.5, 0.9]:
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for s in [0.3, 0.4, 0.7]:
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xp = xa*(1-t) + xb*t
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yp = ya*(1-s) + yb*s
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zp = (+ lut(xa, ya)*(1-t)*(1-s)
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+ lut(xb, ya)*t*(1-s)
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+ lut(xa, yb)*(1-t)*s
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+ lut(xb, yb)*t*s)
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assert_almost_equal(lut(xp,yp), zp)
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def test_integral(self):
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x = [1,1,1,2,2,2,8,8,8]
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y = [1,2,3,1,2,3,1,2,3]
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z = array([0,7,8,3,4,7,1,3,4])
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s = 0.1
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tx = [1+s,3-s]
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ty = [1+s,3-s]
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with suppress_warnings() as sup:
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r = sup.record(UserWarning, "\nThe coefficients of the spline")
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lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
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assert_equal(len(r), 1)
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tx, ty = lut.get_knots()
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tz = lut(tx, ty)
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trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
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* (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
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assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]),
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trpz)
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def test_empty_input(self):
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# Test whether empty inputs returns an empty output. Ticket 1014
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x = [1,1,1,2,2,2,3,3,3]
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y = [1,2,3,1,2,3,1,2,3]
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z = [3,3,3,3,3,3,3,3,3]
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s = 0.1
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tx = [1+s,3-s]
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ty = [1+s,3-s]
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with suppress_warnings() as sup:
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r = sup.record(UserWarning, "\nThe coefficients of the spline")
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lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
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assert_equal(len(r), 1)
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assert_array_equal(lut([], []), np.zeros((0,0)))
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assert_array_equal(lut([], [], grid=False), np.zeros((0,)))
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class TestSmoothBivariateSpline(object):
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def test_linear_constant(self):
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x = [1,1,1,2,2,2,3,3,3]
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y = [1,2,3,1,2,3,1,2,3]
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z = [3,3,3,3,3,3,3,3,3]
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lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
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assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
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assert_array_almost_equal(lut.get_coeffs(),[3,3,3,3])
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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],[1,1.5]),[[3,3],[3,3],[3,3]])
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def test_linear_1d(self):
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x = [1,1,1,2,2,2,3,3,3]
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y = [1,2,3,1,2,3,1,2,3]
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z = [0,0,0,2,2,2,4,4,4]
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lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
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assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
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assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
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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],[1,1.5]),[[0,0],[1,1],[2,2]])
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def test_integral(self):
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x = [1,1,1,2,2,2,4,4,4]
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y = [1,2,3,1,2,3,1,2,3]
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z = array([0,7,8,3,4,7,1,3,4])
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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)
|
||
|
|
|
||
|
|
|
||
|
|
class TestLSQSphereBivariateSpline(object):
|
||
|
|
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,)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestSmoothSphereBivariateSpline(object):
|
||
|
|
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,)))
|
||
|
|
|
||
|
|
|
||
|
|
class TestRectBivariateSpline(object):
|
||
|
|
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_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))
|
||
|
|
|
||
|
|
|
||
|
|
class TestRectSphereBivariateSpline(object):
|
||
|
|
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_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)
|
||
|
|
|
||
|
|
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 _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")
|