from __future__ import division, print_function, absolute_import import itertools import warnings from numpy.testing import (assert_, assert_equal, assert_almost_equal, assert_array_almost_equal, assert_raises, assert_array_equal, dec, TestCase, run_module_suite, assert_allclose) from numpy import mgrid, pi, sin, ogrid, poly1d, linspace import numpy as np from scipy.lib.six import xrange from scipy.lib._version import NumpyVersion from scipy.interpolate import (interp1d, interp2d, lagrange, PPoly, BPoly, ppform, splrep, splev, splantider, splint, sproot, Akima1DInterpolator, RegularGridInterpolator, LinearNDInterpolator, NearestNDInterpolator, RectBivariateSpline, interpn) from scipy.interpolate import _ppoly from scipy.lib._gcutils import assert_deallocated class TestInterp2D(TestCase): def test_interp2d(self): y, x = mgrid[0:2:20j, 0:pi:21j] z = sin(x+0.5*y) I = interp2d(x, y, z) assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2) v,u = ogrid[0:2:24j, 0:pi:25j] assert_almost_equal(I(u.ravel(), v.ravel()), sin(u+0.5*v), decimal=2) def test_interp2d_meshgrid_input(self): # Ticket #703 x = linspace(0, 2, 16) y = linspace(0, pi, 21) z = sin(x[None,:] + y[:,None]/2.) I = interp2d(x, y, z) assert_almost_equal(I(1.0, 2.0), sin(2.0), decimal=2) def test_interp2d_meshgrid_input_unsorted(self): np.random.seed(1234) x = linspace(0, 2, 16) y = linspace(0, pi, 21) z = sin(x[None,:] + y[:,None]/2.) ip1 = interp2d(x.copy(), y.copy(), z, kind='cubic') np.random.shuffle(x) z = sin(x[None,:] + y[:,None]/2.) ip2 = interp2d(x.copy(), y.copy(), z, kind='cubic') np.random.shuffle(x) np.random.shuffle(y) z = sin(x[None,:] + y[:,None]/2.) ip3 = interp2d(x, y, z, kind='cubic') x = linspace(0, 2, 31) y = linspace(0, pi, 30) assert_equal(ip1(x, y), ip2(x, y)) assert_equal(ip1(x, y), ip3(x, y)) def test_interp2d_linear(self): # Ticket #898 a = np.zeros([5, 5]) a[2, 2] = 1.0 x = y = np.arange(5) b = interp2d(x, y, a, 'linear') assert_almost_equal(b(2.0, 1.5), np.array([0.5]), decimal=2) assert_almost_equal(b(2.0, 2.5), np.array([0.5]), decimal=2) def test_interp2d_bounds(self): x = np.linspace(0, 1, 5) y = np.linspace(0, 2, 7) z = x[:,None]**2 + y[None,:] ix = np.linspace(-1, 3, 31) iy = np.linspace(-1, 3, 33) b = interp2d(x, y, z, bounds_error=True) assert_raises(ValueError, b, ix, iy) b = interp2d(x, y, z, fill_value=np.nan) iz = b(ix, iy) mx = (ix < 0) | (ix > 1) my = (iy < 0) | (iy > 2) assert_(np.isnan(iz[my,:]).all()) assert_(np.isnan(iz[:,mx]).all()) assert_(np.isfinite(iz[~my,:][:,~mx]).all()) class TestInterp1D(object): def setUp(self): self.x10 = np.arange(10.) self.y10 = np.arange(10.) self.x25 = self.x10.reshape((2,5)) self.x2 = np.arange(2.) self.y2 = np.arange(2.) self.x1 = np.array([0.]) self.y1 = np.array([0.]) self.y210 = np.arange(20.).reshape((2, 10)) self.y102 = np.arange(20.).reshape((10, 2)) self.fill_value = -100.0 def test_validation(self): # Make sure that appropriate exceptions are raised when invalid values # are given to the constructor. # These should all work. interp1d(self.x10, self.y10, kind='linear') interp1d(self.x10, self.y10, kind='cubic') interp1d(self.x10, self.y10, kind='slinear') interp1d(self.x10, self.y10, kind='quadratic') interp1d(self.x10, self.y10, kind='zero') interp1d(self.x10, self.y10, kind='nearest') interp1d(self.x10, self.y10, kind=0) interp1d(self.x10, self.y10, kind=1) interp1d(self.x10, self.y10, kind=2) interp1d(self.x10, self.y10, kind=3) # x array must be 1D. assert_raises(ValueError, interp1d, self.x25, self.y10) # y array cannot be a scalar. assert_raises(ValueError, interp1d, self.x10, np.array(0)) # Check for x and y arrays having the same length. assert_raises(ValueError, interp1d, self.x10, self.y2) assert_raises(ValueError, interp1d, self.x2, self.y10) assert_raises(ValueError, interp1d, self.x10, self.y102) interp1d(self.x10, self.y210) interp1d(self.x10, self.y102, axis=0) # Check for x and y having at least 1 element. assert_raises(ValueError, interp1d, self.x1, self.y10) assert_raises(ValueError, interp1d, self.x10, self.y1) assert_raises(ValueError, interp1d, self.x1, self.y1) def test_init(self): # Check that the attributes are initialized appropriately by the # constructor. assert_(interp1d(self.x10, self.y10).copy) assert_(not interp1d(self.x10, self.y10, copy=False).copy) assert_(interp1d(self.x10, self.y10).bounds_error) assert_(not interp1d(self.x10, self.y10, bounds_error=False).bounds_error) assert_(np.isnan(interp1d(self.x10, self.y10).fill_value)) assert_equal(interp1d(self.x10, self.y10, fill_value=3.0).fill_value, 3.0) assert_equal(interp1d(self.x10, self.y10).axis, 0) assert_equal(interp1d(self.x10, self.y210).axis, 1) assert_equal( interp1d(self.x10, self.y102, axis=0).axis, 0) assert_array_equal(interp1d(self.x10, self.y10).x, self.x10) assert_array_equal(interp1d(self.x10, self.y10).y, self.y10) assert_array_equal(interp1d(self.x10, self.y210).y, self.y210) def test_assume_sorted(self): # Check for unsorted arrays interp10 = interp1d(self.x10, self.y10) interp10_unsorted = interp1d(self.x10[::-1], self.y10[::-1]) assert_array_almost_equal(interp10_unsorted(self.x10), self.y10) assert_array_almost_equal(interp10_unsorted(1.2), np.array([1.2])) assert_array_almost_equal(interp10_unsorted([2.4, 5.6, 6.0]), interp10([2.4, 5.6, 6.0])) # Check assume_sorted keyword (defaults to False) interp10_assume_kw = interp1d(self.x10[::-1], self.y10[::-1], assume_sorted=False) assert_array_almost_equal(interp10_assume_kw(self.x10), self.y10) interp10_assume_kw2 = interp1d(self.x10[::-1], self.y10[::-1], assume_sorted=True) # Should raise an error for unsorted input if assume_sorted=True assert_raises(ValueError, interp10_assume_kw2, self.x10) # Check that if y is a 2-D array, things are still consistent interp10_y_2d = interp1d(self.x10, self.y210) interp10_y_2d_unsorted = interp1d(self.x10[::-1], self.y210[:, ::-1]) assert_array_almost_equal(interp10_y_2d(self.x10), interp10_y_2d_unsorted(self.x10)) def test_linear(self): # Check the actual implementation of linear interpolation. interp10 = interp1d(self.x10, self.y10) assert_array_almost_equal(interp10(self.x10), self.y10) assert_array_almost_equal(interp10(1.2), np.array([1.2])) assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), np.array([2.4, 5.6, 6.0])) def test_cubic(self): # Check the actual implementation of spline interpolation. interp10 = interp1d(self.x10, self.y10, kind='cubic') assert_array_almost_equal(interp10(self.x10), self.y10) assert_array_almost_equal(interp10(1.2), np.array([1.2])) assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), np.array([2.4, 5.6, 6.0]),) def test_nearest(self): # Check the actual implementation of nearest-neighbour interpolation. interp10 = interp1d(self.x10, self.y10, kind='nearest') assert_array_almost_equal(interp10(self.x10), self.y10) assert_array_almost_equal(interp10(1.2), np.array(1.)) assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), np.array([2., 6., 6.]),) @dec.knownfailureif(True, "zero-order splines fail for the last point") def test_zero(self): # Check the actual implementation of zero-order spline interpolation. interp10 = interp1d(self.x10, self.y10, kind='zero') assert_array_almost_equal(interp10(self.x10), self.y10) assert_array_almost_equal(interp10(1.2), np.array(1.)) assert_array_almost_equal(interp10([2.4, 5.6, 6.0]), np.array([2., 6., 6.])) def _bounds_check(self, kind='linear'): # Test that our handling of out-of-bounds input is correct. extrap10 = interp1d(self.x10, self.y10, fill_value=self.fill_value, bounds_error=False, kind=kind) assert_array_equal(extrap10(11.2), np.array(self.fill_value)) assert_array_equal(extrap10(-3.4), np.array(self.fill_value)) assert_array_equal(extrap10([[[11.2], [-3.4], [12.6], [19.3]]]), np.array(self.fill_value),) assert_array_equal(extrap10._check_bounds( np.array([-1.0, 0.0, 5.0, 9.0, 11.0])), np.array([True, False, False, False, True])) raises_bounds_error = interp1d(self.x10, self.y10, bounds_error=True, kind=kind) assert_raises(ValueError, raises_bounds_error, -1.0) assert_raises(ValueError, raises_bounds_error, 11.0) raises_bounds_error([0.0, 5.0, 9.0]) def _bounds_check_int_nan_fill(self, kind='linear'): x = np.arange(10).astype(np.int_) y = np.arange(10).astype(np.int_) c = interp1d(x, y, kind=kind, fill_value=np.nan, bounds_error=False) yi = c(x - 1) assert_(np.isnan(yi[0])) assert_array_almost_equal(yi, np.r_[np.nan, y[:-1]]) def test_bounds(self): for kind in ('linear', 'cubic', 'nearest', 'slinear', 'zero', 'quadratic'): self._bounds_check(kind) self._bounds_check_int_nan_fill(kind) def _nd_check_interp(self, kind='linear'): # Check the behavior when the inputs and outputs are multidimensional. # Multidimensional input. interp10 = interp1d(self.x10, self.y10, kind=kind) assert_array_almost_equal(interp10(np.array([[3., 5.], [2., 7.]])), np.array([[3., 5.], [2., 7.]])) # Scalar input -> 0-dim scalar array output assert_(isinstance(interp10(1.2), np.ndarray)) assert_equal(interp10(1.2).shape, ()) # Multidimensional outputs. interp210 = interp1d(self.x10, self.y210, kind=kind) assert_array_almost_equal(interp210(1.), np.array([1., 11.])) assert_array_almost_equal(interp210(np.array([1., 2.])), np.array([[1., 2.], [11., 12.]])) interp102 = interp1d(self.x10, self.y102, axis=0, kind=kind) assert_array_almost_equal(interp102(1.), np.array([2.0, 3.0])) assert_array_almost_equal(interp102(np.array([1., 3.])), np.array([[2., 3.], [6., 7.]])) # Both at the same time! x_new = np.array([[3., 5.], [2., 7.]]) assert_array_almost_equal(interp210(x_new), np.array([[[3., 5.], [2., 7.]], [[13., 15.], [12., 17.]]])) assert_array_almost_equal(interp102(x_new), np.array([[[6., 7.], [10., 11.]], [[4., 5.], [14., 15.]]])) def _nd_check_shape(self, kind='linear'): # Check large ndim output shape a = [4, 5, 6, 7] y = np.arange(np.prod(a)).reshape(*a) for n, s in enumerate(a): x = np.arange(s) z = interp1d(x, y, axis=n, kind=kind) assert_array_almost_equal(z(x), y, err_msg=kind) x2 = np.arange(2*3*1).reshape((2,3,1)) / 12. b = list(a) b[n:n+1] = [2,3,1] assert_array_almost_equal(z(x2).shape, b, err_msg=kind) def test_nd(self): for kind in ('linear', 'cubic', 'slinear', 'quadratic', 'nearest'): self._nd_check_interp(kind) self._nd_check_shape(kind) def _check_complex(self, dtype=np.complex_, kind='linear'): x = np.array([1, 2.5, 3, 3.1, 4, 6.4, 7.9, 8.0, 9.5, 10]) y = x * x ** (1 + 2j) y = y.astype(dtype) # simple test c = interp1d(x, y, kind=kind) assert_array_almost_equal(y[:-1], c(x)[:-1]) # check against interpolating real+imag separately xi = np.linspace(1, 10, 31) cr = interp1d(x, y.real, kind=kind) ci = interp1d(x, y.imag, kind=kind) assert_array_almost_equal(c(xi).real, cr(xi)) assert_array_almost_equal(c(xi).imag, ci(xi)) def test_complex(self): for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic', 'zero'): self._check_complex(np.complex64, kind) self._check_complex(np.complex128, kind) @dec.knownfailureif(True, "zero-order splines fail for the last point") def test_nd_zero_spline(self): # zero-order splines don't get the last point right, # see test_zero above #yield self._nd_check_interp, 'zero' #yield self._nd_check_interp, 'zero' pass def test_circular_refs(self): # Test interp1d can be automatically garbage collected x = np.linspace(0, 1) y = np.linspace(0, 1) # Confirm interp can be released from memory after use with assert_deallocated(interp1d, x, y) as interp: new_y = interp([0.1, 0.2]) del interp class TestLagrange(TestCase): def test_lagrange(self): p = poly1d([5,2,1,4,3]) xs = np.arange(len(p.coeffs)) ys = p(xs) pl = lagrange(xs,ys) assert_array_almost_equal(p.coeffs,pl.coeffs) class TestAkima1DInterpolator(TestCase): def test_eval(self): x = np.arange(0., 11.) y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) ak = Akima1DInterpolator(x, y) xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, 8.6, 9.9, 10.]) yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, 4.1363636363636366866103344, 5.9803623910336236590978842, 5.5067291516462386624652936, 5.2031367459745245795943447, 4.1796554159017080820603951, 3.4110386597938129327189927, 3.]) assert_allclose(ak(xi), yi) def test_eval_2d(self): x = np.arange(0., 11.) y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) y = np.column_stack((y, 2. * y)) ak = Akima1DInterpolator(x, y) xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, 8.6, 9.9, 10.]) yi = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, 4.1363636363636366866103344, 5.9803623910336236590978842, 5.5067291516462386624652936, 5.2031367459745245795943447, 4.1796554159017080820603951, 3.4110386597938129327189927, 3.]) yi = np.column_stack((yi, 2. * yi)) assert_allclose(ak(xi), yi) def test_eval_3d(self): x = np.arange(0., 11.) y_ = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) y = np.empty((11, 2, 2)) y[:, 0, 0] = y_ y[:, 1, 0] = 2. * y_ y[:, 0, 1] = 3. * y_ y[:, 1, 1] = 4. * y_ ak = Akima1DInterpolator(x, y) xi = np.array([0., 0.5, 1., 1.5, 2.5, 3.5, 4.5, 5.1, 6.5, 7.2, 8.6, 9.9, 10.]) yi = np.empty((13, 2, 2)) yi_ = np.array([0., 1.375, 2., 1.5, 1.953125, 2.484375, 4.1363636363636366866103344, 5.9803623910336236590978842, 5.5067291516462386624652936, 5.2031367459745245795943447, 4.1796554159017080820603951, 3.4110386597938129327189927, 3.]) yi[:, 0, 0] = yi_ yi[:, 1, 0] = 2. * yi_ yi[:, 0, 1] = 3. * yi_ yi[:, 1, 1] = 4. * yi_ assert_allclose(ak(xi), yi) def test_extend(self): x = np.arange(0., 11.) y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.]) ak = Akima1DInterpolator(x, y) try: ak.extend() except NotImplementedError as e: if str(e) != ("Extending a 1D Akima interpolator is not " "yet implemented"): raise except: raise class TestPPolyCommon(TestCase): # test basic functionality for PPoly and BPoly def test_sort_check(self): c = np.array([[1, 4], [2, 5], [3, 6]]) x = np.array([0, 1, 0.5]) assert_raises(ValueError, PPoly, c, x) assert_raises(ValueError, BPoly, c, x) def test_extend(self): # Test adding new points to the piecewise polynomial np.random.seed(1234) order = 3 x = np.unique(np.r_[0, 10 * np.random.rand(30), 10]) c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1 for cls in (PPoly, BPoly): pp = cls(c[:,:9], x[:10]) pp.extend(c[:,9:], x[10:]) pp2 = cls(c[:,10:], x[10:]) pp2.extend(c[:,:10], x[:10], right=False) pp3 = cls(c, x) assert_array_equal(pp.c, pp3.c) assert_array_equal(pp.x, pp3.x) assert_array_equal(pp2.c, pp3.c) assert_array_equal(pp2.x, pp3.x) def test_extend_diff_orders(self): # Test extending polynomial with different order one np.random.seed(1234) x = np.linspace(0, 1, 6) c = np.random.rand(2, 5) x2 = np.linspace(1, 2, 6) c2 = np.random.rand(4, 5) for cls in (PPoly, BPoly): pp1 = cls(c, x) pp2 = cls(c2, x2) pp_comb = cls(c, x) pp_comb.extend(c2, x2[1:]) # NB. doesn't match to pp1 at the endpoint, because pp1 is not # continuous with pp2 as we took random coefs. xi1 = np.linspace(0, 1, 300, endpoint=False) xi2 = np.linspace(1, 2, 300) assert_allclose(pp1(xi1), pp_comb(xi1)) assert_allclose(pp2(xi2), pp_comb(xi2)) def test_shape(self): np.random.seed(1234) c = np.random.rand(8, 12, 5, 6, 7) x = np.sort(np.random.rand(13)) xp = np.random.rand(3, 4) for cls in (PPoly, BPoly): p = cls(c, x) assert_equal(p(xp).shape, (3, 4, 5, 6, 7)) # 'scalars' for cls in (PPoly, BPoly): p = cls(c[..., 0, 0, 0], x) assert_equal(np.shape(p(0.5)), ()) assert_equal(np.shape(p(np.array(0.5))), ()) if NumpyVersion(np.__version__) >= '1.7.0': # can't use dtype=object (with any numpy; what fails is # constructing the object array here for old numpy) assert_raises(ValueError, p, np.array([[0.1, 0.2], [0.4]])) def test_complex_coef(self): np.random.seed(12345) x = np.sort(np.random.random(13)) c = np.random.random((8, 12)) * (1. + 0.3j) c_re, c_im = c.real, c.imag xp = np.random.random(5) for cls in (PPoly, BPoly): p, p_re, p_im = cls(c, x), cls(c_re, x), cls(c_im, x) for nu in [0, 1, 2]: assert_allclose(p(xp, nu).real, p_re(xp, nu)) assert_allclose(p(xp, nu).imag, p_im(xp, nu)) class TestPolySubclassing(TestCase): class P(PPoly): pass class B(BPoly): pass def _make_polynomials(self): np.random.seed(1234) x = np.sort(np.random.random(3)) c = np.random.random((4, 2)) return self.P(c, x), self.B(c, x) def test_derivative(self): pp, bp = self._make_polynomials() for p in (pp, bp): pd = p.derivative() assert_equal(p.__class__, pd.__class__) ppa = pp.antiderivative() assert_equal(pp.__class__, ppa.__class__) def test_from_spline(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0) pp = self.P.from_spline(spl) assert_equal(pp.__class__, self.P) def test_conversions(self): pp, bp = self._make_polynomials() pp1 = self.P.from_bernstein_basis(bp) assert_equal(pp1.__class__, self.P) bp1 = self.B.from_power_basis(pp) assert_equal(bp1.__class__, self.B) def test_from_derivatives(self): x = [0, 1, 2] y = [[1], [2], [3]] bp = self.B.from_derivatives(x, y) assert_equal(bp.__class__, self.B) class TestPPoly(TestCase): def test_simple(self): c = np.array([[1, 4], [2, 5], [3, 6]]) x = np.array([0, 0.5, 1]) p = PPoly(c, x) assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3) assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6) def test_multi_shape(self): c = np.random.rand(6, 2, 1, 2, 3) x = np.array([0, 0.5, 1]) p = PPoly(c, x) assert_equal(p.x.shape, x.shape) assert_equal(p.c.shape, c.shape) assert_equal(p(0.3).shape, c.shape[2:]) assert_equal(p(np.random.rand(5,6)).shape, (5,6) + c.shape[2:]) dp = p.derivative() assert_equal(dp.c.shape, (5, 2, 1, 2, 3)) ip = p.antiderivative() assert_equal(ip.c.shape, (7, 2, 1, 2, 3)) def test_construct_fast(self): np.random.seed(1234) c = np.array([[1, 4], [2, 5], [3, 6]], dtype=float) x = np.array([0, 0.5, 1]) p = PPoly.construct_fast(c, x) assert_allclose(p(0.3), 1*0.3**2 + 2*0.3 + 3) assert_allclose(p(0.7), 4*(0.7-0.5)**2 + 5*(0.7-0.5) + 6) def test_vs_alternative_implementations(self): np.random.seed(1234) c = np.random.rand(3, 12, 22) x = np.sort(np.r_[0, np.random.rand(11), 1]) p = PPoly(c, x) xp = np.r_[0.3, 0.5, 0.33, 0.6] expected = _ppoly_eval_1(c, x, xp) assert_allclose(p(xp), expected) expected = _ppoly_eval_2(c[:,:,0], x, xp) assert_allclose(p(xp)[:,0], expected) def test_from_spline(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0) pp = PPoly.from_spline(spl) xi = np.linspace(0, 1, 200) assert_allclose(pp(xi), splev(xi, spl)) def test_derivative_simple(self): np.random.seed(1234) c = np.array([[4, 3, 2, 1]]).T dc = np.array([[3*4, 2*3, 2]]).T ddc = np.array([[2*3*4, 1*2*3]]).T x = np.array([0, 1]) pp = PPoly(c, x) dpp = PPoly(dc, x) ddpp = PPoly(ddc, x) assert_allclose(pp.derivative().c, dpp.c) assert_allclose(pp.derivative(2).c, ddpp.c) def test_derivative_eval(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0) pp = PPoly.from_spline(spl) xi = np.linspace(0, 1, 200) for dx in range(0, 3): assert_allclose(pp(xi, dx), splev(xi, spl, dx)) def test_derivative(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0, k=5) pp = PPoly.from_spline(spl) xi = np.linspace(0, 1, 200) for dx in range(0, 10): assert_allclose(pp(xi, dx), pp.derivative(dx)(xi), err_msg="dx=%d" % (dx,)) def test_antiderivative_simple(self): np.random.seed(1234) # [ p1(x) = 3*x**2 + 2*x + 1, # p2(x) = 1.6875] c = np.array([[3, 2, 1], [0, 0, 1.6875]]).T # [ pp1(x) = x**3 + x**2 + x, # pp2(x) = 1.6875*(x - 0.25) + pp1(0.25)] ic = np.array([[1, 1, 1, 0], [0, 0, 1.6875, 0.328125]]).T # [ ppp1(x) = (1/4)*x**4 + (1/3)*x**3 + (1/2)*x**2, # ppp2(x) = (1.6875/2)*(x - 0.25)**2 + pp1(0.25)*x + ppp1(0.25)] iic = np.array([[1/4, 1/3, 1/2, 0, 0], [0, 0, 1.6875/2, 0.328125, 0.037434895833333336]]).T x = np.array([0, 0.25, 1]) pp = PPoly(c, x) ipp = pp.antiderivative() iipp = pp.antiderivative(2) iipp2 = ipp.antiderivative() assert_allclose(ipp.x, x) assert_allclose(ipp.c.T, ic.T) assert_allclose(iipp.c.T, iic.T) assert_allclose(iipp2.c.T, iic.T) def test_antiderivative_vs_derivative(self): np.random.seed(1234) x = np.linspace(0, 1, 30)**2 y = np.random.rand(len(x)) spl = splrep(x, y, s=0, k=5) pp = PPoly.from_spline(spl) for dx in range(0, 10): ipp = pp.antiderivative(dx) # check that derivative is inverse op pp2 = ipp.derivative(dx) assert_allclose(pp.c, pp2.c) # check continuity for k in range(dx): pp2 = ipp.derivative(k) r = 1e-13 endpoint = r*pp2.x[:-1] + (1 - r)*pp2.x[1:] assert_allclose(pp2(pp2.x[1:]), pp2(endpoint), rtol=1e-7, err_msg="dx=%d k=%d" % (dx, k)) def test_antiderivative_vs_spline(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0, k=5) pp = PPoly.from_spline(spl) for dx in range(0, 10): pp2 = pp.antiderivative(dx) spl2 = splantider(spl, dx) xi = np.linspace(0, 1, 200) assert_allclose(pp2(xi), splev(xi, spl2), rtol=1e-7) def test_integrate(self): np.random.seed(1234) x = np.sort(np.r_[0, np.random.rand(11), 1]) y = np.random.rand(len(x)) spl = splrep(x, y, s=0, k=5) pp = PPoly.from_spline(spl) a, b = 0.3, 0.9 ig = pp.integrate(a, b) ipp = pp.antiderivative() assert_allclose(ig, ipp(b) - ipp(a)) assert_allclose(ig, splint(a, b, spl)) a, b = -0.3, 0.9 ig = pp.integrate(a, b, extrapolate=True) assert_allclose(ig, ipp(b) - ipp(a)) assert_(np.isnan(pp.integrate(a, b, extrapolate=False)).all()) def test_roots(self): x = np.linspace(0, 1, 31)**2 y = np.sin(30*x) spl = splrep(x, y, s=0, k=3) pp = PPoly.from_spline(spl) r = pp.roots() r = r[(r >= 0 - 1e-15) & (r <= 1 + 1e-15)] assert_allclose(r, sproot(spl), atol=1e-15) def test_roots_idzero(self): # Roots for piecewise polynomials with identically zero # sections. c = np.array([[-1, 0.25], [0, 0], [-1, 0.25]]).T x = np.array([0, 0.4, 0.6, 1.0]) pp = PPoly(c, x) assert_array_equal(pp.roots(), [0.25, 0.4, np.nan, 0.6 + 0.25]) def test_roots_repeated(self): # Check roots repeated in multiple sections are reported only # once. # [(x + 1)**2 - 1, -x**2] ; x == 0 is a repeated root c = np.array([[1, 0, -1], [-1, 0, 0]]).T x = np.array([-1, 0, 1]) pp = PPoly(c, x) assert_array_equal(pp.roots(), [-2, 0]) assert_array_equal(pp.roots(extrapolate=False), [0]) def test_roots_discont(self): # Check that a discontinuity across zero is reported as root c = np.array([[1], [-1]]).T x = np.array([0, 0.5, 1]) pp = PPoly(c, x) assert_array_equal(pp.roots(), [0.5]) assert_array_equal(pp.roots(discontinuity=False), []) def test_roots_random(self): # Check high-order polynomials with random coefficients np.random.seed(1234) num = 0 for extrapolate in (True, False): for order in range(0, 20): x = np.unique(np.r_[0, 10 * np.random.rand(30), 10]) c = 2*np.random.rand(order+1, len(x)-1, 2, 3) - 1 pp = PPoly(c, x) r = pp.roots(discontinuity=False, extrapolate=extrapolate) for i in range(2): for j in range(3): rr = r[i,j] if rr.size > 0: # Check that the reported roots indeed are roots num += rr.size val = pp(rr, extrapolate=extrapolate)[:,i,j] cmpval = pp(rr, nu=1, extrapolate=extrapolate)[:,i,j] assert_allclose(val/cmpval, 0, atol=1e-7, err_msg="(%r) r = %s" % (extrapolate, repr(rr),)) # Check that we checked a number of roots assert_(num > 100, repr(num)) def test_roots_croots(self): # Test the complex root finding algorithm np.random.seed(1234) for k in range(1, 15): c = np.random.rand(k, 1, 130) if k == 3: # add a case with zero discriminant c[:,0,0] = 1, 2, 1 w = np.empty(c.shape, dtype=complex) _ppoly._croots_poly1(c, w) if k == 1: assert_(np.isnan(w).all()) continue res = 0 cres = 0 for i in range(k): res += c[i,None] * w**(k-1-i) cres += abs(c[i,None] * w**(k-1-i)) res /= cres res = res.ravel() res = res[~np.isnan(res)] assert_allclose(res, 0, atol=1e-10) def test_extrapolate_attr(self): # [ 1 - x**2 ] c = np.array([[-1, 0, 1]]).T x = np.array([0, 1]) for extrapolate in [True, False, None]: pp = PPoly(c, x, extrapolate=extrapolate) pp_d = pp.derivative() pp_i = pp.antiderivative() if extrapolate is False: assert_(np.isnan(pp([-0.1, 1.1])).all()) assert_(np.isnan(pp_i([-0.1, 1.1])).all()) assert_(np.isnan(pp_d([-0.1, 1.1])).all()) assert_equal(pp.roots(), [1]) else: assert_allclose(pp([-0.1, 1.1]), [1-0.1**2, 1-1.1**2]) assert_(not np.isnan(pp_i([-0.1, 1.1])).any()) assert_(not np.isnan(pp_d([-0.1, 1.1])).any()) assert_allclose(pp.roots(), [1, -1]) class TestBPoly(TestCase): def test_simple(self): x = [0, 1] c = [[3]] bp = BPoly(c, x) assert_allclose(bp(0.1), 3.) def test_simple2(self): x = [0, 1] c = [[3], [1]] bp = BPoly(c, x) # 3*(1-x) + 1*x assert_allclose(bp(0.1), 3*0.9 + 1.*0.1) def test_simple3(self): x = [0, 1] c = [[3], [1], [4]] bp = BPoly(c, x) # 3 * (1-x)**2 + 2 * x (1-x) + 4 * x**2 assert_allclose(bp(0.2), 3 * 0.8*0.8 + 1 * 2*0.2*0.8 + 4 * 0.2*0.2) def test_simple4(self): x = [0, 1] c = [[1], [1], [1], [2]] bp = BPoly(c, x) assert_allclose(bp(0.3), 0.7**3 + 3 * 0.7**2 * 0.3 + 3 * 0.7 * 0.3**2 + 2 * 0.3**3) def test_simple5(self): x = [0, 1] c = [[1], [1], [8], [2], [1]] bp = BPoly(c, x) assert_allclose(bp(0.3), 0.7**4 + 4 * 0.7**3 * 0.3 + 8 * 6 * 0.7**2 * 0.3**2 + 2 * 4 * 0.7 * 0.3**3 + 0.3**4) def test_multi_shape(self): c = np.random.rand(6, 2, 1, 2, 3) x = np.array([0, 0.5, 1]) p = BPoly(c, x) assert_equal(p.x.shape, x.shape) assert_equal(p.c.shape, c.shape) assert_equal(p(0.3).shape, c.shape[2:]) assert_equal(p(np.random.rand(5,6)).shape, (5,6)+c.shape[2:]) dp = p.derivative() assert_equal(dp.c.shape, (5, 2, 1, 2, 3)) def test_interval_length(self): x = [0, 2] c = [[3], [1], [4]] bp = BPoly(c, x) xval = 0.1 s = xval / 2 # s = (x - xa) / (xb - xa) assert_allclose(bp(xval), 3 * (1-s)*(1-s) + 1 * 2*s*(1-s) + 4 * s*s) def test_two_intervals(self): x = [0, 1, 3] c = [[3, 0], [0, 0], [0, 2]] bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2] assert_allclose(bp(0.4), 3 * 0.6*0.6) assert_allclose(bp(1.7), 2 * (0.7/2)**2) def test_extrapolate_attr(self): x = [0, 2] c = [[3], [1], [4]] bp = BPoly(c, x) for extrapolate in (True, False, None): bp = BPoly(c, x, extrapolate=extrapolate) bp_d = bp.derivative() if extrapolate is False: assert_(np.isnan(bp([-0.1, 2.1])).all()) assert_(np.isnan(bp_d([-0.1, 2.1])).all()) else: assert_(not np.isnan(bp([-0.1, 2.1])).any()) assert_(not np.isnan(bp_d([-0.1, 2.1])).any()) class TestBPolyCalculus(TestCase): def test_derivative(self): x = [0, 1, 3] c = [[3, 0], [0, 0], [0, 2]] bp = BPoly(c, x) # [3*(1-x)**2, 2*((x-1)/2)**2] bp_der = bp.derivative() assert_allclose(bp_der(0.4), -6*(0.6)) assert_allclose(bp_der(1.7), 0.7) # derivatives in-place assert_allclose([bp(0.4, nu=1), bp(0.4, nu=2), bp(0.4, nu=3)], [-6*(1-0.4), 6., 0.]) assert_allclose([bp(1.7, nu=1), bp(1.7, nu=2), bp(1.7, nu=3)], [0.7, 1., 0]) def test_derivative_ppoly(self): # make sure it's consistent w/ power basis np.random.seed(1234) m, k = 5, 8 # number of intervals, order x = np.sort(np.random.random(m)) c = np.random.random((k, m-1)) bp = BPoly(c, x) pp = PPoly.from_bernstein_basis(bp) for d in range(k): bp = bp.derivative() pp = pp.derivative() xp = np.linspace(x[0], x[-1], 21) assert_allclose(bp(xp), pp(xp)) def test_deriv_inplace(self): np.random.seed(1234) m, k = 5, 8 # number of intervals, order x = np.sort(np.random.random(m)) c = np.random.random((k, m-1)) bp = BPoly(c, x) xp = np.linspace(x[0], x[-1], 21) for i in range(k): assert_allclose(bp(xp, i), bp.derivative(i)(xp)) class TestPolyConversions(TestCase): def test_bp_from_pp(self): x = [0, 1, 3] c = [[3, 2], [1, 8], [4, 3]] pp = PPoly(c, x) bp = BPoly.from_power_basis(pp) pp1 = PPoly.from_bernstein_basis(bp) xp = [0.1, 1.4] assert_allclose(pp(xp), bp(xp)) assert_allclose(pp(xp), pp1(xp)) def test_bp_from_pp_random(self): np.random.seed(1234) m, k = 5, 8 # number of intervals, order x = np.sort(np.random.random(m)) c = np.random.random((k, m-1)) pp = PPoly(c, x) bp = BPoly.from_power_basis(pp) pp1 = PPoly.from_bernstein_basis(bp) xp = np.linspace(x[0], x[-1], 21) assert_allclose(pp(xp), bp(xp)) assert_allclose(pp(xp), pp1(xp)) def test_pp_from_bp(self): x = [0, 1, 3] c = [[3, 3], [1, 1], [4, 2]] bp = BPoly(c, x) pp = PPoly.from_bernstein_basis(bp) bp1 = BPoly.from_power_basis(pp) xp = [0.1, 1.4] assert_allclose(bp(xp), pp(xp)) assert_allclose(bp(xp), bp1(xp)) class TestBPolyFromDerivatives(TestCase): def test_make_poly_1(self): c1 = BPoly._construct_from_derivatives(0, 1, [2], [3]) assert_allclose(c1, [2., 3.]) def test_make_poly_2(self): c1 = BPoly._construct_from_derivatives(0, 1, [1, 0], [1]) assert_allclose(c1, [1., 1., 1.]) # f'(0) = 3 c2 = BPoly._construct_from_derivatives(0, 1, [2, 3], [1]) assert_allclose(c2, [2., 7./2, 1.]) # f'(1) = 3 c3 = BPoly._construct_from_derivatives(0, 1, [2], [1, 3]) assert_allclose(c3, [2., -0.5, 1.]) def test_make_poly_3(self): # f'(0)=2, f''(0)=3 c1 = BPoly._construct_from_derivatives(0, 1, [1, 2, 3], [4]) assert_allclose(c1, [1., 5./3, 17./6, 4.]) # f'(1)=2, f''(1)=3 c2 = BPoly._construct_from_derivatives(0, 1, [1], [4, 2, 3]) assert_allclose(c2, [1., 19./6, 10./3, 4.]) # f'(0)=2, f'(1)=3 c3 = BPoly._construct_from_derivatives(0, 1, [1, 2], [4, 3]) assert_allclose(c3, [1., 5./3, 3., 4.]) def test_make_poly_12(self): np.random.seed(12345) ya = np.r_[0, np.random.random(5)] yb = np.r_[0, np.random.random(5)] c = BPoly._construct_from_derivatives(0, 1, ya, yb) pp = BPoly(c[:, None], [0, 1]) for j in range(6): assert_allclose([pp(0.), pp(1.)], [ya[j], yb[j]]) pp = pp.derivative() def test_raise_degree(self): np.random.seed(12345) x = [0, 1] k, d = 8, 5 c = np.random.random((k, 1, 2, 3, 4)) bp = BPoly(c, x) c1 = BPoly._raise_degree(c, d) bp1 = BPoly(c1, x) xp = np.linspace(0, 1, 11) assert_allclose(bp(xp), bp1(xp)) def test_xi_yi(self): assert_raises(ValueError, BPoly.from_derivatives, [0, 1], [0]) def test_coords_order(self): xi = [0, 0, 1] yi = [[0], [0], [0]] assert_raises(ValueError, BPoly.from_derivatives, xi, yi) def test_zeros(self): xi = [0, 1, 2, 3] yi = [[0, 0], [0], [0, 0], [0, 0]] # NB: will have to raise the degree pp = BPoly.from_derivatives(xi, yi) assert_(pp.c.shape == (4, 3)) ppd = pp.derivative() for xp in [0., 0.1, 1., 1.1, 1.9, 2., 2.5]: assert_allclose([pp(xp), ppd(xp)], [0., 0.]) def _make_random_mk(self, m, k): # k derivatives at each breakpoint np.random.seed(1234) xi = np.asarray([1. * j**2 for j in range(m+1)]) yi = [np.random.random(k) for j in range(m+1)] return xi, yi def test_random_12(self): m, k = 5, 12 xi, yi = self._make_random_mk(m, k) pp = BPoly.from_derivatives(xi, yi) for order in range(k//2): assert_allclose(pp(xi), [yy[order] for yy in yi]) pp = pp.derivative() def test_order_zero(self): m, k = 5, 12 xi, yi = self._make_random_mk(m, k) assert_raises(ValueError, BPoly.from_derivatives, **dict(xi=xi, yi=yi, orders=0)) def test_orders_too_high(self): m, k = 5, 12 xi, yi = self._make_random_mk(m, k) pp = BPoly.from_derivatives(xi, yi, orders=2*k-1) # this is still ok assert_raises(ValueError, BPoly.from_derivatives, # but this is not **dict(xi=xi, yi=yi, orders=2*k)) def test_orders_global(self): m, k = 5, 12 xi, yi = self._make_random_mk(m, k) # ok, this is confusing. Local polynomials will be of the order 5 # which means that up to the 2nd derivatives will be used at each point order = 5 pp = BPoly.from_derivatives(xi, yi, orders=order) for j in range(order//2+1): assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)) pp = pp.derivative() assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))) # now repeat with `order` being even: on each interval, it uses # order//2 'derivatives' @ the right-hand endpoint and # order//2+1 @ 'derivatives' the left-hand endpoint order = 6 pp = BPoly.from_derivatives(xi, yi, orders=order) for j in range(order//2): assert_allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12)) pp = pp.derivative() assert_(not np.allclose(pp(xi[1:-1] - 1e-12), pp(xi[1:-1] + 1e-12))) def test_orders_local(self): m, k = 7, 12 xi, yi = self._make_random_mk(m, k) orders = [o + 1 for o in range(m)] for i, x in enumerate(xi[1:-1]): pp = BPoly.from_derivatives(xi, yi, orders=orders) for j in range(orders[i] // 2 + 1): assert_allclose(pp(x - 1e-12), pp(x + 1e-12)) pp = pp.derivative() assert_(not np.allclose(pp(x - 1e-12), pp(x + 1e-12))) def test_yi_trailing_dims(self): m, k = 7, 5 xi = np.sort(np.random.random(m+1)) yi = np.random.random((m+1, k, 6, 7, 8)) pp = BPoly.from_derivatives(xi, yi) assert_equal(pp.c.shape, (2*k, m, 6, 7, 8)) class TestPpform(TestCase): def test_shape(self): with warnings.catch_warnings(): warnings.simplefilter("ignore", DeprecationWarning) np.random.seed(1234) c = np.random.rand(3, 12, 5, 6, 7) x = np.sort(np.random.rand(13)) p = ppform(c, x) xp = np.random.rand(3, 4) assert_equal(p(xp).shape, (3, 4, 5, 6, 7)) def _ppoly_eval_1(c, x, xps): """Evaluate piecewise polynomial manually""" out = np.zeros((len(xps), c.shape[2])) for i, xp in enumerate(xps): if xp < 0 or xp > 1: out[i,:] = np.nan continue j = np.searchsorted(x, xp) - 1 d = xp - x[j] assert_(x[j] <= xp < x[j+1]) r = sum(c[k,j] * d**(c.shape[0]-k-1) for k in range(c.shape[0])) out[i,:] = r return out def _ppoly_eval_2(coeffs, breaks, xnew, fill=np.nan): """Evaluate piecewise polynomial manually (another way)""" a = breaks[0] b = breaks[-1] K = coeffs.shape[0] saveshape = np.shape(xnew) xnew = np.ravel(xnew) res = np.empty_like(xnew) mask = (xnew >= a) & (xnew <= b) res[~mask] = fill xx = xnew.compress(mask) indxs = np.searchsorted(breaks, xx)-1 indxs = indxs.clip(0, len(breaks)) pp = coeffs diff = xx - breaks.take(indxs) V = np.vander(diff, N=K) values = np.array([np.dot(V[k, :], pp[:, indxs[k]]) for k in xrange(len(xx))]) res[mask] = values res.shape = saveshape return res class TestRegularGridInterpolator(TestCase): def _get_sample_4d(self): # create a 4d grid of 3 points in each dimension points = [(0., .5, 1.)] * 4 values = np.asarray([0., .5, 1.]) values0 = values[:, np.newaxis, np.newaxis, np.newaxis] values1 = values[np.newaxis, :, np.newaxis, np.newaxis] values2 = values[np.newaxis, np.newaxis, :, np.newaxis] values3 = values[np.newaxis, np.newaxis, np.newaxis, :] values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) return points, values def _get_sample_4d_2(self): # create another 4d grid of 3 points in each dimension points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2 values = np.asarray([0., .5, 1.]) values0 = values[:, np.newaxis, np.newaxis, np.newaxis] values1 = values[np.newaxis, :, np.newaxis, np.newaxis] values2 = values[np.newaxis, np.newaxis, :, np.newaxis] values3 = values[np.newaxis, np.newaxis, np.newaxis, :] values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) return points, values def test_list_input(self): points, values = self._get_sample_4d() sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) for method in ['linear', 'nearest']: interp = RegularGridInterpolator(points, values.tolist(), method=method) v1 = interp(sample.tolist()) interp = RegularGridInterpolator(points, values, method=method) v2 = interp(sample) assert_allclose(v1, v2) def test_complex(self): points, values = self._get_sample_4d() values = values - 2j*values sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) for method in ['linear', 'nearest']: interp = RegularGridInterpolator(points, values, method=method) rinterp = RegularGridInterpolator(points, values.real, method=method) iinterp = RegularGridInterpolator(points, values.imag, method=method) v1 = interp(sample) v2 = rinterp(sample) + 1j*iinterp(sample) assert_allclose(v1, v2) def test_linear_xi1d(self): points, values = self._get_sample_4d_2() interp = RegularGridInterpolator(points, values) sample = np.asarray([0.1, 0.1, 10., 9.]) wanted = 1001.1 assert_array_almost_equal(interp(sample), wanted) def test_linear_xi3d(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values) sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) wanted = np.asarray([1001.1, 846.2, 555.5]) assert_array_almost_equal(interp(sample), wanted) def test_nearest(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values, method="nearest") sample = np.asarray([0.1, 0.1, .9, .9]) wanted = 1100. assert_array_almost_equal(interp(sample), wanted) sample = np.asarray([0.1, 0.1, 0.1, 0.1]) wanted = 0. assert_array_almost_equal(interp(sample), wanted) sample = np.asarray([0., 0., 0., 0.]) wanted = 0. assert_array_almost_equal(interp(sample), wanted) sample = np.asarray([1., 1., 1., 1.]) wanted = 1111. assert_array_almost_equal(interp(sample), wanted) sample = np.asarray([0.1, 0.4, 0.6, 0.9]) wanted = 1055. assert_array_almost_equal(interp(sample), wanted) def test_linear_edges(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values) sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]]) wanted = np.asarray([0., 1111.]) assert_array_almost_equal(interp(sample), wanted) def test_valid_create(self): # create a 2d grid of 3 points in each dimension points = [(0., .5, 1.), (0., 1., .5)] values = np.asarray([0., .5, 1.]) values0 = values[:, np.newaxis] values1 = values[np.newaxis, :] values = (values0 + values1 * 10) assert_raises(ValueError, RegularGridInterpolator, points, values) points = [((0., .5, 1.), ), (0., .5, 1.)] assert_raises(ValueError, RegularGridInterpolator, points, values) points = [(0., .5, .75, 1.), (0., .5, 1.)] assert_raises(ValueError, RegularGridInterpolator, points, values) points = [(0., .5, 1.), (0., .5, 1.), (0., .5, 1.)] assert_raises(ValueError, RegularGridInterpolator, points, values) points = [(0., .5, 1.), (0., .5, 1.)] assert_raises(ValueError, RegularGridInterpolator, points, values, method="undefmethod") def test_valid_call(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values) sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.]]) assert_raises(ValueError, interp, sample, "undefmethod") sample = np.asarray([[0., 0., 0.], [1., 1., 1.]]) assert_raises(ValueError, interp, sample) sample = np.asarray([[0., 0., 0., 0.], [1., 1., 1., 1.1]]) assert_raises(ValueError, interp, sample) def test_out_of_bounds_extrap(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values, bounds_error=False, fill_value=None) sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], [21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]]) wanted = np.asarray([0., 1111., 11., 11.]) assert_array_almost_equal(interp(sample, method="nearest"), wanted) wanted = np.asarray([-111.1, 1222.1, -11068., -1186.9]) assert_array_almost_equal(interp(sample, method="linear"), wanted) def test_out_of_bounds_extrap2(self): points, values = self._get_sample_4d_2() interp = RegularGridInterpolator(points, values, bounds_error=False, fill_value=None) sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], [21, 2.1, -1.1, -11], [2.1, 2.1, -1.1, -1.1]]) wanted = np.asarray([0., 11., 11., 11.]) assert_array_almost_equal(interp(sample, method="nearest"), wanted) wanted = np.asarray([-12.1, 133.1, -1069., -97.9]) assert_array_almost_equal(interp(sample, method="linear"), wanted) def test_out_of_bounds_fill(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values, bounds_error=False, fill_value=np.nan) sample = np.asarray([[-.1, -.1, -.1, -.1], [1.1, 1.1, 1.1, 1.1], [2.1, 2.1, -1.1, -1.1]]) wanted = np.asarray([np.nan, np.nan, np.nan]) assert_array_almost_equal(interp(sample, method="nearest"), wanted) assert_array_almost_equal(interp(sample, method="linear"), wanted) sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) wanted = np.asarray([1001.1, 846.2, 555.5]) assert_array_almost_equal(interp(sample), wanted) def test_nearest_compare_qhull(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values, method="nearest") points_qhull = itertools.product(*points) points_qhull = [p for p in points_qhull] points_qhull = np.asarray(points_qhull) values_qhull = values.reshape(-1) interp_qhull = NearestNDInterpolator(points_qhull, values_qhull) sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) assert_array_almost_equal(interp(sample), interp_qhull(sample)) def test_linear_compare_qhull(self): points, values = self._get_sample_4d() interp = RegularGridInterpolator(points, values) points_qhull = itertools.product(*points) points_qhull = [p for p in points_qhull] points_qhull = np.asarray(points_qhull) values_qhull = values.reshape(-1) interp_qhull = LinearNDInterpolator(points_qhull, values_qhull) sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8], [0.5, 0.5, .5, .5]]) assert_array_almost_equal(interp(sample), interp_qhull(sample)) def test_duck_typed_values(self): x = np.linspace(0, 2, 5) y = np.linspace(0, 1, 7) values = MyValue((5, 7)) for method in ('nearest', 'linear'): interp = RegularGridInterpolator((x, y), values, method=method) v1 = interp([0.4, 0.7]) interp = RegularGridInterpolator((x, y), values._v, method=method) v2 = interp([0.4, 0.7]) assert_allclose(v1, v2) def test_invalid_fill_value(self): np.random.seed(1234) x = np.linspace(0, 2, 5) y = np.linspace(0, 1, 7) values = np.random.rand(5, 7) # integers can be cast to floats RegularGridInterpolator((x, y), values, fill_value=1) # complex values cannot assert_raises(ValueError, RegularGridInterpolator, (x, y), values, fill_value=1+2j) class MyValue(object): """ Minimal indexable object """ def __init__(self, shape): self.ndim = 2 self.shape = shape self._v = np.arange(np.prod(shape)).reshape(shape) def __getitem__(self, idx): return self._v[idx] def __array_interface__(self): return None def __array__(self): raise RuntimeError("No array representation") class TestInterpN(TestCase): def _sample_2d_data(self): x = np.arange(1, 6) x = np.array([.5, 2., 3., 4., 5.5]) y = np.arange(1, 6) y = np.array([.5, 2., 3., 4., 5.5]) z = np.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]]) return x, y, z def test_spline_2d(self): x, y, z = self._sample_2d_data() lut = RectBivariateSpline(x, y, z) xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T assert_array_almost_equal(interpn((x, y), z, xi, method="splinef2d"), lut.ev(xi[:, 0], xi[:, 1])) def test_list_input(self): x, y, z = self._sample_2d_data() xi = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T for method in ['nearest', 'linear', 'splinef2d']: v1 = interpn((x, y), z, xi, method=method) v2 = interpn((x.tolist(), y.tolist()), z.tolist(), xi.tolist(), method=method) assert_allclose(v1, v2, err_msg=method) def test_spline_2d_outofbounds(self): x = np.array([.5, 2., 3., 4., 5.5]) y = np.array([.5, 2., 3., 4., 5.5]) z = np.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 = np.array([[1, 2.3, 6.3, 0.5, 3.3, 1.2, 3], [1, 3.3, 1.2, -4.0, 5.0, 1.0, 3]]).T actual = interpn((x, y), z, xi, method="splinef2d", bounds_error=False, fill_value=999.99) expected = lut.ev(xi[:, 0], xi[:, 1]) expected[2:4] = 999.99 assert_array_almost_equal(actual, expected) # no extrapolation for splinef2d assert_raises(ValueError, interpn, (x, y), z, xi, method="splinef2d", bounds_error=False, fill_value=None) def _sample_4d_data(self): points = [(0., .5, 1.)] * 2 + [(0., 5., 10.)] * 2 values = np.asarray([0., .5, 1.]) values0 = values[:, np.newaxis, np.newaxis, np.newaxis] values1 = values[np.newaxis, :, np.newaxis, np.newaxis] values2 = values[np.newaxis, np.newaxis, :, np.newaxis] values3 = values[np.newaxis, np.newaxis, np.newaxis, :] values = (values0 + values1 * 10 + values2 * 100 + values3 * 1000) return points, values def test_linear_4d(self): # create a 4d grid of 3 points in each dimension points, values = self._sample_4d_data() interp_rg = RegularGridInterpolator(points, values) sample = np.asarray([[0.1, 0.1, 10., 9.]]) wanted = interpn(points, values, sample, method="linear") assert_array_almost_equal(interp_rg(sample), wanted) def test_4d_linear_outofbounds(self): # create a 4d grid of 3 points in each dimension points, values = self._sample_4d_data() sample = np.asarray([[0.1, -0.1, 10.1, 9.]]) wanted = 999.99 actual = interpn(points, values, sample, method="linear", bounds_error=False, fill_value=999.99) assert_array_almost_equal(actual, wanted) def test_nearest_4d(self): # create a 4d grid of 3 points in each dimension points, values = self._sample_4d_data() interp_rg = RegularGridInterpolator(points, values, method="nearest") sample = np.asarray([[0.1, 0.1, 10., 9.]]) wanted = interpn(points, values, sample, method="nearest") assert_array_almost_equal(interp_rg(sample), wanted) def test_4d_nearest_outofbounds(self): # create a 4d grid of 3 points in each dimension points, values = self._sample_4d_data() sample = np.asarray([[0.1, -0.1, 10.1, 9.]]) wanted = 999.99 actual = interpn(points, values, sample, method="nearest", bounds_error=False, fill_value=999.99) assert_array_almost_equal(actual, wanted) def test_xi_1d(self): # verify that 1D xi works as expected points, values = self._sample_4d_data() sample = np.asarray([0.1, 0.1, 10., 9.]) v1 = interpn(points, values, sample, bounds_error=False) v2 = interpn(points, values, sample[None,:], bounds_error=False) assert_allclose(v1, v2) def test_xi_nd(self): # verify that higher-d xi works as expected points, values = self._sample_4d_data() np.random.seed(1234) sample = np.random.rand(2, 3, 4) v1 = interpn(points, values, sample, method='nearest', bounds_error=False) assert_equal(v1.shape, (2, 3)) v2 = interpn(points, values, sample.reshape(-1, 4), method='nearest', bounds_error=False) assert_allclose(v1, v2.reshape(v1.shape)) def test_xi_broadcast(self): # verify that the interpolators broadcast xi x, y, values = self._sample_2d_data() points = (x, y) xi = np.linspace(0, 1, 2) yi = np.linspace(0, 3, 3) for method in ['nearest', 'linear', 'splinef2d']: sample = (xi[:,None], yi[None,:]) v1 = interpn(points, values, sample, method=method, bounds_error=False) assert_equal(v1.shape, (2, 3)) xx, yy = np.meshgrid(xi, yi) sample = np.c_[xx.T.ravel(), yy.T.ravel()] v2 = interpn(points, values, sample, method=method, bounds_error=False) assert_allclose(v1, v2.reshape(v1.shape)) def test_nonscalar_values(self): # Verify that non-scalar valued values also works points, values = self._sample_4d_data() np.random.seed(1234) values = np.random.rand(3, 3, 3, 3, 6) sample = np.random.rand(7, 11, 4) for method in ['nearest', 'linear']: v = interpn(points, values, sample, method=method, bounds_error=False) assert_equal(v.shape, (7, 11, 6), err_msg=method) vs = [interpn(points, values[...,j], sample, method=method, bounds_error=False) for j in range(6)] v2 = np.array(vs).transpose(1, 2, 0) assert_allclose(v, v2, err_msg=method) # Vector-valued splines supported with fitpack assert_raises(ValueError, interpn, points, values, sample, method='splinef2d') def test_complex(self): x, y, values = self._sample_2d_data() points = (x, y) values = values - 2j*values sample = np.array([[1, 2.3, 5.3, 0.5, 3.3, 1.2, 3], [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]]).T for method in ['linear', 'nearest']: v1 = interpn(points, values, sample, method=method) v2r = interpn(points, values.real, sample, method=method) v2i = interpn(points, values.imag, sample, method=method) v2 = v2r + 1j*v2i assert_allclose(v1, v2) # Complex-valued data not supported by spline2fd with warnings.catch_warnings(): warnings.simplefilter("error", category=np.ComplexWarning) assert_raises(np.ComplexWarning, interpn, points, values, sample, method='splinef2d') def test_duck_typed_values(self): x = np.linspace(0, 2, 5) y = np.linspace(0, 1, 7) values = MyValue((5, 7)) for method in ('nearest', 'linear'): v1 = interpn((x, y), values, [0.4, 0.7], method=method) v2 = interpn((x, y), values._v, [0.4, 0.7], method=method) assert_allclose(v1, v2) def test_matrix_input(self): x = np.linspace(0, 2, 5) y = np.linspace(0, 1, 7) values = np.matrix(np.random.rand(5, 7)) sample = np.random.rand(3, 7, 2) for method in ('nearest', 'linear', 'splinef2d'): v1 = interpn((x, y), values, sample, method=method) v2 = interpn((x, y), np.asarray(values), sample, method=method) assert_allclose(v1, np.asmatrix(v2)) if __name__ == "__main__": run_module_suite()