2585 lines
95 KiB
Python
2585 lines
95 KiB
Python
from numpy.testing import (assert_, assert_equal, assert_almost_equal,
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assert_array_almost_equal, assert_array_equal,
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assert_allclose, suppress_warnings)
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from pytest import raises as assert_raises
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import pytest
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from numpy import mgrid, pi, sin, ogrid, poly1d, linspace
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import numpy as np
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from scipy.interpolate import (interp1d, interp2d, lagrange, PPoly, BPoly,
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splrep, splev, splantider, splint, sproot, Akima1DInterpolator,
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NdPPoly, BSpline)
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from scipy.special import poch, gamma
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from scipy.interpolate import _ppoly
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from scipy._lib._gcutils import assert_deallocated, IS_PYPY
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from scipy.integrate import nquad
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from scipy.special import binom
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class TestInterp2D:
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def test_interp2d(self):
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y, x = mgrid[0:2:20j, 0:pi:21j]
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z = sin(x+0.5*y)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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II = interp2d(x, y, z)
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assert_almost_equal(II(1.0, 2.0), sin(2.0), decimal=2)
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v, u = ogrid[0:2:24j, 0:pi:25j]
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assert_almost_equal(II(u.ravel(), v.ravel()),
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sin(u+0.5*v), decimal=2)
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def test_interp2d_meshgrid_input(self):
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# Ticket #703
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x = linspace(0, 2, 16)
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y = linspace(0, pi, 21)
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z = sin(x[None, :] + y[:, None]/2.)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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II = interp2d(x, y, z)
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assert_almost_equal(II(1.0, 2.0), sin(2.0), decimal=2)
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def test_interp2d_meshgrid_input_unsorted(self):
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np.random.seed(1234)
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x = linspace(0, 2, 16)
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y = linspace(0, pi, 21)
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z = sin(x[None, :] + y[:, None] / 2.)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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ip1 = interp2d(x.copy(), y.copy(), z, kind='cubic')
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np.random.shuffle(x)
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z = sin(x[None, :] + y[:, None]/2.)
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ip2 = interp2d(x.copy(), y.copy(), z, kind='cubic')
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np.random.shuffle(x)
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np.random.shuffle(y)
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z = sin(x[None, :] + y[:, None] / 2.)
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ip3 = interp2d(x, y, z, kind='cubic')
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x = linspace(0, 2, 31)
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y = linspace(0, pi, 30)
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assert_equal(ip1(x, y), ip2(x, y))
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assert_equal(ip1(x, y), ip3(x, y))
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def test_interp2d_eval_unsorted(self):
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y, x = mgrid[0:2:20j, 0:pi:21j]
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z = sin(x + 0.5*y)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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func = interp2d(x, y, z)
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xe = np.array([3, 4, 5])
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ye = np.array([5.3, 7.1])
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assert_allclose(func(xe, ye), func(xe, ye[::-1]))
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assert_raises(ValueError, func, xe, ye[::-1], 0, 0, True)
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def test_interp2d_linear(self):
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# Ticket #898
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a = np.zeros([5, 5])
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a[2, 2] = 1.0
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x = y = np.arange(5)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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b = interp2d(x, y, a, 'linear')
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assert_almost_equal(b(2.0, 1.5), np.array([0.5]), decimal=2)
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assert_almost_equal(b(2.0, 2.5), np.array([0.5]), decimal=2)
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def test_interp2d_bounds(self):
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x = np.linspace(0, 1, 5)
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y = np.linspace(0, 2, 7)
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z = x[None, :]**2 + y[:, None]
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ix = np.linspace(-1, 3, 31)
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iy = np.linspace(-1, 3, 33)
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with suppress_warnings() as sup:
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sup.filter(DeprecationWarning)
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b = interp2d(x, y, z, bounds_error=True)
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assert_raises(ValueError, b, ix, iy)
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b = interp2d(x, y, z, fill_value=np.nan)
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iz = b(ix, iy)
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mx = (ix < 0) | (ix > 1)
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my = (iy < 0) | (iy > 2)
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assert_(np.isnan(iz[my, :]).all())
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assert_(np.isnan(iz[:, mx]).all())
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assert_(np.isfinite(iz[~my, :][:, ~mx]).all())
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class TestInterp1D:
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def setup_method(self):
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self.x5 = np.arange(5.)
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self.x10 = np.arange(10.)
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self.y10 = np.arange(10.)
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self.x25 = self.x10.reshape((2,5))
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self.x2 = np.arange(2.)
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self.y2 = np.arange(2.)
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self.x1 = np.array([0.])
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self.y1 = np.array([0.])
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self.y210 = np.arange(20.).reshape((2, 10))
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self.y102 = np.arange(20.).reshape((10, 2))
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self.y225 = np.arange(20.).reshape((2, 2, 5))
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self.y25 = np.arange(10.).reshape((2, 5))
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self.y235 = np.arange(30.).reshape((2, 3, 5))
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self.y325 = np.arange(30.).reshape((3, 2, 5))
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# Edge updated test matrix 1
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# array([[ 30, 1, 2, 3, 4, 5, 6, 7, 8, -30],
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# [ 30, 11, 12, 13, 14, 15, 16, 17, 18, -30]])
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self.y210_edge_updated = np.arange(20.).reshape((2, 10))
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self.y210_edge_updated[:, 0] = 30
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self.y210_edge_updated[:, -1] = -30
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# Edge updated test matrix 2
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# array([[ 30, 30],
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# [ 2, 3],
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# [ 4, 5],
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# [ 6, 7],
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# [ 8, 9],
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# [ 10, 11],
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# [ 12, 13],
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# [ 14, 15],
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# [ 16, 17],
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# [-30, -30]])
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self.y102_edge_updated = np.arange(20.).reshape((10, 2))
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self.y102_edge_updated[0, :] = 30
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self.y102_edge_updated[-1, :] = -30
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self.fill_value = -100.0
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def test_validation(self):
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# Make sure that appropriate exceptions are raised when invalid values
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# are given to the constructor.
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# These should all work.
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for kind in ('nearest', 'nearest-up', 'zero', 'linear', 'slinear',
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'quadratic', 'cubic', 'previous', 'next'):
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interp1d(self.x10, self.y10, kind=kind)
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interp1d(self.x10, self.y10, kind=kind, fill_value="extrapolate")
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interp1d(self.x10, self.y10, kind='linear', fill_value=(-1, 1))
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interp1d(self.x10, self.y10, kind='linear',
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fill_value=np.array([-1]))
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interp1d(self.x10, self.y10, kind='linear',
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fill_value=(-1,))
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interp1d(self.x10, self.y10, kind='linear',
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fill_value=-1)
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interp1d(self.x10, self.y10, kind='linear',
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fill_value=(-1, -1))
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interp1d(self.x10, self.y10, kind=0)
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interp1d(self.x10, self.y10, kind=1)
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interp1d(self.x10, self.y10, kind=2)
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interp1d(self.x10, self.y10, kind=3)
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interp1d(self.x10, self.y210, kind='linear', axis=-1,
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fill_value=(-1, -1))
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interp1d(self.x2, self.y210, kind='linear', axis=0,
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fill_value=np.ones(10))
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interp1d(self.x2, self.y210, kind='linear', axis=0,
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fill_value=(np.ones(10), np.ones(10)))
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interp1d(self.x2, self.y210, kind='linear', axis=0,
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fill_value=(np.ones(10), -1))
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# x array must be 1D.
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assert_raises(ValueError, interp1d, self.x25, self.y10)
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# y array cannot be a scalar.
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assert_raises(ValueError, interp1d, self.x10, np.array(0))
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# Check for x and y arrays having the same length.
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assert_raises(ValueError, interp1d, self.x10, self.y2)
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assert_raises(ValueError, interp1d, self.x2, self.y10)
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assert_raises(ValueError, interp1d, self.x10, self.y102)
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interp1d(self.x10, self.y210)
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interp1d(self.x10, self.y102, axis=0)
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# Check for x and y having at least 1 element.
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assert_raises(ValueError, interp1d, self.x1, self.y10)
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assert_raises(ValueError, interp1d, self.x10, self.y1)
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# Bad fill values
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=(-1, -1, -1)) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=[-1, -1, -1]) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=np.array((-1, -1, -1))) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=[[-1]]) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=[-1, -1]) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=np.array([])) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x10, self.y10, kind='linear',
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fill_value=()) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear',
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axis=0, fill_value=[-1, -1]) # doesn't broadcast
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assert_raises(ValueError, interp1d, self.x2, self.y210, kind='linear',
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axis=0, fill_value=(0., [-1, -1])) # above doesn't bc
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def test_init(self):
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# Check that the attributes are initialized appropriately by the
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# constructor.
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assert_(interp1d(self.x10, self.y10).copy)
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assert_(not interp1d(self.x10, self.y10, copy=False).copy)
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assert_(interp1d(self.x10, self.y10).bounds_error)
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assert_(not interp1d(self.x10, self.y10, bounds_error=False).bounds_error)
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assert_(np.isnan(interp1d(self.x10, self.y10).fill_value))
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assert_equal(interp1d(self.x10, self.y10, fill_value=3.0).fill_value,
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3.0)
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assert_equal(interp1d(self.x10, self.y10, fill_value=(1.0, 2.0)).fill_value,
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(1.0, 2.0))
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assert_equal(interp1d(self.x10, self.y10).axis, 0)
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assert_equal(interp1d(self.x10, self.y210).axis, 1)
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assert_equal(interp1d(self.x10, self.y102, axis=0).axis, 0)
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assert_array_equal(interp1d(self.x10, self.y10).x, self.x10)
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assert_array_equal(interp1d(self.x10, self.y10).y, self.y10)
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assert_array_equal(interp1d(self.x10, self.y210).y, self.y210)
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def test_assume_sorted(self):
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# Check for unsorted arrays
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interp10 = interp1d(self.x10, self.y10)
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interp10_unsorted = interp1d(self.x10[::-1], self.y10[::-1])
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assert_array_almost_equal(interp10_unsorted(self.x10), self.y10)
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assert_array_almost_equal(interp10_unsorted(1.2), np.array([1.2]))
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assert_array_almost_equal(interp10_unsorted([2.4, 5.6, 6.0]),
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interp10([2.4, 5.6, 6.0]))
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# Check assume_sorted keyword (defaults to False)
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interp10_assume_kw = interp1d(self.x10[::-1], self.y10[::-1],
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assume_sorted=False)
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assert_array_almost_equal(interp10_assume_kw(self.x10), self.y10)
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interp10_assume_kw2 = interp1d(self.x10[::-1], self.y10[::-1],
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assume_sorted=True)
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# Should raise an error for unsorted input if assume_sorted=True
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assert_raises(ValueError, interp10_assume_kw2, self.x10)
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# Check that if y is a 2-D array, things are still consistent
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interp10_y_2d = interp1d(self.x10, self.y210)
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interp10_y_2d_unsorted = interp1d(self.x10[::-1], self.y210[:, ::-1])
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assert_array_almost_equal(interp10_y_2d(self.x10),
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interp10_y_2d_unsorted(self.x10))
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def test_linear(self):
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for kind in ['linear', 'slinear']:
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self._check_linear(kind)
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def _check_linear(self, kind):
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# Check the actual implementation of linear interpolation.
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interp10 = interp1d(self.x10, self.y10, kind=kind)
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assert_array_almost_equal(interp10(self.x10), self.y10)
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assert_array_almost_equal(interp10(1.2), np.array([1.2]))
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assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
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np.array([2.4, 5.6, 6.0]))
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# test fill_value="extrapolate"
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extrapolator = interp1d(self.x10, self.y10, kind=kind,
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fill_value='extrapolate')
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assert_allclose(extrapolator([-1., 0, 9, 11]),
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[-1, 0, 9, 11], rtol=1e-14)
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opts = dict(kind=kind,
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fill_value='extrapolate',
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bounds_error=True)
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assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
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def test_linear_dtypes(self):
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# regression test for gh-5898, where 1D linear interpolation has been
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# delegated to numpy.interp for all float dtypes, and the latter was
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# not handling e.g. np.float128.
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for dtyp in [np.float16,
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np.float32,
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np.float64,
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np.longdouble]:
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x = np.arange(8, dtype=dtyp)
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y = x
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yp = interp1d(x, y, kind='linear')(x)
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assert_equal(yp.dtype, dtyp)
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assert_allclose(yp, y, atol=1e-15)
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# regression test for gh-14531, where 1D linear interpolation has been
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# has been extended to delegate to numpy.interp for integer dtypes
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x = [0, 1, 2]
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y = [np.nan, 0, 1]
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yp = interp1d(x, y)(x)
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assert_allclose(yp, y, atol=1e-15)
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def test_slinear_dtypes(self):
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# regression test for gh-7273: 1D slinear interpolation fails with
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# float32 inputs
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dt_r = [np.float16, np.float32, np.float64]
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dt_rc = dt_r + [np.complex64, np.complex128]
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spline_kinds = ['slinear', 'zero', 'quadratic', 'cubic']
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for dtx in dt_r:
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x = np.arange(0, 10, dtype=dtx)
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for dty in dt_rc:
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y = np.exp(-x/3.0).astype(dty)
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for dtn in dt_r:
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xnew = x.astype(dtn)
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for kind in spline_kinds:
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f = interp1d(x, y, kind=kind, bounds_error=False)
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assert_allclose(f(xnew), y, atol=1e-7,
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err_msg=f"{dtx}, {dty} {dtn}")
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def test_cubic(self):
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# Check the actual implementation of spline interpolation.
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interp10 = interp1d(self.x10, self.y10, kind='cubic')
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assert_array_almost_equal(interp10(self.x10), self.y10)
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assert_array_almost_equal(interp10(1.2), np.array([1.2]))
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assert_array_almost_equal(interp10(1.5), np.array([1.5]))
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assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
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np.array([2.4, 5.6, 6.0]),)
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def test_nearest(self):
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# Check the actual implementation of nearest-neighbour interpolation.
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# Nearest asserts that half-integer case (1.5) rounds down to 1
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interp10 = interp1d(self.x10, self.y10, kind='nearest')
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assert_array_almost_equal(interp10(self.x10), self.y10)
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assert_array_almost_equal(interp10(1.2), np.array(1.))
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assert_array_almost_equal(interp10(1.5), np.array(1.))
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assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
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np.array([2., 6., 6.]),)
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# test fill_value="extrapolate"
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extrapolator = interp1d(self.x10, self.y10, kind='nearest',
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fill_value='extrapolate')
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assert_allclose(extrapolator([-1., 0, 9, 11]),
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[0, 0, 9, 9], rtol=1e-14)
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opts = dict(kind='nearest',
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fill_value='extrapolate',
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bounds_error=True)
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assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
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def test_nearest_up(self):
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# Check the actual implementation of nearest-neighbour interpolation.
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# Nearest-up asserts that half-integer case (1.5) rounds up to 2
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interp10 = interp1d(self.x10, self.y10, kind='nearest-up')
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assert_array_almost_equal(interp10(self.x10), self.y10)
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assert_array_almost_equal(interp10(1.2), np.array(1.))
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assert_array_almost_equal(interp10(1.5), np.array(2.))
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assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
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np.array([2., 6., 6.]),)
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# test fill_value="extrapolate"
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extrapolator = interp1d(self.x10, self.y10, kind='nearest-up',
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fill_value='extrapolate')
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assert_allclose(extrapolator([-1., 0, 9, 11]),
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[0, 0, 9, 9], rtol=1e-14)
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opts = dict(kind='nearest-up',
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fill_value='extrapolate',
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bounds_error=True)
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assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
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def test_previous(self):
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# Check the actual implementation of previous interpolation.
|
|
interp10 = interp1d(self.x10, self.y10, kind='previous')
|
|
assert_array_almost_equal(interp10(self.x10), self.y10)
|
|
assert_array_almost_equal(interp10(1.2), np.array(1.))
|
|
assert_array_almost_equal(interp10(1.5), np.array(1.))
|
|
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
|
|
np.array([2., 5., 6.]),)
|
|
|
|
# test fill_value="extrapolate"
|
|
extrapolator = interp1d(self.x10, self.y10, kind='previous',
|
|
fill_value='extrapolate')
|
|
assert_allclose(extrapolator([-1., 0, 9, 11]),
|
|
[np.nan, 0, 9, 9], rtol=1e-14)
|
|
|
|
# Tests for gh-9591
|
|
interpolator1D = interp1d(self.x10, self.y10, kind="previous",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator1D([-1, -2, 5, 8, 12, 25]),
|
|
[np.nan, np.nan, 5, 8, 9, 9])
|
|
|
|
interpolator2D = interp1d(self.x10, self.y210, kind="previous",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]),
|
|
[[np.nan, np.nan, 5, 8, 9, 9],
|
|
[np.nan, np.nan, 15, 18, 19, 19]])
|
|
|
|
interpolator2DAxis0 = interp1d(self.x10, self.y102, kind="previous",
|
|
axis=0, fill_value='extrapolate')
|
|
assert_allclose(interpolator2DAxis0([-2, 5, 12]),
|
|
[[np.nan, np.nan],
|
|
[10, 11],
|
|
[18, 19]])
|
|
|
|
opts = dict(kind='previous',
|
|
fill_value='extrapolate',
|
|
bounds_error=True)
|
|
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
|
|
|
|
# Tests for gh-16813
|
|
interpolator1D = interp1d([0, 1, 2],
|
|
[0, 1, -1], kind="previous",
|
|
fill_value='extrapolate',
|
|
assume_sorted=True)
|
|
assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]),
|
|
[np.nan, np.nan, 0, 1, -1, -1, -1])
|
|
|
|
interpolator1D = interp1d([2, 0, 1], # x is not ascending
|
|
[-1, 0, 1], kind="previous",
|
|
fill_value='extrapolate',
|
|
assume_sorted=False)
|
|
assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]),
|
|
[np.nan, np.nan, 0, 1, -1, -1, -1])
|
|
|
|
interpolator2D = interp1d(self.x10, self.y210_edge_updated,
|
|
kind="previous",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]),
|
|
[[np.nan, np.nan, 5, 8, -30, -30],
|
|
[np.nan, np.nan, 15, 18, -30, -30]])
|
|
|
|
interpolator2DAxis0 = interp1d(self.x10, self.y102_edge_updated,
|
|
kind="previous",
|
|
axis=0, fill_value='extrapolate')
|
|
assert_allclose(interpolator2DAxis0([-2, 5, 12]),
|
|
[[np.nan, np.nan],
|
|
[10, 11],
|
|
[-30, -30]])
|
|
|
|
def test_next(self):
|
|
# Check the actual implementation of next interpolation.
|
|
interp10 = interp1d(self.x10, self.y10, kind='next')
|
|
assert_array_almost_equal(interp10(self.x10), self.y10)
|
|
assert_array_almost_equal(interp10(1.2), np.array(2.))
|
|
assert_array_almost_equal(interp10(1.5), np.array(2.))
|
|
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
|
|
np.array([3., 6., 6.]),)
|
|
|
|
# test fill_value="extrapolate"
|
|
extrapolator = interp1d(self.x10, self.y10, kind='next',
|
|
fill_value='extrapolate')
|
|
assert_allclose(extrapolator([-1., 0, 9, 11]),
|
|
[0, 0, 9, np.nan], rtol=1e-14)
|
|
|
|
# Tests for gh-9591
|
|
interpolator1D = interp1d(self.x10, self.y10, kind="next",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator1D([-1, -2, 5, 8, 12, 25]),
|
|
[0, 0, 5, 8, np.nan, np.nan])
|
|
|
|
interpolator2D = interp1d(self.x10, self.y210, kind="next",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]),
|
|
[[0, 0, 5, 8, np.nan, np.nan],
|
|
[10, 10, 15, 18, np.nan, np.nan]])
|
|
|
|
interpolator2DAxis0 = interp1d(self.x10, self.y102, kind="next",
|
|
axis=0, fill_value='extrapolate')
|
|
assert_allclose(interpolator2DAxis0([-2, 5, 12]),
|
|
[[0, 1],
|
|
[10, 11],
|
|
[np.nan, np.nan]])
|
|
|
|
opts = dict(kind='next',
|
|
fill_value='extrapolate',
|
|
bounds_error=True)
|
|
assert_raises(ValueError, interp1d, self.x10, self.y10, **opts)
|
|
|
|
# Tests for gh-16813
|
|
interpolator1D = interp1d([0, 1, 2],
|
|
[0, 1, -1], kind="next",
|
|
fill_value='extrapolate',
|
|
assume_sorted=True)
|
|
assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]),
|
|
[0, 0, 0, 1, -1, np.nan, np.nan])
|
|
|
|
interpolator1D = interp1d([2, 0, 1], # x is not ascending
|
|
[-1, 0, 1], kind="next",
|
|
fill_value='extrapolate',
|
|
assume_sorted=False)
|
|
assert_allclose(interpolator1D([-2, -1, 0, 1, 2, 3, 5]),
|
|
[0, 0, 0, 1, -1, np.nan, np.nan])
|
|
|
|
interpolator2D = interp1d(self.x10, self.y210_edge_updated,
|
|
kind="next",
|
|
fill_value='extrapolate')
|
|
assert_allclose(interpolator2D([-1, -2, 5, 8, 12, 25]),
|
|
[[30, 30, 5, 8, np.nan, np.nan],
|
|
[30, 30, 15, 18, np.nan, np.nan]])
|
|
|
|
interpolator2DAxis0 = interp1d(self.x10, self.y102_edge_updated,
|
|
kind="next",
|
|
axis=0, fill_value='extrapolate')
|
|
assert_allclose(interpolator2DAxis0([-2, 5, 12]),
|
|
[[30, 30],
|
|
[10, 11],
|
|
[np.nan, np.nan]])
|
|
|
|
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(1.5), np.array(1.))
|
|
assert_array_almost_equal(interp10([2.4, 5.6, 6.0]),
|
|
np.array([2., 5., 6.]))
|
|
|
|
def bounds_check_helper(self, interpolant, test_array, fail_value):
|
|
# Asserts that a ValueError is raised and that the error message
|
|
# contains the value causing this exception.
|
|
assert_raises(ValueError, interpolant, test_array)
|
|
try:
|
|
interpolant(test_array)
|
|
except ValueError as err:
|
|
assert (f"{fail_value}" in str(err))
|
|
|
|
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, False],
|
|
[False, False, False, False, True]]))
|
|
|
|
raises_bounds_error = interp1d(self.x10, self.y10, bounds_error=True,
|
|
kind=kind)
|
|
|
|
self.bounds_check_helper(raises_bounds_error, -1.0, -1.0)
|
|
self.bounds_check_helper(raises_bounds_error, 11.0, 11.0)
|
|
self.bounds_check_helper(raises_bounds_error, [0.0, -1.0, 0.0], -1.0)
|
|
self.bounds_check_helper(raises_bounds_error, [0.0, 1.0, 21.0], 21.0)
|
|
|
|
raises_bounds_error([0.0, 5.0, 9.0])
|
|
|
|
def _bounds_check_int_nan_fill(self, kind='linear'):
|
|
x = np.arange(10).astype(int)
|
|
y = np.arange(10).astype(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', 'previous', 'next',
|
|
'slinear', 'zero', 'quadratic'):
|
|
self._bounds_check(kind)
|
|
self._bounds_check_int_nan_fill(kind)
|
|
|
|
def _check_fill_value(self, kind):
|
|
interp = interp1d(self.x10, self.y10, kind=kind,
|
|
fill_value=(-100, 100), bounds_error=False)
|
|
assert_array_almost_equal(interp(10), 100)
|
|
assert_array_almost_equal(interp(-10), -100)
|
|
assert_array_almost_equal(interp([-10, 10]), [-100, 100])
|
|
|
|
# Proper broadcasting:
|
|
# interp along axis of length 5
|
|
# other dim=(2, 3), (3, 2), (2, 2), or (2,)
|
|
|
|
# one singleton fill_value (works for all)
|
|
for y in (self.y235, self.y325, self.y225, self.y25):
|
|
interp = interp1d(self.x5, y, kind=kind, axis=-1,
|
|
fill_value=100, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), 100)
|
|
assert_array_almost_equal(interp(-10), 100)
|
|
assert_array_almost_equal(interp([-10, 10]), 100)
|
|
|
|
# singleton lower, singleton upper
|
|
interp = interp1d(self.x5, y, kind=kind, axis=-1,
|
|
fill_value=(-100, 100), bounds_error=False)
|
|
assert_array_almost_equal(interp(10), 100)
|
|
assert_array_almost_equal(interp(-10), -100)
|
|
if y.ndim == 3:
|
|
result = [[[-100, 100]] * y.shape[1]] * y.shape[0]
|
|
else:
|
|
result = [[-100, 100]] * y.shape[0]
|
|
assert_array_almost_equal(interp([-10, 10]), result)
|
|
|
|
# one broadcastable (3,) fill_value
|
|
fill_value = [100, 200, 300]
|
|
for y in (self.y325, self.y225):
|
|
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2)
|
|
assert_array_almost_equal(interp(-10), [[100, 200, 300]] * 2)
|
|
assert_array_almost_equal(interp([-10, 10]), [[[100, 100],
|
|
[200, 200],
|
|
[300, 300]]] * 2)
|
|
|
|
# one broadcastable (2,) fill_value
|
|
fill_value = [100, 200]
|
|
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for y in (self.y225, self.y325, self.y25):
|
|
interp = interp1d(self.x5, y, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
result = [100, 200]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp(10), result)
|
|
assert_array_almost_equal(interp(-10), result)
|
|
result = [[100, 100], [200, 200]]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp([-10, 10]), result)
|
|
|
|
# broadcastable (3,) lower, singleton upper
|
|
fill_value = (np.array([-100, -200, -300]), 100)
|
|
for y in (self.y325, self.y225):
|
|
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), 100)
|
|
assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2)
|
|
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
|
|
[-200, 100],
|
|
[-300, 100]]] * 2)
|
|
|
|
# broadcastable (2,) lower, singleton upper
|
|
fill_value = (np.array([-100, -200]), 100)
|
|
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for y in (self.y225, self.y325, self.y25):
|
|
interp = interp1d(self.x5, y, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), 100)
|
|
result = [-100, -200]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp(-10), result)
|
|
result = [[-100, 100], [-200, 100]]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp([-10, 10]), result)
|
|
|
|
# broadcastable (3,) lower, broadcastable (3,) upper
|
|
fill_value = ([-100, -200, -300], [100, 200, 300])
|
|
for y in (self.y325, self.y225):
|
|
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for ii in range(2): # check ndarray as well as list here
|
|
if ii == 1:
|
|
fill_value = tuple(np.array(f) for f in fill_value)
|
|
interp = interp1d(self.x5, self.y235, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), [[100, 200, 300]] * 2)
|
|
assert_array_almost_equal(interp(-10), [[-100, -200, -300]] * 2)
|
|
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
|
|
[-200, 200],
|
|
[-300, 300]]] * 2)
|
|
# broadcastable (2,) lower, broadcastable (2,) upper
|
|
fill_value = ([-100, -200], [100, 200])
|
|
assert_raises(ValueError, interp1d, self.x5, self.y235, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for y in (self.y325, self.y225, self.y25):
|
|
interp = interp1d(self.x5, y, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
result = [100, 200]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp(10), result)
|
|
result = [-100, -200]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp(-10), result)
|
|
result = [[-100, 100], [-200, 200]]
|
|
if y.ndim == 3:
|
|
result = [result] * y.shape[0]
|
|
assert_array_almost_equal(interp([-10, 10]), result)
|
|
|
|
# one broadcastable (2, 2) array-like
|
|
fill_value = [[100, 200], [1000, 2000]]
|
|
for y in (self.y235, self.y325, self.y25):
|
|
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for ii in range(2):
|
|
if ii == 1:
|
|
fill_value = np.array(fill_value)
|
|
interp = interp1d(self.x5, self.y225, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]])
|
|
assert_array_almost_equal(interp(-10), [[100, 200], [1000, 2000]])
|
|
assert_array_almost_equal(interp([-10, 10]), [[[100, 100],
|
|
[200, 200]],
|
|
[[1000, 1000],
|
|
[2000, 2000]]])
|
|
|
|
# broadcastable (2, 2) lower, broadcastable (2, 2) upper
|
|
fill_value = ([[-100, -200], [-1000, -2000]],
|
|
[[100, 200], [1000, 2000]])
|
|
for y in (self.y235, self.y325, self.y25):
|
|
assert_raises(ValueError, interp1d, self.x5, y, kind=kind,
|
|
axis=-1, fill_value=fill_value, bounds_error=False)
|
|
for ii in range(2):
|
|
if ii == 1:
|
|
fill_value = (np.array(fill_value[0]), np.array(fill_value[1]))
|
|
interp = interp1d(self.x5, self.y225, kind=kind, axis=-1,
|
|
fill_value=fill_value, bounds_error=False)
|
|
assert_array_almost_equal(interp(10), [[100, 200], [1000, 2000]])
|
|
assert_array_almost_equal(interp(-10), [[-100, -200],
|
|
[-1000, -2000]])
|
|
assert_array_almost_equal(interp([-10, 10]), [[[-100, 100],
|
|
[-200, 200]],
|
|
[[-1000, 1000],
|
|
[-2000, 2000]]])
|
|
|
|
def test_fill_value(self):
|
|
# test that two-element fill value works
|
|
for kind in ('linear', 'nearest', 'cubic', 'slinear', 'quadratic',
|
|
'zero', 'previous', 'next'):
|
|
self._check_fill_value(kind)
|
|
|
|
def test_fill_value_writeable(self):
|
|
# backwards compat: fill_value is a public writeable attribute
|
|
interp = interp1d(self.x10, self.y10, fill_value=123.0)
|
|
assert_equal(interp.fill_value, 123.0)
|
|
interp.fill_value = 321.0
|
|
assert_equal(interp.fill_value, 321.0)
|
|
|
|
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 N-D 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',
|
|
'zero', 'previous', 'next'):
|
|
self._nd_check_interp(kind)
|
|
self._nd_check_shape(kind)
|
|
|
|
def _check_complex(self, dtype=np.complex128, 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', 'previous', 'next'):
|
|
self._check_complex(np.complex64, kind)
|
|
self._check_complex(np.complex128, kind)
|
|
|
|
@pytest.mark.skipif(IS_PYPY, reason="Test not meaningful on PyPy")
|
|
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:
|
|
interp([0.1, 0.2])
|
|
del interp
|
|
|
|
def test_overflow_nearest(self):
|
|
# Test that the x range doesn't overflow when given integers as input
|
|
for kind in ('nearest', 'previous', 'next'):
|
|
x = np.array([0, 50, 127], dtype=np.int8)
|
|
ii = interp1d(x, x, kind=kind)
|
|
assert_array_almost_equal(ii(x), x)
|
|
|
|
def test_local_nans(self):
|
|
# check that for local interpolation kinds (slinear, zero) a single nan
|
|
# only affects its local neighborhood
|
|
x = np.arange(10).astype(float)
|
|
y = x.copy()
|
|
y[6] = np.nan
|
|
for kind in ('zero', 'slinear'):
|
|
ir = interp1d(x, y, kind=kind)
|
|
vals = ir([4.9, 7.0])
|
|
assert_(np.isfinite(vals).all())
|
|
|
|
def test_spline_nans(self):
|
|
# Backwards compat: a single nan makes the whole spline interpolation
|
|
# return nans in an array of the correct shape. And it doesn't raise,
|
|
# just quiet nans because of backcompat.
|
|
x = np.arange(8).astype(float)
|
|
y = x.copy()
|
|
yn = y.copy()
|
|
yn[3] = np.nan
|
|
|
|
for kind in ['quadratic', 'cubic']:
|
|
ir = interp1d(x, y, kind=kind)
|
|
irn = interp1d(x, yn, kind=kind)
|
|
for xnew in (6, [1, 6], [[1, 6], [3, 5]]):
|
|
xnew = np.asarray(xnew)
|
|
out, outn = ir(x), irn(x)
|
|
assert_(np.isnan(outn).all())
|
|
assert_equal(out.shape, outn.shape)
|
|
|
|
def test_all_nans(self):
|
|
# regression test for gh-11637: interp1d core dumps with all-nan `x`
|
|
x = np.ones(10) * np.nan
|
|
y = np.arange(10)
|
|
with assert_raises(ValueError):
|
|
interp1d(x, y, kind='cubic')
|
|
|
|
def test_read_only(self):
|
|
x = np.arange(0, 10)
|
|
y = np.exp(-x / 3.0)
|
|
xnew = np.arange(0, 9, 0.1)
|
|
# Check both read-only and not read-only:
|
|
for xnew_writeable in (True, False):
|
|
xnew.flags.writeable = xnew_writeable
|
|
x.flags.writeable = False
|
|
for kind in ('linear', 'nearest', 'zero', 'slinear', 'quadratic',
|
|
'cubic'):
|
|
f = interp1d(x, y, kind=kind)
|
|
vals = f(xnew)
|
|
assert_(np.isfinite(vals).all())
|
|
|
|
@pytest.mark.parametrize(
|
|
"kind", ("linear", "nearest", "nearest-up", "previous", "next")
|
|
)
|
|
def test_single_value(self, kind):
|
|
# https://github.com/scipy/scipy/issues/4043
|
|
f = interp1d([1.5], [6], kind=kind, bounds_error=False,
|
|
fill_value=(2, 10))
|
|
assert_array_equal(f([1, 1.5, 2]), [2, 6, 10])
|
|
# check still error if bounds_error=True
|
|
f = interp1d([1.5], [6], kind=kind, bounds_error=True)
|
|
with assert_raises(ValueError, match="x_new is above"):
|
|
f(2.0)
|
|
|
|
|
|
class TestLagrange:
|
|
|
|
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:
|
|
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_mod(self):
|
|
# Reference values generated with the following MATLAB code:
|
|
# format longG
|
|
# x = 0:10; y = [0. 2. 1. 3. 2. 6. 5.5 5.5 2.7 5.1 3.];
|
|
# xi = [0. 0.5 1. 1.5 2.5 3.5 4.5 5.1 6.5 7.2 8.6 9.9 10.];
|
|
# makima(x, y, xi)
|
|
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, method="makima")
|
|
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([
|
|
0.0, 1.34471153846154, 2.0, 1.44375, 1.94375, 2.51939102564103,
|
|
4.10366931918656, 5.98501550899192, 5.51756330960439, 5.1757231914014,
|
|
4.12326636931311, 3.32931513157895, 3.0])
|
|
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_degenerate_case_multidimensional(self):
|
|
# This test is for issue #5683.
|
|
x = np.array([0, 1, 2])
|
|
y = np.vstack((x, x**2)).T
|
|
ak = Akima1DInterpolator(x, y)
|
|
x_eval = np.array([0.5, 1.5])
|
|
y_eval = ak(x_eval)
|
|
assert_allclose(y_eval, np.vstack((x_eval, x_eval**2)).T)
|
|
|
|
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)
|
|
match = "Extending a 1-D Akima interpolator is not yet implemented"
|
|
with pytest.raises(NotImplementedError, match=match):
|
|
ak.extend(None, None)
|
|
|
|
def test_mod_invalid_method(self):
|
|
x = np.arange(0., 11.)
|
|
y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
|
|
match = "`method`=invalid is unsupported."
|
|
with pytest.raises(NotImplementedError, match=match):
|
|
Akima1DInterpolator(x, y, method="invalid") # type: ignore
|
|
|
|
def test_complex(self):
|
|
# Complex-valued data deprecated
|
|
x = np.arange(0., 11.)
|
|
y = np.array([0., 2., 1., 3., 2., 6., 5.5, 5.5, 2.7, 5.1, 3.])
|
|
y = y - 2j*y
|
|
# actually raises ComplexWarning, which subclasses RuntimeWarning, see
|
|
# https://github.com/numpy/numpy/blob/main/numpy/exceptions.py
|
|
msg = "Passing an array with a complex.*|Casting complex values to real.*"
|
|
with pytest.warns((RuntimeWarning, DeprecationWarning), match=msg):
|
|
Akima1DInterpolator(x, y)
|
|
|
|
|
|
class TestPPolyCommon:
|
|
# 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_ctor_c(self):
|
|
# wrong shape: `c` must be at least 2D
|
|
with assert_raises(ValueError):
|
|
PPoly([1, 2], [0, 1])
|
|
|
|
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])
|
|
|
|
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_extend_descending(self):
|
|
np.random.seed(0)
|
|
|
|
order = 3
|
|
x = np.sort(np.random.uniform(0, 10, 20))
|
|
c = np.random.rand(order + 1, x.shape[0] - 1, 2, 3)
|
|
|
|
for cls in (PPoly, BPoly):
|
|
p = cls(c, x)
|
|
|
|
p1 = cls(c[:, :9], x[:10])
|
|
p1.extend(c[:, 9:], x[10:])
|
|
|
|
p2 = cls(c[:, 10:], x[10:])
|
|
p2.extend(c[:, :10], x[:10])
|
|
|
|
assert_array_equal(p1.c, p.c)
|
|
assert_array_equal(p1.x, p.x)
|
|
assert_array_equal(p2.c, p.c)
|
|
assert_array_equal(p2.x, p.x)
|
|
|
|
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))), ())
|
|
|
|
assert_raises(ValueError, p, np.array([[0.1, 0.2], [0.4]], dtype=object))
|
|
|
|
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))
|
|
|
|
def test_axis(self):
|
|
np.random.seed(12345)
|
|
c = np.random.rand(3, 4, 5, 6, 7, 8)
|
|
c_s = c.shape
|
|
xp = np.random.random((1, 2))
|
|
for axis in (0, 1, 2, 3):
|
|
m = c.shape[axis+1]
|
|
x = np.sort(np.random.rand(m+1))
|
|
for cls in (PPoly, BPoly):
|
|
p = cls(c, x, axis=axis)
|
|
assert_equal(p.c.shape,
|
|
c_s[axis:axis+2] + c_s[:axis] + c_s[axis+2:])
|
|
res = p(xp)
|
|
targ_shape = c_s[:axis] + xp.shape + c_s[2+axis:]
|
|
assert_equal(res.shape, targ_shape)
|
|
|
|
# deriv/antideriv does not drop the axis
|
|
for p1 in [cls(c, x, axis=axis).derivative(),
|
|
cls(c, x, axis=axis).derivative(2),
|
|
cls(c, x, axis=axis).antiderivative(),
|
|
cls(c, x, axis=axis).antiderivative(2)]:
|
|
assert_equal(p1.axis, p.axis)
|
|
|
|
# c array needs two axes for the coefficients and intervals, so
|
|
# 0 <= axis < c.ndim-1; raise otherwise
|
|
for axis in (-1, 4, 5, 6):
|
|
for cls in (BPoly, PPoly):
|
|
assert_raises(ValueError, cls, **dict(c=c, x=x, axis=axis))
|
|
|
|
|
|
class TestPolySubclassing:
|
|
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:
|
|
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_periodic(self):
|
|
c = np.array([[1, 4], [2, 5], [3, 6]])
|
|
x = np.array([0, 0.5, 1])
|
|
p = PPoly(c, x, extrapolate='periodic')
|
|
|
|
assert_allclose(p(1.3), 1 * 0.3 ** 2 + 2 * 0.3 + 3)
|
|
assert_allclose(p(-0.3), 4 * (0.7 - 0.5) ** 2 + 5 * (0.7 - 0.5) + 6)
|
|
|
|
assert_allclose(p(1.3, 1), 2 * 0.3 + 2)
|
|
assert_allclose(p(-0.3, 1), 8 * (0.7 - 0.5) + 5)
|
|
|
|
def test_read_only(self):
|
|
c = np.array([[1, 4], [2, 5], [3, 6]])
|
|
x = np.array([0, 0.5, 1])
|
|
xnew = np.array([0, 0.1, 0.2])
|
|
PPoly(c, x, extrapolate='periodic')
|
|
|
|
for writeable in (True, False):
|
|
x.flags.writeable = writeable
|
|
c.flags.writeable = writeable
|
|
f = PPoly(c, x)
|
|
vals = f(xnew)
|
|
assert_(np.isfinite(vals).all())
|
|
|
|
def test_descending(self):
|
|
def binom_matrix(power):
|
|
n = np.arange(power + 1).reshape(-1, 1)
|
|
k = np.arange(power + 1)
|
|
B = binom(n, k)
|
|
return B[::-1, ::-1]
|
|
|
|
np.random.seed(0)
|
|
|
|
power = 3
|
|
for m in [10, 20, 30]:
|
|
x = np.sort(np.random.uniform(0, 10, m + 1))
|
|
ca = np.random.uniform(-2, 2, size=(power + 1, m))
|
|
|
|
h = np.diff(x)
|
|
h_powers = h[None, :] ** np.arange(power + 1)[::-1, None]
|
|
B = binom_matrix(power)
|
|
cap = ca * h_powers
|
|
cdp = np.dot(B.T, cap)
|
|
cd = cdp / h_powers
|
|
|
|
pa = PPoly(ca, x, extrapolate=True)
|
|
pd = PPoly(cd[:, ::-1], x[::-1], extrapolate=True)
|
|
|
|
x_test = np.random.uniform(-10, 20, 100)
|
|
assert_allclose(pa(x_test), pd(x_test), rtol=1e-13)
|
|
assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13)
|
|
|
|
pa_d = pa.derivative()
|
|
pd_d = pd.derivative()
|
|
|
|
assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13)
|
|
|
|
# Antiderivatives won't be equal because fixing continuity is
|
|
# done in the reverse order, but surely the differences should be
|
|
# equal.
|
|
pa_i = pa.antiderivative()
|
|
pd_i = pd.antiderivative()
|
|
for a, b in np.random.uniform(-10, 20, (5, 2)):
|
|
int_a = pa.integrate(a, b)
|
|
int_d = pd.integrate(a, b)
|
|
assert_allclose(int_a, int_d, rtol=1e-13)
|
|
assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a),
|
|
rtol=1e-13)
|
|
|
|
roots_d = pd.roots()
|
|
roots_a = pa.roots()
|
|
assert_allclose(roots_a, np.sort(roots_d), rtol=1e-12)
|
|
|
|
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))
|
|
|
|
# make sure .from_spline accepts BSpline objects
|
|
b = BSpline(*spl)
|
|
ppp = PPoly.from_spline(b)
|
|
assert_allclose(ppp(xi), b(xi))
|
|
|
|
# BSpline's extrapolate attribute propagates unless overridden
|
|
t, c, k = spl
|
|
for extrap in (None, True, False):
|
|
b = BSpline(t, c, k, extrapolate=extrap)
|
|
p = PPoly.from_spline(b)
|
|
assert_equal(p.extrapolate, b.extrapolate)
|
|
|
|
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_of_constant(self):
|
|
# https://github.com/scipy/scipy/issues/4216
|
|
p = PPoly([[1.]], [0, 1])
|
|
assert_equal(p.antiderivative().c, PPoly([[1], [0]], [0, 1]).c)
|
|
assert_equal(p.antiderivative().x, PPoly([[1], [0]], [0, 1]).x)
|
|
|
|
def test_antiderivative_regression_4355(self):
|
|
# https://github.com/scipy/scipy/issues/4355
|
|
p = PPoly([[1., 0.5]], [0, 1, 2])
|
|
q = p.antiderivative()
|
|
assert_equal(q.c, [[1, 0.5], [0, 1]])
|
|
assert_equal(q.x, [0, 1, 2])
|
|
assert_allclose(p.integrate(0, 2), 1.5)
|
|
assert_allclose(q(2) - q(0), 1.5)
|
|
|
|
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_antiderivative_continuity(self):
|
|
c = np.array([[2, 1, 2, 2], [2, 1, 3, 3]]).T
|
|
x = np.array([0, 0.5, 1])
|
|
|
|
p = PPoly(c, x)
|
|
ip = p.antiderivative()
|
|
|
|
# check continuity
|
|
assert_allclose(ip(0.5 - 1e-9), ip(0.5 + 1e-9), rtol=1e-8)
|
|
|
|
# check that only lowest order coefficients were changed
|
|
p2 = ip.derivative()
|
|
assert_allclose(p2.c, p.c)
|
|
|
|
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_integrate_readonly(self):
|
|
x = np.array([1, 2, 4])
|
|
c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]])
|
|
|
|
for writeable in (True, False):
|
|
x.flags.writeable = writeable
|
|
|
|
P = PPoly(c, x)
|
|
vals = P.integrate(1, 4)
|
|
|
|
assert_(np.isfinite(vals).all())
|
|
|
|
def test_integrate_periodic(self):
|
|
x = np.array([1, 2, 4])
|
|
c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]])
|
|
|
|
P = PPoly(c, x, extrapolate='periodic')
|
|
I = P.antiderivative()
|
|
|
|
period_int = I(4) - I(1)
|
|
|
|
assert_allclose(P.integrate(1, 4), period_int)
|
|
assert_allclose(P.integrate(-10, -7), period_int)
|
|
assert_allclose(P.integrate(-10, -4), 2 * period_int)
|
|
|
|
assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5))
|
|
assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5))
|
|
assert_allclose(P.integrate(3.5 + 12, 5 + 12),
|
|
I(2) - I(1) + I(4) - I(3.5))
|
|
assert_allclose(P.integrate(3.5, 5 + 12),
|
|
I(2) - I(1) + I(4) - I(3.5) + 4 * period_int)
|
|
|
|
assert_allclose(P.integrate(0, -1), I(2) - I(3))
|
|
assert_allclose(P.integrate(-9, -10), I(2) - I(3))
|
|
assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int)
|
|
|
|
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])
|
|
|
|
# ditto for p.solve(const) with sections identically equal const
|
|
const = 2.
|
|
c1 = c.copy()
|
|
c1[1, :] += const
|
|
pp1 = PPoly(c1, x)
|
|
|
|
assert_array_equal(pp1.solve(const),
|
|
[0.25, 0.4, np.nan, 0.6 + 0.25])
|
|
|
|
def test_roots_all_zero(self):
|
|
# test the code path for the polynomial being identically zero everywhere
|
|
c = [[0], [0]]
|
|
x = [0, 1]
|
|
p = PPoly(c, x)
|
|
assert_array_equal(p.roots(), [0, np.nan])
|
|
assert_array_equal(p.solve(0), [0, np.nan])
|
|
assert_array_equal(p.solve(1), [])
|
|
|
|
c = [[0, 0], [0, 0]]
|
|
x = [0, 1, 2]
|
|
p = PPoly(c, x)
|
|
assert_array_equal(p.roots(), [0, np.nan, 1, np.nan])
|
|
assert_array_equal(p.solve(0), [0, np.nan, 1, np.nan])
|
|
assert_array_equal(p.solve(1), [])
|
|
|
|
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), [])
|
|
|
|
# ditto for a discontinuity across y:
|
|
assert_array_equal(pp.solve(0.5), [0.5])
|
|
assert_array_equal(pp.solve(0.5, discontinuity=False), [])
|
|
|
|
assert_array_equal(pp.solve(1.5), [])
|
|
assert_array_equal(pp.solve(1.5, 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)
|
|
for y in [0, np.random.random()]:
|
|
r = pp.solve(y, 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]
|
|
msg = f"({extrapolate!r}) r = {repr(rr)}"
|
|
assert_allclose((val-y) / cmpval, 0, atol=1e-7,
|
|
err_msg=msg)
|
|
|
|
# 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
|
|
|
|
for y in [0, np.random.random()]:
|
|
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))
|
|
with np.errstate(invalid='ignore'):
|
|
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:
|
|
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_periodic(self):
|
|
x = [0, 1, 3]
|
|
c = [[3, 0], [0, 0], [0, 2]]
|
|
# [3*(1-x)**2, 2*((x-1)/2)**2]
|
|
bp = BPoly(c, x, extrapolate='periodic')
|
|
|
|
assert_allclose(bp(3.4), 3 * 0.6**2)
|
|
assert_allclose(bp(-1.3), 2 * (0.7/2)**2)
|
|
|
|
assert_allclose(bp(3.4, 1), -6 * 0.6)
|
|
assert_allclose(bp(-1.3, 1), 2 * (0.7/2))
|
|
|
|
def test_descending(self):
|
|
np.random.seed(0)
|
|
|
|
power = 3
|
|
for m in [10, 20, 30]:
|
|
x = np.sort(np.random.uniform(0, 10, m + 1))
|
|
ca = np.random.uniform(-0.1, 0.1, size=(power + 1, m))
|
|
# We need only to flip coefficients to get it right!
|
|
cd = ca[::-1].copy()
|
|
|
|
pa = BPoly(ca, x, extrapolate=True)
|
|
pd = BPoly(cd[:, ::-1], x[::-1], extrapolate=True)
|
|
|
|
x_test = np.random.uniform(-10, 20, 100)
|
|
assert_allclose(pa(x_test), pd(x_test), rtol=1e-13)
|
|
assert_allclose(pa(x_test, 1), pd(x_test, 1), rtol=1e-13)
|
|
|
|
pa_d = pa.derivative()
|
|
pd_d = pd.derivative()
|
|
|
|
assert_allclose(pa_d(x_test), pd_d(x_test), rtol=1e-13)
|
|
|
|
# Antiderivatives won't be equal because fixing continuity is
|
|
# done in the reverse order, but surely the differences should be
|
|
# equal.
|
|
pa_i = pa.antiderivative()
|
|
pd_i = pd.antiderivative()
|
|
for a, b in np.random.uniform(-10, 20, (5, 2)):
|
|
int_a = pa.integrate(a, b)
|
|
int_d = pd.integrate(a, b)
|
|
assert_allclose(int_a, int_d, rtol=1e-12)
|
|
assert_allclose(pa_i(b) - pa_i(a), pd_i(b) - pd_i(a),
|
|
rtol=1e-12)
|
|
|
|
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:
|
|
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))
|
|
|
|
# test both real and complex coefficients
|
|
for cc in [c.copy(), c*(1. + 2.j)]:
|
|
bp = BPoly(cc, x)
|
|
xp = np.linspace(x[0], x[-1], 21)
|
|
for i in range(k):
|
|
assert_allclose(bp(xp, i), bp.derivative(i)(xp))
|
|
|
|
def test_antiderivative_simple(self):
|
|
# f(x) = x for x \in [0, 1),
|
|
# (x-1)/2 for x \in [1, 3]
|
|
#
|
|
# antiderivative is then
|
|
# F(x) = x**2 / 2 for x \in [0, 1),
|
|
# 0.5*x*(x/2 - 1) + A for x \in [1, 3]
|
|
# where A = 3/4 for continuity at x = 1.
|
|
x = [0, 1, 3]
|
|
c = [[0, 0], [1, 1]]
|
|
|
|
bp = BPoly(c, x)
|
|
bi = bp.antiderivative()
|
|
|
|
xx = np.linspace(0, 3, 11)
|
|
assert_allclose(bi(xx),
|
|
np.where(xx < 1, xx**2 / 2.,
|
|
0.5 * xx * (xx/2. - 1) + 3./4),
|
|
atol=1e-12, rtol=1e-12)
|
|
|
|
def test_der_antider(self):
|
|
np.random.seed(1234)
|
|
x = np.sort(np.random.random(11))
|
|
c = np.random.random((4, 10, 2, 3))
|
|
bp = BPoly(c, x)
|
|
|
|
xx = np.linspace(x[0], x[-1], 100)
|
|
assert_allclose(bp.antiderivative().derivative()(xx),
|
|
bp(xx), atol=1e-12, rtol=1e-12)
|
|
|
|
def test_antider_ppoly(self):
|
|
np.random.seed(1234)
|
|
x = np.sort(np.random.random(11))
|
|
c = np.random.random((4, 10, 2, 3))
|
|
bp = BPoly(c, x)
|
|
pp = PPoly.from_bernstein_basis(bp)
|
|
|
|
xx = np.linspace(x[0], x[-1], 10)
|
|
|
|
assert_allclose(bp.antiderivative(2)(xx),
|
|
pp.antiderivative(2)(xx), atol=1e-12, rtol=1e-12)
|
|
|
|
def test_antider_continuous(self):
|
|
np.random.seed(1234)
|
|
x = np.sort(np.random.random(11))
|
|
c = np.random.random((4, 10))
|
|
bp = BPoly(c, x).antiderivative()
|
|
|
|
xx = bp.x[1:-1]
|
|
assert_allclose(bp(xx - 1e-14),
|
|
bp(xx + 1e-14), atol=1e-12, rtol=1e-12)
|
|
|
|
def test_integrate(self):
|
|
np.random.seed(1234)
|
|
x = np.sort(np.random.random(11))
|
|
c = np.random.random((4, 10))
|
|
bp = BPoly(c, x)
|
|
pp = PPoly.from_bernstein_basis(bp)
|
|
assert_allclose(bp.integrate(0, 1),
|
|
pp.integrate(0, 1), atol=1e-12, rtol=1e-12)
|
|
|
|
def test_integrate_extrap(self):
|
|
c = [[1]]
|
|
x = [0, 1]
|
|
b = BPoly(c, x)
|
|
|
|
# default is extrapolate=True
|
|
assert_allclose(b.integrate(0, 2), 2., atol=1e-14)
|
|
|
|
# .integrate argument overrides self.extrapolate
|
|
b1 = BPoly(c, x, extrapolate=False)
|
|
assert_(np.isnan(b1.integrate(0, 2)))
|
|
assert_allclose(b1.integrate(0, 2, extrapolate=True), 2., atol=1e-14)
|
|
|
|
def test_integrate_periodic(self):
|
|
x = np.array([1, 2, 4])
|
|
c = np.array([[0., 0.], [-1., -1.], [2., -0.], [1., 2.]])
|
|
|
|
P = BPoly.from_power_basis(PPoly(c, x), extrapolate='periodic')
|
|
I = P.antiderivative()
|
|
|
|
period_int = I(4) - I(1)
|
|
|
|
assert_allclose(P.integrate(1, 4), period_int)
|
|
assert_allclose(P.integrate(-10, -7), period_int)
|
|
assert_allclose(P.integrate(-10, -4), 2 * period_int)
|
|
|
|
assert_allclose(P.integrate(1.5, 2.5), I(2.5) - I(1.5))
|
|
assert_allclose(P.integrate(3.5, 5), I(2) - I(1) + I(4) - I(3.5))
|
|
assert_allclose(P.integrate(3.5 + 12, 5 + 12),
|
|
I(2) - I(1) + I(4) - I(3.5))
|
|
assert_allclose(P.integrate(3.5, 5 + 12),
|
|
I(2) - I(1) + I(4) - I(3.5) + 4 * period_int)
|
|
|
|
assert_allclose(P.integrate(0, -1), I(2) - I(3))
|
|
assert_allclose(P.integrate(-9, -10), I(2) - I(3))
|
|
assert_allclose(P.integrate(0, -10), I(2) - I(3) - 3 * period_int)
|
|
|
|
def test_antider_neg(self):
|
|
# .derivative(-nu) ==> .andiderivative(nu) and vice versa
|
|
c = [[1]]
|
|
x = [0, 1]
|
|
b = BPoly(c, x)
|
|
|
|
xx = np.linspace(0, 1, 21)
|
|
|
|
assert_allclose(b.derivative(-1)(xx), b.antiderivative()(xx),
|
|
atol=1e-12, rtol=1e-12)
|
|
assert_allclose(b.derivative(1)(xx), b.antiderivative(-1)(xx),
|
|
atol=1e-12, rtol=1e-12)
|
|
|
|
|
|
class TestPolyConversions:
|
|
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))
|
|
|
|
def test_broken_conversions(self):
|
|
# regression test for gh-10597: from_power_basis only accepts PPoly etc.
|
|
x = [0, 1, 3]
|
|
c = [[3, 3], [1, 1], [4, 2]]
|
|
pp = PPoly(c, x)
|
|
with assert_raises(TypeError):
|
|
PPoly.from_bernstein_basis(pp)
|
|
|
|
bp = BPoly(c, x)
|
|
with assert_raises(TypeError):
|
|
BPoly.from_power_basis(bp)
|
|
|
|
|
|
class TestBPolyFromDerivatives:
|
|
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)
|
|
|
|
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))
|
|
|
|
def test_gh_5430(self):
|
|
# At least one of these raises an error unless gh-5430 is
|
|
# fixed. In py2k an int is implemented using a C long, so
|
|
# which one fails depends on your system. In py3k there is only
|
|
# one arbitrary precision integer type, so both should fail.
|
|
orders = np.int32(1)
|
|
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
|
|
assert_almost_equal(p(0), 0)
|
|
orders = np.int64(1)
|
|
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
|
|
assert_almost_equal(p(0), 0)
|
|
orders = 1
|
|
# This worked before; make sure it still works
|
|
p = BPoly.from_derivatives([0, 1], [[0], [0]], orders=orders)
|
|
assert_almost_equal(p(0), 0)
|
|
orders = 1
|
|
|
|
|
|
class TestNdPPoly:
|
|
def test_simple_1d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5)
|
|
x = np.linspace(0, 1, 5+1)
|
|
|
|
xi = np.random.rand(200)
|
|
|
|
p = NdPPoly(c, (x,))
|
|
v1 = p((xi,))
|
|
|
|
v2 = _ppoly_eval_1(c[:,:,None], x, xi).ravel()
|
|
assert_allclose(v1, v2)
|
|
|
|
def test_simple_2d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5, 6, 7)
|
|
x = np.linspace(0, 1, 6+1)
|
|
y = np.linspace(0, 1, 7+1)**2
|
|
|
|
xi = np.random.rand(200)
|
|
yi = np.random.rand(200)
|
|
|
|
v1 = np.empty([len(xi), 1], dtype=c.dtype)
|
|
v1.fill(np.nan)
|
|
_ppoly.evaluate_nd(c.reshape(4*5, 6*7, 1),
|
|
(x, y),
|
|
np.array([4, 5], dtype=np.intc),
|
|
np.c_[xi, yi],
|
|
np.array([0, 0], dtype=np.intc),
|
|
1,
|
|
v1)
|
|
v1 = v1.ravel()
|
|
v2 = _ppoly2d_eval(c, (x, y), xi, yi)
|
|
assert_allclose(v1, v2)
|
|
|
|
p = NdPPoly(c, (x, y))
|
|
for nu in (None, (0, 0), (0, 1), (1, 0), (2, 3), (9, 2)):
|
|
v1 = p(np.c_[xi, yi], nu=nu)
|
|
v2 = _ppoly2d_eval(c, (x, y), xi, yi, nu=nu)
|
|
assert_allclose(v1, v2, err_msg=repr(nu))
|
|
|
|
def test_simple_3d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5, 6, 7, 8, 9)
|
|
x = np.linspace(0, 1, 7+1)
|
|
y = np.linspace(0, 1, 8+1)**2
|
|
z = np.linspace(0, 1, 9+1)**3
|
|
|
|
xi = np.random.rand(40)
|
|
yi = np.random.rand(40)
|
|
zi = np.random.rand(40)
|
|
|
|
p = NdPPoly(c, (x, y, z))
|
|
|
|
for nu in (None, (0, 0, 0), (0, 1, 0), (1, 0, 0), (2, 3, 0),
|
|
(6, 0, 2)):
|
|
v1 = p((xi, yi, zi), nu=nu)
|
|
v2 = _ppoly3d_eval(c, (x, y, z), xi, yi, zi, nu=nu)
|
|
assert_allclose(v1, v2, err_msg=repr(nu))
|
|
|
|
def test_simple_4d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5, 6, 7, 8, 9, 10, 11)
|
|
x = np.linspace(0, 1, 8+1)
|
|
y = np.linspace(0, 1, 9+1)**2
|
|
z = np.linspace(0, 1, 10+1)**3
|
|
u = np.linspace(0, 1, 11+1)**4
|
|
|
|
xi = np.random.rand(20)
|
|
yi = np.random.rand(20)
|
|
zi = np.random.rand(20)
|
|
ui = np.random.rand(20)
|
|
|
|
p = NdPPoly(c, (x, y, z, u))
|
|
v1 = p((xi, yi, zi, ui))
|
|
|
|
v2 = _ppoly4d_eval(c, (x, y, z, u), xi, yi, zi, ui)
|
|
assert_allclose(v1, v2)
|
|
|
|
def test_deriv_1d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5)
|
|
x = np.linspace(0, 1, 5+1)
|
|
|
|
p = NdPPoly(c, (x,))
|
|
|
|
# derivative
|
|
dp = p.derivative(nu=[1])
|
|
p1 = PPoly(c, x)
|
|
dp1 = p1.derivative()
|
|
assert_allclose(dp.c, dp1.c)
|
|
|
|
# antiderivative
|
|
dp = p.antiderivative(nu=[2])
|
|
p1 = PPoly(c, x)
|
|
dp1 = p1.antiderivative(2)
|
|
assert_allclose(dp.c, dp1.c)
|
|
|
|
def test_deriv_3d(self):
|
|
np.random.seed(1234)
|
|
|
|
c = np.random.rand(4, 5, 6, 7, 8, 9)
|
|
x = np.linspace(0, 1, 7+1)
|
|
y = np.linspace(0, 1, 8+1)**2
|
|
z = np.linspace(0, 1, 9+1)**3
|
|
|
|
p = NdPPoly(c, (x, y, z))
|
|
|
|
# differentiate vs x
|
|
p1 = PPoly(c.transpose(0, 3, 1, 2, 4, 5), x)
|
|
dp = p.derivative(nu=[2])
|
|
dp1 = p1.derivative(2)
|
|
assert_allclose(dp.c,
|
|
dp1.c.transpose(0, 2, 3, 1, 4, 5))
|
|
|
|
# antidifferentiate vs y
|
|
p1 = PPoly(c.transpose(1, 4, 0, 2, 3, 5), y)
|
|
dp = p.antiderivative(nu=[0, 1, 0])
|
|
dp1 = p1.antiderivative(1)
|
|
assert_allclose(dp.c,
|
|
dp1.c.transpose(2, 0, 3, 4, 1, 5))
|
|
|
|
# differentiate vs z
|
|
p1 = PPoly(c.transpose(2, 5, 0, 1, 3, 4), z)
|
|
dp = p.derivative(nu=[0, 0, 3])
|
|
dp1 = p1.derivative(3)
|
|
assert_allclose(dp.c,
|
|
dp1.c.transpose(2, 3, 0, 4, 5, 1))
|
|
|
|
def test_deriv_3d_simple(self):
|
|
# Integrate to obtain function x y**2 z**4 / (2! 4!)
|
|
|
|
c = np.ones((1, 1, 1, 3, 4, 5))
|
|
x = np.linspace(0, 1, 3+1)**1
|
|
y = np.linspace(0, 1, 4+1)**2
|
|
z = np.linspace(0, 1, 5+1)**3
|
|
|
|
p = NdPPoly(c, (x, y, z))
|
|
ip = p.antiderivative((1, 0, 4))
|
|
ip = ip.antiderivative((0, 2, 0))
|
|
|
|
xi = np.random.rand(20)
|
|
yi = np.random.rand(20)
|
|
zi = np.random.rand(20)
|
|
|
|
assert_allclose(ip((xi, yi, zi)),
|
|
xi * yi**2 * zi**4 / (gamma(3)*gamma(5)))
|
|
|
|
def test_integrate_2d(self):
|
|
np.random.seed(1234)
|
|
c = np.random.rand(4, 5, 16, 17)
|
|
x = np.linspace(0, 1, 16+1)**1
|
|
y = np.linspace(0, 1, 17+1)**2
|
|
|
|
# make continuously differentiable so that nquad() has an
|
|
# easier time
|
|
c = c.transpose(0, 2, 1, 3)
|
|
cx = c.reshape(c.shape[0], c.shape[1], -1).copy()
|
|
_ppoly.fix_continuity(cx, x, 2)
|
|
c = cx.reshape(c.shape)
|
|
c = c.transpose(0, 2, 1, 3)
|
|
c = c.transpose(1, 3, 0, 2)
|
|
cx = c.reshape(c.shape[0], c.shape[1], -1).copy()
|
|
_ppoly.fix_continuity(cx, y, 2)
|
|
c = cx.reshape(c.shape)
|
|
c = c.transpose(2, 0, 3, 1).copy()
|
|
|
|
# Check integration
|
|
p = NdPPoly(c, (x, y))
|
|
|
|
for ranges in [[(0, 1), (0, 1)],
|
|
[(0, 0.5), (0, 1)],
|
|
[(0, 1), (0, 0.5)],
|
|
[(0.3, 0.7), (0.6, 0.2)]]:
|
|
|
|
ig = p.integrate(ranges)
|
|
ig2, err2 = nquad(lambda x, y: p((x, y)), ranges,
|
|
opts=[dict(epsrel=1e-5, epsabs=1e-5)]*2)
|
|
assert_allclose(ig, ig2, rtol=1e-5, atol=1e-5,
|
|
err_msg=repr(ranges))
|
|
|
|
def test_integrate_1d(self):
|
|
np.random.seed(1234)
|
|
c = np.random.rand(4, 5, 6, 16, 17, 18)
|
|
x = np.linspace(0, 1, 16+1)**1
|
|
y = np.linspace(0, 1, 17+1)**2
|
|
z = np.linspace(0, 1, 18+1)**3
|
|
|
|
# Check 1-D integration
|
|
p = NdPPoly(c, (x, y, z))
|
|
|
|
u = np.random.rand(200)
|
|
v = np.random.rand(200)
|
|
a, b = 0.2, 0.7
|
|
|
|
px = p.integrate_1d(a, b, axis=0)
|
|
pax = p.antiderivative((1, 0, 0))
|
|
assert_allclose(px((u, v)), pax((b, u, v)) - pax((a, u, v)))
|
|
|
|
py = p.integrate_1d(a, b, axis=1)
|
|
pay = p.antiderivative((0, 1, 0))
|
|
assert_allclose(py((u, v)), pay((u, b, v)) - pay((u, a, v)))
|
|
|
|
pz = p.integrate_1d(a, b, axis=2)
|
|
paz = p.antiderivative((0, 0, 1))
|
|
assert_allclose(pz((u, v)), paz((u, v, b)) - paz((u, v, a)))
|
|
|
|
|
|
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 range(len(xx))])
|
|
res[mask] = values
|
|
res.shape = saveshape
|
|
return res
|
|
|
|
|
|
def _dpow(x, y, n):
|
|
"""
|
|
d^n (x**y) / dx^n
|
|
"""
|
|
if n < 0:
|
|
raise ValueError("invalid derivative order")
|
|
elif n > y:
|
|
return 0
|
|
else:
|
|
return poch(y - n + 1, n) * x**(y - n)
|
|
|
|
|
|
def _ppoly2d_eval(c, xs, xnew, ynew, nu=None):
|
|
"""
|
|
Straightforward evaluation of 2-D piecewise polynomial
|
|
"""
|
|
if nu is None:
|
|
nu = (0, 0)
|
|
|
|
out = np.empty((len(xnew),), dtype=c.dtype)
|
|
|
|
nx, ny = c.shape[:2]
|
|
|
|
for jout, (x, y) in enumerate(zip(xnew, ynew)):
|
|
if not ((xs[0][0] <= x <= xs[0][-1]) and
|
|
(xs[1][0] <= y <= xs[1][-1])):
|
|
out[jout] = np.nan
|
|
continue
|
|
|
|
j1 = np.searchsorted(xs[0], x) - 1
|
|
j2 = np.searchsorted(xs[1], y) - 1
|
|
|
|
s1 = x - xs[0][j1]
|
|
s2 = y - xs[1][j2]
|
|
|
|
val = 0
|
|
|
|
for k1 in range(c.shape[0]):
|
|
for k2 in range(c.shape[1]):
|
|
val += (c[nx-k1-1,ny-k2-1,j1,j2]
|
|
* _dpow(s1, k1, nu[0])
|
|
* _dpow(s2, k2, nu[1]))
|
|
|
|
out[jout] = val
|
|
|
|
return out
|
|
|
|
|
|
def _ppoly3d_eval(c, xs, xnew, ynew, znew, nu=None):
|
|
"""
|
|
Straightforward evaluation of 3-D piecewise polynomial
|
|
"""
|
|
if nu is None:
|
|
nu = (0, 0, 0)
|
|
|
|
out = np.empty((len(xnew),), dtype=c.dtype)
|
|
|
|
nx, ny, nz = c.shape[:3]
|
|
|
|
for jout, (x, y, z) in enumerate(zip(xnew, ynew, znew)):
|
|
if not ((xs[0][0] <= x <= xs[0][-1]) and
|
|
(xs[1][0] <= y <= xs[1][-1]) and
|
|
(xs[2][0] <= z <= xs[2][-1])):
|
|
out[jout] = np.nan
|
|
continue
|
|
|
|
j1 = np.searchsorted(xs[0], x) - 1
|
|
j2 = np.searchsorted(xs[1], y) - 1
|
|
j3 = np.searchsorted(xs[2], z) - 1
|
|
|
|
s1 = x - xs[0][j1]
|
|
s2 = y - xs[1][j2]
|
|
s3 = z - xs[2][j3]
|
|
|
|
val = 0
|
|
for k1 in range(c.shape[0]):
|
|
for k2 in range(c.shape[1]):
|
|
for k3 in range(c.shape[2]):
|
|
val += (c[nx-k1-1,ny-k2-1,nz-k3-1,j1,j2,j3]
|
|
* _dpow(s1, k1, nu[0])
|
|
* _dpow(s2, k2, nu[1])
|
|
* _dpow(s3, k3, nu[2]))
|
|
|
|
out[jout] = val
|
|
|
|
return out
|
|
|
|
|
|
def _ppoly4d_eval(c, xs, xnew, ynew, znew, unew, nu=None):
|
|
"""
|
|
Straightforward evaluation of 4-D piecewise polynomial
|
|
"""
|
|
if nu is None:
|
|
nu = (0, 0, 0, 0)
|
|
|
|
out = np.empty((len(xnew),), dtype=c.dtype)
|
|
|
|
mx, my, mz, mu = c.shape[:4]
|
|
|
|
for jout, (x, y, z, u) in enumerate(zip(xnew, ynew, znew, unew)):
|
|
if not ((xs[0][0] <= x <= xs[0][-1]) and
|
|
(xs[1][0] <= y <= xs[1][-1]) and
|
|
(xs[2][0] <= z <= xs[2][-1]) and
|
|
(xs[3][0] <= u <= xs[3][-1])):
|
|
out[jout] = np.nan
|
|
continue
|
|
|
|
j1 = np.searchsorted(xs[0], x) - 1
|
|
j2 = np.searchsorted(xs[1], y) - 1
|
|
j3 = np.searchsorted(xs[2], z) - 1
|
|
j4 = np.searchsorted(xs[3], u) - 1
|
|
|
|
s1 = x - xs[0][j1]
|
|
s2 = y - xs[1][j2]
|
|
s3 = z - xs[2][j3]
|
|
s4 = u - xs[3][j4]
|
|
|
|
val = 0
|
|
for k1 in range(c.shape[0]):
|
|
for k2 in range(c.shape[1]):
|
|
for k3 in range(c.shape[2]):
|
|
for k4 in range(c.shape[3]):
|
|
val += (c[mx-k1-1,my-k2-1,mz-k3-1,mu-k4-1,j1,j2,j3,j4]
|
|
* _dpow(s1, k1, nu[0])
|
|
* _dpow(s2, k2, nu[1])
|
|
* _dpow(s3, k3, nu[2])
|
|
* _dpow(s4, k4, nu[3]))
|
|
|
|
out[jout] = val
|
|
|
|
return out
|