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387 lines
13 KiB
Python
387 lines
13 KiB
Python
import os
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import numpy as np
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from numpy.testing import (assert_equal, assert_allclose, assert_almost_equal,
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suppress_warnings)
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from pytest import raises as assert_raises
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import pytest
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import scipy.interpolate.interpnd as interpnd
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import scipy.spatial.qhull as qhull
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import pickle
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def data_file(basename):
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return os.path.join(os.path.abspath(os.path.dirname(__file__)),
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'data', basename)
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class TestLinearNDInterpolation(object):
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def test_smoketest(self):
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# Test at single points
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x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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yi = interpnd.LinearNDInterpolator(x, y)(x)
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assert_almost_equal(y, yi)
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def test_smoketest_alternate(self):
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# Test at single points, alternate calling convention
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x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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yi = interpnd.LinearNDInterpolator((x[:,0], x[:,1]), y)(x[:,0], x[:,1])
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assert_almost_equal(y, yi)
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def test_complex_smoketest(self):
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# Test at single points
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x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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yi = interpnd.LinearNDInterpolator(x, y)(x)
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assert_almost_equal(y, yi)
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def test_tri_input(self):
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# Test at single points
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x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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yi = interpnd.LinearNDInterpolator(tri, y)(x)
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assert_almost_equal(y, yi)
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def test_square(self):
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# Test barycentric interpolation on a square against a manual
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# implementation
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points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.double)
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values = np.array([1., 2., -3., 5.], dtype=np.double)
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# NB: assume triangles (0, 1, 3) and (1, 2, 3)
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#
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# 1----2
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# | \ |
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# | \ |
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# 0----3
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def ip(x, y):
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t1 = (x + y <= 1)
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t2 = ~t1
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x1 = x[t1]
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y1 = y[t1]
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x2 = x[t2]
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y2 = y[t2]
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z = 0*x
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z[t1] = (values[0]*(1 - x1 - y1)
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+ values[1]*y1
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+ values[3]*x1)
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z[t2] = (values[2]*(x2 + y2 - 1)
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+ values[1]*(1 - x2)
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+ values[3]*(1 - y2))
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return z
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xx, yy = np.broadcast_arrays(np.linspace(0, 1, 14)[:,None],
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np.linspace(0, 1, 14)[None,:])
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xx = xx.ravel()
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yy = yy.ravel()
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xi = np.array([xx, yy]).T.copy()
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zi = interpnd.LinearNDInterpolator(points, values)(xi)
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assert_almost_equal(zi, ip(xx, yy))
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def test_smoketest_rescale(self):
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# Test at single points
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x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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yi = interpnd.LinearNDInterpolator(x, y, rescale=True)(x)
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assert_almost_equal(y, yi)
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def test_square_rescale(self):
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# Test barycentric interpolation on a rectangle with rescaling
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# agaings the same implementation without rescaling
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points = np.array([(0,0), (0,100), (10,100), (10,0)], dtype=np.double)
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values = np.array([1., 2., -3., 5.], dtype=np.double)
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xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None],
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np.linspace(0, 100, 14)[None,:])
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xx = xx.ravel()
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yy = yy.ravel()
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xi = np.array([xx, yy]).T.copy()
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zi = interpnd.LinearNDInterpolator(points, values)(xi)
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zi_rescaled = interpnd.LinearNDInterpolator(points, values,
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rescale=True)(xi)
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assert_almost_equal(zi, zi_rescaled)
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def test_tripoints_input_rescale(self):
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# Test at single points
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x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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yi = interpnd.LinearNDInterpolator(tri.points, y)(x)
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yi_rescale = interpnd.LinearNDInterpolator(tri.points, y,
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rescale=True)(x)
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assert_almost_equal(yi, yi_rescale)
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def test_tri_input_rescale(self):
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# Test at single points
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x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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match = ("Rescaling is not supported when passing a "
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"Delaunay triangulation as ``points``.")
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with pytest.raises(ValueError, match=match):
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interpnd.LinearNDInterpolator(tri, y, rescale=True)(x)
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def test_pickle(self):
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# Test at single points
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np.random.seed(1234)
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x = np.random.rand(30, 2)
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y = np.random.rand(30) + 1j*np.random.rand(30)
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ip = interpnd.LinearNDInterpolator(x, y)
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ip2 = pickle.loads(pickle.dumps(ip))
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assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
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class TestEstimateGradients2DGlobal(object):
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def test_smoketest(self):
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x = np.array([(0, 0), (0, 2),
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(1, 0), (1, 2), (0.25, 0.75), (0.6, 0.8)], dtype=float)
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tri = qhull.Delaunay(x)
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# Should be exact for linear functions, independent of triangulation
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funcs = [
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(lambda x, y: 0*x + 1, (0, 0)),
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(lambda x, y: 0 + x, (1, 0)),
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(lambda x, y: -2 + y, (0, 1)),
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(lambda x, y: 3 + 3*x + 14.15*y, (3, 14.15))
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]
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for j, (func, grad) in enumerate(funcs):
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z = func(x[:,0], x[:,1])
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dz = interpnd.estimate_gradients_2d_global(tri, z, tol=1e-6)
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assert_equal(dz.shape, (6, 2))
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assert_allclose(dz, np.array(grad)[None,:] + 0*dz,
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rtol=1e-5, atol=1e-5, err_msg="item %d" % j)
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def test_regression_2359(self):
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# Check regression --- for certain point sets, gradient
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# estimation could end up in an infinite loop
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points = np.load(data_file('estimate_gradients_hang.npy'))
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values = np.random.rand(points.shape[0])
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tri = qhull.Delaunay(points)
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# This should not hang
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with suppress_warnings() as sup:
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sup.filter(interpnd.GradientEstimationWarning,
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"Gradient estimation did not converge")
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interpnd.estimate_gradients_2d_global(tri, values, maxiter=1)
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class TestCloughTocher2DInterpolator(object):
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def _check_accuracy(self, func, x=None, tol=1e-6, alternate=False, rescale=False, **kw):
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np.random.seed(1234)
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if x is None:
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x = np.array([(0, 0), (0, 1),
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(1, 0), (1, 1), (0.25, 0.75), (0.6, 0.8),
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(0.5, 0.2)],
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dtype=float)
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if not alternate:
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ip = interpnd.CloughTocher2DInterpolator(x, func(x[:,0], x[:,1]),
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tol=1e-6, rescale=rescale)
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else:
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ip = interpnd.CloughTocher2DInterpolator((x[:,0], x[:,1]),
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func(x[:,0], x[:,1]),
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tol=1e-6, rescale=rescale)
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p = np.random.rand(50, 2)
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if not alternate:
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a = ip(p)
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else:
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a = ip(p[:,0], p[:,1])
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b = func(p[:,0], p[:,1])
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try:
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assert_allclose(a, b, **kw)
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except AssertionError:
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print("_check_accuracy: abs(a-b):", abs(a - b))
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print("ip.grad:", ip.grad)
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raise
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def test_linear_smoketest(self):
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# Should be exact for linear functions, independent of triangulation
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funcs = [
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lambda x, y: 0*x + 1,
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lambda x, y: 0 + x,
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lambda x, y: -2 + y,
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lambda x, y: 3 + 3*x + 14.15*y,
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]
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for j, func in enumerate(funcs):
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self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
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err_msg="Function %d" % j)
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self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
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alternate=True,
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err_msg="Function (alternate) %d" % j)
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# check rescaling
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self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
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err_msg="Function (rescaled) %d" % j, rescale=True)
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self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
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alternate=True, rescale=True,
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err_msg="Function (alternate, rescaled) %d" % j)
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def test_quadratic_smoketest(self):
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# Should be reasonably accurate for quadratic functions
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funcs = [
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lambda x, y: x**2,
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lambda x, y: y**2,
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lambda x, y: x**2 - y**2,
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lambda x, y: x*y,
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]
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for j, func in enumerate(funcs):
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self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
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err_msg="Function %d" % j)
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self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
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err_msg="Function %d" % j, rescale=True)
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def test_tri_input(self):
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# Test at single points
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x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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yi = interpnd.CloughTocher2DInterpolator(tri, y)(x)
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assert_almost_equal(y, yi)
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def test_tri_input_rescale(self):
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# Test at single points
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x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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match = ("Rescaling is not supported when passing a "
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"Delaunay triangulation as ``points``.")
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with pytest.raises(ValueError, match=match):
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interpnd.CloughTocher2DInterpolator(tri, y, rescale=True)(x)
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def test_tripoints_input_rescale(self):
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# Test at single points
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x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
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dtype=np.double)
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y = np.arange(x.shape[0], dtype=np.double)
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y = y - 3j*y
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tri = qhull.Delaunay(x)
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yi = interpnd.CloughTocher2DInterpolator(tri.points, y)(x)
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yi_rescale = interpnd.CloughTocher2DInterpolator(tri.points, y, rescale=True)(x)
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assert_almost_equal(yi, yi_rescale)
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def test_dense(self):
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# Should be more accurate for dense meshes
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funcs = [
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lambda x, y: x**2,
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lambda x, y: y**2,
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lambda x, y: x**2 - y**2,
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lambda x, y: x*y,
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lambda x, y: np.cos(2*np.pi*x)*np.sin(2*np.pi*y)
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]
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np.random.seed(4321) # use a different seed than the check!
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grid = np.r_[np.array([(0,0), (0,1), (1,0), (1,1)], dtype=float),
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np.random.rand(30*30, 2)]
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for j, func in enumerate(funcs):
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self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
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err_msg="Function %d" % j)
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self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
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err_msg="Function %d" % j, rescale=True)
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def test_wrong_ndim(self):
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x = np.random.randn(30, 3)
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y = np.random.randn(30)
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assert_raises(ValueError, interpnd.CloughTocher2DInterpolator, x, y)
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def test_pickle(self):
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# Test at single points
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np.random.seed(1234)
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x = np.random.rand(30, 2)
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y = np.random.rand(30) + 1j*np.random.rand(30)
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ip = interpnd.CloughTocher2DInterpolator(x, y)
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ip2 = pickle.loads(pickle.dumps(ip))
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assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
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def test_boundary_tri_symmetry(self):
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# Interpolation at neighbourless triangles should retain
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# symmetry with mirroring the triangle.
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# Equilateral triangle
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points = np.array([(0, 0), (1, 0), (0.5, np.sqrt(3)/2)])
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values = np.array([1, 0, 0])
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ip = interpnd.CloughTocher2DInterpolator(points, values)
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# Set gradient to zero at vertices
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ip.grad[...] = 0
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# Interpolation should be symmetric vs. bisector
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alpha = 0.3
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p1 = np.array([0.5 * np.cos(alpha), 0.5 * np.sin(alpha)])
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p2 = np.array([0.5 * np.cos(np.pi/3 - alpha), 0.5 * np.sin(np.pi/3 - alpha)])
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v1 = ip(p1)
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v2 = ip(p2)
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assert_allclose(v1, v2)
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# ... and affine invariant
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np.random.seed(1)
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A = np.random.randn(2, 2)
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b = np.random.randn(2)
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points = A.dot(points.T).T + b[None,:]
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p1 = A.dot(p1) + b
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p2 = A.dot(p2) + b
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ip = interpnd.CloughTocher2DInterpolator(points, values)
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ip.grad[...] = 0
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w1 = ip(p1)
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w2 = ip(p2)
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assert_allclose(w1, v1)
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assert_allclose(w2, v2)
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