You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
389 lines
13 KiB
Python
389 lines
13 KiB
Python
from __future__ import division, print_function, absolute_import
|
|
|
|
import os
|
|
|
|
import numpy as np
|
|
from numpy.testing import assert_equal, assert_allclose, assert_almost_equal
|
|
from pytest import raises as assert_raises
|
|
import pytest
|
|
from scipy._lib._numpy_compat import suppress_warnings
|
|
|
|
import scipy.interpolate.interpnd as interpnd
|
|
import scipy.spatial.qhull as qhull
|
|
|
|
import pickle
|
|
|
|
|
|
def data_file(basename):
|
|
return os.path.join(os.path.abspath(os.path.dirname(__file__)),
|
|
'data', basename)
|
|
|
|
|
|
class TestLinearNDInterpolation(object):
|
|
def test_smoketest(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
|
|
yi = interpnd.LinearNDInterpolator(x, y)(x)
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_smoketest_alternate(self):
|
|
# Test at single points, alternate calling convention
|
|
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
|
|
yi = interpnd.LinearNDInterpolator((x[:,0], x[:,1]), y)(x[:,0], x[:,1])
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_complex_smoketest(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
yi = interpnd.LinearNDInterpolator(x, y)(x)
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_tri_input(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
yi = interpnd.LinearNDInterpolator(tri, y)(x)
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_square(self):
|
|
# Test barycentric interpolation on a square against a manual
|
|
# implementation
|
|
|
|
points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.double)
|
|
values = np.array([1., 2., -3., 5.], dtype=np.double)
|
|
|
|
# NB: assume triangles (0, 1, 3) and (1, 2, 3)
|
|
#
|
|
# 1----2
|
|
# | \ |
|
|
# | \ |
|
|
# 0----3
|
|
|
|
def ip(x, y):
|
|
t1 = (x + y <= 1)
|
|
t2 = ~t1
|
|
|
|
x1 = x[t1]
|
|
y1 = y[t1]
|
|
|
|
x2 = x[t2]
|
|
y2 = y[t2]
|
|
|
|
z = 0*x
|
|
|
|
z[t1] = (values[0]*(1 - x1 - y1)
|
|
+ values[1]*y1
|
|
+ values[3]*x1)
|
|
|
|
z[t2] = (values[2]*(x2 + y2 - 1)
|
|
+ values[1]*(1 - x2)
|
|
+ values[3]*(1 - y2))
|
|
return z
|
|
|
|
xx, yy = np.broadcast_arrays(np.linspace(0, 1, 14)[:,None],
|
|
np.linspace(0, 1, 14)[None,:])
|
|
xx = xx.ravel()
|
|
yy = yy.ravel()
|
|
|
|
xi = np.array([xx, yy]).T.copy()
|
|
zi = interpnd.LinearNDInterpolator(points, values)(xi)
|
|
|
|
assert_almost_equal(zi, ip(xx, yy))
|
|
|
|
def test_smoketest_rescale(self):
|
|
# Test at single points
|
|
x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
|
|
yi = interpnd.LinearNDInterpolator(x, y, rescale=True)(x)
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_square_rescale(self):
|
|
# Test barycentric interpolation on a rectangle with rescaling
|
|
# agaings the same implementation without rescaling
|
|
|
|
points = np.array([(0,0), (0,100), (10,100), (10,0)], dtype=np.double)
|
|
values = np.array([1., 2., -3., 5.], dtype=np.double)
|
|
|
|
xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None],
|
|
np.linspace(0, 100, 14)[None,:])
|
|
xx = xx.ravel()
|
|
yy = yy.ravel()
|
|
xi = np.array([xx, yy]).T.copy()
|
|
zi = interpnd.LinearNDInterpolator(points, values)(xi)
|
|
zi_rescaled = interpnd.LinearNDInterpolator(points, values,
|
|
rescale=True)(xi)
|
|
|
|
assert_almost_equal(zi, zi_rescaled)
|
|
|
|
def test_tripoints_input_rescale(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
yi = interpnd.LinearNDInterpolator(tri.points, y)(x)
|
|
yi_rescale = interpnd.LinearNDInterpolator(tri.points, y,
|
|
rescale=True)(x)
|
|
assert_almost_equal(yi, yi_rescale)
|
|
|
|
def test_tri_input_rescale(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
match = ("Rescaling is not supported when passing a "
|
|
"Delaunay triangulation as ``points``.")
|
|
with pytest.raises(ValueError, match=match):
|
|
interpnd.LinearNDInterpolator(tri, y, rescale=True)(x)
|
|
|
|
def test_pickle(self):
|
|
# Test at single points
|
|
np.random.seed(1234)
|
|
x = np.random.rand(30, 2)
|
|
y = np.random.rand(30) + 1j*np.random.rand(30)
|
|
|
|
ip = interpnd.LinearNDInterpolator(x, y)
|
|
ip2 = pickle.loads(pickle.dumps(ip))
|
|
|
|
assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
|
|
|
|
|
|
class TestEstimateGradients2DGlobal(object):
|
|
def test_smoketest(self):
|
|
x = np.array([(0, 0), (0, 2),
|
|
(1, 0), (1, 2), (0.25, 0.75), (0.6, 0.8)], dtype=float)
|
|
tri = qhull.Delaunay(x)
|
|
|
|
# Should be exact for linear functions, independent of triangulation
|
|
|
|
funcs = [
|
|
(lambda x, y: 0*x + 1, (0, 0)),
|
|
(lambda x, y: 0 + x, (1, 0)),
|
|
(lambda x, y: -2 + y, (0, 1)),
|
|
(lambda x, y: 3 + 3*x + 14.15*y, (3, 14.15))
|
|
]
|
|
|
|
for j, (func, grad) in enumerate(funcs):
|
|
z = func(x[:,0], x[:,1])
|
|
dz = interpnd.estimate_gradients_2d_global(tri, z, tol=1e-6)
|
|
|
|
assert_equal(dz.shape, (6, 2))
|
|
assert_allclose(dz, np.array(grad)[None,:] + 0*dz,
|
|
rtol=1e-5, atol=1e-5, err_msg="item %d" % j)
|
|
|
|
def test_regression_2359(self):
|
|
# Check regression --- for certain point sets, gradient
|
|
# estimation could end up in an infinite loop
|
|
points = np.load(data_file('estimate_gradients_hang.npy'))
|
|
values = np.random.rand(points.shape[0])
|
|
tri = qhull.Delaunay(points)
|
|
|
|
# This should not hang
|
|
with suppress_warnings() as sup:
|
|
sup.filter(interpnd.GradientEstimationWarning,
|
|
"Gradient estimation did not converge")
|
|
interpnd.estimate_gradients_2d_global(tri, values, maxiter=1)
|
|
|
|
|
|
class TestCloughTocher2DInterpolator(object):
|
|
|
|
def _check_accuracy(self, func, x=None, tol=1e-6, alternate=False, rescale=False, **kw):
|
|
np.random.seed(1234)
|
|
if x is None:
|
|
x = np.array([(0, 0), (0, 1),
|
|
(1, 0), (1, 1), (0.25, 0.75), (0.6, 0.8),
|
|
(0.5, 0.2)],
|
|
dtype=float)
|
|
|
|
if not alternate:
|
|
ip = interpnd.CloughTocher2DInterpolator(x, func(x[:,0], x[:,1]),
|
|
tol=1e-6, rescale=rescale)
|
|
else:
|
|
ip = interpnd.CloughTocher2DInterpolator((x[:,0], x[:,1]),
|
|
func(x[:,0], x[:,1]),
|
|
tol=1e-6, rescale=rescale)
|
|
|
|
p = np.random.rand(50, 2)
|
|
|
|
if not alternate:
|
|
a = ip(p)
|
|
else:
|
|
a = ip(p[:,0], p[:,1])
|
|
b = func(p[:,0], p[:,1])
|
|
|
|
try:
|
|
assert_allclose(a, b, **kw)
|
|
except AssertionError:
|
|
print(abs(a - b))
|
|
print(ip.grad)
|
|
raise
|
|
|
|
def test_linear_smoketest(self):
|
|
# Should be exact for linear functions, independent of triangulation
|
|
funcs = [
|
|
lambda x, y: 0*x + 1,
|
|
lambda x, y: 0 + x,
|
|
lambda x, y: -2 + y,
|
|
lambda x, y: 3 + 3*x + 14.15*y,
|
|
]
|
|
|
|
for j, func in enumerate(funcs):
|
|
self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
|
|
err_msg="Function %d" % j)
|
|
self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
|
|
alternate=True,
|
|
err_msg="Function (alternate) %d" % j)
|
|
# check rescaling
|
|
self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
|
|
err_msg="Function (rescaled) %d" % j, rescale=True)
|
|
self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
|
|
alternate=True, rescale=True,
|
|
err_msg="Function (alternate, rescaled) %d" % j)
|
|
|
|
def test_quadratic_smoketest(self):
|
|
# Should be reasonably accurate for quadratic functions
|
|
funcs = [
|
|
lambda x, y: x**2,
|
|
lambda x, y: y**2,
|
|
lambda x, y: x**2 - y**2,
|
|
lambda x, y: x*y,
|
|
]
|
|
|
|
for j, func in enumerate(funcs):
|
|
self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
|
|
err_msg="Function %d" % j)
|
|
self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
|
|
err_msg="Function %d" % j, rescale=True)
|
|
|
|
def test_tri_input(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
yi = interpnd.CloughTocher2DInterpolator(tri, y)(x)
|
|
assert_almost_equal(y, yi)
|
|
|
|
def test_tri_input_rescale(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
match = ("Rescaling is not supported when passing a "
|
|
"Delaunay triangulation as ``points``.")
|
|
with pytest.raises(ValueError, match=match):
|
|
interpnd.CloughTocher2DInterpolator(tri, y, rescale=True)(x)
|
|
|
|
def test_tripoints_input_rescale(self):
|
|
# Test at single points
|
|
x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
|
|
dtype=np.double)
|
|
y = np.arange(x.shape[0], dtype=np.double)
|
|
y = y - 3j*y
|
|
|
|
tri = qhull.Delaunay(x)
|
|
yi = interpnd.CloughTocher2DInterpolator(tri.points, y)(x)
|
|
yi_rescale = interpnd.CloughTocher2DInterpolator(tri.points, y, rescale=True)(x)
|
|
assert_almost_equal(yi, yi_rescale)
|
|
|
|
def test_dense(self):
|
|
# Should be more accurate for dense meshes
|
|
funcs = [
|
|
lambda x, y: x**2,
|
|
lambda x, y: y**2,
|
|
lambda x, y: x**2 - y**2,
|
|
lambda x, y: x*y,
|
|
lambda x, y: np.cos(2*np.pi*x)*np.sin(2*np.pi*y)
|
|
]
|
|
|
|
np.random.seed(4321) # use a different seed than the check!
|
|
grid = np.r_[np.array([(0,0), (0,1), (1,0), (1,1)], dtype=float),
|
|
np.random.rand(30*30, 2)]
|
|
|
|
for j, func in enumerate(funcs):
|
|
self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
|
|
err_msg="Function %d" % j)
|
|
self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
|
|
err_msg="Function %d" % j, rescale=True)
|
|
|
|
def test_wrong_ndim(self):
|
|
x = np.random.randn(30, 3)
|
|
y = np.random.randn(30)
|
|
assert_raises(ValueError, interpnd.CloughTocher2DInterpolator, x, y)
|
|
|
|
def test_pickle(self):
|
|
# Test at single points
|
|
np.random.seed(1234)
|
|
x = np.random.rand(30, 2)
|
|
y = np.random.rand(30) + 1j*np.random.rand(30)
|
|
|
|
ip = interpnd.CloughTocher2DInterpolator(x, y)
|
|
ip2 = pickle.loads(pickle.dumps(ip))
|
|
|
|
assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
|
|
|
|
def test_boundary_tri_symmetry(self):
|
|
# Interpolation at neighbourless triangles should retain
|
|
# symmetry with mirroring the triangle.
|
|
|
|
# Equilateral triangle
|
|
points = np.array([(0, 0), (1, 0), (0.5, np.sqrt(3)/2)])
|
|
values = np.array([1, 0, 0])
|
|
|
|
ip = interpnd.CloughTocher2DInterpolator(points, values)
|
|
|
|
# Set gradient to zero at vertices
|
|
ip.grad[...] = 0
|
|
|
|
# Interpolation should be symmetric vs. bisector
|
|
alpha = 0.3
|
|
p1 = np.array([0.5 * np.cos(alpha), 0.5 * np.sin(alpha)])
|
|
p2 = np.array([0.5 * np.cos(np.pi/3 - alpha), 0.5 * np.sin(np.pi/3 - alpha)])
|
|
|
|
v1 = ip(p1)
|
|
v2 = ip(p2)
|
|
assert_allclose(v1, v2)
|
|
|
|
# ... and affine invariant
|
|
np.random.seed(1)
|
|
A = np.random.randn(2, 2)
|
|
b = np.random.randn(2)
|
|
|
|
points = A.dot(points.T).T + b[None,:]
|
|
p1 = A.dot(p1) + b
|
|
p2 = A.dot(p2) + b
|
|
|
|
ip = interpnd.CloughTocher2DInterpolator(points, values)
|
|
ip.grad[...] = 0
|
|
|
|
w1 = ip(p1)
|
|
w2 = ip(p2)
|
|
assert_allclose(w1, v1)
|
|
assert_allclose(w2, v2)
|