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import numpy as np
from numpy.testing import assert_equal, assert_allclose, assert_almost_equal, \
run_module_suite, assert_raises
import scipy.interpolate.interpnd as interpnd
import scipy.spatial.qhull as qhull
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_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))
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)
class TestCloughTocher2DInterpolator(object):
def _check_accuracy(self, func, x=None, tol=1e-6, alternate=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)
else:
ip = interpnd.CloughTocher2DInterpolator((x[:,0], x[:,1]),
func(x[:,0], x[:,1]),
tol=1e-6)
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)
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)
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)
def test_wrong_ndim(self):
x = np.random.randn(30, 3)
y = np.random.randn(30)
assert_raises(ValueError, interpnd.CloughTocher2DInterpolator, x, y)
if __name__ == "__main__":
run_module_suite()
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