1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191
|
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()
|