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_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_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_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_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)
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)
try:
interpnd.CloughTocher2DInterpolator(tri, y, rescale=True)(x)
except ValueError as a:
if str(a) != ("Rescaling is not supported when passing a "
"Delaunay triangulation as ``points``."):
raise
except:
raise
