def test_gradients_returned_by_xi(self):
# verifies that gradients with respect to xi are returned if cached
points, values, func, df = self._get_sample_2d()
np.random.seed(4321)
for method in self.valid_methods:
interp = InterpND(points, values, method)
x = np.array([0.9, 0.1])
interp._xi = x
dy = np.array([0.997901, 0.08915])
interp._d_dx = dy
assert_almost_equal(interp.gradient(x), dy)
def test_gradients_returned_by_xi(self):
# verifies that gradients with respect to xi are returned if cached
points, values, func, df = self._get_sample_2d()
np.random.seed(4321)
for method in self.interp_methods:
interp = InterpND(method=method, points=points, values=values)
x = np.array([0.9, 0.1])
interp._xi = x
dy = np.array([0.997901, 0.08915])
interp._d_dx = dy
assert_near_equal(interp.gradient(x), dy, tolerance=1e-7)
def test_auto_reduce_spline_order(self):
# if a spline method is used and spline_dim_error=False and a dimension
# does not have enough points, the spline order for that dimension
# should be automatically reduced
np.random.seed(314)
# x dimension is too small for cubic, should fall back to linear
x = [0, 1]
y = np.linspace(-10, 4, 10)
z = np.linspace(1000, 2000, 20)
points = [x, y, z]
values = np.random.randn(2, 10, 20)
interp = InterpND(points, values, interp_method='scipy_cubic')
# first dimension (x) should be reduced to k=1 (linear)
self.assertEqual(interp.table._ki[0], 1)
# should operate as normal
x = np.array([0.5, 0, 1001])
result = interp.interpolate(x)
assert_almost_equal(result, -0.046325695741704434, decimal=5)
interp = InterpND(points, values, interp_method='scipy_slinear')
value1 = interp.interpolate(x)
# cycle through different methods that require order reduction
# in the first dimension
interp = InterpND(points, values, interp_method='scipy_quintic')
value2 = interp.interpolate(x)
interp.gradient(x)
interp = InterpND(points, values, interp_method='scipy_cubic')
value3 = interp.interpolate(x)
interp.gradient(x)
# values from different methods should be different
self.assertTrue(value1[0] != value2[0])
self.assertTrue(value2[0] != value3[0])
def test_spline_deriv_xi1d(self):
# tests gradient values
points, values, func, df = self._get_sample_2d()
np.random.seed(1234)
test_pt = np.random.uniform(0, 3, 2)
actual = np.array(df(*test_pt))
for method in self.valid_methods:
interp = InterpND(points, values, method)
computed = interp.gradient(test_pt)
r_err = rel_error(actual, computed)
assert r_err < self.tol[method]
# test that gradients have been cached
assert_array_equal(interp._xi, test_pt)
assert_array_equal(interp._d_dx.flatten(), computed.flatten())
def test_spline_out_of_bounds_extrap(self):
points, values, func, df = self._get_sample_2d()
np.random.seed(5)
test_pt = np.random.uniform(3, 3.1, 2)
actual = func(*test_pt)
gradient = np.array(df(*test_pt))
for method in self.valid_methods:
k = self.interp_configs[method]
interp = InterpND(points, values, method, bounds_error=False)
computed = interp.interpolate(test_pt)
computed_grad = interp.gradient(test_pt)
r_err = rel_error(actual, computed)
assert r_err < 1e3 * self.tol[method]
r_err = rel_error(gradient, computed_grad)
# extrapolated gradients are even trickier, but usable still
assert r_err < 2e3 * self.tol[method]
def test_spline_out_of_bounds_extrap(self):
points, values, func, df = self. _get_sample_2d()
np.random.seed(5)
test_pt = np.random.uniform(3, 3.1, 2)
actual = func(*test_pt)
gradient = np.array(df(*test_pt))
tol = 1e-1
for method in self.interp_methods:
k = self.interp_configs[method]
if method == 'slinear':
tol = 2
interp = InterpND(method=method, points=points, values=values,
extrapolate=True)
computed, computed_grad = interp.interpolate(test_pt, compute_derivative=True)
computed_grad = interp.gradient(test_pt)
r_err = rel_error(actual, computed)
assert r_err < tol
r_err = rel_error(gradient, computed_grad)
# extrapolated gradients are even trickier, but usable still
assert r_err < 2 * tol
