def test_invalid_fill_value(self):
np.random.seed(1234)
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = np.random.rand(5, 7)
# integers can be cast to floats
_RegularGridInterp((x, y), values, fill_value=1)
# complex values cannot
self.assertRaises(ValueError, _RegularGridInterp,
(x, y), values, fill_value=1 + 2j)
def test_list_input(self):
points, values = self._get_sample_4d_large()
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
for method in self.valid_methods:
interp = _RegularGridInterp(points, values.tolist(), method=method)
v1 = interp(sample.tolist(), compute_gradients=False)
interp = _RegularGridInterp(points, values, method=method)
v2 = interp(sample, compute_gradients=False)
assert_allclose(v1, v2)
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)
# verify that this raises error with dimension checking
self.assertRaises(ValueError, _RegularGridInterp, points, values,
'cubic')
interp = _RegularGridInterp(points,
values,
method='cubic',
spline_dim_error=False)
# first dimension (x) should be reduced to k=1 (linear)
assert_equal(interp._ki[0], 1)
# should operate as normal
x = [0.5, 0, 1001]
result = interp(x)
assert_almost_equal(result, -0.046325695741704434, decimal=5)
interp = _RegularGridInterp(points,
values,
method='slinear',
spline_dim_error=False)
value1 = interp(x)
# cycle through different methods that require order reduction
# in the first dimension
value2 = interp(x, method='quintic')
interp.gradient(x, method='quintic')
value3 = interp(x, method='cubic')
interp.gradient(x, method='cubic')
# use default method again
value4 = interp(x)
# values from different methods should be different
self.assertRaises(AssertionError, assert_equal, value1, value2)
self.assertRaises(AssertionError, assert_equal, value2, value3)
# first value should match last with no side effects from the
# order reduction or gradient caluclations
assert_equal(value1, value4)
def test_invalid_fill_value(self):
np.random.seed(1234)
x = np.linspace(0, 2, 5)
y = np.linspace(0, 1, 7)
values = np.random.rand(5, 7)
# integers can be cast to floats
_RegularGridInterp((x, y), values, fill_value=1)
# complex values cannot
self.assertRaises(ValueError,
_RegularGridInterp, (x, y),
values,
fill_value=1 + 2j)
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)
# verify that this raises error with dimension checking
self.assertRaises(ValueError, _RegularGridInterp,
points, values, 'cubic')
interp = _RegularGridInterp(
points, values, method='cubic', spline_dim_error=False)
# first dimension (x) should be reduced to k=1 (linear)
assert_equal(interp._ki[0], 1)
# should operate as normal
x = [0.5, 0, 1001]
result = interp(x)
assert_almost_equal(result, -0.046325695741704434, decimal=5)
interp = _RegularGridInterp(
points, values, method='slinear', spline_dim_error=False)
value1 = interp(x)
# cycle through different methods that require order reduction
# in the first dimension
value2 = interp(x, method='quintic')
interp.gradient(x, method='quintic')
value3 = interp(x, method='cubic')
interp.gradient(x, method='cubic')
# use default method again
value4 = interp(x)
# values from different methods should be different
self.assertRaises(AssertionError, assert_equal, value1, value2)
self.assertRaises(AssertionError, assert_equal, value2, value3)
# first value should match last with no side effects from the
# order reduction or gradient caluclations
assert_equal(value1, value4)
def test_list_input(self):
points, values = self._get_sample_4d_large()
sample = np.asarray([[0.1, 0.1, 1., .9], [0.2, 0.1, .45, .8],
[0.5, 0.5, .5, .5]])
for method in self.valid_methods:
interp = _RegularGridInterp(points,
values.tolist(),
method=method)
v1 = interp(sample.tolist(), compute_gradients=False)
interp = _RegularGridInterp(points,
values,
method=method)
v2 = interp(sample, compute_gradients=False)
assert_allclose(v1, v2)
def test_out_of_bounds_fill2(self):
points, values, func, df = self. _get_sample_2d()
np.random.seed(1)
test_pt = np.random.uniform(3, 3.1, 2)
actual = np.asarray([np.nan])
methods = self.valid_methods
for method in methods:
interp = _RegularGridInterp(points, values, method,
bounds_error=False,
fill_value=np.nan)
computed = interp(test_pt, compute_gradients=False)
assert_array_almost_equal(computed, actual)
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.spline_methods:
interp = _RegularGridInterp(points, values, method)
x = np.array([0.9, 0.1])
interp._xi = x
interp._gmethod = method
dy = np.array([0.997901, 0.08915])
interp._all_gradients = 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.spline_methods:
interp = _RegularGridInterp(points, values, method)
x = np.array([0.9, 0.1])
interp._xi = x
interp._gmethod = method
dy = np.array([0.997901, 0.08915])
interp._all_gradients = dy
assert_almost_equal(interp.gradient(x), dy)
def test_spline_xi3d(self):
points, values, func, df = self. _get_sample_2d()
np.random.seed(1)
test_pt = np.random.uniform(0, 3, 6).reshape(3, 2)
actual = func(*test_pt.T)
for method in self.spline_methods:
tol = 1e-1
if method == 'slinear':
tol = 0.5
interp = _RegularGridInterp(points, values, method)
computed = interp(test_pt, compute_gradients=False)
r_err = rel_error(actual, computed)
assert r_err < tol
def test_spline_xi3d(self):
points, values, func, df = self._get_sample_2d()
np.random.seed(1)
test_pt = np.random.uniform(0, 3, 6).reshape(3, 2)
actual = func(*test_pt.T)
for method in self.spline_methods:
tol = 1e-1
if method == 'slinear':
tol = 0.5
interp = _RegularGridInterp(points, values, method)
computed = interp(test_pt, compute_gradients=False)
r_err = rel_error(actual, computed)
assert r_err < tol
def test_out_of_bounds_fill2(self):
points, values, func, df = self._get_sample_2d()
np.random.seed(1)
test_pt = np.random.uniform(3, 3.1, 2)
actual = np.asarray([np.nan])
methods = self.valid_methods
for method in methods:
interp = _RegularGridInterp(points,
values,
method,
bounds_error=False,
fill_value=np.nan)
computed = interp(test_pt, compute_gradients=False)
assert_array_almost_equal(computed, actual)
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))
tol = 1e-1
for method in self.spline_methods:
if method == 'slinear':
tol = 1.5
interp = _RegularGridInterp(points, values, method)
computed = interp.gradient(test_pt)
r_err = rel_error(actual, computed)
assert r_err < tol
# test that gradients have been cached
assert_array_equal(interp._xi, test_pt)
assert_array_equal(
interp._all_gradients.flatten(), computed.flatten())
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))
tol = 1e-1
for method in self.spline_methods:
if method == 'slinear':
tol = 1.5
interp = _RegularGridInterp(points, values, method)
computed = interp.gradient(test_pt)
r_err = rel_error(actual, computed)
assert r_err < tol
# test that gradients have been cached
assert_array_equal(interp._xi, test_pt)
assert_array_equal(interp._all_gradients.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))
tol = 1e-1
for method in self.spline_methods:
k = self.interp_configs[method]
if method == 'slinear':
tol = 2
interp = _RegularGridInterp(points, values, method,
bounds_error=False,
fill_value=None)
computed = interp(test_pt)
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
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.spline_methods:
k = self.interp_configs[method]
if method == 'slinear':
tol = 2
interp = _RegularGridInterp(points,
values,
method,
bounds_error=False,
fill_value=None)
computed = interp(test_pt)
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
def test_method_switching(self):
# should be able to switch interpolation methods on each __call__
# and gradient call, without overriding defaults permenantly.
# exceptions and gradient caching should work as expected.
np.random.seed(314)
x = np.linspace(-100, 2, 10)
y = np.linspace(-10, 4, 6)
z = np.linspace(1000, 2000, 50)
points = [x, y, z]
values = np.random.randn(10, 6, 50)
x = [0.5, 0, 1001]
# create as cubic
interp = _RegularGridInterp(
points, values, method='cubic')
# value and gradient work as expected
result1 = interp(x)
gradient1 = interp.gradient(x)
result_actual_1 = 0.2630309995970872
result_gradient_1 = np.array([0.22505535, -0.46465198, 0.02523666])
assert_almost_equal(result1, result_actual_1)
assert_almost_equal(gradient1, result_gradient_1)
# changing the method should work as expected
result2 = interp(x, method='slinear')
gradient2 = interp.gradient(x, method='slinear')
result_actual_2 = 0.27801704674026684
result_gradient_2 = np.array([0.12167214, -0.44221416, -0.00323078])
assert_almost_equal(result2, result_actual_2)
assert_almost_equal(gradient2, result_gradient_2)
# should be able to switch back and get the original results without
# explicitly setting the method
result3 = interp(x)
gradient3 = interp.gradient(x)
assert_almost_equal(result3, result_actual_1)
assert_almost_equal(gradient3, result_gradient_1)
# new interpolator and evaluation point
interp = _RegularGridInterp(
points, values, method='slinear')
# values will be cast to float for splines/gradient methods
# otherwise, will get null vector gradient [0,0,0] at all pts
x = [-50, 0, 1501]
result6 = interp(x)
result_actual_6 = 0.3591176338294626
assert_almost_equal(result6, result_actual_6)
# should be able to switch and get value and gradient
result7 = interp(x, method='quintic')
gradient7 = interp.gradient(x, method='quintic')
result_actual_7 = 0.6157594079479937
result_gradient_7 = np.array([-0.35731922, 0.23131539, -0.14088582])
assert_almost_equal(result7, result_actual_7)
assert_almost_equal(gradient7, result_gradient_7)
# switch again; gradient should be different
gradient8 = interp.gradient(x, method='slinear')
result_gradient_8 = np.array([-0.11299396, 0.24352342, -0.07446338])
assert_almost_equal(gradient8, result_gradient_8)
# should be able to switch back to original without setting it
result9 = interp(x)
assert_almost_equal(result9, result6)
def test_method_switching(self):
# should be able to switch interpolation methods on each __call__
# and gradient call, without overriding defaults permenantly.
# exceptions and gradient caching should work as expected.
np.random.seed(314)
x = np.linspace(-100, 2, 10)
y = np.linspace(-10, 4, 6)
z = np.linspace(1000, 2000, 50)
points = [x, y, z]
values = np.random.randn(10, 6, 50)
x = [0.5, 0, 1001]
# create as cubic
interp = _RegularGridInterp(points, values, method='cubic')
# value and gradient work as expected
result1 = interp(x)
gradient1 = interp.gradient(x)
result_actual_1 = 0.2630309995970872
result_gradient_1 = np.array([0.22505535, -0.46465198, 0.02523666])
assert_almost_equal(result1, result_actual_1)
assert_almost_equal(gradient1, result_gradient_1)
# changing the method should work as expected
result2 = interp(x, method='slinear')
gradient2 = interp.gradient(x, method='slinear')
result_actual_2 = 0.27801704674026684
result_gradient_2 = np.array([0.12167214, -0.44221416, -0.00323078])
assert_almost_equal(result2, result_actual_2)
assert_almost_equal(gradient2, result_gradient_2)
# should be able to switch back and get the original results without
# explicitly setting the method
result3 = interp(x)
gradient3 = interp.gradient(x)
assert_almost_equal(result3, result_actual_1)
assert_almost_equal(gradient3, result_gradient_1)
# new interpolator and evaluation point
interp = _RegularGridInterp(points, values, method='slinear')
# values will be cast to float for splines/gradient methods
# otherwise, will get null vector gradient [0,0,0] at all pts
x = [-50, 0, 1501]
result6 = interp(x)
result_actual_6 = 0.3591176338294626
assert_almost_equal(result6, result_actual_6)
# should be able to switch and get value and gradient
result7 = interp(x, method='quintic')
gradient7 = interp.gradient(x, method='quintic')
result_actual_7 = 0.6157594079479937
result_gradient_7 = np.array([-0.35731922, 0.23131539, -0.14088582])
assert_almost_equal(result7, result_actual_7)
assert_almost_equal(gradient7, result_gradient_7)
# switch again; gradient should be different
gradient8 = interp.gradient(x, method='slinear')
result_gradient_8 = np.array([-0.11299396, 0.24352342, -0.07446338])
assert_almost_equal(gradient8, result_gradient_8)
# should be able to switch back to original without setting it
result9 = interp(x)
assert_almost_equal(result9, result6)