def test_piecewise_linear_sens_scalar_x():
"""Test shape of output when asked for derivative of scalar."""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
eval_at = 0.5 * (x[4] + x[5])
sens = pl_sens.node_derivative(eval_at)
assert(sens.ndim == 1)
assert(sens.shape == (len(x),))
def test_piecewise_linear_sens_1d_x():
"""Test shape of output when asked for derivative of 1D array."""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
eval_at = x + 0.5
eval_shape = eval_at.shape
sens = pl_sens.node_derivative(eval_at)
assert(sens.ndim == 2)
assert(sens.shape == (eval_shape + (len(x),)))
def test_piecewise_linear_sens_3d_x():
"""Test shape of output when asked for derivative of 3D array."""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
eval_shape = (2, 3, 4)
eval_at = np.random.random(eval_shape) * x.max()
sens = pl_sens.node_derivative(eval_at)
assert(sens.ndim == 4)
assert(sens.shape == (eval_shape + (len(x),)))
def test_piecewise_linear_sens_locality():
"""Test that y(x) is sensitive only to its nearest nodes,
the one to its left and the one to its right."""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
sens_inner = pl_sens.node_derivative(0.5 * (x[4] + x[5]))
assert(np.isclose(sens_inner[4], 0.5))
assert (np.isclose(sens_inner[5], 0.5))
assert (np.isclose(np.sum(sens_inner[:4]), 0.0))
assert (np.isclose(np.sum(sens_inner[5+1:]), 0.0))
def test_order_of_outputs():
""" Confirm output shape is consistent for PiecewiseLinear and Spline."""
pl = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
cs = CubicSplineWithNodeSens(x, y, bc_type='clamped')
eval_shape = (3, 5)
eval_at = np.random.random(eval_shape) * x.max()
pl_sens = pl.node_derivative(eval_at)
cs_sens = cs.node_derivative(eval_at)
assert(pl_sens.shape == cs_sens.shape)
def test_piecewise_linear_unit_sens_when_x_is_a_node():
"""Sanity check of unit sensitivity"""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
ix = np.arange(len(x))
sens_inner_node = pl_sens.node_derivative(x[4])
assert np.isclose(sens_inner_node[4], 1.0)
assert np.allclose(sens_inner_node[ix != 4], 0.0)
assert np.isclose(1.0, np.sum(sens_inner_node))
sens_first_node = pl_sens.node_derivative(x[0])
assert np.isclose(sens_first_node[0], 1.0)
assert np.allclose(sens_first_node[ix != 0], 0.0)
assert np.isclose(1.0, np.sum(sens_first_node))
sens_last_node = pl_sens.node_derivative(x[-1])
assert np.isclose(sens_last_node[-1], 1.0)
assert np.allclose(sens_last_node[ix != (n-1)], 0.0)
assert np.isclose(1.0, np.sum(sens_last_node))
def test_piecewise_linear_sens_extrap():
"""Test extrapolation of PiecewiseLinear."""
pl_sens = PiecewiseLinear(x, y, extrapolate=('clamped', 'natural'))
eval_at = np.array([x[0] - 100.0, x[-1] + 2.0])
sens = pl_sens.node_derivative(eval_at)
assert(sens.ndim == 2)
assert(sens.shape == (2, len(x)))
# Test left extrapolation.
# As it is 'clamped', all should be 0, except for 0'th node, == 1
assert(np.isclose(np.sum(sens[0][1:]), 0.0))
assert (np.isclose(sens[0][0], 1.0))
# Test right extrapolation
# As it is 'natural', it will be sensitive to the 2 nearest nodes
z = x[-1] + 2
sens_m1 = 1 + (z - x[-1]) / (x[-1] - x[-2])
sens_m2 = - (z - x[-1]) / (x[-1] - x[-2])
assert (np.isclose(sens[1][-1], sens_m1))
assert (np.isclose(sens[1][-2], sens_m2))