Flat2dDetector.surface_deriv

Flat2dDetector.surface_deriv(param)

Return the surface derivative at param.

This is a constant function evaluating to axes everywhere.

Parameters:

paramarray-like or sequence

Parameter value(s) at which to evaluate. A sequence of parameters must have length 2.

Returns:

derivnumpy.ndarray

Array containing the derivative vectors. The first dimension enumerates the axes, i.e., has always length 2. If param is a single parameter, the returned array has shape (2, 3), otherwise broadcast(*param).shape + (2, 3).

Notes

To get an array that enumerates the derivative vectors in the first dimension, move the second-to-last axis to the first position:

deriv = surface_deriv(param)
axes_enumeration = np.moveaxis(deriv, -2, 0)

Examples

The method works with a single parameter, resulting in a 2-tuple of vectors:

>>> part = odl.uniform_partition([0, 0], [1, 1], (10, 10))
>>> det = Flat2dDetector(part, axes=[(1, 0, 0), (0, 0, 1)])
>>> det.surface_deriv([0, 0])
array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])
>>> det.surface_deriv([1, 1])
array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])

It is also vectorized, i.e., it can be called with multiple parameters at once (or n-dimensional arrays of parameters):

>>> # 2 pairs of parameters, resulting in 3 vectors for each axis
>>> deriv = det.surface_deriv([[0, 1],
...                            [0, 1]])
>>> deriv[0]  # first pair of vectors
array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])
>>> deriv[1]  # second pair of vectors
array([[ 1.,  0.,  0.],
       [ 0.,  0.,  1.]])
>>> # Pairs of parameters in a (4, 5) array each
>>> param = (np.zeros((4, 5)), np.zeros((4, 5)))  # pairs of params
>>> det.surface_deriv(param).shape
(4, 5, 2, 3)
>>> # Using broadcasting for "outer product" type result
>>> param = (np.zeros((4, 1)), np.zeros((1, 5)))  # broadcasting
>>> det.surface_deriv(param).shape
(4, 5, 2, 3)