uniform_discr_fromdiscr

odl.discr.discr_space.uniform_discr_fromdiscr(discr, min_pt=None, max_pt=None, shape=None, cell_sides=None, **kwargs)

Return a discretization based on an existing one.

The parameters that are explicitly given are used to create the new discretization, and the missing information is taken from the template space. See Notes for the exact functionality.

Parameters:

discrDiscretizedSpace

Uniformly discretized space used as a template.

min_pt, max_pt: float or sequence of floats, optional

Desired minimum/maximum corners of the new space domain.

shapeint or sequence of ints, optional

Desired number of samples per axis of the new space.

cell_sidesfloat or sequence of floats, optional

Desired cell side lenghts of the new space's partition.

Other Parameters:

nodes_on_bdrybool or sequence, optional

If a sequence is provided, it determines per axis whether to place the last grid point on the boundary (True) or shift it by half a cell size into the interior (False). In each axis, an entry may consist in a single bool or a 2-tuple of bool. In the latter case, the first tuple entry decides for the left, the second for the right boundary. The length of the sequence must be discr.ndim.

A single boolean is interpreted as a global choice for all boundaries.

Default: False.

kwargs

Additional keyword parameters passed to the DiscretizedSpace initializer.

See also

uniform_discr

implicit uniform Lp discretization

odl.discr.partition.uniform_partition

underlying domain partitioning scheme

Notes

The parameters min_pt, max_pt, shape and cell_sides can be combined in the following ways (applies in each axis individually):

0 arguments:

Return a copy of discr

1 argument:

[min,max]_pt -> keep sampling but translate domain so it starts/ends at [min,max]_pt

shape/cell_sides -> keep domain but change sampling. See uniform_partition for restrictions.

2 arguments:

min_pt + max_pt -> translate and resample with the same number of samples

[min,max]_pt + shape/cell_sides -> translate and resample

shape + cell_sides -> error due to ambiguity (keep min_pt or max_pt?)

3+ arguments:

The underlying partition is uniquely determined by the new parameters. See uniform_partition.

Examples

>>> discr = odl.uniform_discr([0, 0], [1, 2], (10, 5))
>>> discr.cell_sides
array([ 0.1,  0.4])

If no additional argument is given, a copy of discr is returned:

>>> odl.uniform_discr_fromdiscr(discr) == discr
True
>>> odl.uniform_discr_fromdiscr(discr) is discr
False

Giving min_pt or max_pt results in a translation, while for the other two options, the domain is kept but re-partitioned:

>>> odl.uniform_discr_fromdiscr(discr, min_pt=[1, 1])
uniform_discr([ 1.,  1.], [ 2.,  3.], (10, 5))
>>> odl.uniform_discr_fromdiscr(discr, max_pt=[0, 0])
uniform_discr([-1., -2.], [ 0.,  0.], (10, 5))
>>> odl.uniform_discr_fromdiscr(discr, cell_sides=[1, 1])
uniform_discr([ 0.,  0.], [ 1.,  2.], (1, 2))
>>> odl.uniform_discr_fromdiscr(discr, shape=[5, 5])
uniform_discr([ 0.,  0.], [ 1.,  2.], (5, 5))
>>> odl.uniform_discr_fromdiscr(discr, shape=[5, 5]).cell_sides
array([ 0.2,  0.4])

The cases with 2 or more additional arguments and the syntax for specifying quantities per axis is illustrated in the following:

# axis 0: translate to match max_pt = 3 # axis 1: recompute max_pt using the original shape with the # new min_pt and cell_sides >>> new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=[None, 1], ... max_pt=[3, None], ... cell_sides=[None, 0.25]) >>> new_discr uniform_discr([ 2., 1.], [ 3. , 2.25], (10, 5)) >>> new_discr.cell_sides array([ 0.1 , 0.25])

# axis 0: recompute min_pt from old cell_sides and new # max_pt and shape # axis 1: use new min_pt, shape and cell_sides only >>> new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=[None, 1], ... max_pt=[3, None], ... shape=[5, 5], ... cell_sides=[None, 0.25]) >>> new_discr uniform_discr([ 2.5, 1. ], [ 3. , 2.25], (5, 5)) >>> new_discr.cell_sides array([ 0.1 , 0.25])