uniform_partition

odl.discr.partition.uniform_partition(min_pt=None, max_pt=None, shape=None, cell_sides=None, nodes_on_bdry=False)

Return a partition with equally sized cells.

Parameters:

min_pt, max_ptfloat or sequence of float, optional

Vectors defining the lower/upper limits of the intervals in an IntervalProd (a rectangular box). None entries mean "compute the value".

shapeint or sequence of ints, optional

Number of nodes per axis. None entries mean "compute the value".

cell_sidesfloat or sequence of floats, optional

Side length of the partition cells per axis. None entries mean "compute the value".

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 array.ndim.

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

See also

uniform_partition_fromintv

partition an existing set

uniform_partition_fromgrid

use an existing grid as basis

Notes

In each axis, 3 of the 4 possible parameters min_pt, max_pt, shape and cell_sides must be given. If all four are provided, they are checked for consistency.

Examples

Any combination of three of the four parameters can be used for creation of a partition:

>>> part = odl.uniform_partition(min_pt=0, max_pt=2, shape=4)
>>> part.cell_boundary_vecs
(array([ 0. ,  0.5,  1. ,  1.5,  2. ]),)
>>> part = odl.uniform_partition(min_pt=0, shape=4, cell_sides=0.5)
>>> part.cell_boundary_vecs
(array([ 0. ,  0.5,  1. ,  1.5,  2. ]),)
>>> part = odl.uniform_partition(max_pt=2, shape=4, cell_sides=0.5)
>>> part.cell_boundary_vecs
(array([ 0. ,  0.5,  1. ,  1.5,  2. ]),)
>>> part = odl.uniform_partition(min_pt=0, max_pt=2, cell_sides=0.5)
>>> part.cell_boundary_vecs
(array([ 0. ,  0.5,  1. ,  1.5,  2. ]),)

In higher dimensions, the parameters can be given differently in each axis. Where None is given, the value will be computed:

>>> part = odl.uniform_partition(min_pt=[0, 0], max_pt=[1, 2],
...                              shape=[4, 2])
>>> part.cell_boundary_vecs
(array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ]), array([ 0.,  1.,  2.]))
>>> part = odl.uniform_partition(min_pt=[0, 0], max_pt=[1, 2],
...                              shape=[None, 2], cell_sides=[0.25, None])
>>> part.cell_boundary_vecs
(array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ]), array([ 0.,  1.,  2.]))
>>> part = odl.uniform_partition(min_pt=[0, None], max_pt=[None, 2],
...                              shape=[4, 2], cell_sides=[0.25, 1])
>>> part.cell_boundary_vecs
(array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ]), array([ 0.,  1.,  2.]))

By default, no grid points are placed on the boundary:

>>> part = odl.uniform_partition(0, 1, 4)
>>> part.nodes_on_bdry
False
>>> part.cell_boundary_vecs
(array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ]),)
>>> part.grid.coord_vectors
(array([ 0.125,  0.375,  0.625,  0.875]),)

This can be changed with the nodes_on_bdry parameter:

>>> part = odl.uniform_partition(0, 1, 3, nodes_on_bdry=True)
>>> part.nodes_on_bdry
True
>>> part.cell_boundary_vecs
(array([ 0.  ,  0.25,  0.75,  1.  ]),)
>>> part.grid.coord_vectors
(array([ 0. ,  0.5,  1. ]),)

We can specify this per axis, too. In this case we choose both in the first axis and only the rightmost in the second:

>>> part = odl.uniform_partition([0, 0], [1, 1], (3, 3),
...                              nodes_on_bdry=(True, (False, True)))
...
>>> part.cell_boundary_vecs[0]  # first axis, as above
array([ 0.  ,  0.25,  0.75,  1.  ])
>>> part.grid.coord_vectors[0]
array([ 0. ,  0.5,  1. ])
>>> part.cell_boundary_vecs[1]  # second, asymmetric axis
array([ 0. ,  0.4,  0.8,  1. ])
>>> part.grid.coord_vectors[1]
array([ 0.2,  0.6,  1. ])