core.reference.coordinate_map

Module: core.reference.coordinate_map

Inheritance diagram for nipy.core.reference.coordinate_map:

Inheritance diagram of nipy.core.reference.coordinate_map

This module describes two types of mappings:

  • CoordinateMap: a general function from a domain to a range, with a possible
    inverse function.
  • AffineTransform: an affine function from a domain to a range, not
    necessarily of the same dimension, hence not always invertible.

Each of these objects is meant to encapsulate a tuple of (domain, range, function). Each of the mapping objects contain all the details about their domain CoordinateSystem, their range CoordinateSystem and the mapping between them.

Common API

They are separate classes, neither one inheriting from the other. They do, however, share some parts of an API, each having methods:

  • renamed_domain : rename on the coordinates of the domain (returns a new mapping)
  • renamed_range : rename the coordinates of the range (returns a new mapping)
  • reordered_domain : reorder the coordinates of the domain (returns a new mapping)
  • reordered_range : reorder the coordinates of the range (returns a new mapping)
  • inverse : when appropriate, return the inverse mapping

These methods are implemented by module level functions of the same name.

They also share some attributes:

  • ndims : the dimensions of the domain and range, respectively
  • function_domain : CoordinateSystem describing the domain
  • function_range : CoordinateSystem describing the range

Operations on mappings (module level functions)

  • compose : Take a sequence of mappings (either CoordinateMaps or
    AffineTransforms) and return their composition. If they are all AffineTransforms, an AffineTransform is returned. This checks to ensure that domains and ranges of the various mappings agree.
  • product : Take a sequence of mappings (either CoordinateMaps or
    AffineTransforms) and return a new mapping that has domain and range given by the concatenation of their domains and ranges, and the mapping simply concatenates the output of each of the individual mappings. If they are all AffineTransforms, an AffineTransform is returned. If they are all AffineTransforms that are in fact linear (i.e. origin=0) then can is represented as a block matrix with the size of the blocks determined by
  • concat : Take a mapping and prepend a coordinate to its domain and
    range. For mapping m, this is the same as product(AffineTransform.identity(‘concat’), m)

Classes

AffineTransform

class nipy.core.reference.coordinate_map.AffineTransform(function_domain, function_range, affine)

Bases: object

Class for affine transformation from domain to a range

This class has an affine attribute, which is a matrix representing the affine transformation in homogeneous coordinates. This matrix is used to evaluate the function, rather than having an explicit function (as is the case for a CoordinateMap).

Examples

>>> inp_cs = CoordinateSystem('ijk')
>>> out_cs = CoordinateSystem('xyz')
>>> cm = AffineTransform(inp_cs, out_cs, np.diag([1, 2, 3, 1]))
>>> cm
AffineTransform(
   function_domain=CoordinateSystem(coord_names=('i', 'j', 'k'), name='', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x', 'y', 'z'), name='', coord_dtype=float64),
   affine=array([[ 1.,  0.,  0.,  0.],
                 [ 0.,  2.,  0.,  0.],
                 [ 0.,  0.,  3.,  0.],
                 [ 0.,  0.,  0.,  1.]])
)
>>> cm.affine
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  2.,  0.,  0.],
       [ 0.,  0.,  3.,  0.],
       [ 0.,  0.,  0.,  1.]])
>>> cm([1,1,1])
array([ 1.,  2.,  3.])
>>> icm = cm.inverse()
>>> icm([1,2,3])
array([ 1.,  1.,  1.])
__init__(function_domain, function_range, affine)

Initialize AffineTransform

Parameters:

function_domain : CoordinateSystem

input coordinates

function_range : CoordinateSystem

output coordinates

affine : array-like

affine homogenous coordinate matrix

Notes

The dtype of the resulting matrix is determined by finding a safe typecast for the function_domain, function_range and affine.

affine = array([[3, 0, 0, 0], [0, 4, 0, 0], [0, 0, 5, 0], [0, 0, 0, 1]])
static from_params(innames, outnames, params, domain_name='', range_name='')

Create AffineTransform from innames and outnames

Parameters:

innames : sequence of str or str

The names of the axes of the domain. If str, then names given by list(innames)

outnames : seqence of str or str

The names of the axes of the range. If str, then names given by list(outnames)

params : AffineTransform, array or (array, array)

An affine function between the domain and range. This can be represented either by a single ndarray (which is interpreted as the representation of the function in homogeneous coordinates) or an (A,b) tuple.

domain_name : str, optional

Name of domain CoordinateSystem

range_name : str, optional

Name of range CoordinateSystem

Returns:

aff : AffineTransform

Notes

Precondition:len(shape) == len(names)
Raises ValueError:
 if len(shape) != len(names)
static from_start_step(innames, outnames, start, step, domain_name='', range_name='')

New AffineTransform from names, start and step.

Parameters:

innames : sequence of str or str

The names of the axes of the domain. If str, then names given by list(innames)

outnames : seqence of str or str

The names of the axes of the range. If str, then names given by list(outnames)

start : sequence of float

Start vector used in constructing affine transformation

step : sequence of float

Step vector used in constructing affine transformation

domain_name : str, optional

Name of domain CoordinateSystem

range_name : str, optional

Name of range CoordinateSystem

Returns:

cm : CoordinateMap

Notes

len(names) == len(start) == len(step)

Examples

>>> cm = AffineTransform.from_start_step('ijk', 'xyz', [1, 2, 3], [4, 5, 6])
>>> cm.affine
array([[ 4.,  0.,  0.,  1.],
       [ 0.,  5.,  0.,  2.],
       [ 0.,  0.,  6.,  3.],
       [ 0.,  0.,  0.,  1.]])
function_domain = CoordinateSystem(coord_names=('x',), name='', coord_dtype=float64)
function_range = CoordinateSystem(coord_names=('y',), name='', coord_dtype=float64)
static identity(coord_names, name='')

Return an identity coordmap of the given shape

Parameters:

coord_names : sequence of str or str

The names of the axes of the domain. If str, then names given by list(coord_names)

name : str, optional

Name of origin of coordinate system

Returns:

cm : CoordinateMap

CoordinateMap with CoordinateSystem domain and an identity transform, with identical domain and range.

Examples

>>> cm = AffineTransform.identity('ijk', 'somewhere')
>>> cm.affine
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  1.]])
>>> cm.function_domain
CoordinateSystem(coord_names=('i', 'j', 'k'), name='somewhere', coord_dtype=float64)
>>> cm.function_range
CoordinateSystem(coord_names=('i', 'j', 'k'), name='somewhere', coord_dtype=float64)
inverse(preserve_dtype=False)

Return coordinate map with inverse affine transform or None

Parameters:

preserve_dtype : bool

If False, return affine mapping from inverting the affine. The domain / range dtypes for the inverse may then change as a function of the dtype of the inverted affine. If True, try to invert our affine, and see if it can be cast to the needed data type, which is self.function_domain.coord_dtype. We need this dtype in order for the inverse to preserve the coordinate system dtypes.

Returns:

aff_cm_inv : AffineTransform instance or None

AffineTransform mapping from the range of input self to the domain of input self - the inverse of self. If self.affine was not invertible return None. If preserve_dtype is True, and the inverse of self.affine cannot be cast to self.function_domain.coord_dtype, then return None. Otherwise return AffineTransform inverse mapping. If preserve_dtype is False, the domain / range dtypes of the return inverse may well be different from those of the input self.

Examples

>>> input_cs = CoordinateSystem('ijk', coord_dtype=np.int)
>>> output_cs = CoordinateSystem('xyz', coord_dtype=np.int)
>>> affine = np.array([[1,0,0,1],
...                    [0,1,0,1],
...                    [0,0,1,1],
...                    [0,0,0,1]])
>>> affine_transform = AffineTransform(input_cs, output_cs, affine)
>>> affine_transform([2,3,4]) 
array([3, 4, 5])

The inverse transform, by default, generates a floating point inverse matrix and therefore floating point output:

>>> affine_transform_inv = affine_transform.inverse()
>>> affine_transform_inv([2, 6, 12])
array([  1.,   5.,  11.])

You can force it to preserve the coordinate system dtype with the preserve_dtype flag:

>>> at_inv_preserved = affine_transform.inverse(preserve_dtype=True)
>>> at_inv_preserved([2, 6, 12]) 
array([  1,   5,  11])

If you preserve_dtype, and there is no inverse affine preserving the dtype, the inverse is None:

>>> affine2 = affine.copy()
>>> affine2[0, 0] = 2 # now inverse can't be integer
>>> aff_t = AffineTransform(input_cs, output_cs, affine2)
>>> aff_t.inverse(preserve_dtype=True) is None
True
ndims = (3, 3)
renamed_domain(newnames, name='')

New AffineTransform with function_domain renamed

Parameters:

newnames : dict

A dictionary whose keys are integers or are in mapping.function_domain.coord_names and whose values are the new names.

Returns:

newmapping : AffineTransform

A new AffineTransform with renamed function_domain.

Examples

>>> affine_domain = CoordinateSystem('ijk')
>>> affine_range = CoordinateSystem('xyz')
>>> affine_matrix = np.identity(4)
>>> affine_mapping = AffineTransform(affine_domain, affine_range, affine_matrix)
>>> new_affine_mapping = affine_mapping.renamed_domain({'i':'phase','k':'freq','j':'slice'})
>>> new_affine_mapping.function_domain
CoordinateSystem(coord_names=('phase', 'slice', 'freq'), name='', coord_dtype=float64)
>>> new_affine_mapping = affine_mapping.renamed_domain({'i':'phase','k':'freq','l':'slice'})
Traceback (most recent call last):
   ...
ValueError: no domain coordinate named l
renamed_range(newnames, name='')

New AffineTransform with renamed function_domain

Parameters:

newnames : dict

A dictionary whose keys are integers or are in mapping.function_range.coord_names and whose values are the new names.

Returns:

newmapping : AffineTransform

A new AffineTransform with renamed function_range.

Examples

>>> affine_domain = CoordinateSystem('ijk')
>>> affine_range = CoordinateSystem('xyz')
>>> affine_matrix = np.identity(4)
>>> affine_mapping = AffineTransform(affine_domain, affine_range, affine_matrix)
>>> new_affine_mapping = affine_mapping.renamed_range({'x':'u'})
>>> new_affine_mapping.function_range
CoordinateSystem(coord_names=('u', 'y', 'z'), name='', coord_dtype=float64)
>>> new_affine_mapping = affine_mapping.renamed_range({'w':'u'})
Traceback (most recent call last):
   ...
ValueError: no range coordinate named w
reordered_domain(order=None)

New AffineTransform with function_domain reordered

Default behaviour is to reverse the order of the coordinates.

Parameters:

order : sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_domain.coord_names.

Returns:

newmapping :AffineTransform

A new AffineTransform with the coordinates of function_domain reordered.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = AffineTransform(input_cs, output_cs, np.identity(4))
>>> cm.reordered_domain('ikj').function_domain
CoordinateSystem(coord_names=('i', 'k', 'j'), name='', coord_dtype=float64)
reordered_range(order=None)

New AffineTransform with function_range reordered

Defaults to reversing the coordinates of function_range.

Parameters:

order : sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_range.coord_names.

Returns:

newmapping : AffineTransform

A new AffineTransform with the coordinates of function_range reordered.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = AffineTransform(input_cs, output_cs, np.identity(4))
>>> cm.reordered_range('xzy').function_range
CoordinateSystem(coord_names=('x', 'z', 'y'), name='', coord_dtype=float64)
>>> cm.reordered_range([0,2,1]).function_range.coord_names
('x', 'z', 'y')
>>> newcm = cm.reordered_range('yzx')
>>> newcm.function_range.coord_names
('y', 'z', 'x')
similar_to(other)

Does other have similar coordinate systems and same mappings?

A “similar” coordinate system is one with the same coordinate names and data dtype, but ignoring the coordinate system name.

AxisError

class nipy.core.reference.coordinate_map.AxisError

Bases: exceptions.Exception

Error for incorrect axis selection

__init__()

x.__init__(…) initializes x; see help(type(x)) for signature

CoordMapMaker

class nipy.core.reference.coordinate_map.CoordMapMaker(domain_maker, range_maker)

Bases: object

Class to create coordinate maps of different dimensions

__init__(domain_maker, range_maker)

Create coordinate map maker

Parameters:

domain_maker : callable

A coordinate system maker, returning a coordinate system with input argument only N, an integer giving the length of the coordinate map.

range_maker : callable

A coordinate system maker, returning a coordinate system with input argument only N, an integer giving the length of the coordinate map.

Examples

>>> from nipy.core.reference.coordinate_system import CoordSysMaker
>>> dmaker = CoordSysMaker('ijkl', 'generic-array')
>>> rmaker = CoordSysMaker('xyzt', 'generic-scanner')
>>> cm_maker = CoordMapMaker(dmaker, rmaker)
affine_maker

alias of AffineTransform

generic_maker

alias of CoordinateMap

make_affine(affine, append_zooms=(), append_offsets=())

Create affine coordinate map

Parameters:

affine : (M, N) array-like

Array expressing the affine tranformation

append_zooms : scalar or sequence length E

If scalar, converted to sequence length E==1. Append E entries to the diagonal of affine (see examples)

append_offsets : scalar or sequence length F

If scalar, converted to sequence length F==1. If F==0, and E!=0, use sequence of zeros length E. Append E entries to the translations (final column) of affine (see examples).

Returns:

affmap : AffineTransform coordinate map

Examples

>>> from nipy.core.reference.coordinate_system import CoordSysMaker
>>> dmaker = CoordSysMaker('ijkl', 'generic-array')
>>> rmaker = CoordSysMaker('xyzt', 'generic-scanner')
>>> cm_maker = CoordMapMaker(dmaker, rmaker)
>>> cm_maker.make_affine(np.diag([2,3,4,1]))
AffineTransform(
   function_domain=CoordinateSystem(coord_names=('i', 'j', 'k'), name='generic-array', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x', 'y', 'z'), name='generic-scanner', coord_dtype=float64),
   affine=array([[ 2.,  0.,  0.,  0.],
                 [ 0.,  3.,  0.,  0.],
                 [ 0.,  0.,  4.,  0.],
                 [ 0.,  0.,  0.,  1.]])
)

We can add extra orthogonal dimensions, by specifying the diagonal elements:

>>> cm_maker.make_affine(np.diag([2,3,4,1]), 6)
AffineTransform(
   function_domain=CoordinateSystem(coord_names=('i', 'j', 'k', 'l'), name='generic-array', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x', 'y', 'z', 't'), name='generic-scanner', coord_dtype=float64),
   affine=array([[ 2.,  0.,  0.,  0.,  0.],
                 [ 0.,  3.,  0.,  0.,  0.],
                 [ 0.,  0.,  4.,  0.,  0.],
                 [ 0.,  0.,  0.,  6.,  0.],
                 [ 0.,  0.,  0.,  0.,  1.]])
)

Or the diagonal elements and the offset elements:

>>> cm_maker.make_affine(np.diag([2,3,4,1]), [6], [9])
AffineTransform(
   function_domain=CoordinateSystem(coord_names=('i', 'j', 'k', 'l'), name='generic-array', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x', 'y', 'z', 't'), name='generic-scanner', coord_dtype=float64),
   affine=array([[ 2.,  0.,  0.,  0.,  0.],
                 [ 0.,  3.,  0.,  0.,  0.],
                 [ 0.,  0.,  4.,  0.,  0.],
                 [ 0.,  0.,  0.,  6.,  9.],
                 [ 0.,  0.,  0.,  0.,  1.]])
)
make_cmap(domain_N, xform, inv_xform=None)

Coordinate map with transform function xform

Parameters:

domain_N : int

Number of domain coordinates

xform : callable

Function that transforms points of dimension domain_N

inv_xform : None or callable, optional

Function, such that inv_xform(xform(pts)) returns pts

Returns:

cmap : CoordinateMap

Examples

>>> from nipy.core.reference.coordinate_system import CoordSysMaker
>>> dmaker = CoordSysMaker('ijkl', 'generic-array')
>>> rmaker = CoordSysMaker('xyzt', 'generic-scanner')
>>> cm_maker = CoordMapMaker(dmaker, rmaker)
>>> cm_maker.make_cmap(4, lambda x : x+1) 
CoordinateMap(
   function_domain=CoordinateSystem(coord_names=('i', 'j', 'k', 'l'), name='generic-array', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x', 'y', 'z', 't'), name='generic-scanner', coord_dtype=float64),
   function=<function <lambda> at ...>
  )

CoordMapMakerError

class nipy.core.reference.coordinate_map.CoordMapMakerError

Bases: exceptions.Exception

__init__()

x.__init__(…) initializes x; see help(type(x)) for signature

CoordinateMap

class nipy.core.reference.coordinate_map.CoordinateMap(function_domain, function_range, function, inverse_function=None)

Bases: object

A set of domain and range CoordinateSystems and a function between them.

For example, the function may represent the mapping of a voxel (the domain of the function) to real space (the range). The function may be an affine or non-affine transformation.

Examples

>>> function_domain = CoordinateSystem('ijk', 'voxels')
>>> function_range = CoordinateSystem('xyz', 'world')
>>> mni_orig = np.array([-90.0, -126.0, -72.0])
>>> function = lambda x: x + mni_orig
>>> inv_function = lambda x: x - mni_orig
>>> cm = CoordinateMap(function_domain, function_range, function, inv_function)

Map the first 3 voxel coordinates, along the x-axis, to mni space:

>>> x = np.array([[0,0,0], [1,0,0], [2,0,0]])
>>> cm.function(x)
array([[ -90., -126.,  -72.],
       [ -89., -126.,  -72.],
       [ -88., -126.,  -72.]])
>>> x = CoordinateSystem('x')
>>> y = CoordinateSystem('y')
>>> m = CoordinateMap(x, y, np.exp, np.log)
>>> m
CoordinateMap(
   function_domain=CoordinateSystem(coord_names=('x',), name='', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('y',), name='', coord_dtype=float64),
   function=<ufunc 'exp'>,
   inverse_function=<ufunc 'log'>
  )
>>> m.inverse()
CoordinateMap(
   function_domain=CoordinateSystem(coord_names=('y',), name='', coord_dtype=float64),
   function_range=CoordinateSystem(coord_names=('x',), name='', coord_dtype=float64),
   function=<ufunc 'log'>,
   inverse_function=<ufunc 'exp'>
  )

Attributes

function(x, /[, out, where, casting, order, …])
inverse_function(x, /[, out, where, …])
function_domain (CoordinateSystem instance) The input coordinate system.
function_range (CoordinateSystem instance) The output coordinate system.
__init__(function_domain, function_range, function, inverse_function=None)

Create a CoordinateMap given function, domain and range.

Parameters:

function_domain : CoordinateSystem

The input coordinate system.

function_range : CoordinateSystem

The output coordinate system

function : callable

The function between function_domain and function_range. It should be a callable that accepts arrays of shape (N, function_domain.ndim) and returns arrays of shape (N, function_range.ndim), where N is the number of points for transformation.

inverse_function : None or callable, optional

The optional inverse of function, with the intention being x = inverse_function(function(x)). If the function is affine and invertible, then this is true for all x. The default is None

Returns:

coordmap : CoordinateMap

function(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'exp'>
function_domain = CoordinateSystem(coord_names=('x',), name='', coord_dtype=float64)
function_range = CoordinateSystem(coord_names=('y',), name='', coord_dtype=float64)
inverse()

New CoordinateMap with the functions reversed

inverse_function(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'log'>
ndims = (1, 1)
renamed_domain(newnames, name='')

New CoordinateMap with function_domain renamed

Parameters:

newnames : dict

A dictionary whose keys are integers or are in mapping.function_domain.coord_names and whose values are the new names.

Returns:

newmaping : CoordinateMap

A new CoordinateMap with renamed function_domain.

Examples

>>> domain = CoordinateSystem('ijk')
>>> range = CoordinateSystem('xyz')
>>> cm = CoordinateMap(domain, range, lambda x:x+1)
>>> new_cm = cm.renamed_domain({'i':'phase','k':'freq','j':'slice'})
>>> new_cm.function_domain
CoordinateSystem(coord_names=('phase', 'slice', 'freq'), name='', coord_dtype=float64)
>>> new_cm = cm.renamed_domain({'i':'phase','k':'freq','l':'slice'})
Traceback (most recent call last):
   ...
ValueError: no domain coordinate named l
renamed_range(newnames, name='')

New CoordinateMap with function_domain renamed

Parameters:

newnames : dict

A dictionary whose keys are integers or are in mapping.function_range.coord_names and whose values are the new names.

Returns:

newmapping : CoordinateMap

A new CoordinateMap with renamed function_range.

Examples

>>> domain = CoordinateSystem('ijk')
>>> range = CoordinateSystem('xyz')
>>> cm = CoordinateMap(domain, range, lambda x:x+1)
>>> new_cm = cm.renamed_range({'x':'u'})
>>> new_cm.function_range
CoordinateSystem(coord_names=('u', 'y', 'z'), name='', coord_dtype=float64)
>>> new_cm = cm.renamed_range({'w':'u'})
Traceback (most recent call last):
   ...
ValueError: no range coordinate named w
reordered_domain(order=None)

Create a new CoordinateMap with the coordinates of function_domain reordered. Default behaviour is to reverse the order of the coordinates.

Parameters:

order : sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_domain.coord_names.

Returns:

newmapping : CoordinateMap

A new CoordinateMap with the coordinates of function_domain reordered.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = CoordinateMap(input_cs, output_cs, lambda x:x+1)
>>> cm.reordered_domain('ikj').function_domain
CoordinateSystem(coord_names=('i', 'k', 'j'), name='', coord_dtype=float64)
reordered_range(order=None)

Nnew CoordinateMap with function_range reordered.

Defaults to reversing the coordinates of function_range.

Parameters:

order : sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_range.coord_names.

Returns:

newmapping : CoordinateMap

A new CoordinateMap with the coordinates of function_range reordered.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = CoordinateMap(input_cs, output_cs, lambda x:x+1)
>>> cm.reordered_range('xzy').function_range
CoordinateSystem(coord_names=('x', 'z', 'y'), name='', coord_dtype=float64)
>>> cm.reordered_range([0,2,1]).function_range.coord_names
('x', 'z', 'y')
>>> newcm = cm.reordered_range('yzx')
>>> newcm.function_range.coord_names
('y', 'z', 'x')
similar_to(other)

Does other have similar coordinate systems and same mappings?

A “similar” coordinate system is one with the same coordinate names and data dtype, but ignoring the coordinate system name.

Functions

nipy.core.reference.coordinate_map.append_io_dim(cm, in_name, out_name, start=0, step=1)

Append input and output dimension to coordmap

Parameters:

cm : Affine

Affine coordinate map instance to which to append dimension

in_name : str

Name for new input dimension

out_name : str

Name for new output dimension

start : float, optional

Offset for transformed values in new dimension

step : float, optional

Step, or scale factor for transformed values in new dimension

Returns:

cm_plus : Affine

New coordinate map with appended dimension

Examples

Typical use is creating a 4D coordinate map from a 3D

>>> cm3d = AffineTransform.from_params('ijk', 'xyz', np.diag([1,2,3,1]))
>>> cm4d = append_io_dim(cm3d, 'l', 't', 9, 5)
>>> cm4d.affine
array([[ 1.,  0.,  0.,  0.,  0.],
       [ 0.,  2.,  0.,  0.,  0.],
       [ 0.,  0.,  3.,  0.,  0.],
       [ 0.,  0.,  0.,  5.,  9.],
       [ 0.,  0.,  0.,  0.,  1.]])
nipy.core.reference.coordinate_map.axmap(coordmap, direction='in2out', fix0=True)

Return mapping between input and output axes

Parameters:

coordmap : Affine

Affine coordinate map instance for which to get axis mappings

direction : {‘in2out’, ‘out2in’, ‘both’}

direction to find mapping. If ‘in2out’, returned mapping will have keys from the input axis (names and indices) and values of corresponding output axes. If ‘out2in’ the keys will be output axis names, indices and the values will be input axis indices. If both, return both mappings.

fix0: bool, optional

Whether to fix potential 0 TR in affine

Returns:

map : dict or tuple

  • if direction == ‘in2out’ - mapping with keys of input names and input indices, values of output indices. Mapping is to closest matching axis. None means there appears to be no matching axis
  • if direction == ‘out2in’ - mapping with keys of output names and input indices, values of input indices, as above.
  • if direction == ‘both’ - tuple of (input to output mapping, output to input mapping)
nipy.core.reference.coordinate_map.compose(*cmaps)

Return the composition of two or more CoordinateMaps.

Parameters:

cmaps : sequence of CoordinateMaps

Returns:

cmap : CoordinateMap

The resulting CoordinateMap has function_domain == cmaps[-1].function_domain and function_range == cmaps[0].function_range

Examples

>>> cmap = AffineTransform.from_params('i', 'x', np.diag([2.,1.]))
>>> cmapi = cmap.inverse()
>>> id1 = compose(cmap,cmapi)
>>> id1.affine
array([[ 1.,  0.],
       [ 0.,  1.]])
>>> id2 = compose(cmapi,cmap)
>>> id1.function_domain.coord_names
('x',)
>>> id2.function_domain.coord_names
('i',)
nipy.core.reference.coordinate_map.drop_io_dim(cm, axis_id, fix0=True)

Drop dimensions axis_id from coordinate map, if orthogonal to others

If you specify an input dimension, drop that dimension and any corresponding output dimension, as long as all other outputs are orthogonal to dropped input. If you specify an output dimension, drop that dimension and any corresponding input dimension, as long as all other inputs are orthogonal to dropped output.

Parameters:

cm : class:AffineTransform

Affine coordinate map instance

axis_id : int or str

If int, gives index of input axis to drop. If str, gives name of input or output axis to drop. When specifying an input axis: if given input axis does not affect any output axes, just drop input axis. If input axis affects only one output axis, drop both input and corresponding output. Similarly when specifying an output axis. If axis_id is a str, it must be unambiguous - if the named axis exists in both input and output, and they do not correspond, raises a AxisError. See Raises section for checks

fix0: bool, optional

Whether to fix potential 0 TR in affine

Returns:

cm_redux : Affine

Affine coordinate map with orthogonal input + output dimension dropped

Raises:

AxisError: if `axis_id` is a str and does not match any no input or output

coordinate names.

AxisError: if specified `axis_id` affects more than a single input / output

axis.

AxisError: if the named `axis_id` exists in both input and output, and they

do not correspond.

Examples

Typical use is in getting a 3D coordinate map from 4D

>>> cm4d = AffineTransform.from_params('ijkl', 'xyzt', np.diag([1,2,3,4,1]))
>>> cm3d = drop_io_dim(cm4d, 't')
>>> cm3d.affine
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  2.,  0.,  0.],
       [ 0.,  0.,  3.,  0.],
       [ 0.,  0.,  0.,  1.]])
nipy.core.reference.coordinate_map.equivalent(mapping1, mapping2)

A test to see if mapping1 is equal to mapping2 after possibly reordering the domain and range of mapping.

Parameters:

mapping1 : CoordinateMap or AffineTransform

mapping2 : CoordinateMap or AffineTransform

Returns:

are_they_equal : bool

Examples

>>> ijk = CoordinateSystem('ijk')
>>> xyz = CoordinateSystem('xyz')
>>> T = np.random.standard_normal((4,4))
>>> T[-1] = [0,0,0,1] # otherwise AffineTransform raises
...                   # an exception because
...                   # it's supposed to represent an
...                   # affine transform in homogeneous
...                   # coordinates
>>> A = AffineTransform(ijk, xyz, T)
>>> B = A.reordered_domain('ikj').reordered_range('xzy')
>>> C = B.renamed_domain({'i':'slice'})
>>> equivalent(A, B)
True
>>> equivalent(A, C)
False
>>> equivalent(B, C)
False
>>>
>>> D = CoordinateMap(ijk, xyz, np.exp)
>>> equivalent(D, D)
True
>>> E = D.reordered_domain('kij').reordered_range('xzy')
>>> # no non-AffineTransform will ever be
>>> # equivalent to a reordered version of itself,
>>> # because their functions don't evaluate as equal
>>> equivalent(D, E)
False
>>> equivalent(E, E)
True
>>>
>>> # This has not changed the order
>>> # of the axes, so the function is still the same
>>>
>>> F = D.reordered_range('xyz').reordered_domain('ijk')
>>> equivalent(F, D)
True
>>> id(F) == id(D)
False
nipy.core.reference.coordinate_map.input_axis_index(coordmap, axis_id, fix0=True)

Return input axis index for axis_id

axis_id can be integer, or a name of an input axis, or it can be the name of an output axis which maps to an input axis.

Parameters:

coordmap : AffineTransform

axis_id : int or str

If int, then an index of an input axis. Can be negative, so that -2 refers to the second to last input axis. If a str can be the name of an input axis, or the name of an output axis that should have a corresponding input axis (see Raises section).

fix0: bool, optional

Whether to fix potential single 0 on diagonal of affine. This often happens when loading nifti images with TR set to 0.

Returns:

inax : int

index of matching input axis. If axis_id is the name of an output axis, then inax will be the input axis that had a ‘best’ match with this output axis. The ‘best’ match algorithm ensures that there can only be one input axis paired with one output axis.

Raises:

AxisError: if no matching name found

AxisError : if name exists in both input and output and they do not map to

each other

AxisError : if name present in output but no matching input

nipy.core.reference.coordinate_map.io_axis_indices(coordmap, axis_id, fix0=True)

Return input and output axis index for id axis_id in coordmap

Parameters:

cm : class:AffineTransform

Affine coordinate map instance

axis_id : int or str

If int, gives index of input axis. Can be negative, so that -2 refers to the second from last input axis. If str, gives name of input or output axis. If axis_id is a str, it must be unambiguous - if the named axis exists in both input and output, and they do not correspond, raises a AxisError. See Raises section for checks

fix0: bool, optional

Whether to fix potential 0 column / row in affine

Returns:

in_index : None or int

index of input axis that corresponds to axis_id

out_index : None or int

index of output axis that corresponds to axis_id

Raises:

AxisError: if `axis_id` is a str and does not match any input or output

coordinate names.

AxisError: if the named `axis_id` exists in both input and output, and they

do not correspond.

Examples

>>> aff = [[0, 1, 0, 10], [1, 0, 0, 11], [0, 0, 1, 12], [0, 0, 0, 1]]
>>> cmap = AffineTransform('ijk', 'xyz', aff)
>>> io_axis_indices(cmap, 0)
(0, 1)
>>> io_axis_indices(cmap, 1)
(1, 0)
>>> io_axis_indices(cmap, -1)
(2, 2)
>>> io_axis_indices(cmap, 'j')
(1, 0)
>>> io_axis_indices(cmap, 'y')
(0, 1)
nipy.core.reference.coordinate_map.orth_axes(in_ax, out_ax, affine, allow_zero=True, tol=1e-05)

True if in_ax related only to out_ax in affine and vice versa

Parameters:

in_ax : int

Input axis index

out_ax : int

Output axis index

affine : array-like

Affine transformation matrix

allow_zero : bool, optional

Whether to allow zero in affine[out_ax, in_ax]. This means that the two axes are not related, but nor is this pair related to any other part of the affine.

Returns:

tf : bool

True if in_ax, out_ax pair are orthogonal to the rest of affine, unless allow_zero is False, in which case require in addition that affine[out_ax, in_ax] != 0.

Examples

>>> aff = np.eye(4)
>>> orth_axes(1, 1, aff)
True
>>> orth_axes(1, 2, aff)
False
nipy.core.reference.coordinate_map.product(*cmaps, **kwargs)

“topological” product of two or more mappings

The mappings can be either AffineTransforms or CoordinateMaps.

If they are all AffineTransforms, the result is an AffineTransform, else it is a CoordinateMap.

Parameters:cmaps : sequence of CoordinateMaps or AffineTransforms
Returns:cmap : CoordinateMap

Examples

>>> inc1 = AffineTransform.from_params('i', 'x', np.diag([2,1]))
>>> inc2 = AffineTransform.from_params('j', 'y', np.diag([3,1]))
>>> inc3 = AffineTransform.from_params('k', 'z', np.diag([4,1]))
>>> cmap = product(inc1, inc3, inc2)
>>> cmap.function_domain.coord_names
('i', 'k', 'j')
>>> cmap.function_range.coord_names
('x', 'z', 'y')
>>> cmap.affine
array([[ 2.,  0.,  0.,  0.],
       [ 0.,  4.,  0.,  0.],
       [ 0.,  0.,  3.,  0.],
       [ 0.,  0.,  0.,  1.]])
>>> A1 = AffineTransform.from_params('ij', 'xyz', np.array([[2,3,1,0],[3,4,5,0],[7,9,3,1]]).T)
>>> A2 = AffineTransform.from_params('xyz', 'de', np.array([[8,6,7,4],[1,-1,13,3],[0,0,0,1]]))
>>> A1.affine
array([[ 2.,  3.,  7.],
       [ 3.,  4.,  9.],
       [ 1.,  5.,  3.],
       [ 0.,  0.,  1.]])
>>> A2.affine
array([[  8.,   6.,   7.,   4.],
       [  1.,  -1.,  13.,   3.],
       [  0.,   0.,   0.,   1.]])
>>> p=product(A1, A2)
>>> p.affine
array([[  2.,   3.,   0.,   0.,   0.,   7.],
       [  3.,   4.,   0.,   0.,   0.,   9.],
       [  1.,   5.,   0.,   0.,   0.,   3.],
       [  0.,   0.,   8.,   6.,   7.,   4.],
       [  0.,   0.,   1.,  -1.,  13.,   3.],
       [  0.,   0.,   0.,   0.,   0.,   1.]])
>>> np.allclose(p.affine[:3,:2], A1.affine[:3,:2])
True
>>> np.allclose(p.affine[:3,-1], A1.affine[:3,-1])
True
>>> np.allclose(p.affine[3:5,2:5], A2.affine[:2,:3])
True
>>> np.allclose(p.affine[3:5,-1], A2.affine[:2,-1])
True
>>>
>>> A1([3,4])
array([ 25.,  34.,  26.])
>>> A2([5,6,7])
array([ 129.,   93.])
>>> p([3,4,5,6,7])
array([  25.,   34.,   26.,  129.,   93.])
nipy.core.reference.coordinate_map.renamed_domain(mapping, newnames, name='')

New coordmap with the coordinates of function_domain renamed

Parameters:

newnames: dict

A dictionary whose keys are integers or are in mapping.function_range.coord_names and whose values are the new names.

Returns:

newmapping : CoordinateMap or AffineTransform

A new mapping with renamed function_domain. If isinstance(mapping, AffineTransform), newmapping is also an AffineTransform. Otherwise, it is a CoordinateMap.

Examples

>>> affine_domain = CoordinateSystem('ijk')
>>> affine_range = CoordinateSystem('xyz')
>>> affine_matrix = np.identity(4)
>>> affine_mapping = AffineTransform(affine_domain, affine_range, affine_matrix)
>>> new_affine_mapping = affine_mapping.renamed_domain({'i':'phase','k':'freq','j':'slice'})
>>> new_affine_mapping.function_domain
CoordinateSystem(coord_names=('phase', 'slice', 'freq'), name='', coord_dtype=float64)
>>> new_affine_mapping = affine_mapping.renamed_domain({'i':'phase','k':'freq','l':'slice'})
Traceback (most recent call last):
   ...
ValueError: no domain coordinate named l
nipy.core.reference.coordinate_map.renamed_range(mapping, newnames)

New coordmap with the coordinates of function_range renamed

Parameters:

newnames : dict

A dictionary whose keys are integers or in mapping.function_range.coord_names and whose values are the new names.

Returns:

newmapping : CoordinateMap or AffineTransform

A new CoordinateMap with the coordinates of function_range renamed. If isinstance(mapping, AffineTransform), newmapping is also an AffineTransform. Otherwise, it is a CoordinateMap.

Examples

>>> affine_domain = CoordinateSystem('ijk')
>>> affine_range = CoordinateSystem('xyz')
>>> affine_matrix = np.identity(4)
>>> affine_mapping = AffineTransform(affine_domain, affine_range, affine_matrix)
>>> new_affine_mapping = affine_mapping.renamed_range({'x':'u'})
>>> new_affine_mapping.function_range
CoordinateSystem(coord_names=('u', 'y', 'z'), name='', coord_dtype=float64)
>>> new_affine_mapping = affine_mapping.renamed_range({'w':'u'})
Traceback (most recent call last):
   ...
ValueError: no range coordinate named w
nipy.core.reference.coordinate_map.reordered_domain(mapping, order=None)

New coordmap with the coordinates of function_domain reordered

Default behaviour is to reverse the order of the coordinates.

Parameters:

order: sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_domain.coord_names.

Returns:

newmapping : CoordinateMap or AffineTransform

A new CoordinateMap with the coordinates of function_domain reordered. If isinstance(mapping, AffineTransform), newmapping is also an AffineTransform. Otherwise, it is a CoordinateMap.

Notes

If no reordering is to be performed, it returns a copy of mapping.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = AffineTransform(input_cs, output_cs, np.identity(4))
>>> cm.reordered_domain('ikj').function_domain
CoordinateSystem(coord_names=('i', 'k', 'j'), name='', coord_dtype=float64)
nipy.core.reference.coordinate_map.reordered_range(mapping, order=None)

New coordmap with the coordinates of function_range reordered

Defaults to reversing the coordinates of function_range.

Parameters:

order: sequence

Order to use, defaults to reverse. The elements can be integers, strings or 2-tuples of strings. If they are strings, they should be in mapping.function_range.coord_names.

Returns:

newmapping : CoordinateMap or AffineTransform

A new CoordinateMap with the coordinates of function_range reordered. If isinstance(mapping, AffineTransform), newmapping is also an AffineTransform. Otherwise, it is a CoordinateMap.

Notes

If no reordering is to be performed, it returns a copy of mapping.

Examples

>>> input_cs = CoordinateSystem('ijk')
>>> output_cs = CoordinateSystem('xyz')
>>> cm = AffineTransform(input_cs, output_cs, np.identity(4))
>>> cm.reordered_range('xzy').function_range
CoordinateSystem(coord_names=('x', 'z', 'y'), name='', coord_dtype=float64)
>>> cm.reordered_range([0,2,1]).function_range.coord_names
('x', 'z', 'y')
>>> newcm = cm.reordered_range('yzx')
>>> newcm.function_range.coord_names
('y', 'z', 'x')
nipy.core.reference.coordinate_map.shifted_domain_origin(mapping, difference_vector, new_origin)

Shift the origin of the domain

Parameters:

difference_vector : array

Representing the difference shifted_origin-current_origin in the domain’s basis.

Examples

>>> A = np.random.standard_normal((5,6))
>>> A[-1] = [0,0,0,0,0,1]
>>> affine_transform = AffineTransform(CS('ijklm', 'oldorigin'), CS('xyzt'), A)
>>> affine_transform.function_domain
CoordinateSystem(coord_names=('i', 'j', 'k', 'l', 'm'), name='oldorigin', coord_dtype=float64)

A random change of origin

>>> difference = np.random.standard_normal(5)

The same affine transforation with a different origin for its domain

>>> shifted_affine_transform = shifted_domain_origin(affine_transform, difference, 'neworigin')
>>> shifted_affine_transform.function_domain
CoordinateSystem(coord_names=('i', 'j', 'k', 'l', 'm'), name='neworigin', coord_dtype=float64)

Let’s check that things work

>>> point_in_old_basis = np.random.standard_normal(5)

This is the relation ship between coordinates in old and new origins

>>> np.allclose(shifted_affine_transform(point_in_old_basis), affine_transform(point_in_old_basis+difference))
True
>>> np.allclose(shifted_affine_transform(point_in_old_basis-difference), affine_transform(point_in_old_basis))
True
nipy.core.reference.coordinate_map.shifted_range_origin(mapping, difference_vector, new_origin)

Shift the origin of the range.

Parameters:

difference_vector : array

Representing the difference shifted_origin-current_origin in the range’s basis.

Examples

>>> A = np.random.standard_normal((5,6))
>>> A[-1] = [0,0,0,0,0,1]
>>> affine_transform = AffineTransform(CS('ijklm'), CS('xyzt', 'oldorigin'), A)
>>> affine_transform.function_range
CoordinateSystem(coord_names=('x', 'y', 'z', 't'), name='oldorigin', coord_dtype=float64)

Make a random shift of the origin in the range

>>> difference = np.random.standard_normal(4)
>>> shifted_affine_transform = shifted_range_origin(affine_transform, difference, 'neworigin')
>>> shifted_affine_transform.function_range
CoordinateSystem(coord_names=('x', 'y', 'z', 't'), name='neworigin', coord_dtype=float64)
>>>

Evaluate the transform and verify it does as expected

>>> point_in_domain = np.random.standard_normal(5)

Check that things work

>>> np.allclose(shifted_affine_transform(point_in_domain), affine_transform(point_in_domain) - difference)
True
>>> np.allclose(shifted_affine_transform(point_in_domain) + difference, affine_transform(point_in_domain))
True