core.reference.coordinate_map¶
Module: core.reference.coordinate_map
¶
Inheritance diagram for 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.])
Methods
__call__
(x)Return mapping evaluated at x from_params
(innames, outnames, params[, …])Create AffineTransform from innames and outnames from_start_step
(innames, outnames, start, step)New AffineTransform from names, start and step. identity
(coord_names[, name])Return an identity coordmap of the given shape inverse
([preserve_dtype])Return coordinate map with inverse affine transform or None renamed_domain
(newnames[, name])New AffineTransform with function_domain renamed renamed_range
(newnames[, name])New AffineTransform with renamed function_domain reordered_domain
([order])New AffineTransform with function_domain reordered reordered_range
([order])New AffineTransform with function_range reordered similar_to
(other)Does other have similar coordinate systems and same mappings? -
__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
withCoordinateSystem
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 invertedaffine
. If True, try to invert ouraffine
, and see if it can be cast to the needed data type, which isself.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 NoneAffineTransform
mapping from the range of input self to the domain of input self - the inverse of self. Ifself.affine
was not invertible return None. If preserve_dtype is True, and the inverse ofself.affine
cannot be cast toself.function_domain.coord_dtype
, then return None. Otherwise returnAffineTransform
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.
-
CoordMapMaker
¶
-
class
nipy.core.reference.coordinate_map.
CoordMapMaker
(domain_maker, range_maker)¶ Bases:
object
Class to create coordinate maps of different dimensions
Methods
__call__
(*args, **kwargs)Create affine or non-affine coordinate map affine_maker
alias of AffineTransform
generic_maker
alias of CoordinateMap
make_affine
(affine[, append_zooms, …])Create affine coordinate map make_cmap
(domain_N, xform[, inv_xform])Coordinate map with transform function xform -
__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 mapExamples
>>> 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))
returnspts
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 ...> )
-
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_domain
function_range
function
(x, /[, out, where, casting, order, …])inverse_function
(x, /[, out, where, …])Methods
__call__
(x)Return mapping evaluated at x function
(x, /[, out, where, casting, order, …])inverse
()New CoordinateMap with the functions reversed inverse_function
(x, /[, out, where, …])renamed_domain
(newnames[, name])New CoordinateMap with function_domain renamed renamed_range
(newnames[, name])New CoordinateMap with function_domain renamed reordered_domain
([order])Create a new CoordinateMap with the coordinates of function_domain reordered. reordered_range
([order])Nnew CoordinateMap with function_range reordered. similar_to
(other)Does other have similar coordinate systems and same mappings? -
__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 NoneReturns: 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',)
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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.]])
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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
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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
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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)
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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
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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.])
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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
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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
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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)
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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')
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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
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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