algorithms.statistics.utils¶
Module: algorithms.statistics.utils
¶
Functions¶
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nipy.algorithms.statistics.utils.
complex
(maximal=[(0, 3, 2, 7), (0, 6, 2, 7), (0, 7, 5, 4), (0, 7, 5, 1), (0, 7, 4, 6), (0, 3, 1, 7)])¶ Faces from simplices
Take a list of maximal simplices (by default a triangulation of a cube into 6 tetrahedra) and computes all faces
Parameters: maximal : sequence of sequences, optional
Default is triangulation of cube into tetrahedra
Returns: faces : dict
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nipy.algorithms.statistics.utils.
cube_with_strides_center
(center=[0, 0, 0], strides=[4, 2, 1])¶ Cube in an array of voxels with a given center and strides.
This triangulates a cube with vertices [center[i] + 1].
The dimension of the cube is determined by len(center) which should agree with len(center).
The allowable dimensions are [1,2,3].
Parameters: center : (d,) sequence of int, optional
Default is [0, 0, 0]
strides : (d,) sequence of int, optional
Default is [4, 2, 1]. These are the strides given by
np.ones((2,2,2), np.bool).strides
Returns: complex : dict
A dictionary with integer keys representing a simplicial complex. The vertices of the simplicial complex are the indices of the corners of the cube in a ‘flattened’ array with specified strides.
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nipy.algorithms.statistics.utils.
decompose2d
(shape, dim=3)¶ Return all (dim-1)-dimensional simplices in a triangulation of a square of a given shape. The vertices in the triangulation are indices in a ‘flattened’ array of the specified shape.
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nipy.algorithms.statistics.utils.
decompose3d
(shape, dim=4)¶ Return all (dim-1)-dimensional simplices in a triangulation of a cube of a given shape. The vertices in the triangulation are indices in a ‘flattened’ array of the specified shape.
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nipy.algorithms.statistics.utils.
join_complexes
(*complexes)¶ Join a sequence of simplicial complexes.
Returns the union of all the particular faces.
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nipy.algorithms.statistics.utils.
multiple_fast_inv
(a)¶ Compute the inverse of a set of arrays in-place
Parameters: a: array_like of shape (n_samples, M, M) :
Set of square matrices to be inverted. a is changed in place.
Returns: a: ndarray shape (n_samples, M, M) :
The input array a, overwritten with the inverses of the original 2D arrays in
a[0], a[1], ...
. Thusa[0]
replaced withinv(a[0])
etc.Raises: LinAlgError : :
If a is singular.
ValueError : :
If a is not square, or not 2-dimensional.
Notes
This function is copied from scipy.linalg.inv, but with some customizations for speed-up from operating on multiple arrays. It also has some conditionals to work with different scipy versions.
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nipy.algorithms.statistics.utils.
multiple_mahalanobis
(effect, covariance)¶ Returns the squared Mahalanobis distance for a given set of samples
Parameters: effect: array of shape (n_features, n_samples), :
Each column represents a vector to be evaluated
covariance: array of shape (n_features, n_features, n_samples), :
Corresponding covariance models stacked along the last axis
Returns: sqd: array of shape (n_samples,) :
the squared distances (one per sample)
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nipy.algorithms.statistics.utils.
test_EC2
(shape)¶
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nipy.algorithms.statistics.utils.
test_EC3
(shape)¶
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nipy.algorithms.statistics.utils.
z_score
(pvalue)¶ Return the z-score corresponding to a given p-value.