# algorithms.statistics.utils¶

## Functions¶

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 faces : dict
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 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.
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.

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.

nipy.algorithms.statistics.utils.join_complexes(*complexes)

Join a sequence of simplicial complexes.

Returns the union of all the particular faces.

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. 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], .... Thus a[0] replaced with inv(a[0]) etc. 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.

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 sqd: array of shape (n_samples,) the squared distances (one per sample)
nipy.algorithms.statistics.utils.test_EC2(shape)
nipy.algorithms.statistics.utils.test_EC3(shape)
nipy.algorithms.statistics.utils.z_score(pvalue)

Return the z-score corresponding to a given p-value.