Utils

morphopy.neurontree.utils.angle_between(v1, v2)

Returns the angle in radians between vectors ‘v1’ and ‘v2’:

>>> angle_between((1, 0, 0), (0, 1, 0))
1.5707963267948966
>>> angle_between((1, 0, 0), (1, 0, 0))
0.0
>>> angle_between((1, 0, 0), (-1, 0, 0))
3.141592653589793

Parameters:

• v1 – numpy.array d-dimensional vector
• v2 – numpy.array d-dimensional vector

Returns:

theta - float angle btw v1 and v2 in radians

morphopy.neurontree.utils.commuteDist(A)

Returns the commute distance within a graph given by adjacency matrix A

Parameters:A – adjacency matrix (NxN) Returns:B (NxN) containing the commute distances from each node to each other

morphopy.neurontree.utils.computeStat(statType, W, d, maxDist)

computes a graph key on (sub)graph given by W

Parameters:

• statType – string ‘maxDist’ : maximal distance ‘maxDist_norm’ : normalized maximal distance ‘meanEdgeLength’ : mean edge length ‘meanEdgeLength_norm’ : normalized mean edge length ‘4starMotif’ : 4 star motif ‘branchPoints’ : number of branch points
• W – (KxK) adjacency matrix of graph
• d – (Kx1) shortest path distances of nodes in W
• maxDist – float maximal shortest path distance in graph of which W is a sub-graph of.

Returns:

stat: float key calculated according to statType

morphopy.neurontree.utils.eulerAnglesToRotationMatrix(theta)

Calculates the rotation matrix from given euler angles

Parameters:theta – 3D vector with eulerangles for x,y and z axis Returns:rotation matrix R [3x3]

morphopy.neurontree.utils.get_A(x)

Returns matrix A. Used for rotation matrix calculation

Parameters:x – 3D numpy.array rotation axis Returns:A - 3x3 numpy.array

morphopy.neurontree.utils.get_axis(v1, v2)

Returns the axis between two vectors v1 and v2

Parameters:

• v1 – numpy.array d-dimensional
• v2 – numpy.array d-dimensional

Returns:

axis - numpy.array d-dimensional axis btw v1 and v2

morphopy.neurontree.utils.get_rotation_matrix(a, b)

Returns the rotation matrix to rotate vector a onto vector b.

Parameters:

• a – numpy.array (2 or 3 dimensional)
• b – numpy.array (2 or 3 dimensional)

Returns:

R (2x2 or 3x3) rotation matrix to rotate a onto b

morphopy.neurontree.utils.get_standardized_swc(swc, scaling=1.0, soma_radius=None, soma_center=True, pca_rot=False)

This function collapses all soma points to a single node located at the centroid of the convex hull of the original soma nodes. It can also scale the coordinates, merge nodes into the soma that have a bigger radius than soma_radius and return the xyz coordinates of the swc file in their PCA rotation.

Parameters:

• swc – swc file, as pandas.DataFrame.
• scaling – float, (default=1), allows for a uniform scaling of x, y and z
• soma_radius – float (default=None), if set, then all nodes with a radius greater or equal to soma radius are set to be somatic (type=1). In a subsequent step these nodes will be merged to one. Careful! If this radius is set too small this leads to faulty skeletons.
• soma_center – bool (default=True), if True, x,y,z are soma centered.
• pca_rot – bool (default=False), if True, the x,y,z coordinates in the given swc file are rotated into their PCA frame. Then x corresponds to the direction of highest and z to the direction of lowest variance.

Returns:

pandas.DataFrame

morphopy.neurontree.utils.isRotationMatrix(R)

Checks if R is a valid rotation matrix.

Parameters:R – [3x3] rotation matrix Returns:boolean. Returns True when R is a valid rotation matrix, otherwise False.

morphopy.neurontree.utils.rotationMatrixToEulerAngles(R)

Calculates rotation matrix to euler angles

Parameters:R – rotation matrix [3x3] Returns:vector of euler angles (rotations around x,y and z axis)

morphopy.neurontree.utils.shortpathFW(A)

Returns matrix B of shortest path distances from each node to each other node in the graph. If the graph is undirected, B will be symmetric. B[:,0] corresponds to all shortest paths from reached from node 0. Algorithm after Floyd and Warshall

Parameters:

• A – adjacency matrix of a graph (NxN)
• gpu – default True. If True, calculation is performed on GPU.

Returns:

B (NxN) matrix of shortest paths

morphopy.neurontree.utils.smooth_gaussian(data, dim, sigma=2)

Smooths the given data using a gaussian. This method only works for stacked one or two dimensional data so far! Smoothing in 3D is not implemented.

Parameters:

• data – (X,Y,N) numpy.array 1,2 or 3 dimensional.
• dim – int Dimension of the passed data. Used to determine if data is a single image or stacked.
• sigma – int The standard deviation of the smoothing gaussian used.

Returns:

Xb: same dimension as the input array. Smoothed data.

morphopy.neurontree.utils.sphereFit(spX, spY, spZ)

fit a sphere to X,Y, and Z data points returns the radius and center points of the best fit sphere.

Implementation by http://jekel.me/2015/Least-Squares-Sphere-Fit/

Parameters:

• spX –
• spY –
• spZ –

Returns:

morphopy.neurontree.utils.unit_vector(vector)

Returns the unit vector of the vector.

Parameters:vector – numpy.array d-dimensional vector Returns:u numpy.array d-dimensional unit vector of ‘vector’