cdipaolo

import numpy as np
import scipy.linalg

def kronsolve(A, y):
    """Given a list of positive definite matrices A = [Ar,...,A1]
    and a vector y, return x so that (Ar o ... o A1)x = y where o is
    the Kronecker product.

    Note
    ----

cdipaolo

import numpy as np

def kronmatvec(A, x):
    """Given a list of matrices A = [Ar,...,A1] and a vector x,
    return (Ar o ... o A1)x where o is the Kronecker product.

    Note
    ----
    This function assumes each A[i] is square, and that the vector
    x is of suitable dimension to make the matrix-vector product

cdipaolo

#Python 3.6.5 (default, Jun 17 2018, 12:13:06) 
#Type 'copyright', 'credits' or 'license' for more information
#IPython 6.4.0 -- An enhanced Interactive Python. Type '?' for help.
#Using matplotlib backend: MacOSX

In [6]: import scipy

In [7]: from scipy import linalg

In [1]: n, p = 10**5, 10**2

cdipaolo

import numpy as np

def whiten(X):
    '''whiten
    Takes a data matrix X in R^{n\times p} and returns a matrix
    Y with zero column mean and identity covariance. Assumes
    your data has full column rank. For speed, if n is 10000
    and p is 400, this takes about 150ms, for example.
    
    :param X: Data matrix where rows are samples and cols are features.

cdipaolo

This is free and unencumbered software released into the public domain.

Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.

In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit

cdipaolo

// haversin(θ) function
func hsin(theta float64) float64 {
	return math.Pow(math.Sin(theta/2), 2)
}

// Distance function returns the distance (in meters) between two points of
//     a given longitude and latitude relatively accurately (using a spherical
//     approximation of the Earth) through the Haversin Distance Formula for
//     great arc distance on a sphere with accuracy for small distances
//

cdipaolo

extension UIBezierPath {
    
    // creates an arrow shaped path with middle of base as start point and pointed end as end point
    class func arrowPath(tailLength: CGFloat, tailWidth: CGFloat, headWidth: CGFloat) -> UIBezierPath {
        
        let midY: CGFloat = tailWidth / 2
        
        var polygonPath = UIBezierPath()
        polygonPath.moveToPoint(CGPointMake(0, 0))
        polygonPath.addLineToPoint(CGPointMake( 0, -midY))