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import math

def is_prime(n):
    """Determine if `n` is prime."""
    if (n%2==0 or n%3==0): return(False)
    threshold = math.floor(math.sqrt(n))

    # all primes are of the form 6k+/-1 =>
    plus_tst  = any(n%i for i in
                    (6*k+1 for k in

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Using pip behind a Web Proxy

pip is a package management system used primarily to install and maintain third-party libraries written for Python. pip will not work in an enterprise setting behind a web proxy without first setting environmental variables specifying the user's authentication details, in addition to the url and port of the proxy server. This post walks through how to setup and use pip from behind a web proxy on Windows.

Setting HTTP_PROXY & HTTPS_PROXY Environmental Variables

The first step is to set two environmental variables from the command line: HTTP_PROXY and HTTPS_PROXY. The required format is:

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import numpy as np

fpath = "challenger.csv"

# Setting dtype to `None` forces genfromtxt to determine
# the datatypes of each column =>
res = np.genfromtxt(fname=fpath, 
                    dtype=None, 
                    delimiter=",",
                    autostrip=True, 

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### `getLogisticCoefficients_1` tracks the development of the coefficent vector and 
### Information matrix across iterations, and identifies them as `information_progression` 
### and coefficients_progression` in the returned list `returnList` ===>
getLogisticCoefficients_1 <- function(design_matrix, response_vector, epsilon=.0001) {
    
    # ===================================================================
    # design_matrix      (X)     => n-by-(p+1)                          |
    # response_vector    (y)     => n-by-1                              |
    # probability_vector (p)     => n-by-1                              |
    # weights_matrix     (W)     => n-by-n                              |

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def get_coefficients(design_matrix, response_vector, epsilon=.001):
    """
    Determine Logistic Regression coefficents using Fisher Scoring algorithm.
    Iteration ceases once changes between elements in coefficent matrix across
    consecutive iterations is less than epsilon.
    # =========================================================================
    # design_matrix      `X`     => n-by-(p+1)                                |
    # response_vector    `y`     => n-by-1                                    |
    # probability_vector `p`     => n-by-1                                    |
    # weights_matrix     `W`     => n-by-n                                    |

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getCoefficients <- function(design_matrix, response_vector, epsilon=.0001) {
    # =========================================================================
    # design_matrix      `X`     => n-by-(p+1)                                |
    # response_vector    `y`     => n-by-1                                    |
    # probability_vector `p`     => n-by-1                                    |
    # weights_matrix     `W`     => n-by-n                                    |
    # epsilon                    => threshold above which iteration continues |
    # =========================================================================
    # n                          => # of observations                         |
    # (p + 1)                    => # of parameterss, +1 for intercept term   |