Numpy

import numpy as np

• Casting list to a np array:

np.array([1,2,3])

arange

Returns integers given a start, stop (not included), and stepsize (default is 1):

np.arange(start=0,stop=10,step=2)

returns: array([0,2,4,6,8])

zeros and ones:

• zeros

np.zeros((3,4))

returns:

array([[0.,0.,0.,0.],
	[0.,0.,0.,0.],
	[0.,0.,0.,0.]])

• ones

np.ones((3))

returns:

array([1.,1.,1.])

• another arbitrary number by multiplying times ones

np.ones((4))*5

returns:

array([5.,5.,5.,5.])

linspace:

Evenly spaced numbers over a specified interval. Includes stop value.

np.linspace(0,10,3)

returns

array([0., 5., 10.])

Identity matrix:

np.eye(3)

returns

array([[1., 0., 0.],
	[0., 1., 0.],
	[0., 0., 1.]])

Percentiles

q75, q25 = np.percentile(sample,[75,25])

Reshaping

arr = np.arange(24)
arr.shape # --> (25,)
arr = arr.reshape(5,5) # Not permanent. Need to reassign.
arr.shape # --> (5,5)

max and argmax:

arr.max() # --> Returns max value in the array
arr.argmax() # --> Returns the index location of the max value in the array

• similar with min and argmin.

Data types:

arr.dtype # --> Returns, e.g.dtype('int32')

Random sampling

Seed

np.random.seed(101)

Uniform sampling:

The line below returns three random numbers in the range [0,1) sampled uniformly:

np.random.rand(3)

• The following gives a shape of 3 rows by 4 columns:

np.random.rand(3,4)

Normal sampling:

• standard normal distribution (mean=0, variance=1):

np.random.randn(3)

• more general normal distribution:

np.random.normal(mean,std_dev,shape)

Random integers:

np.random.randint(start,stop,shape)

Numpy operations

arr = np.array(0,1,2)
arr + 5

this returns array([5,6,7]) as the operation is done on an element-by-element basis.

• Similar with array-array operations:

arr = np.array(2,3,4)
arr*arr

this returns: array([4,9,16]).

• Universal array functions

Covariance matrix, eigenvalues and eigenvectors:

covariance_matrix = np.cov(scaled_X,rowvar=False)
eigen_values, eigen_vectors = np.linalg.eig(covariance_matrix)