NumPy

NumPy is a fundamental library for computation in Python.

Additional resources:

• NumPy Quickstart

• NumPy absolute basics

• NumPy for MATLAB users

import numpy as np

Python list

Lets’s compare regular Python lists and NumPy arrays.

# A list is created with [.., ..]
myvals = [1.0, 2.0, 1.5]
myvals

[1.0, 2.0, 1.5]

type(myvals)

list

Numpy 1D array (vector)

myvals_np = np.array([1.2, 3.0, 4.0])

myvals_np

array([1.2, 3. , 4. ])

type(myvals_np)

numpy.ndarray

myvals_np.dtype

dtype('float64')

myvals_np.sum()

8.2

Indexing

x = np.array([1.0,1.5, 2.0, 5.3]) 
x

array([1. , 1.5, 2. , 5.3])

x[1]

1.5

x[-1]

5.3

x[1] = 2.0 # modify the second value in the array
x

array([1. , 2. , 2. , 5.3])

Slicing

x[:2]

array([1., 2.])

Inline exercise

1. Create an array x with three values: 1, 2, 3

2. What is is the data type of x?

3. Create a new array: y = x/2

4. What is the data type of y?`

Math operations

Python is a general purpose language not designed with numerical computing in mind.

However, NumPy is designed for numerical computing!

[1.2, 4.5] + [2.3, 4.3] # is this the result you expected??

[1.2, 4.5, 2.3, 4.3]

np.array([1.2, 4.5]) + np.array([2.3, 4.3]) 

array([3.5, 8.8])

np.array([1.2, 4.5]) * np.array([2.3, 4.3]) 

array([ 2.76, 19.35])

Note for Matlab users, all operators such as * are element wise

np.array([1.2, 4.5]) @ np.array([2.3, 4.3]) # in case you actually wanted to do a dot product

22.11

x = np.arange(5, 100, 5)
x

array([ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85,
       90, 95])

x.dtype # Integers!

dtype('int64')

x + 1 # add 1!

array([ 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86,
       91, 96])

x = x + 3.0 # add a float to some integers, can we do that?
x

array([ 8., 13., 18., 23., 28., 33., 38., 43., 48., 53., 58., 63., 68.,
       73., 78., 83., 88., 93., 98.])

x.dtype # but now it became floats!

dtype('float64')

xr = np.random.random(10)
xr

array([0.35768268, 0.6889755 , 0.1592107 , 0.63488875, 0.32039466,
       0.03918149, 0.16808186, 0.06856908, 0.765837  , 0.60742217])

xr.mean()

0.38102438833192964

xr.std()

0.2592044030162411

xr.max()

0.7658370025427886

xr - xr.mean()

array([-0.02334171,  0.30795111, -0.22181369,  0.25386436, -0.06062973,
       -0.3418429 , -0.21294253, -0.31245531,  0.38481261,  0.22639778])

xn = np.random.normal(loc=5.0, scale=2.0, size=100)
xn[30] = 99.0

mu = xn.mean()
sigma = xn.std()

xn[xn < mu - 3*sigma]

array([], dtype=float64)

xn[xn > mu + 3*sigma]

array([99.])

Missing values (delete values)

NumPy has support for missing values.

y = np.random.random(10)
y

array([0.77554858, 0.95861717, 0.48472919, 0.06205427, 0.27357326,
       0.9851281 , 0.63129154, 0.89431399, 0.683834  , 0.5429035 ])

y[5:] = np.nan
y

array([0.77554858, 0.95861717, 0.48472919, 0.06205427, 0.27357326,
              nan,        nan,        nan,        nan,        nan])

y.mean()

nan

np.nanmean(y)

0.5109044940187875

y * np.pi

array([2.43645773, 3.01158467, 1.52282166, 0.19494923, 0.85945573,
              nan,        nan,        nan,        nan,        nan])

Boolean indexing

z = np.random.normal(loc=0.0, scale=3.0, size=10)

z_sorted = np.sort(z)
z_sorted

array([-5.15264602, -4.00480408, -3.2023718 ,  0.25670486,  0.6500434 ,
        1.00857388,  2.66170335,  4.42462713,  5.44320422,  5.5993012 ])

z<0.0

array([False, False,  True, False, False, False, False,  True, False,
        True])

z_sorted<0.0

array([ True,  True,  True, False, False, False, False, False, False,
       False])

z_sorted[z_sorted<0.0]

array([-5.15264602, -4.00480408, -3.2023718 ])

z_sorted[z_sorted<0.0] = 0.0

z_sorted

array([0.        , 0.        , 0.        , 0.25670486, 0.6500434 ,
       1.00857388, 2.66170335, 4.42462713, 5.44320422, 5.5993012 ])

np.where(z<0.0)

(array([2, 7, 9]),)

xn = np.random.normal(loc=5.0, scale=2.0, size=100)

xn[30] = 99.0 # outlier

median = np.median(xn)
sigma = xn.std()

sigma # sample std affected by outlier

9.567980749793008

xn[xn > median + 3*sigma] # but 1 abnormally high value

array([99.])

xn[xn > median + 3*sigma] = np.nan

np.nanstd(xn) # much closer to the true std==2.0

2.1388685746394196

2D arrays

X = np.array([
              [0.0, 1.0, 2.0],
              [3.0, 4.0, 5.0]
])
    

X

array([[0., 1., 2.],
       [3., 4., 5.]])

X.shape

(2, 3)

nrows = X.shape[0]
nrows

2

ncols = X.shape[1]
ncols

3

X[0,0]

0.0

X[1,1]

4.0

X[-1,-1]

5.0

X[0,:]

array([0., 1., 2.])

X[0]

array([0., 1., 2.])

X.mean()

2.5

colmeans = X.mean(axis=0)
colmeans

array([1.5, 2.5, 3.5])

colmeans.shape

(3,)

rowmeans = X.mean(axis=1)
rowmeans

array([1., 4.])

X - colmeans

array([[-1.5, -1.5, -1.5],
       [ 1.5,  1.5,  1.5]])

X - rowmeans    # this will fail

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[63], line 1
----> 1 X - rowmeans    # this will fail

ValueError: operands could not be broadcast together with shapes (2,3) (2,) 

NumPy broadcasting (detailed explanation of how arrays can be used in expressions)

R = rowmeans[:, np.newaxis] # add a new dimension to create a 2D array
R

np.expand_dims(rowmeans, 1) # same result

X.shape

R.shape

X - R

Reshaping

x = X.flatten()

x

x.reshape(2,3)