NumPy Array Arithmetic

Table of Contents

• Introduction
• NumPy Addition +
• NumPy Subtraction -
• NumPy Negation -
• NumPy Multiplication *
• NumPy Division /
• NumPy Floor Division //
• NumPy Power **
• NumPy Modulus/Remainder %
• Compound ufunc Operations
• Commonly Used Mathematical Functions

Introduction

NumPy’s ufuncs make use of Python’s built-in arithmetic operators such as +, -, * and / and are therefore very convenient to implement. By using the ufuncs, an operation on the array is equivalent to the same operation applied to each and every element.

The following table lists the basic arithmetic operators in NumPy.

Note that the arithmetic operators (first column) are simply convenient wrappers for the corresponding NumPy ufuncs. For example, the + operator is a wrapper for the np.add function.

We will present examples of the above arithmetic operations in the following sections. First, let’s create two arrays using the numpy.arange function.

1import numpy as np
2a= np.arange(11,20)
3b= np.arange(1,10)
4print(a)
5print(b)

[11 12 13 14 15 16 17 18 19]

[1 2 3 4 5 6 7 8 9]

NumPy Addition +

Example

1print(a+2)
2print(a+b)

[13 14 15 16 17 18 19 20 21]

[12 14 16 18 20 22 24 26 28]

The same operations could have been accomplished using np.add.

1print(np.add(a,2))
2print(np.add(a,b))

[13 14 15 16 17 18 19 20 21]

[12 14 16 18 20 22 24 26 28]

NumPy Subtraction -

Example

1print(a-2)
2print(a-b)

[ 9 10 11 12 13 14 15 16 17]

[10 10 10 10 10 10 10 10 10]

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NumPy Negation -

Example

1print(-a)
2print(-b)
3print(--a) # applied twice

[-11 -12 -13 -14 -15 -16 -17 -18 -19]

[-1 -2 -3 -4 -5 -6 -7 -8 -9]

[11 12 13 14 15 16 17 18 19]

NumPy Multiplication *

Example

1print(a*2)
2print(a*b)

[22 24 26 28 30 32 34 36 38]

[ 11  24  39  56  75  96 119 144 171]

In the first example, each element of array a is multiplied by 2. In the second example, each element of array a is multiplied by the corresponding element in array b.

Example

1print(2*a)

[22 24 26 28 30 32 34 36 38]

In the above example, the number 2 is multiplied by each element of array a. This is the same as the previous example when each element of array a is multiplied by 2.

NumPy Division /

Example

1print(a/2)
2print(a/b)

[5.5   6.  6.5   7.  7.5   8.  8.5   9.  9.5]

[11.          6.     4.33333333      3.5     3.     2.66666667
2.42857143  2.25     2.11111111]

NumPy Floor Division //

Example

1print(a//2)
2print(a//b)

    [5 6 6 7 7 8 8 9 9]

    [11  6  4  3  3  2  2  2  2]

Compare the current outputs with the outputs from the previous example. The numbers here are simply truncated at the decimal point to return the largest possible integer.

NumPy Power **

Example

1print(a**2)
2print(a**b)

[121 144 169 196 225 256 289 324 361]

[         11         144        2197       38416      759375    16777216
410338673 -1864941312   565150579]

In fact a**2 is equivalent to

$$[{11}^2~ {12}^2~ {13}^2~ {14}^2~ {15}^2~ {16}^2~ {17}^2~ {18}^2~ {19}^2]$$

whereas 2**a is equivalent to

$$[2^{11}~ 2^{12}~ 2^{13}~ 2^{14}~ 2^{15}~ 2^{16}~ 2^{17}~ 2^{18}~ 2^{19}]$$

The following example computes 2**a.

1print(2**a)

[  2048   4096   8192  16384  32768  65536 131072 262144 524288]

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NumPy Modulus/Remainder %

The % operator computes the remainder when the first input a is divided by the second input b. The numpy.mod ufunc can also take floats as arguments.

Example

1print(a%2)
2print(a%2.3)

[1 0 1 0 1 0 1 0 1]

[1.8 0.5 1.5 0.2 1.2 2.2 0.9 1.9 0.6]

For the first element of the second example, 11 % 2.3 = 1.8 since the remainder of $\frac{11}{2.3}$ can be computed as:

$$ 11 - 4\times 2.3 = 1.8 $$

In fact, the quotient 4.0 above can be obtained using floor division: 11//2.3=4.0.

Compound ufunc Operations

In case you encounter several operators in a single line, just follow the PEDMAS rule.

Example

1print(a-b*2)
2print(a*b-2)

[9 8 7 6 5 4 3 2 1]

[  9  22  37  54  73  94 117 142 169]

Commonly Used Mathematical Functions

Other commonly used mathematical functions include: