## 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.

Note
Ufuncs exist as two types:
• unary ufuncs: operate on a single input.
• binary ufuncs: operate on two inputs.

The following table lists the basic arithmetic operators in NumPy.

Operator ufunc Type Description Output
+ np.add(a,b) binary Addition a+b
- np.subtract(a,b) binary Subtraction a-b
- np.negative(a) unary Unary negation -a
* np.multiply(a,b) binary Multiplication a*b
/ np.divide(a,b) binary Division a/b
/ np.reciprocal(a) unary Reciprocal 1/a
// np.floor_divide(a,b) binary Floor division a//b
** np.power(a,b) binary Exponentiation a**b
% np.mod(a,b) binary Modulus/remainder a%b

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]


Example

NumPy addition with +.

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))

[13 14 15 16 17 18 19 20 21]

[12 14 16 18 20 22 24 26 28]


## NumPy Subtraction -

Example

NumPy subtraction with -.

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

[ 9 10 11 12 13 14 15 16 17]

[10 10 10 10 10 10 10 10 10]


## NumPy Negation -

Example

NumPy negation with -.

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

NumPy multiplication with *.

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.

Note

Both inputs in a binary ufunc can be either a scalar or an array.

Example

NumPy multiplication with *.

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

NumPy division with /.

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

NumPy floor division with //.

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

NumPy power with **.

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

[121 144 169 196 225 256 289 324 361]

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

Caution

a**2 is not the same as 2**a.

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]


## 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

NumPy Modulus/Remainder with %.

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.

👀 Review

Example

Compund operations with ufuncs.

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]

Tip

Whenever possible, always use parentheses to precisely define the order of operations you desire.

## Commonly Used Mathematical Functions

Other commonly used mathematical functions include:

ufunc Type Description Math Expression
np.sqrt(a) unary Square root $\sqrt{a}$
np.square(a) unary Square $a^2$
np.cbrt(a) unary Cube root $\sqrt{a}$
np.abs(a) unary Absolute value $| a |$