Arithmetic Operations and Universal Functions in Numpy¶

Numpy provides support for large, multi-dimensional arrays and matrices, along with a collection of mathematical functions to operate on them efficiently. Understanding how to perform arithmetic operations and utilize universal functions (ufuncs) is essential for data analysis, machine learning, and scientific computations.

Importing NumPy¶

Before you begin working with NumPy, you need to import the library. It's standard practice to import NumPy using the alias np for convenience.

In [1]:

import numpy as np

import numpy as np

Basic Arithmetic Operations¶

NumPy allows you to perform element-wise arithmetic operations on arrays. These operations are applied to each corresponding element of the arrays involved.

Creating Arrays¶

First, let's create two NumPy arrays:

In [2]:

# Creating two arrays
arr1 = np.arange(0, 5)
arr2 = np.arange(6, 11)

# Creating two arrays arr1 = np.arange(0, 5) arr2 = np.arange(6, 11)

• arr1 will contain [0, 1, 2, 3, 4].
• arr2 will contain [6, 7, 8, 9, 10].

Addition¶

You can add two arrays element-wise using the + operator:

In [3]:

# Element-wise addition
addition_result = arr1 + arr2
addition_result

# Element-wise addition addition_result = arr1 + arr2 addition_result

Out[3]:

array([ 6,  8, 10, 12, 14])

This operation adds each element of arr1 to the corresponding element in arr2.

Subtraction¶

Subtraction is also performed element-wise using the - operator:

In [4]:

# Element-wise subtraction
subtraction_result = arr2 - arr1

# Element-wise subtraction subtraction_result = arr2 - arr1

This subtracts each element of arr1 from the corresponding element in arr2.

Multiplication¶

Element-wise multiplication uses the *** operator:

In [5]:

# Element-wise multiplication
multiplication_result = arr1 * arr2

# Element-wise multiplication multiplication_result = arr1 * arr2

Each element in arr1 is multiplied by the corresponding element in arr2.

Division¶

Element-wise division is performed using the / operator:

In [6]:

# Element-wise division
division_result = arr1 / arr2

# Element-wise division division_result = arr1 / arr2

This divides each element in arr1 by the corresponding element in arr2.

Note: Be cautious of division by zero. In this example, arr1 starts with 0, but since arr2 does not contain zero, division by zero does not occur.

Exponentiation (Squaring)¶

You can raise each element of an array to a power using the **** operator:

In [7]:

# Element-wise exponentiation (squaring arr1)
squared_result = arr1 ** 2

# Element-wise exponentiation (squaring arr1) squared_result = arr1 ** 2

This squares each element in arr1.

Universal Functions (ufuncs)¶

Universal functions, or ufuncs, are functions that operate element-wise on arrays. They are highly optimized and support broadcasting, typecasting, and several other features.

Mathematical Functions¶

NumPy provides a range of mathematical functions that operate element-wise.

Addition (np.add)¶

In [8]:

# Using np.add to add two arrays
addition_result = np.add(arr1, arr2)

# Using np.add to add two arrays addition_result = np.add(arr1, arr2)

This function performs element-wise addition of arr1 and arr2.

Subtraction (np.subtract)¶

In [20]:

# Using np.subtract to subtract arr2 from arr1
subtraction_result = np.subtract(arr1, arr2)
subtraction_result

# Using np.subtract to subtract arr2 from arr1 subtraction_result = np.subtract(arr1, arr2) subtraction_result

Out[20]:

array([-6, -6, -6, -6, -6])

Subtracts each element in arr2 from the corresponding element in arr1.

Multiplication (np.multiply)¶

In [10]:

# Using np.multiply to multiply two arrays
multiplication_result = np.multiply(arr1, arr2)

# Using np.multiply to multiply two arrays multiplication_result = np.multiply(arr1, arr2)

Multiplies each element in arr1 by the corresponding element in arr2.

Division (np.divide)¶

In [11]:

# Using np.divide to divide arr1 by arr2
division_result = np.divide(arr1, arr2)

# Using np.divide to divide arr1 by arr2 division_result = np.divide(arr1, arr2)

Divides each element in arr1 by the corresponding element in arr2.

Power (np.power)¶

In [21]:

# Using np.power to raise elements of arr1 to powers from arr2
power_result = np.power(arr1, arr2)
power_result

# Using np.power to raise elements of arr1 to powers from arr2 power_result = np.power(arr1, arr2) power_result

Out[21]:

array([      0,       1,     256,   19683, 1048576])

Raises each element in arr1 to the power of the corresponding element in arr2. For example, arr1[0] raised to arr2[0] (i.e., 06**).

Trigonometric Functions¶

NumPy offers trigonometric functions that operate on arrays. The input values are assumed to be in radians.

Sine (np.sin)¶

In [13]:

# Calculating the sine of each element in arr1
sine_result = np.sin(arr1)

# Calculating the sine of each element in arr1 sine_result = np.sin(arr1)

Computes the sine of each element in arr1.

Cosine (np.cos)¶

In [14]:

# Calculating the cosine of each element in arr1
cosine_result = np.cos(arr1)

# Calculating the cosine of each element in arr1 cosine_result = np.cos(arr1)

Computes the cosine of each element in arr1.

Tangent (np.tan)¶

In [15]:

# Calculating the tangent of each element in arr2
tangent_result = np.tan(arr2)

# Calculating the tangent of each element in arr2 tangent_result = np.tan(arr2)

Computes the tangent of each element in arr2.

Note: Trigonometric functions expect input in radians. If you have degrees, convert them using np.deg2rad().

Exponential and Logarithmic Functions¶

Exponential (np.exp)¶

In [16]:

# Calculating the exponential (e^x) of each element in arr2
exponential_result = np.exp(arr2)

# Calculating the exponential (e^x) of each element in arr2 exponential_result = np.exp(arr2)

Computes the exponential of each element in arr2.

Logarithm (np.log)¶

In [17]:

# Calculating the natural logarithm of each element in arr2
logarithm_result = np.log(arr2)

# Calculating the natural logarithm of each element in arr2 logarithm_result = np.log(arr2)

Computes the natural logarithm (base e) of each element in arr2.

Note: All elements in arr2 must be positive for np.log to work properly.

Comparison Functions¶

Comparison functions perform element-wise comparisons and return boolean arrays.

Greater (np.greater)¶

In [18]:

# Comparing elements of arr1 and arr2
greater_result = np.greater(arr1, arr2)

# Comparing elements of arr1 and arr2 greater_result = np.greater(arr1, arr2)

Returns True where elements in arr1 are greater than those in arr2, else False.

Less (np.less)¶

In [19]:

# Checking if elements in arr1 are less than those in arr2
less_result = np.less(arr1, arr2)

# Checking if elements in arr1 are less than those in arr2 less_result = np.less(arr1, arr2)

Returns True where elements in arr1 are less than those in arr2, else False.

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