Python

# Numpy Dot Product

The Numpy dot product of Python will be discussed in this section. The dot() method in Numpy calculates the dot product for n-dimensional arrays in Numpy. The numpy.dot() operation takes two numpy arrays as input, computes the dot product between them, and returns the output. For 1D arrays, it is essentially the inner creation of the vectors. It does the dot product on two-dimensional arrays by treating them as matrices.

As a consequence, multiply them with matrix multiplication. We will explore how the numpy.dot() function works with vectors, scalars, matrices, and arrays.  Before we go any further, let us give you a quick rundown on the Numpy dot product’s syntax and return type in Python. You will get a hand on a guide on how to calculate the dot product in Python using Numpy in this post. The numpy.dot() method has the following syntax.

In this case, ‘a’ and ‘b’ are the two input arrays. Both arrays should be one-dimensional or two-dimensional. The output parameter for the 1-D array scalar to be returned is out. It returns the dot product of a and b arrays, respectively. The dot() function does the inner product of vectors and returns a scalar result if both arrays, in our example ‘a’ and ‘b,’ are 1-D arrays. The dot() method executes matrix multiplication if both arrays are 2-D arrays. The dot() method executes the sum-product across the last axis of a and b if ‘a’ is an N-dimensional array while ‘b’ is a 1-dimensional array. It is a product of the last axis of ‘a’ and the second-last axis of the specified variable ‘b’ over N-dimensional arrays. In machine learning, knowing how to interpret and calculate the dot product among vectors and scalars is crucial. This essay will explain what actually the dot product is and how to calculate it in detail. You will discover how to compute the dot product of two 1-dimensional arrays, a 1-dimensional array and a scalar, and two 2-dimensional arrays.

## Example 1:

In the preceding example, two scalar values are supplied as arguments to the np.dot() function. As a result, this numpy dot method multiplies two scalar values to get the dot product. np.dot() produces 24 when one = 6 and two = 4.

import numpy as np

one = 6

two = 4

res = np.dot(one,two)

print(res)

The following is the result of the scalar numpy dot product.

## Example 2:

The NumPy dot function determines the dot sum of two complex vectors in this example. Because ‘one’ and ‘two’ are complex, a complex conjugate of one of the two complex vectors is required. The complex conjugate of ‘two’ is employed in this case (6 + 7j) and (6_7j). The dot product is calculated using the np.dot() function as 3(6 + 7j) + 2j(6 – 7j). 18+ 21j + 12j – 14 = 4+33j is the #complex conjugate of ‘two’. As a result of supplying ‘one’ and ‘two’ as parameters to the np.dot() function, the output is (4+33j).

import numpy as np

one = 3 + 2j

two = 6 + 7j

res= np.dot(one, two)

print("Output : ", res)

The output of the preceding code is attached.

## Example 3:

The dot product of 1D Arrays is demonstrated in this example. To begin, two arrays are created by supplying the values for ‘one’ and ‘two’ to the np.array() method. The arrays declared as ‘one’ and ‘two’ are basically one-dimensional arrays. The dot product for these two 1D arrays is calculated using the NumPy dot function as follows:

[2, 3, 1, 6]. [1, 2, 3, 4] = 2*1 + 3*2 + 1*3 + 6*4 = 35

As a result of giving A and B one-dimensional arrays to the np.dot() function, the output is a scalar value of 35.

import numpy as np

one = np.array([2, 3, 1, 6])

two = np.array([1, 2, 3, 4])

res = np.dot(one, two)

print(res)

Refer to the attached screenshot to see the output.

## Example 4:

The Dot product over 2D arrays is our final example. The np.array() technique creates two arrays, one and two, in this case. The ‘one’ and ‘two’ arrays that have been constructed are two-dimensional arrays. The dot product of two input arrays is returned when two two-dimensional arrays are multiplied by a matrix. The dot product of 3D arrays is calculated as:

[[1, 0], [4, 3]].[[2, 3], [6, 7]]

= [[1*2+0*6, 1*3+0*7], [4*2+3*6, 4*3+3*7]]

= [[2, 3], [26, 33]

The resultant output is also a 2D array when one and two 2D arrays are passed to the np.dot() function.

import numpy as np

one = np.array([[1, 0], [4, 3]])

two = np.array([[2, 3], [6, 7]])

res = np.dot(one, two)

print(res)

The output, which is a 2D array, can be seen here.

## Conclusion:

NumPy is the most important Python package for numerical computation. It’s a numerical operations library that’s been efficient. NumPy’s support makes the job a lot easier. When used with NumPy, several libraries such as OpenCV, SciPy, and Matplotlib expand your programming knowledge. In this article, we learned about Python’s dot product. Python’s numpy.dot() feature returns the dot manufactured from two arrays. We included a way to discover the dot product from scalars and complex vectors. With thorough examples, we additionally discovered the way to use the NumPy dot characteristic on 1D and 2d arrays.