Numpy dot Product

Numpy is one of the Powerful Python Data Science Libraries. It comes with a built-in robust Array data structure that can be used for many mathematical operations. The numpy library supports many methods and numpy.dot() is one of those. Using the numpy dot() method, we can calculate the dot product of two arrays. The numpy dot(array1,array2) method accepts two arrays as a parameter and returns their dot product or matrix multiplication.

Numpy dot() syntax

numpy.dot(array1, array2, out=None)

Parameters

arrray1 and array2 represent the array-like structure. The out parameter represents the output argument. By default, its value is None, and if specified explicitly, it needs to be the exact kind of return output of the dot() method.

Return value

The dot() product returns a ndarray.

Python numpy dot() method examples

Example1:

Python dot() product if both array1 and array2 are 1-D arrays.

>>> import numpy as np
>>> array1 = [1,2,3]
>>> array2 = [4,5,6]
>>> print(np.dot(array1, array2))
32

If both the arrays are 1D, the dot() method performs the inner product between the arrays and returns the output as a number.

>>>1*4 + 2*5 + 3*6
>>>4+10+18
32

Example 2: Python dot() product if both array1 and array2 are 2-D arrays

>>> import numpy as np
>>> array1 = [[4,0], [1,-9]]
>>> array2 = [[8,0],[2,-18]]
>>> print(np.dot(array1, array2))
[[ 32 0]
[-10 162]]

If both arrays are 2D, the dot will perform the matrix multiplication between them.

>>>[[4*8 + 0*2, 4*0 + 0*-18 ]
 [1*8 + -9*2, 1*0 + -9*-18 ]

>>>[[32, 0]
    [-10, 162]]

Note: As a matrix multiplication, the row size of array1 must be equal to the column size of array2 else, the dot() method throws a ValueError.

Example3:

Python dot() product if either of array1 or array2 is a 0-D(scalar) array

>>> import numpy as np
>>> array1 = 10
>>> array2 = [[8,0],[2,-18]]
>>> print(np.dot(array1, array2))
[[ 80 0]
[ 20 -180]]

If one array of either is a 0-D array, the dot() multiply the 0-D array with the other array.

Summary

The numpy dot() method finds out the product of two arrays based on their shape. Here are some important facts about dot(array1, array2) method of how it computes the product for different array shapes.

• If array1, and array2 are 1-D array, the dot() method performs inner product between both the arrays.
• If array1 and array2 are 2D arrays, the numpy dot() method performs matrix multiplication between them.
• If anyone between the array1 or array2 is a scalar or 1d array, the numpy dot() method will multiply that 1d or scalar number with another array.
• If array1 is an N-D array and array2 is a 1-D array, then the numpy dot() method will calculate the sum-product over the last axis of array1 and array2.
• If array1 is an N-D array and array2 is an M-D array (M>=2 ), then the dot() method will calculate the sum-product over the last axis of array1 and second to the last axis of array2.

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