Python:NumPy .dot()

The .dot() method computes the dot product of an array with another array or scalar. For one-dimensional arrays, it calculates the standard inner product of vectors. When applied to two-dimensional arrays, it performs matrix multiplication. For arrays with higher dimensions, it executes a sum-product over the last axis of the first array and the second-to-last axis of the second array.

Syntax

ndarray.dot(b, out=None)

Parameters:

• ndarray: The first array (A) in the dot product operation (A $\cdot$ B).
• b: The second array (B) or scalar in the dot product operation.
• out (optional): An alternative output array to place the result in. It must have the same shape and buffer length as the expected output, but the type will be cast if necessary.

Return value:

Returns the dot product as a scalar, 2-D array, or ndarray, depending on the input dimensions.

Example

This example shows how to use the .dot() method for matrix multiplication between two 2D NumPy arrays, matrix_a and matrix_b:

# Import NumPy
import numpy as np

# Create the first 2x3 matrix
matrix_a = np.array([[1, 2, 3],
                     [4, 5, 6]])

# Create the second 3x2 matrix
matrix_b = np.array([[7, 8],
                     [9, 10],
                     [11, 12]])

# Use the '.dot()' method for matrix multiplication (2x3 @ 3x2 = 2x2)
result_matrix = matrix_a.dot(matrix_b)

print("Matrix A:")
print(matrix_a)
print("\nMatrix B:")
print(matrix_b)
print("\nResult (A.dot(B)):")
print(result_matrix)

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The output of the above code will be:

Matrix A:
[[1 2 3]
 [4 5 6]]

Matrix B:
[[ 7  8]
 [ 9 10]
 [11 12]]

Result (A.dot(B)):
[[ 58  64]
 [139 154]]

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Codebyte Example

In the following codebyte example, the .dot() method is used to calculate the inner product (dot product) of two one-dimensional vectors, vector_x and vector_y:

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Calculation breakdown:

$$\vec{x} \cdot \vec{y} = (1 \times 5) + (2 \times 6) + (3 \times 7) = 5 + 12 + 21 = 38$$