Numpy matrix multiply python

Numpy | Array Creation
numpy.arange() in Python
numpy.zeros() in Python
Create a Numpy array filled with all ones
numpy.linspace() in Python
numpy.eye() in Python
Creating a one-dimensional NumPy array
How to create an empty and a full NumPy array?
Create a Numpy array filled with all zeros | Python
How to generate 2-D Gaussian array using NumPy?
How to create a vector in Python using NumPy
Python | Numpy fromrecords() method

Copy and View in NumPy Array
How to Copy NumPy array into another array?
Appending values at the end of an NumPy array
How to swap columns of a given NumPy array?
Insert a new axis within a NumPy array
numpy.hstack() in Python
numpy.vstack() in python
Joining NumPy Array
Combining a one and a two-dimensional NumPy Array
Python | Numpy np.ma.concatenate() method
Python | Numpy dstack() method
Splitting Arrays in NumPy
How to compare two NumPy arrays?
Find the union of two NumPy arrays
Find unique rows in a NumPy array
Python | Numpy np.unique() method
numpy.trim_zeros() in Python

Matrix manipulation in Python
numpy matrix operations | empty() function
numpy matrix operations | zeros() function
numpy matrix operations | ones() function
numpy matrix operations | eye() function
numpy matrix operations | identity() function
Adding and Subtracting Matrices in Python
Matrix Multiplication in NumPy
Numpy ndarray.dot() function | Python
NumPy | Vector Multiplication
How to calculate dot product of two vectors in Python?
Multiplication of two Matrices in Single line using Numpy in Python
Python | Numpy np.eigvals() method
How to Calculate the determinant of a matrix using NumPy?
Python | Numpy matrix.transpose()
Python | Numpy matrix.var()
Compute the inverse of a matrix using NumPy

Reshape NumPy Array
Python | Numpy matrix.resize()
Python | Numpy matrix.reshape()
NumPy Array Shape
Change the dimension of a NumPy array
numpy.ndarray.resize() function – Python
Flatten a Matrix in Python using NumPy
numpy.moveaxis() function | Python
numpy.swapaxes() function | Python
Python | Numpy matrix.swapaxes()
numpy.vsplit() function | Python
numpy.hsplit() function | Python
Numpy MaskedArray.reshape() function | Python
Python | Numpy matrix.squeeze()

Random sampling in numpy | ranf() function
Random sampling in numpy | random() function
Random sampling in numpy | random_sample() function
Random sampling in numpy | sample() function
Random sampling in numpy | random_integers() function
Random sampling in numpy | randint() function
numpy.random.choice() in Python
How to choose elements from the list with different probability using NumPy?
How to get weighted random choice in Python?
numpy.random.shuffle() in python
numpy.random.geometric() in Python
numpy.random.permutation() in Python

Numpy | Array Creation
numpy.arange() in Python
numpy.zeros() in Python
Create a Numpy array filled with all ones
numpy.linspace() in Python
numpy.eye() in Python
Creating a one-dimensional NumPy array
How to create an empty and a full NumPy array?
Create a Numpy array filled with all zeros | Python
How to generate 2-D Gaussian array using NumPy?
How to create a vector in Python using NumPy
Python | Numpy fromrecords() method

Copy and View in NumPy Array
How to Copy NumPy array into another array?
Appending values at the end of an NumPy array
How to swap columns of a given NumPy array?
Insert a new axis within a NumPy array
numpy.hstack() in Python
numpy.vstack() in python
Joining NumPy Array
Combining a one and a two-dimensional NumPy Array
Python | Numpy np.ma.concatenate() method
Python | Numpy dstack() method
Splitting Arrays in NumPy
How to compare two NumPy arrays?
Find the union of two NumPy arrays
Find unique rows in a NumPy array
Python | Numpy np.unique() method
numpy.trim_zeros() in Python

Matrix manipulation in Python
numpy matrix operations | empty() function
numpy matrix operations | zeros() function
numpy matrix operations | ones() function
numpy matrix operations | eye() function
numpy matrix operations | identity() function
Adding and Subtracting Matrices in Python
Matrix Multiplication in NumPy
Numpy ndarray.dot() function | Python
NumPy | Vector Multiplication
How to calculate dot product of two vectors in Python?
Multiplication of two Matrices in Single line using Numpy in Python
Python | Numpy np.eigvals() method
How to Calculate the determinant of a matrix using NumPy?
Python | Numpy matrix.transpose()
Python | Numpy matrix.var()
Compute the inverse of a matrix using NumPy

Reshape NumPy Array
Python | Numpy matrix.resize()
Python | Numpy matrix.reshape()
NumPy Array Shape
Change the dimension of a NumPy array
numpy.ndarray.resize() function – Python
Flatten a Matrix in Python using NumPy
numpy.moveaxis() function | Python
numpy.swapaxes() function | Python
Python | Numpy matrix.swapaxes()
numpy.vsplit() function | Python
numpy.hsplit() function | Python
Numpy MaskedArray.reshape() function | Python
Python | Numpy matrix.squeeze()

Random sampling in numpy | ranf() function
Random sampling in numpy | random() function
Random sampling in numpy | random_sample() function
Random sampling in numpy | sample() function
Random sampling in numpy | random_integers() function
Random sampling in numpy | randint() function
numpy.random.choice() in Python
How to choose elements from the list with different probability using NumPy?
How to get weighted random choice in Python?
numpy.random.shuffle() in python
numpy.random.geometric() in Python
numpy.random.permutation() in Python

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numpy.matmul#

A location into which the result is stored. If provided, it must have a shape that matches the signature (n,k),(k,m)->(n,m). If not provided or None, a freshly-allocated array is returned.

For other keyword-only arguments, see the ufunc docs .

New in version 1.16: Now handles ufunc kwargs

The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors.

If the last dimension of x1 is not the same size as the second-to-last dimension of x2.

If a scalar value is passed in.

Complex-conjugating dot product.

Sum products over arbitrary axes.

Einstein summation convention.

alternative matrix product with different broadcasting rules.

The behavior depends on the arguments in the following way.

If both arguments are 2-D they are multiplied like conventional matrices.
If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly.
If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed.
If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed.

matmul differs from dot in two important ways:

Multiplication by scalars is not allowed, use * instead.
Stacks of matrices are broadcast together as if the matrices were elements, respecting the signature (n,k),(k,m)->(n,m) :

>>> a = np.ones([9, 5, 7, 4]) >>> c = np.ones([9, 5, 4, 3]) >>> np.dot(a, c).shape (9, 5, 7, 9, 5, 3) >>> np.matmul(a, c).shape (9, 5, 7, 3) >>> # n is 7, k is 4, m is 3

The matmul function implements the semantics of the @ operator introduced in Python 3.5 following PEP 465.

It uses an optimized BLAS library when possible (see numpy.linalg ).

For 2-D arrays it is the matrix product:

>>> a = np.array([[1, 0], . [0, 1]]) >>> b = np.array([[4, 1], . [2, 2]]) >>> np.matmul(a, b) array([[4, 1], [2, 2]])

For 2-D mixed with 1-D, the result is the usual.

>>> a = np.array([[1, 0], . [0, 1]]) >>> b = np.array([1, 2]) >>> np.matmul(a, b) array([1, 2]) >>> np.matmul(b, a) array([1, 2])

Broadcasting is conventional for stacks of arrays

>>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4)) >>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2)) >>> np.matmul(a,b).shape (2, 2, 2) >>> np.matmul(a, b)[0, 1, 1] 98 >>> sum(a[0, 1, :] * b[0 , :, 1]) 98

Vector, vector returns the scalar inner product, but neither argument is complex-conjugated:

Scalar multiplication raises an error.

>>> np.matmul([1,2], 3) Traceback (most recent call last): . ValueError: matmul: Input operand 1 does not have enough dimensions .

The @ operator can be used as a shorthand for np.matmul on ndarrays.

>>> x1 = np.array([2j, 3j]) >>> x2 = np.array([2j, 3j]) >>> x1 @ x2 (-13+0j)

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NumPy matrix multiplication: Get started in 5 minutes

NumPy is a popular Python library that offers a range of powerful mathematical functions. The library is widely used in quantitative fields, such as data science, machine learning, and deep learning. We can use NumPy to perform complex mathematical calculations, such as matrix multiplication.

NumPy matrix multiplication can help give us quick approximations of very complicated calculations. It can help us with network theory, linear systems of equations, population modeling, and much more. In this tutorial, we’ll explore some basic computations with NumPy matrix multiplication and matrix operations.

Learn to code today.

What is NumPy?

NumPy is an open-source Python library that we can use to perform high-level mathematical operations with arrays, matrices, linear algebra, Fourier analysis, and more. The NumPy library is very popular in scientific computing, data science, and machine learning. NumPy is compatible with various data types and other popular data science libraries like pandas, matplotlib, and Scikit-learn. It’s much faster than Python lists because it integrates faster codes, such as C and C++, in Python. It also breaks down our tasks into multiple pieces and processes each piece concurrently.

Installing and importing NumPy

Before we get started, let’s make sure we have NumPy installed. If you already have Python, you can install NumPy with one of the following commands:

To import NumPy into our Python code, we can use the following command:

If you’re looking to learn Python data structures, start off with this helpful Python tutorial!

What is a NumPy matrix?

A matrix is a 2-D array. Each element in the array has two indices. Let’s look at an example in NumPy:

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NumPy Matrix Multiplication

While we believe that this content benefits our community, we have not yet thoroughly reviewed it. If you have any suggestions for improvements, please let us know by clicking the “report an issue“ button at the bottom of the tutorial.

multiply(): element-wise matrix multiplication.
matmul(): matrix product of two arrays.
dot(): dot product of two arrays.

1. NumPy Matrix Multiplication Element Wise

If you want element-wise matrix multiplication, you can use multiply() function.

import numpy as np arr1 = np.array([[1, 2], [3, 4]]) arr2 = np.array([[5, 6], [7, 8]]) arr_result = np.multiply(arr1, arr2) print(arr_result)

The below image shows the multiplication operation performed to get the result matrix.

2. Matrix Product of Two NumPy Arrays

If you want the matrix product of two arrays, use matmul() function.

import numpy as np arr1 = np.array([[1, 2], [3, 4]]) arr2 = np.array([[5, 6], [7, 8]]) arr_result = np.matmul(arr1, arr2) print(f'Matrix Product of arr1 and arr2 is:\n') arr_result = np.matmul(arr2, arr1) print(f'Matrix Product of arr2 and arr1 is:\n')

Matrix Product of arr1 and arr2 is: [[19 22] [43 50]] Matrix Product of arr2 and arr1 is: [[23 34] [31 46]]

The below diagram explains the matrix product operations for every index in the result array. For simplicity, take the row from the first array and the column from the second array for each index. Then multiply the corresponding elements and then add them to reach the matrix product value.

The matrix product of two arrays depends on the argument position. So matmul(A, B) might be different from matmul(B, A).

3. Dot Product of Two NumPy Arrays

The numpy dot() function returns the dot product of two arrays. The result is the same as the matmul() function for one-dimensional and two-dimensional arrays.

import numpy as np arr1 = np.array([[1, 2], [3, 4]]) arr2 = np.array([[5, 6], [7, 8]]) arr_result = np.dot(arr1, arr2) print(f'Dot Product of arr1 and arr2 is:\n') arr_result = np.dot(arr2, arr1) print(f'Dot Product of arr2 and arr1 is:\n') arr_result = np.dot([1, 2], [5, 6]) print(f'Dot Product of two 1-D arrays is:\n')

Dot Product of arr1 and arr2 is: [[19 22] [43 50]] Dot Product of arr2 and arr1 is: [[23 34] [31 46]] Dot Product of two 1-D arrays is: 17

References

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