NumPy Matrix Library (Matrix)

NumPy contains a matrix librarynumpy.matlib, the functions in this module return a matrix, not an ndarray object.

numpy.matlibIt is specifically used to create and manipulate matrix objects. Although NumPy's core supports multi-dimensional arrays (ndarray), numpy.matlib provides some convenient functions that specifically return matrix types, making it easier for users to perform traditional linear algebra operations.

Amatrix is a rectangular array arranged byrowsand columns of elements.

The elements in a matrix can be numbers, symbols, or mathematical expressions. The following is a 2-row, 3-column matrix consisting of 6 numeric elements:

Transpose Matrix

In NumPy, besides using the numpy.transpose function to swap the dimensions of an array, you can also use theTattribute.

For example, given a matrix with m rows and n columns, using the t() function converts it into a matrix with n rows and m columns.

Example

import numpy as np a = np.arange(12).reshape(3,4) print ('Original array:') print (a) print ('\n') print ('Transposed array:') print (a.T)

The output result is as follows:

原数组：
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]


转置数组：
[[ 0  4  8]
 [ 1  5  9]
 [ 2  6 10]
 [ 3  7 11]]

matlib.empty()

The matlib.empty() function returns a new matrix, with the syntax format:

numpy.matlib.empty(shape, dtype, order)

Parameter description:

  • shape: Integer or tuple of integers defining the shape of the new matrix
  • Dtype: Optional, data type
  • order: C (row-major order) or F (column-major order)

Example

import numpy.matlib import numpy as np print (np.matlib.empty((2,2))) # Fill with random data

The output result is:

[[-1.49166815e-154 -1.49166815e-154]
 [ 2.17371491e-313  2.52720790e-212]]

numpy.matlib.zeros()

The numpy.matlib.zeros() function creates a matrix filled with 0s.

Example

import numpy.matlib import numpy as np print (np.matlib.zeros((2,2)))

The output result is:

[[0. 0.]
 [0. 0.]]

numpy.matlib.ones()

The numpy.matlib.ones() function creates a matrix filled with 1s.

Example

import numpy.matlib import numpy as np print (np.matlib.ones((2,2)))

The output result is:

[[1. 1.]
 [1. 1.]]

numpy.matlib.eye()

The numpy.matlib.eye() function returns a matrix with diagonal elements equal to 1 and all other positions equal to 0.

numpy.matlib.eye(n, M,k, dtype)

Parameter description:

  • n: Number of rows of the returned matrix
  • M: Number of columns of the returned matrix, default is n
  • k: Index of the diagonal
  • dtype: Data type

Example

import numpy.matlib import numpy as np print (np.matlib.eye(n = 3, M = 4, k = 0, dtype = float))

The output result is:

[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]

numpy.matlib.identity()

The numpy.matlib.identity() function returns an identity matrix of a given size.

An identity matrix is a square matrix. The elements on the diagonal from the upper-left to the lower-right (called the main diagonal) are all 1, and all other elements are 0.

Example

import numpy.matlib import numpy as np # Size is 5, type is floating-point print (np.matlib.identity(5, dtype = float))

The output result is:

[[ 1.  0.  0.  0.  0.] 
 [ 0.  1.  0.  0.  0.] 
 [ 0.  0.  1.  0.  0.] 
 [ 0.  0.  0.  1.  0.] 
 [ 0.  0.  0.  0.  1.]]

numpy.matlib.rand()

The numpy.matlib.rand() function creates a matrix of a given size, with data filled randomly.

Example

import numpy.matlib import numpy as np print (np.matlib.rand(3,3))

The output result is:

[[0.23966718 0.16147628 0.14162   ]
 [0.28379085 0.59934741 0.62985825]
 [0.99527238 0.11137883 0.41105367]]

Matrices are always two-dimensional, while ndarray is an n-dimensional array. The two objects are interchangeable.

Example

import numpy.matlib import numpy as np i = np.matrix('1,2;3,4') print (i)

The output result is:

[[1  2] 
 [3  4]]

Example

import numpy.matlib import numpy as np j = np.asarray(i) print (j)

The output result is:

[[1  2] 
 [3  4]]

Example

import numpy.matlib import numpy as np k = np.asmatrix (j) print (k)

The output result is:

[[1  2] 
 [3  4]]

The following functions also exist in the NumPy namespace, but they return matrix objects.

Function Name Parameter Description Function Description
matrix(data[, dtype, copy]) data: array-like or string, dtype: data type, copy: whether to copy Create a matrix object from an array or string
asmatrix(data[, dtype]) data: input data, dtype: data type (optional) Convert the input to a matrix object
bmat(obj[, ldict, gdict]) obj: string or nested sequence, ldict, gdict: namespace dictionaries (optional) Build a matrix from a string, nested sequence, or array
empty(shape[, dtype, order]) shape: shape, dtype: data type, order: storage order Create a matrix with uninitialized elements
zeros(shape[, dtype, order]) shape: shape, dtype: data type, order: storage order Create an all-zero matrix
ones(shape[, dtype, order]) shape: shape, dtype: data type, order: storage order Create an all-ones matrix
eye(n[, M, k, dtype, order]) n: number of rows, M: number of columns, k: diagonal offset, dtype: data type, order: storage order Create a matrix with 1s on the diagonal and 0s elsewhere
identity(n[, dtype]) n: size, dtype: data type (optional) Create an identity square matrix
repmat(a, m, n) a: array or matrix, m, n: number of repetitions Repeat the array or matrix for m rows and n columns
rand(args) args: Specify the matrix shape Generate a uniformly distributed random matrix of the specified shape
randn(args) args: Specify the matrix shape Generate a standard normal distribution random matrix of the specified shape

Notes

  • Althoughnumpy.matlibis convenient, the official NumPy recommendation is to use thendarrayand@operator to perform matrix operations, becausematrixthe type has some limitations and may be deprecated in future versions.
  • For new code, it is recommended to usendarrayfirst to ensure better compatibility and flexibility.
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