
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
PyTorch – How to compute Singular Value Decomposition (SVD) of a matrix?
torch.linalg.svd() computes the singular value decomposition (SVD) of a matrix or a batch of matrices. Singular value decomposition is represented as a named tuple (U, S, Vh).
U and Vh are orthogonal for real matrix and unitary for input complex matrix.
Vh is transpose of V when V is a real value and conjugate transpose when V is complex.
S is always real valued even when the input is complex.
Syntax
U, S, Vh = torch.linalg.svd(A, full_matrices=True)
Parameters
A – PyTorch tensor (matrix or batch of matrices).
full_matrices – If True, the output is a full SVD, else a reduced SVD. Default is True.
Output
It returns a named tuple (U, S, Vh).
Steps
Import the required library.
import torch
Create a matrix or batch of matrices.
A = torch.randn(3,4)
Compute the SVD of above-created matrix or batch of matrices.
U, S, Vh = torch.linalg.svd(A)
Display U, S and Vh.
print("U:
",U) print("S:
",S) print("Vh:
",Vh)
Example 1
The following Python program shows how to compute the SVD of a matrix.
# import necessary library import torch # create a matrix A = torch.randn(3,4) print("Matrix:
", A) # compute SVD U, S, Vh = torch.linalg.svd(A) # print U, S, and Vh print("U:
",U) print("S:
",S) print("Vh:
",Vh)
Output
Matrix: tensor([[-1.5122, -0.4714, -0.1173, -0.3914], [ 0.4288, -1.9329, 0.9171, -1.0288], [ 0.1143, 0.1989, 0.3290, 0.3031]]) U: tensor([[ 0.1769, 0.9716, 0.1569], [ 0.9815, -0.1860, 0.0448], [-0.0728, -0.1460, 0.9866]]) S: tensor([2.4383, 1.6226, 0.4119]) Vh: tensor([[ 0.0595, -0.8182, 0.3508, -0.4516], [-0.9649, -0.0787, -0.2050, -0.1438], [-0.2554, 0.0864, 0.8433, 0.4650], [ 0.0092, -0.5629, -0.3519, 0.7478]])
Example 2
The following Python program shows how to compute the SVD of a complex matrix.
# import necessary library import torch # create a matrix of complex random number A = torch.randn(2,2, dtype = torch.cfloat) print("Complex Matrix:
", A) # compute SVD U, S, Vh = torch.linalg.svd(A) # print U, S, and Vh print("U:
",U) print("S:
",S) print("Vh:
",Vh)
Output
Complex Matrix: tensor([[-0.2761-0.6619j, -1.4248-0.3026j], [-0.2797+0.2036j, 0.2143+1.3459j]]) U: tensor([[-0.2670-0.7083j, 0.3372+0.5597j], [-0.4943+0.4273j, -0.4737+0.5905j]]) S: tensor([2.1358, 0.2259]) Vh: tensor([[ 0.3595+0.0000j, 0.4981-0.7891j], [-0.9332+0.0000j, 0.1919-0.3040j]])
Example 3
The following Python program shows how to compute the SVD of a batch of three matrices.
# import necessary library import torch # create a batch of three 2x3 matrices A = torch.randn(3,2,3) print("Matrices:
", A) # compute SVD U, S, Vh = torch.linalg.svd(A) #print U, S, and Vh print("U:
",U) print("S:
",S) print("Vh:
",Vh)
Output
Matrices: tensor([[[ 0.2195, -1.3015, -1.0770], [-0.5884, -0.8269, 0.0135]], [[ 1.0753, -1.7080, -0.3692], [-1.3024, 0.2581, -1.2018]], [[-0.3576, -1.0531, -0.6192], [ 0.8453, 0.4187, -0.1622]]]) U: tensor([[[ 0.9242, -0.3818], [ 0.3818, 0.9242]], [[ 0.8178, 0.5755], [-0.5755, 0.8178]], [[ 0.8604, 0.5097], [-0.5097, 0.8604]]]) S: tensor([[1.8131, 0.8030], [2.2789, 1.4912], [1.4146, 0.7317]]) Vh: tensor([[[-0.0120, -0.8376, -0.5462], [-0.7815, -0.3329, 0.5276], [ 0.6237, -0.4332, 0.6506]], [[ 0.7148, -0.6781, 0.1710], [-0.2993, -0.5176, -0.8015], [-0.6321, -0.5217, 0.5730]], [[-0.5221, -0.7913, -0.3182], [ 0.7448, -0.2413, -0.6221], [ 0.4155, -0.5617, 0.7154]]])