PyTorch torch.linalg.pinv Function
Pytorch torch Reference Manual
torch.linalg.pinvIt is a function in the PyTorch linear algebra module used to compute the Moore-Penrose pseudo-inverse of a matrix. For non-square or singular matrices, the pseudo-inverse is an important tool.
Function Definition
torch.linalg.pinv(A, rcond=None, hermitian=False, out=None)
Parameters:
A(Tensor): The input matrix.rcond(float, optional): Singular value truncation threshold.hermitian(bool, optional): If True, the matrix is assumed to be Hermitian. Defaults to False.out(Tensor, optional): The output tensor.
Return Value:
torch.Tensor: Returns the pseudo-inverse of the matrix.
Usage Example
Example
import torch
# Create a non-square matrix
A = torch.tensor([[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]], dtype=torch.float64)
# Compute the pseudo-inverse
A_pinv = torch.linalg.pinv(A)
print("Matrix A:")
print(A)
print("nPseudo-inverse A^+:")
print(A_pinv)
print("nVerification: A @ A^+ @ A ≈ A")
print(A @ A_pinv @ A)
# Create a non-square matrix
A = torch.tensor([[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0]], dtype=torch.float64)
# Compute the pseudo-inverse
A_pinv = torch.linalg.pinv(A)
print("Matrix A:")
print(A)
print("nPseudo-inverse A^+:")
print(A_pinv)
print("nVerification: A @ A^+ @ A ≈ A")
print(A @ A_pinv @ A)
The output result is:
矩阵 A:
tensor([[1., 2., 3.],
[4., 5., 6.]], dtype=torch.float64)
伪逆 A^+:
tensor([[-0.9444, 0.4444],
[-0.2778, 0.2778],
[ 0.3889, 0.1111]], dtype=float64)
验证: A @ A^+ @ A ≈ A
tensor([[ 1.0000e+00, 2.0000e+00, 3.0000e+00],
[ 4.0000e+00, 5.0000e+00, 6.0000e+00]], dtype=float64)
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