la_pseudoinverse::pinv Interface Reference

Compute the pseudo-inverse of a matrix. More...

Public Member Functions
real(sp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_s (a, rtol, err)
real(dp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_d (a, rtol, err)
real(qp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_q (a, rtol, err)
complex(sp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_c (a, rtol, err)
complex(dp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_z (a, rtol, err)
complex(qp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pseudoinverse_w (a, rtol, err)

Detailed Description

Compute the pseudo-inverse of a matrix.

This function computes the Moore-Penrose pseudo-inverse of a real or complex matrix $A$. The pseudo-inverse is computed using Singular Value Decomposition (SVD):

$A^+ = V \Sigma^+ U^T$

where $U$ and $V$ are unitary matrices, and $\Sigma^+$ is the pseudo-inverse of the singular values.

Parameters

[in]	A	The input matrix of size $[m, n]$.
[in]	rtol	(Optional) Relative tolerance for singular value truncation. If not provided, a default value is used.
[out]	err	(Optional) A state return flag. If an error occurs and err is not provided, the function will stop execution.

Returns

The pseudo-inverse matrix $A^+$ of size $[n, m]$.

Note

This function relies on LAPACK's SVD routines (GESVD or GESDD).

Warning

If rtol is too large, important singular values may be discarded, leading to inaccurate results.

Compute the pseudo-inverse of a matrix (subroutine version).

This subroutine computes the Moore-Penrose pseudo-inverse of a real or complex matrix $A$, storing the result in a pre-allocated output matrix $A^+$. The computation is based on Singular Value Decomposition (SVD):

$A^+ = V \Sigma^+ U^T$

where $U$ and $V$ are unitary matrices, and $\Sigma^+$ is the pseudo-inverse of the singular values.

Parameters

[in,out]	A	The input matrix of size $[m, n]$. Its contents may be modified.
[out]	pinva	The output pseudo-inverse matrix of size $[n, m]$.
[in]	rtol	(Optional) Relative tolerance for singular value truncation.
[out]	err	(Optional) A state return flag. If an error occurs and err is not provided, the function will stop execution.

Note

This subroutine is useful when the output matrix pinva is already allocated and avoids memory allocation inside the routine.

Warning

The input matrix A may be modified during computation.

Compute the pseudo-inverse of a matrix using the .pinv. operator.

This operator computes the Moore-Penrose pseudo-inverse of a real or complex matrix $A$ using Singular Value Decomposition (SVD):

$A^+ = V \Sigma^+ U^T$

where $U$ and $V$ are unitary matrices, and $\Sigma^+$ is the pseudo-inverse of the singular values.

Parameters

[in]

A

The input matrix of size $[m, n]$.

Returns

The pseudo-inverse matrix $A^+$ of size $[n, m]$.

Note

This operator is a shorthand for calling pinv(A), allowing expressions such as: $X = .pinv.A$

Warning

The accuracy of the pseudo-inverse depends on the condition number of $A$.

Compute the pseudo-inverse of a matrix.

This function computes the Moore-Penrose pseudo-inverse of a real or complex matrix $A$. The pseudo-inverse is computed using Singular Value Decomposition (SVD):

$A^+ = V \Sigma^+ U^T$

where $U$ and $V$ are unitary matrices, and $\Sigma^+$ is the pseudo-inverse of the singular values.

Parameters

[in]	A	The input matrix of size $[m, n]$.
[in]	rtol	(Optional) Relative tolerance for singular value truncation. If not provided, a default value is used.
[out]	err	(Optional) A state return flag. If an error occurs and err is not provided, the function will stop execution.

Returns

The pseudo-inverse matrix $A^+$ of size $[n, m]$.

Note

This function relies on LAPACK's SVD routines (*GESVD or *GESDD).

Warning

If rtol is too large, important singular values may be discarded, leading to inaccurate results.

Member Function/Subroutine Documentation

la_pseudoinverse_c()

complex(sp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_c	(	complex(sp), dimension(:,:), intent(in), target	a,
		real(sp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

la_pseudoinverse_d()

real(dp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_d	(	real(dp), dimension(:,:), intent(in), target	a,
		real(dp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

la_pseudoinverse_q()

real(qp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_q	(	real(qp), dimension(:,:), intent(in), target	a,
		real(qp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

la_pseudoinverse_s()

real(sp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_s	(	real(sp), dimension(:,:), intent(in), target	a,
		real(sp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

la_pseudoinverse_w()

complex(qp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_w	(	complex(qp), dimension(:,:), intent(in), target	a,
		real(qp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

la_pseudoinverse_z()

complex(dp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::pinv::la_pseudoinverse_z	(	complex(dp), dimension(:,:), intent(in), target	a,
		real(dp), intent(in), optional	rtol,
		type(la_state), intent(out), optional	err )

Parameters

[in]	a	Input matrix a[m,n]
[in]	rtol	[optional] ....
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns

Matrix pseudo-inverse

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The documentation for this interface was generated from the following file:

• la_pinv.f90