la_pseudoinverse::operator(.pinv.) Interface Reference

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

Public Member Functions
real(sp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_s_operator (a)
real(dp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_d_operator (a)
real(qp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_q_operator (a)
complex(sp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_c_operator (a)
complex(dp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_z_operator (a)
complex(qp) function, dimension(size(a, 2, kind=ilp), size(a, 1, kind=ilp))	la_pinv_w_operator (a)

Detailed Description

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 $A$.

Member Function/Subroutine Documentation

la_pinv_c_operator()

complex(sp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_c_operator

(

complex(sp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

la_pinv_d_operator()

real(dp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_d_operator

(

real(dp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

la_pinv_q_operator()

real(qp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_q_operator

(

real(qp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

la_pinv_s_operator()

real(sp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_s_operator

(

real(sp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

la_pinv_w_operator()

complex(qp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_w_operator

(

complex(qp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

la_pinv_z_operator()

complex(dp) function, dimension(size(a,2,kind=ilp),size(a,1,kind=ilp)) la_pseudoinverse::operator(.pinv.)::la_pinv_z_operator

(

complex(dp), dimension(:,:), intent(in), target

a

)

Parameters

[in]

a

Input matrix a[m,n]

Returns

Result matrix

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

• la_pinv.f90