la_inverse::inv Interface Reference

Compute the inverse of a square matrix. More...

Public Member Functions
real(sp) function, dimension(:,:), allocatable	la_inverse_s (a, err)
real(dp) function, dimension(:,:), allocatable	la_inverse_d (a, err)
real(qp) function, dimension(:,:), allocatable	la_inverse_q (a, err)
complex(sp) function, dimension(:,:), allocatable	la_inverse_c (a, err)
complex(dp) function, dimension(:,:), allocatable	la_inverse_z (a, err)
complex(qp) function, dimension(:,:), allocatable	la_inverse_w (a, err)

Detailed Description

Compute the inverse of a square matrix.

This function computes the inverse of a real or complex square matrix \( A \). The inverse is computed using an LU decomposition with partial pivoting.

Parameters

[in]	A	The input square matrix of size \( [n, n] \).
[out]	err	(Optional) A state return flag. If an error occurs and err is not provided, the function will stop execution.

Returns

The inverse matrix \( A^{-1} \) of size \( [n, n] \).

Note

This function relies on LAPACK's LU decomposition routines (GETRF and GETRI).

Warning

The matrix \( A \) must be non-singular. If it is singular or nearly singular, the function will fail.

Compute the inverse of a square matrix.

This subroutine computes the inverse of a real or complex square matrix \( A \), either in-place or into a second matrix inva of the same shape. The inverse is computed using an LU decomposition with partial pivoting. Storage for the pivot indices may be provided, so that a repeated call performs no internal allocation of the pivot array.

Parameters

[in,out]	A	The input square matrix of size \( [n, n] \). In the in-place form it is replaced by its inverse \( A^{-1} \); in the split form it is read only.
[out]	inva	(Split form only) The inverse matrix \( A^{-1} \), of size \( [n, n] \).
[in,out]	pivot	(Optional) Storage array for the n diagonal pivot indices.
[out]	err	(Optional) A state return flag. If an error occurs and err is not provided, the function will stop execution.

Note

The in-place form is useful when memory efficiency is a priority, as it avoids additional allocations.

Warning

The matrix \( A \) must be non-singular. If it is singular or nearly singular, the computation will fail.

Compute the inverse of a square matrix using the .inv. operator.

This operator computes the inverse of a real or complex square matrix \( A \) using an LU decomposition with partial pivoting.

Parameters

[in]

A

The input square matrix of size \( [n, n] \).

Returns

The inverse matrix \( A^{-1} \) of size \( [n, n] \).

Note

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

Warning

The matrix \( A \) must be non-singular. If it is singular or nearly singular, the computation will fail.

Member Function/Subroutine Documentation

la_inverse_c()

complex(sp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_c	(	complex(sp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

la_inverse_d()

real(dp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_d	(	real(dp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

la_inverse_q()

real(qp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_q	(	real(qp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

la_inverse_s()

real(sp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_s	(	real(sp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

la_inverse_w()

complex(qp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_w	(	complex(qp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

la_inverse_z()

complex(dp) function, dimension(:,:), allocatable la_inverse::inv::la_inverse_z	(	complex(dp), dimension(:,:), intent(in)	a,
		type(la_state), intent(out), optional	err )

Parameters

[in]

a

Input matrix a[n,n]

Returns

Output matrix inverse

Parameters

[out]

err

[optional] state return flag. On error if not requested, the code will stop

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

• la_inverse.f90