Compute the QR factorization of a matrix. More...

Public Member Functions
pure subroutine	la_s_qr (a, q, r, overwrite_a, storage, err)

pure subroutine	la_d_qr (a, q, r, overwrite_a, storage, err)

pure subroutine	la_q_qr (a, q, r, overwrite_a, storage, err)

pure subroutine	la_c_qr (a, q, r, overwrite_a, storage, err)

pure subroutine	la_z_qr (a, q, r, overwrite_a, storage, err)

pure subroutine	la_w_qr (a, q, r, overwrite_a, storage, err)

Detailed Description

Compute the QR factorization of a matrix.

This subroutine computes the QR factorization of a real or complex matrix:

$A = Q \cdot R$

where $A$ is a matrix of size $[m,n]$ with $m \ge n$ , $Q$ is an orthonormal matrix, and $R$ is an upper-triangular matrix. The result is returned in the output matrices $Q$ and $R$ , which are of the same type and kind as $A$ . The function can solve both full and reduced problems depending on the sizes of the matrices.

Parameters

[in,out]	a	The input matrix of size $[m,n]$ . If `overwrite_a` is true, the contents of `a` may be modified during computation.
[out]	q	The orthonormal matrix $Q$ , with shape $[m,m]$ for the full problem or $[m,k]$ for the reduced problem.
[out]	r	The upper-triangular matrix $R$ , with shape $[m,n]$ for the full problem or $[k,n]$ for the reduced problem.
[in]	overwrite_a	(Optional) A logical flag that determines whether matrix `a` may be overwritten. Default is false.
[in,out]	storage	(Optional) Pre-allocated workspace array for intermediate calculations. Its size is checked with `qr_space`.
[out]	err	(Optional) A state return flag. If an error occurs and `err` is not provided, the function will stop execution.

Returns: The QR factorization matrices $Q$ and $R$ are returned in the corresponding output arguments.

Note: This subroutine uses LAPACK's QR decomposition algorithm *GEQRF to compute the factorization.

Warning: If overwrite_a is enabled, the original contents of a may be lost during computation.

Get the required workspace size for QR factorization.

This subroutine returns the minimum workspace size required for performing QR factorization. It computes the size of the workspace array that is necessary for both QR factorization and solving the reduced problem, depending on the input matrix.

Parameters

[in]	a	The input matrix of size $[m,n]$ . This matrix is used to determine the required workspace size.
[out]	lwork	The minimum size of the workspace array needed for QR operations.
[out]	err	(Optional) A state return flag. If an error occurs and `err` is not provided, the function will stop execution.

Returns: The size of the workspace array lwork that should be allocated before calling the QR factorization routine.

Note: This subroutine is useful for preallocating memory for QR factorization in large systems.

Warning: If err is not provided, the function will stop execution on error.

Member Function/Subroutine Documentation

◆ la_c_qr()

pure subroutine la_qr::qr::la_c_qr	(	complex(sp), dimension(:,:), intent(inout), target	a,
		complex(sp), dimension(:,:), intent(out), target, contiguous	q,
		complex(sp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		complex(sp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

◆ la_d_qr()

pure subroutine la_qr::qr::la_d_qr	(	real(dp), dimension(:,:), intent(inout), target	a,
		real(dp), dimension(:,:), intent(out), target, contiguous	q,
		real(dp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		real(dp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

◆ la_q_qr()

pure subroutine la_qr::qr::la_q_qr	(	real(qp), dimension(:,:), intent(inout), target	a,
		real(qp), dimension(:,:), intent(out), target, contiguous	q,
		real(qp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		real(qp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

◆ la_s_qr()

pure subroutine la_qr::qr::la_s_qr	(	real(sp), dimension(:,:), intent(inout), target	a,
		real(sp), dimension(:,:), intent(out), target, contiguous	q,
		real(sp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		real(sp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

◆ la_w_qr()

pure subroutine la_qr::qr::la_w_qr	(	complex(qp), dimension(:,:), intent(inout), target	a,
		complex(qp), dimension(:,:), intent(out), target, contiguous	q,
		complex(qp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		complex(qp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

◆ la_z_qr()

pure subroutine la_qr::qr::la_z_qr	(	complex(dp), dimension(:,:), intent(inout), target	a,
		complex(dp), dimension(:,:), intent(out), target, contiguous	q,
		complex(dp), dimension(:,:), intent(out), target, contiguous	r,
		logical(lk), intent(in), optional	overwrite_a,
		complex(dp), dimension(:), intent(inout), optional, target	storage,
		type(la_state), intent(out), optional	err )

Parameters

[in,out]	a	Input matrix a[m,n]
[out]	q	Orthogonal matrix Q ([m,m], or [m,k] if reduced)
[out]	r	Upper triangular matrix R ([m,n], or [k,n] if reduced)
[in]	overwrite_a	[optional] Can A data be overwritten and destroyed?
[in,out]	storage	[optional] Provide pre-allocated workspace, size to be checked with qr_space
[out]	err	[optional] state return flag. On error if not requested, the code will stop

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

la_qr.f90

Public Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ la_c_qr()

◆ la_d_qr()

◆ la_q_qr()

◆ la_s_qr()

◆ la_w_qr()

◆ la_z_qr()