Compute a least squares solution to system $A \cdot x = b$ , i.e. such that the 2-norm $\|b - A \cdot x\|$ is minimized. More...

Public Member Functions
real(sp) function, dimension(:), allocatable, target	la_slstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(sp) system of linear equations Ax = B.

real(dp) function, dimension(:), allocatable, target	la_dlstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(dp) system of linear equations Ax = B.

real(qp) function, dimension(:), allocatable, target	la_qlstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(qp) system of linear equations Ax = B.

complex(sp) function, dimension(:), allocatable, target	la_clstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(sp) system of linear equations Ax = B.

complex(dp) function, dimension(:), allocatable, target	la_zlstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(dp) system of linear equations Ax = B.

complex(qp) function, dimension(:), allocatable, target	la_wlstsq_one (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(qp) system of linear equations Ax = B.

real(sp) function, dimension(:,:), allocatable, target	la_slstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(sp) system of linear equations Ax = B.

real(dp) function, dimension(:,:), allocatable, target	la_dlstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(dp) system of linear equations Ax = B.

real(qp) function, dimension(:,:), allocatable, target	la_qlstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a real(qp) system of linear equations Ax = B.

complex(sp) function, dimension(:,:), allocatable, target	la_clstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(sp) system of linear equations Ax = B.

complex(dp) function, dimension(:,:), allocatable, target	la_zlstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(dp) system of linear equations Ax = B.

complex(qp) function, dimension(:,:), allocatable, target	la_wlstsq_multiple (a, b, cond, overwrite_a, rank, err)
	Compute the least-squares solution to a complex(qp) system of linear equations Ax = B.

Detailed Description

Compute a least squares solution to system $A \cdot x = b$ , i.e. such that the 2-norm $\|b - A \cdot x\|$ is minimized.

This function computes the least-squares solution to a real system of linear equations:

$A \cdot x = b$

where A is an n x n matrix and b is either a vector (n) or a matrix (n x nrhs). The solution x is returned as an allocatable array.

Parameters

[in,out]	a	The input matrix of size `n x n`. If `overwrite_a` is true, the contents of A may be modified during computation.
[in]	b	The right-hand side vector (`n`) or matrix (`n x nrhs`).
[in]	cond	(Optional) A cutoff for rank evaluation: singular values $s(i)$ such that $s(i) \leq \text{cond} \cdot \max(s)$ are considered zero.
[in]	overwrite_a	(Optional) If true, A and B may be overwritten and destroyed. Default is false.
[out]	rank	(Optional) The rank of the matrix A.
[out]	err	(Optional) A state return flag. If an error occurs and `err` is not provided, the function will stop execution.

Returns: Solution matrix x of size n (for a single right-hand side) or n x nrhs.

Note: This function relies on LAPACK least-squares solvers such as [*GELSS](@ref la_lapack::gelss).

Warning: If overwrite_a is enabled, the original contents of A and B may be lost.

Member Function/Subroutine Documentation

◆ la_clstsq_multiple()

complex(sp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_clstsq_multiple	(	complex(sp), dimension(:,:), intent(inout), target	a,
		complex(sp), dimension(:,:), intent(in)	b,
		real(sp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(sp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_clstsq_one()

complex(sp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_clstsq_one	(	complex(sp), dimension(:,:), intent(inout), target	a,
		complex(sp), dimension(:), intent(in)	b,
		real(sp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(sp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_dlstsq_multiple()

real(dp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_dlstsq_multiple	(	real(dp), dimension(:,:), intent(inout), target	a,
		real(dp), dimension(:,:), intent(in)	b,
		real(dp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(dp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_dlstsq_one()

real(dp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_dlstsq_one	(	real(dp), dimension(:,:), intent(inout), target	a,
		real(dp), dimension(:), intent(in)	b,
		real(dp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(dp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_qlstsq_multiple()

real(qp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_qlstsq_multiple	(	real(qp), dimension(:,:), intent(inout), target	a,
		real(qp), dimension(:,:), intent(in)	b,
		real(qp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(qp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_qlstsq_one()

real(qp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_qlstsq_one	(	real(qp), dimension(:,:), intent(inout), target	a,
		real(qp), dimension(:), intent(in)	b,
		real(qp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(qp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_slstsq_multiple()

real(sp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_slstsq_multiple	(	real(sp), dimension(:,:), intent(inout), target	a,
		real(sp), dimension(:,:), intent(in)	b,
		real(sp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(sp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_slstsq_one()

real(sp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_slstsq_one	(	real(sp), dimension(:,:), intent(inout), target	a,
		real(sp), dimension(:), intent(in)	b,
		real(sp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a real(sp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_wlstsq_multiple()

complex(qp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_wlstsq_multiple	(	complex(qp), dimension(:,:), intent(inout), target	a,
		complex(qp), dimension(:,:), intent(in)	b,
		real(qp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(qp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_wlstsq_one()

complex(qp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_wlstsq_one	(	complex(qp), dimension(:,:), intent(inout), target	a,
		complex(qp), dimension(:), intent(in)	b,
		real(qp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(qp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_zlstsq_multiple()

complex(dp) function, dimension(:,:), allocatable, target la_least_squares::lstsq::la_zlstsq_multiple	(	complex(dp), dimension(:,:), intent(inout), target	a,
		complex(dp), dimension(:,:), intent(in)	b,
		real(dp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(dp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

◆ la_zlstsq_one()

complex(dp) function, dimension(:), allocatable, target la_least_squares::lstsq::la_zlstsq_one	(	complex(dp), dimension(:,:), intent(inout), target	a,
		complex(dp), dimension(:), intent(in)	b,
		real(dp), intent(in), optional	cond,
		logical(lk), intent(in), optional	overwrite_a,
		integer(ilp), intent(out), optional	rank,
		type(la_state), intent(out), optional	err )

Compute the least-squares solution to a complex(dp) system of linear equations Ax = B.

Parameters

[in,out]	a	Input matrix a[n,n]
[in]	b	Right hand side vector or array, b[n] or b[n,nrhs]
[in]	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
[in]	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
[out]	rank	[optional] Return rank of A
[out]	err	[optional] state return flag. On error if not requested, the code will stop

Returns: Result array/matrix x[n] or x[n,nrhs]

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

la_least_squares.f90

Public Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ la_clstsq_multiple()

◆ la_clstsq_one()

◆ la_dlstsq_multiple()

◆ la_dlstsq_one()

◆ la_qlstsq_multiple()

◆ la_qlstsq_one()

◆ la_slstsq_multiple()

◆ la_slstsq_one()

◆ la_wlstsq_multiple()

◆ la_wlstsq_one()

◆ la_zlstsq_multiple()

◆ la_zlstsq_one()