linalg_least_squares

Uses

- iso_fortran_env
- lapack
- linalg_errors

Interfaces

public interface solve_least_squares

private pure function solve_least_squares_mtx(a, b) result(x)

Solves the system of equations $A X = B$ assuming matrix $A$ is of full rank.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_mtx_cmplx(a, b) result(x)

Solves the system of equations $A X = B$ assuming matrix $A$ is of full rank.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value complex(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_vec(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ assuming matrix $A$ is of full rank.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value real(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

private pure function solve_least_squares_vec_cmplx(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ assuming matrix $A$ is of full rank.

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value complex(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

public interface solve_least_squares_full

private pure function solve_least_squares_mtx_pvt(a, b) result(x)

Solves the system of equations $A X = B$ using a full orthogonal factorization of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_mtx_pvt_cmplx(a, b) result(x)

Solves the system of equations $A X = B$ using a full orthogonal factorization of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value complex(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_vec_pvt(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ using a full orthogonal factorization of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value real(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

private pure function solve_least_squares_vec_pvt_cmplx(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ using a full orthogonal factorization of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value complex(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

public interface solve_least_squares_svd

private pure function solve_least_squares_mtx_svd(a, b) result(x)

Solves the system of equations $A X = B$ using a singular value decomposition of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_mtx_svd_cmplx(a, b) result(x)

Solves the system of equations $A X = B$ using a singular value decomposition of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:,:)	::	b	The M-by-NRHS matrix $B$ .

Return Value complex(kind=real64), allocatable, dimension(:,:)

The N-by-NRHS matrix $X$ .

private pure function solve_least_squares_vec_svd(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ using a singular value decomposition of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
real(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value real(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

private pure function solve_least_squares_vec_svd_cmplx(a, b) result(x)

Solves the system of equations $A \vec{x} = \vec{b}$ using a singular value decomposition of $A$ .

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=real64),	intent(in),		dimension(:,:)	::	a	The M-by-N matrix $A$ .
complex(kind=real64),	intent(in),		dimension(:)	::	b	The M-element vector $\vec{b}$ .

Return Value complex(kind=real64), allocatable, dimension(:)

The N-element vector $\vec{x}$ .

linalg_least_squares Module

Contents

Interfaces

Uses

Interfaces

public interface solve_least_squares

private pure function solve_least_squares_mtx(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_mtx_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_vec(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

private pure function solve_least_squares_vec_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)

public interface solve_least_squares_full

private pure function solve_least_squares_mtx_pvt(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_mtx_pvt_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_vec_pvt(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

private pure function solve_least_squares_vec_pvt_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)

public interface solve_least_squares_svd

private pure function solve_least_squares_mtx_svd(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_mtx_svd_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:,:)

private pure function solve_least_squares_vec_svd(a, b) result(x)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

private pure function solve_least_squares_vec_svd_cmplx(a, b) result(x)

Arguments

Return Value complex(kind=real64), allocatable, dimension(:)