lstsq Interface

experimental
74 statements
Source File

public interface lstsq

Computes the squares solution to system $A \cdot x = b$ . (Specification)

Summary

Interface for computing least squares, i.e. the 2-norm $|| (b-A \cdot x ||_2$ minimizing solution.

Description

This interface provides methods for computing the least squares of a linear matrix system. Supported data types include real and complex.

Note

The solution is based on LAPACK's singular value decomposition *GELSD methods.

Functions

private module function stdlib_linalg_c_lstsq_many(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
complex(kind=sp),	intent(in)			::	b(:,:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=sp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value complex(kind=sp), allocatable, target, (:,:)

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

private module function stdlib_linalg_c_lstsq_one(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=sp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
complex(kind=sp),	intent(in)			::	b(:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=sp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value complex(kind=sp), allocatable, target, (:)

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

private module function stdlib_linalg_d_lstsq_many(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
real(kind=dp),	intent(in)			::	b(:,:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=dp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value real(kind=dp), allocatable, target, (:,:)

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

private module function stdlib_linalg_d_lstsq_one(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
real(kind=dp),	intent(in)			::	b(:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=dp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value real(kind=dp), allocatable, target, (:)

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

private module function stdlib_linalg_s_lstsq_many(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
real(kind=sp),	intent(in)			::	b(:,:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=sp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value real(kind=sp), allocatable, target, (:,:)

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

private module function stdlib_linalg_s_lstsq_one(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=sp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
real(kind=sp),	intent(in)			::	b(:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=sp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value real(kind=sp), allocatable, target, (:)

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

private module function stdlib_linalg_z_lstsq_many(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
complex(kind=dp),	intent(in)			::	b(:,:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=dp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value complex(kind=dp), allocatable, target, (:,:)

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

private module function stdlib_linalg_z_lstsq_one(a, b, cond, overwrite_a, rank, err) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
complex(kind=dp),	intent(inout),		target	::	a(:,:)	Input matrix a[n,n]
complex(kind=dp),	intent(in)			::	b(:)	Right hand side vector or array, b[n] or b[n,nrhs]
real(kind=dp),	intent(in),	optional		::	cond	[optional] cutoff for rank evaluation: singular values s(i)<=cond*maxval(s) are considered 0.
logical(kind=lk),	intent(in),	optional		::	overwrite_a	[optional] Can A,b data be overwritten and destroyed?
integer(kind=ilp),	intent(out),	optional		::	rank	[optional] Return rank of A
type(linalg_state_type),	intent(out),	optional		::	err	[optional] state return flag. On error if not requested, the code will stop

Return Value complex(kind=dp), allocatable, target, (:)

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