la_lapack::ggglm Interface Reference

GGGLM: solves a general Gauss-Markov linear model (GLM) problem: minimize || y ||_2 subject to d = A*x + B*y x where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and rank(A) = M and rank( A B ) = N. Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by A = Q*(R), B = Q*T*Z. (0) In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem minimize || inv(B)*(d-A*x) ||_2 x where inv(B) denotes the inverse of B. More...

Public Member Functions
pure subroutine	cggglm (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)
	la_cggglm
pure subroutine	dggglm (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)
	la_dggglm
	la_qggglm
pure subroutine	sggglm (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)
	la_sggglm
	la_wggglm
pure subroutine	zggglm (n, m, p, a, lda, b, ldb, d, x, y, work, lwork, info)
	la_zggglm

Detailed Description

GGGLM: solves a general Gauss-Markov linear model (GLM) problem: minimize || y ||_2 subject to d = A*x + B*y x where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and rank(A) = M and rank( A B ) = N. Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by A = Q*(R), B = Q*T*Z. (0) In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem minimize || inv(B)*(d-A*x) ||_2 x where inv(B) denotes the inverse of B.

Member Function/Subroutine Documentation

cggglm()

pure subroutine la_lapack::ggglm::cggglm	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		complex(sp), dimension(*), intent(inout)	d,
		complex(sp), dimension(*), intent(out)	x,
		complex(sp), dimension(*), intent(out)	y,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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dggglm()

pure subroutine la_lapack::ggglm::dggglm	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		real(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		real(dp), dimension(*), intent(inout)	d,
		real(dp), dimension(*), intent(out)	x,
		real(dp), dimension(*), intent(out)	y,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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la_cggglm()

la_lapack::ggglm::la_cggglm

la_dggglm()

la_lapack::ggglm::la_dggglm

la_qggglm()

la_lapack::ggglm::la_qggglm

la_sggglm()

la_lapack::ggglm::la_sggglm

la_wggglm()

la_lapack::ggglm::la_wggglm

la_zggglm()

la_lapack::ggglm::la_zggglm

sggglm()

pure subroutine la_lapack::ggglm::sggglm	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		real(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		real(sp), dimension(*), intent(inout)	d,
		real(sp), dimension(*), intent(out)	x,
		real(sp), dimension(*), intent(out)	y,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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zggglm()

pure subroutine la_lapack::ggglm::zggglm	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		complex(dp), dimension(*), intent(inout)	d,
		complex(dp), dimension(*), intent(out)	x,
		complex(dp), dimension(*), intent(out)	y,
		complex(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90