la_lapack::gelsy Interface Reference

GELSY: computes the minimum-norm solution to a complex linear least squares problem: minimize || A * X - B || using a complete orthogonal factorization of A. A is an M-by-N matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. The routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ 0 R22 ] with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A. Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization: A * P = Q * [ T11 0 ] * Z [ 0 0 ] The minimum-norm solution is then X = P * Z**H [ inv(T11)*Q1**H*B ] [ 0 ] where Q1 consists of the first RANK columns of Q. This routine is basically identical to the original xGELSX except three differences: o The permutation of matrix B (the right hand side) is faster and more simple. o The call to the subroutine xGEQPF has been substituted by the the call to the subroutine xGEQP3. This subroutine is a Blas-3 version of the QR factorization with column pivoting. o Matrix B (the right hand side) is updated with Blas-3. More...

Public Member Functions
subroutine	cgelsy (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, lwork, rwork, info)
	la_cgelsy
subroutine	dgelsy (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, lwork, info)
	la_dgelsy
	la_qgelsy
subroutine	sgelsy (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, lwork, info)
	la_sgelsy
	la_wgelsy
subroutine	zgelsy (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, lwork, rwork, info)
	la_zgelsy

Detailed Description

GELSY: computes the minimum-norm solution to a complex linear least squares problem: minimize || A * X - B || using a complete orthogonal factorization of A. A is an M-by-N matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. The routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ 0 R22 ] with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A. Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization: A * P = Q * [ T11 0 ] * Z [ 0 0 ] The minimum-norm solution is then X = P * Z**H [ inv(T11)*Q1**H*B ] [ 0 ] where Q1 consists of the first RANK columns of Q. This routine is basically identical to the original xGELSX except three differences: o The permutation of matrix B (the right hand side) is faster and more simple. o The call to the subroutine xGEQPF has been substituted by the the call to the subroutine xGEQP3. This subroutine is a Blas-3 version of the QR factorization with column pivoting. o Matrix B (the right hand side) is updated with Blas-3.

Member Function/Subroutine Documentation

cgelsy()

subroutine la_lapack::gelsy::cgelsy	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	nrhs,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		integer(ilp), dimension(*), intent(inout)	jpvt,
		real(sp), intent(in)	rcond,
		integer(ilp), intent(out)	rank,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(sp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(out)	info
	)

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dgelsy()

subroutine la_lapack::gelsy::dgelsy	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	nrhs,
		real(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		integer(ilp), dimension(*), intent(inout)	jpvt,
		real(dp), intent(in)	rcond,
		integer(ilp), intent(out)	rank,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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la_cgelsy()

la_lapack::gelsy::la_cgelsy

la_dgelsy()

la_lapack::gelsy::la_dgelsy

la_qgelsy()

la_lapack::gelsy::la_qgelsy

la_sgelsy()

la_lapack::gelsy::la_sgelsy

la_wgelsy()

la_lapack::gelsy::la_wgelsy

la_zgelsy()

la_lapack::gelsy::la_zgelsy

sgelsy()

subroutine la_lapack::gelsy::sgelsy	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	nrhs,
		real(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		integer(ilp), dimension(*), intent(inout)	jpvt,
		real(sp), intent(in)	rcond,
		integer(ilp), intent(out)	rank,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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zgelsy()

subroutine la_lapack::gelsy::zgelsy	(	integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	nrhs,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		integer(ilp), dimension(*), intent(inout)	jpvt,
		real(dp), intent(in)	rcond,
		integer(ilp), intent(out)	rank,
		complex(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(dp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90