la_lapack::gsvj1 Interface Reference

GSVJ1: is called from CGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as CGESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. Further Details ~~~~~~~~~~~~~~~ GSVJ1 applies few sweeps of Jacobi rotations in the column space of the input M-by-N matrix A. The pivot pairs are taken from the (1,2) off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The block-entries (tiles) of the (1,2) off-diagonal block are marked by the [x]'s in the following scheme: | * * * [x] [x] [x]| | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. |[x] [x] [x] * * * | |[x] [x] [x] * * * | |[x] [x] [x] * * * | In terms of the columns of A, the first N1 columns are rotated 'against' the remaining N-N1 columns, trying to increase the angle between the corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter. The number of sweeps is given in NSWEEP and the orthogonality threshold is given in TOL. More...

Public Member Functions
pure subroutine	cgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
	la_cgsvj1
pure subroutine	dgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
	la_dgsvj1
	la_qgsvj1
pure subroutine	sgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
	la_sgsvj1
	la_wgsvj1
pure subroutine	zgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)
	la_zgsvj1

Detailed Description

GSVJ1: is called from CGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as CGESVJ does, but it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. Further Details ~~~~~~~~~~~~~~~ GSVJ1 applies few sweeps of Jacobi rotations in the column space of the input M-by-N matrix A. The pivot pairs are taken from the (1,2) off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The block-entries (tiles) of the (1,2) off-diagonal block are marked by the [x]'s in the following scheme: | * * * [x] [x] [x]| | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. |[x] [x] [x] * * * | |[x] [x] [x] * * * | |[x] [x] [x] * * * | In terms of the columns of A, the first N1 columns are rotated 'against' the remaining N-N1 columns, trying to increase the angle between the corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter. The number of sweeps is given in NSWEEP and the orthogonality threshold is given in TOL.

Member Function/Subroutine Documentation

cgsvj1()

pure subroutine la_lapack::gsvj1::cgsvj1	(	character, intent(in)	jobv,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	n1,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(n), intent(inout)	d,
		real(sp), dimension(n), intent(inout)	sva,
		integer(ilp), intent(in)	mv,
		complex(sp), dimension(ldv,*), intent(inout)	v,
		integer(ilp), intent(in)	ldv,
		real(sp), intent(in)	eps,
		real(sp), intent(in)	sfmin,
		real(sp), intent(in)	tol,
		integer(ilp), intent(in)	nsweep,
		complex(sp), dimension(lwork), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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dgsvj1()

pure subroutine la_lapack::gsvj1::dgsvj1	(	character, intent(in)	jobv,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	n1,
		real(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(n), intent(inout)	d,
		real(dp), dimension(n), intent(inout)	sva,
		integer(ilp), intent(in)	mv,
		real(dp), dimension(ldv,*), intent(inout)	v,
		integer(ilp), intent(in)	ldv,
		real(dp), intent(in)	eps,
		real(dp), intent(in)	sfmin,
		real(dp), intent(in)	tol,
		integer(ilp), intent(in)	nsweep,
		real(dp), dimension(lwork), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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la_cgsvj1()

la_lapack::gsvj1::la_cgsvj1

la_dgsvj1()

la_lapack::gsvj1::la_dgsvj1

la_qgsvj1()

la_lapack::gsvj1::la_qgsvj1

la_sgsvj1()

la_lapack::gsvj1::la_sgsvj1

la_wgsvj1()

la_lapack::gsvj1::la_wgsvj1

la_zgsvj1()

la_lapack::gsvj1::la_zgsvj1

sgsvj1()

pure subroutine la_lapack::gsvj1::sgsvj1	(	character, intent(in)	jobv,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	n1,
		real(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(n), intent(inout)	d,
		real(sp), dimension(n), intent(inout)	sva,
		integer(ilp), intent(in)	mv,
		real(sp), dimension(ldv,*), intent(inout)	v,
		integer(ilp), intent(in)	ldv,
		real(sp), intent(in)	eps,
		real(sp), intent(in)	sfmin,
		real(sp), intent(in)	tol,
		integer(ilp), intent(in)	nsweep,
		real(sp), dimension(lwork), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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zgsvj1()

pure subroutine la_lapack::gsvj1::zgsvj1	(	character, intent(in)	jobv,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	n1,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(n), intent(inout)	d,
		real(dp), dimension(n), intent(inout)	sva,
		integer(ilp), intent(in)	mv,
		complex(dp), dimension(ldv,*), intent(inout)	v,
		integer(ilp), intent(in)	ldv,
		real(dp), intent(in)	eps,
		real(dp), intent(in)	sfmin,
		real(dp), intent(in)	tol,
		integer(ilp), intent(in)	nsweep,
		complex(dp), dimension(lwork), 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