QL decompostion. More...

Modules
module	mpqldec
	QL data.

Functions/Subroutines
subroutine	qlini (n, m, l, k)
	Initialize QL decomposition. More...

subroutine	qldec (a)
	QL decomposition (as single block). More...

subroutine	qldecb (a, bpar, bcon)
	QL decomposition (for disjoint block matrix). More...

subroutine	qlmlq (x, m, t)
	Multiply left by Q(t) (per block). More...

subroutine	qlmrq (x, m, t)
	Multiply right by Q(t). More...

subroutine	qlsmq (x, t)
	Similarity transformation by Q(t). More...

subroutine	qlssq (aprod, A, t)
	Similarity transformation by Q(t). More...

subroutine	qlpssq (aprod, B, m, t)
	Partial similarity transformation by Q(t). More...

subroutine	qlgete (emin, emax)
	Get eigenvalues. More...

subroutine	qlbsub (d, y)
	Backward substitution (per block). More...

subroutine	qlsetb (ib)
	Set block. More...

subroutine	qldump ()
	Print statistics. More...

Variables
integer(mpi)	mpqldec::npar
	number of parameters More...

integer(mpi)	mpqldec::ncon
	number of constraints More...

integer(mpi)	mpqldec::nblock
	number of blocks More...

integer(mpi)	mpqldec::iblock
	active block More...

integer(mpi)	mpqldec::monpg
	flag for progress monitoring More...

integer(mpi), dimension(:), allocatable	mpqldec::sparsev
	sparsity structure matV More...

real(mpd), dimension(:), allocatable	mpqldec::matv
	unit normals (v_i) of Householder reflectors More...

real(mpd), dimension(:), allocatable	mpqldec::matl
	lower diagonal matrix L More...

real(mpd), dimension(:), allocatable	mpqldec::vecn
	normal vector More...

integer(mpi), dimension(:), allocatable	mpqldec::nparblock
	number of parameters in block More...

integer(mpi), dimension(:), allocatable	mpqldec::ioffblock
	block offset (1. More...

Detailed Description

QL decompostion.

Author: Claus Kleinwort, DESY, 2015 (Claus.nosp@m..Kle.nosp@m.inwor.nosp@m.t@de.nosp@m.sy.de)

Copyright: Copyright (c) 2015-2020 Deutsches Elektronen-Synchroton, Member of the Helmholtz Association, (DESY), HAMBURG, GERMANY

This library is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more details.

You should have received a copy of the GNU Library General Public License along with this program (see the file COPYING.LIB for more details); if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

QL decomposition of constraints matrix by Householder transformations for solution by elimination. Optionally split into disjoint blocks.

Definition in file mpqldec.f90.

Function/Subroutine Documentation

◆ qlbsub()

subroutine qlbsub	(	real(mpd), dimension(*), intent(in)	d,
		real(mpd), dimension(*), intent(out)	y
	)

Backward substitution (per block).

Get y from L^t*y=d.

Parameters

[in]	d	Ncon vector, resdiduals
[out]	y	Ncon vector, solution

Definition at line 750 of file mpqldec.f90.

References mpqldec::iblock, mpqldec::ioffblock, mpqldec::matl, and mpqldec::ncon.

Referenced by mchdec(), mdiags(), minver(), mminrs(), and mminrsqlp().

◆ qldec()

subroutine qldec ( real(mpd), dimension(*), intent(in) a )

QL decomposition (as single block).

QL decomposition with Householder transformations. Decompose N-By-M matrix A into orthogonal N-by-N matrix Q and a N-by-M matrix containing zeros except for a lower triangular M-by-M matrix L (at the bottom):

         | 0 |
 A = Q * |   |
         | L |

The decomposition is stored in a N-by-M matrix matV containing the unit normal vectors v_i of the hyperplanes (Householder reflectors) defining Q. The lower triangular matrix L is stored in the M-by-M matrix matL.

Parameters

[in] a Npar-by-Ncon matrix

Definition at line 104 of file mpqldec.f90.

References mpqldec::ioffblock, mpqldec::matl, mpqldec::matv, mpqldec::monpg, monpgs(), mpqldec::nblock, mpqldec::ncon, mpqldec::npar, mpqldec::nparblock, mpqldec::sparsev, and mpqldec::vecn.

◆ qldecb()

subroutine qldecb	(	real(mpd), dimension(*), intent(in)	a,
		integer(mpi), dimension(2,*), intent(in)	bpar,
		integer(mpi), dimension(3,*), intent(in)	bcon
	)

QL decomposition (for disjoint block matrix).

QL decomposition with Householder transformations. Decompose N-By-M matrix A into orthogonal N-by-N matrix Q and a N-by-M matrix containing zeros except for a lower triangular M-by-M matrix L (at the bottom):

         | 0 |
 A = Q * |   |
         | L |

The decomposition is stored in a N-by-M matrix matV containing the unit normal vectors v_i of the hyperplanes (Householder reflectors) defining Q. The lower triangular matrix L is stored in the M-by-M matrix matL.

Parameters

[in]	a	block compressed Npar-by-Ncon matrix
[in]	bpar	2-by-NparBlock+1 matrix (with parameter block definition)
[in]	bcon	3-by-NconBlock+1 matrix (with constraint block definition)

Definition at line 194 of file mpqldec.f90.

References mpqldec::ioffblock, mpqldec::matl, mpqldec::matv, mpqldec::monpg, monpgs(), mpqldec::nblock, mpqldec::ncon, mpqldec::npar, mpqldec::nparblock, mpqldec::sparsev, and mpqldec::vecn.

Referenced by feasma().

◆ qldump()

subroutine qldump

Print statistics.

Definition at line 789 of file mpqldec.f90.

References mpqldec::matl, mpqldec::matv, mpqldec::ncon, and mpqldec::npar.

◆ qlgete()

subroutine qlgete	(	real(mpd), intent(out)	emin,
		real(mpd), intent(out)	emax
	)

Get eigenvalues.

Get smallest and largest |eigenvalue| of L.

Parameters

[out]	emin	eigenvalue with smallest absolute value
[out]	emax	eigenvalue with largest absolute value

Definition at line 714 of file mpqldec.f90.

References mpqldec::ioffblock, mpqldec::matl, mpqldec::nblock, and mpqldec::ncon.

Referenced by feasma().

◆ qlini()

subroutine qlini	(	integer(mpi), intent(in)	n,
		integer(mpi), intent(in)	m,
		integer(mpi), intent(in)	l,
		integer(mpi), intent(in)	k
	)

Initialize QL decomposition.

Parameters

[in]	n	number of rows (parameters)
[in]	m	number of columns (constraints)
[in]	l	number of disjoint blocks
[in]	k	flag for progress monitoring

Definition at line 52 of file mpqldec.f90.

References mpqldec::iblock, mpqldec::ioffblock, mpqldec::matl, mpqldec::matv, mpqldec::monpg, mpqldec::nblock, mpqldec::ncon, mpqldec::npar, mpqldec::nparblock, mpqldec::sparsev, and mpqldec::vecn.

Referenced by feasma().

◆ qlmlq()

subroutine qlmlq	(	real(mpd), dimension(*), intent(inout)	x,
		integer(mpi), intent(in)	m,
		logical, intent(in)	t
	)

Multiply left by Q(t) (per block).

Multiply left by Q(t) from QL decomposition.

Parameters

[in,out]	x	NparBlock-by-M matrix, overwritten with QX (t=false) or Q^tX (t=true)
[in]	m	number of columns
[in]	t	use transposed of Q

Definition at line 340 of file mpqldec.f90.

References mpqldec::iblock, mpqldec::ioffblock, mpqldec::matv, mpqldec::npar, and mpqldec::nparblock.

Referenced by avprod(), mchdec(), mdiags(), minver(), mminrs(), mminrsqlp(), and zdiags().

◆ qlmrq()

subroutine qlmrq	(	real(mpd), dimension(*), intent(inout)	x,
		integer(mpi), intent(in)	m,
		logical, intent(in)	t
	)

Multiply right by Q(t).

Multiply right by Q(t) from QL decomposition.

Parameters

[in,out]	x	M-by-Npar matrix, overwritten with XQ (t=false) or XQ^t (t=true)
[in]	m	number of rows
[in]	t	use transposed of Q

Definition at line 392 of file mpqldec.f90.

References mpqldec::matv, mpqldec::ncon, and mpqldec::npar.

◆ qlpssq()

subroutine qlpssq	(		aprod,
		real(mpd), dimension(*), intent(inout)	B,
		integer(mpi), intent(in)	m,
		logical, intent(in)	t
	)

Partial similarity transformation by Q(t).

Partial similarity transformation for symmetric matrix by Q from QL decomposition. Calculate corrections to band part of matrix.

Parameters

[in]	aprod	external procedure to calculate A*v
[in,out]	B	band part of symmetric Npar-by-Npar matrix A in symmetric storage mode, overwritten with band part of Q^tAQ (t=false) or Q^tAQ (t=true)
[in]	m	band width (including diagonal)
[in]	t	use transposed of Q

Definition at line 585 of file mpqldec.f90.

References mpqldec::matv, mpqldec::monpg, monpgs(), mpqldec::ncon, mpqldec::npar, and mpqldec::sparsev.

Referenced by mminrs(), and mminrsqlp().

◆ qlsetb()

subroutine qlsetb ( integer(mpi), intent(in) ib )

Set block.

Definition at line 777 of file mpqldec.f90.

References mpqldec::iblock.

Referenced by mchdec(), and minver().

◆ qlsmq()

subroutine qlsmq	(	real(mpd), dimension(*), intent(inout)	x,
		logical, intent(in)	t
	)

Similarity transformation by Q(t).

Similarity transformation by Q from QL decomposition.

Parameters

[in,out]	x	Npar-by-Npar matrix, overwritten with QXQ^t (t=false) or Q^tXQ (t=true)
[in]	t	use transposed of Q

Definition at line 434 of file mpqldec.f90.

References mpqldec::matv, mpqldec::monpg, monpgs(), mpqldec::ncon, and mpqldec::npar.

◆ qlssq()

subroutine qlssq	(		aprod,
		real(mpd), dimension(*), intent(inout)	A,
		logical, intent(in)	t
	)

Similarity transformation by Q(t).

Similarity transformation for symmetric matrix by Q from QL decomposition.

Parameters

[in]	aprod	external procedure to calculate A*v
[in,out]	A	symmetric Npar-by-Npar matrix A in symmetric storage mode (V(1) = V11, V(2) = V12, V(3) = V22, V(4) = V13, ...), overwritten with QAQ^t (t=false) or Q^tAQ (t=true)
[in]	t	use transposed of Q

Definition at line 487 of file mpqldec.f90.

References mpqldec::ioffblock, mpqldec::matv, mpqldec::monpg, monpgs(), mpqldec::nblock, mpqldec::npar, and mpqldec::nparblock.

Referenced by mchdec(), mdiags(), minver(), and xloopn().

Modules

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ qlbsub()

◆ qldec()

◆ qldecb()

◆ qldump()

◆ qlgete()

◆ qlini()

◆ qlmlq()

◆ qlmrq()

◆ qlpssq()

◆ qlsetb()

◆ qlsmq()

◆ qlssq()