/usr/include/estnorm.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
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Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program 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 General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _estnorm_h
#define _estnorm_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Matrix norm estimation
The algorithm estimates the 1-norm of square matrix A on the assumption
that the multiplication of matrix A by the vector is available (the
iterative method is used). It is recommended to use this algorithm if it
is hard to calculate matrix elements explicitly (for example, when
estimating the inverse matrix norm).
The algorithm uses back communication for multiplying the vector by the
matrix. If KASE=0 after returning from a subroutine, its execution was
completed successfully, otherwise it is required to multiply the returned
vector by matrix A and call the subroutine again.
The DemoIterativeEstimateNorm subroutine shows a simple example.
Parameters:
N - size of matrix A.
V - vector. It is initialized by the subroutine on the first
call. It is then passed into it on repeated calls.
X - if KASE<>0, it contains the vector to be replaced by:
A * X, if KASE=1
A^T * X, if KASE=2
Array whose index ranges within [1..N].
ISGN - vector. It is initialized by the subroutine on the first
call. It is then passed into it on repeated calls.
EST - if KASE=0, it contains the lower boundary of the matrix
norm estimate.
KASE - on the first call, it should be equal to 0. After the last
return, it is equal to 0 (EST contains the matrix norm),
on intermediate returns it can be equal to 1 or 2 depending
on the operation to be performed on vector X.
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
*************************************************************************/
void iterativeestimate1norm(int n,
ap::real_1d_array& v,
ap::real_1d_array& x,
ap::integer_1d_array& isgn,
double& est,
int& kase);
/*************************************************************************
Example of usage of an IterativeEstimateNorm subroutine
Input parameters:
A - matrix.
Array whose indexes range within [1..N, 1..N].
Return:
Matrix norm estimated by the subroutine.
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
double demoiterativeestimate1norm(const ap::real_2d_array& a, int n);
#endif
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