/usr/include/rheolef/cg.h is in librheolef-dev 5.93-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 | # ifndef _SKIT_CG_H
# define _SKIT_CG_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef 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; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
/*D:cg
NAME: @code{cg} -- conjugate gradient algorithm.
@findex cg
@cindex conjugate gradient algorithm
@cindex iterative solver
SYNOPSIS:
@example
template <class Matrix, class Vector, class Preconditioner, class Real>
int cg (const Matrix &A, Vector &x, const Vector &b,
const Preconditioner &M, int &max_iter, Real &tol);
@end example
EXAMPLE:
@noindent
The simplest call to 'cg' has the folling form:
@example
int status = cg(a, x, b, EYE, 100, 1e-7);
@end example
DESCRIPTION:
@noindent
@code{cg} solves the symmetric positive definite linear
system Ax=b using the Conjugate Gradient method.
@noindent
The return value indicates convergence within max_iter (input)
iterations (0), or no convergence within max_iter iterations (1).
Upon successful return, output arguments have the following values:
@table @code
@itemx x
approximate solution to Ax = b
@itemx max_iter
the number of iterations performed before the tolerance was reached
@itemx tol
the residual after the final iteration
@end table
NOTE:
@noindent
@code{cg} is an iterative template routine.
@noindent
@code{cg} follows the algorithm described on p. 15 in
@quotation
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods,
2nd Edition,
R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout,
R. Pozo, C. Romine, H. Van der Vorst,
SIAM, 1994,
@url{ftp.netlib.org/templates/templates.ps}.
@end quotation
@noindent
The present implementation is inspired from
@code{IML++ 1.2} iterative method library,
@url{http://math.nist.gov/iml++}.
AUTHOR:
Pierre Saramito
| Pierre.Saramito@imag.fr
LMC-IMAG, 38041 Grenoble cedex 9, France
DATE:
28 february 1997
METHODS: @cg
End:
*/
// ========== [ method implementation ] ====================================
namespace rheolef {
template < class Matrix, class Vector, class Preconditioner, class Real>
int cg(const Matrix &A, Vector &x, const Vector &b,
const Preconditioner &M, int &max_iter, Real &tol)
{
Real resid;
Vector p, q;
Real alpha, beta, rho, rho_1 = 0;
Real normb = norm(b);
Vector r = b - A*x;
if (normb == Real(0))
normb = 1;
if ((resid = norm(r) / normb) <= tol) {
tol = resid;
max_iter = 0;
return 0;
}
for (int i = 1; i <= max_iter; i++) {
if (i == 1) {
Vector z = M.solve(r);
rho = dot(r, z);
p = z;
} else {
Vector z = M.solve(r);
rho = dot(r, z);
beta = rho / rho_1;
p = z + beta * p;
}
q = A*p;
alpha = rho / dot(p, q);
x += alpha * p;
r -= alpha * q;
if ((resid = norm(r) / normb) <= tol) {
tol = resid;
max_iter = i;
return 0;
}
rho_1 = rho;
}
tol = resid;
return 1;
}
}// namespace rheolef
# endif // _SKIT_CG_H
|