/usr/include/rheolef/newton-backtrack.h is in librheolef-dev 6.5-1build1.
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 | # ifndef _RHEO_NEWTON_BACKTRACK_H
# define _RHEO_NEWTON_BACKTRACK_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
///
/// =========================================================================
namespace rheolef {
template <class Problem, class Preconditioner, class Field, class Real>
int newton_backtrack (
Problem P, Preconditioner T,
Field u_old, Float Tu_old, Field delta_u, Real slope, Real norm_delta_u_max,
Field& u, Field& Fu, Real& Tu, Real& lambda)
{
const Float alpha = 1e-4; // 1e-8 when strongly nonlinear
const Float eps_mach = std::numeric_limits<Float>::epsilon();
Float norm_delta_u = P.space_norm(delta_u);
if (norm_delta_u > norm_delta_u_max) {
Float c = norm_delta_u_max/norm_delta_u;
warning_macro ("delta_u bounded by factor " << c);
delta_u = c*delta_u;
}
// compute lambda_min
Float norm_u = P.space_norm(u);
if (norm_u < norm_delta_u) norm_u = norm_delta_u;
Float lambda_min = eps_mach*norm_u/norm_delta_u;
if (lambda_min > 1) { // machine precision problem detected
u = u_old;
return 1;
}
lambda = 1;
Float lambda_prev = 0;
Float Tu_prev = 0;
Float Tu_prev_old = 0;
for (size_t k = 0; true; k++) {
u = u_old + lambda*delta_u;
Fu = P.residue(u);
Tu = T(P,Fu);
Float lambda_next;
if (lambda < lambda_min) { // machine precision problem detected
u = u_old;
return 1;
} else if (Tu <= Tu_old + alpha*lambda*slope) {
return 0; // have a valid lambda
} else if (lambda == 1) {
// first iteration: first order recursion
lambda_next = - 0.5*slope/(Tu - Tu_old - slope);
} else {
// second and more iterations: second order recursion
Float z = Tu - Tu_old - lambda*slope;
Float z_prev = Tu_prev - Tu_prev_old - lambda_prev*slope;
Float a = ( z/sqr(lambda) - z_prev/sqr(lambda_prev))/(lambda - lambda_prev);
Float b = (- z*lambda_prev/sqr(lambda) + z_prev*lambda/sqr(lambda_prev))
/(lambda - lambda_prev);
if (a == 0) {
lambda_next = - slope/(2*b);
} else {
Float Delta = sqr(b) - 3*a*slope;
if (Delta < 0) {
warning_macro("newton/backtrack: machine precision problem detected");
return 1;
}
lambda_next = (-b + ::sqrt(Delta))/(3*a);
}
lambda_next = std::min (lambda/2, lambda_next);
}
lambda_prev = lambda;
Tu_prev = Tu;
Tu_prev_old = Tu_old;
lambda = std::max (lambda/10, lambda_next);
}
return 0;
}
}// namespace rheolef
# endif // _RHEO_NEWTON_BACKTRACK_H
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