/usr/share/octave/packages/bim-1.1.5/bim2c_norm.m is in octave-bim 1.1.5-4.
This file is owned by root:root, with mode 0o644.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 | ## Copyright (C) 2006-2013 Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
## BIM - Diffusion Advection Reaction PDE Solver
##
## BIM 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.
##
## BIM 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 BIM; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Matteo Porro <meoo85 _AT_ users.sourceforge.net>
## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{norm_u}]} = @
## bim2c_norm(@var{mesh},@var{u},@var{norm_type})
##
## Compute the @var{norm_type}-norm of function @var{u} on the domain described
## by the triangular grid @var{mesh}.
##
## The input function @var{u} can be either a piecewise linear conforming scalar
## function or an elementwise constant scalar or vector function.
##
## The string parameter @var{norm_type} can be one among 'L2', 'H1' and 'inf'.
##
## Should the input function be piecewise constant, the H1 norm will not be
## computed and the function will return an error message.
##
## For the numerical integration of the L2 norm the second order middle point
## quadrature rule is used.
##
## @seealso{bim1c_norm, bim3c_norm}
##
## @end deftypefn
function [norm_u] = bim2c_norm (m, u, norm_type)
## Check input
if (nargin != 3)
error ("bim2c_norm: wrong number of input parameters.");
elseif (! (isstruct (m) && isfield (m,"p")
&& isfield (m, "t")
&& isfield (m, "e")))
error ("bim2c_norm: first input is not a valid mesh structure.");
endif
nnodes = columns (m.p);
nel = columns (m.t);
if (isequal (size (u), [2, nel]))
u = u';
endif
if ((numel (u) != nnodes) && (rows (u) != nel))
error ("bim2c_norm: numel(u) != nnodes and rows(u) != nel.");
endif
if (! (strcmp (norm_type,'L2')
|| strcmp (norm_type,'inf')
|| strcmp (norm_type,'H1')))
error ("bim2c_norm: invalid norm type parameter.");
endif
if (strcmp (norm_type,'inf'))
norm_u = max (abs (u(:)));
else
if (numel (u) == nnodes)
M = __mass_matrix__ (m);
if (strcmp (norm_type, 'H1'))
A = bim2a_laplacian (m, 1, 1);
M += A;
endif
norm_u = sqrt(u' * M * u);
else
if (strcmp (norm_type, 'H1'))
error (["bim2c_norm: cannot compute the H1 norm ", ...
"of an elementwise constant function."]);
endif
norm_u = m.area' * (norm (u, 2, 'rows').^2);
norm_u = sqrt (norm_u);
endif
endif
endfunction
function M = __mass_matrix__ (mesh)
t = mesh.t;
nnodes = columns (mesh.p);
nelem = columns (t);
## Local contributions
Mref = 1/12 * [2 1 1; 1 2 1; 1 1 2];
area = reshape (mesh.area, 1, 1, nelem);
## Computation
for inode = 1:3
for jnode = 1:3
ginode(inode,jnode,:) = t(inode,:);
gjnode(inode,jnode,:) = t(jnode,:);
endfor
endfor
Mloc = area .* Mref;
## assemble global matrix
M = sparse (ginode(:), gjnode(:), Mloc(:), nnodes, nnodes);
endfunction
%!test
%!shared L, V, x, y, m
%! L = rand (1); V = rand (1); x = linspace (0,L,4); y = x;
%! m = msh2m_structured_mesh (x,y,1,1:4);
%! m.area = msh2m_geometrical_properties (m, 'area');
%! m.shg = msh2m_geometrical_properties (m, 'shg');
%! u = V * ones (columns(m.p),1);
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2 = bim2c_norm (m, u, 'L2');
%! uH1 = bim2c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], [V, V*L, V*L], 1e-12);
%!test
%! u = V * (m.p(1,:) + 2*m.p(2,:))';
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2 = bim2c_norm (m, u, 'L2');
%! uH1 = bim2c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1],
%! [3*L*V, V*L^2*sqrt(8/3), V*sqrt(8/3*L^4 + 5*L^2)],
%! 1e-12);
%!test
%! u = V * ones (columns(m.t),1);
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2 = bim2c_norm (m, u, 'L2');
%! assert ([uinf, uL2], [V, V*L], 1e-12);
%!test
%! u = V * ones (columns(m.t),1);
%! uvect = [u, 2*u];
%! uinf = bim2c_norm (m, uvect, 'inf');
%! uL2 = bim2c_norm (m, uvect, 'L2');
%! assert ([uinf, uL2], [2*V, V*L*sqrt(5)], 1e-12);
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