/usr/share/octave/packages/3.2/linear-algebra-2.1.0/funm.m is in octave-linear-algebra 2.1.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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## Copyright (C) 2001 Paul Kienzle <pkienzle@users.sf.net>
##
## 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; 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.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{B} =} funm (@var{A}, @var{F})
## Compute matrix equivalent of function F; F can be a function name or
## a function handle.
##
## For trigonometric and hyperbolic functions, @code{thfm} is automatically
## invoked as that is based on @code{expm} and diagonalization is avoided.
## For other functions diagonalization is invoked, which implies that
## -depending on the properties of input matrix @var{A}- the results
## can be very inaccurate @emph{without any warning}. For easy diagonizable and
## stable matrices results of funm will be sufficiently accurate.
##
## Note that you should not use funm for 'sqrt', 'log' or 'exp'; instead
## use sqrtm, logm and expm as these are more robust.
##
## Examples:
##
## @example
## B = funm (A, sin);
## (Compute matrix equivalent of sin() )
## @end example
##
## @example
## function bk1 = besselk1 (x)
## bk1 = besselk(x, 1);
## endfunction
## B = funm (A, besselk1);
## (Compute matrix equivalent of bessel function K1(); a helper function
## is needed here to convey extra args for besselk() )
## @end example
##
## @seealso{thfm, expm, logm, sqrtm}
## @end deftypefn
## Author: P.R. Nienhuis <prnienhuis@users.sf.net> (somewhere in 2000)
## Additions by P. Kienzle, .........
## 2001-03-01 Paul Kienzle
## * Many code improvements
## 2011-03-27 Philip Nienhuis
## * Function handles
## * Texinfo header
## * Fallback to thfm for trig & hyperb funcs to avoid diagonalization
## 2011-07-29 Philip Nienhuis
## * Layout, cleanup (tabs, alignment, ...)
function B = funm (A, name)
persistent thfuncs = {"cos", "sin", "tan", "sec", "csc", "cot", ...
"cosh", "sinh", "tanh", "sech", "csch", "coth", ...
"acos", "asin", "atan", "asec", "acsc", "acot", ...
"acosh", "asinh", "atanh", "asech", "acsch", "acoth", ...
}
## Function handle supplied?
try
ishndl = isstruct (functions (name));
fname = functions (name).function;
catch
ishdnl = 0;
fname = ' '
end_try_catch
if (nargin < 2 || (!(ischar (name) || ishndl)) || ischar (A))
usage ("B = funm (A, 'f' where A = square matrix and f = function name");
endif
if (~isempty (find (ismember (thfuncs, fname))))
## Use more robust thfm ()
if (ishndl); name = fname; endif
B = thfm (A, name);
else
## Simply invoke eigenvalues. Note: risk for repeated eigenvalues!!
## Modeled after suggestion by N. Higham (based on R. Davis, 2007)
## FIXME Do we need automatic setting of TOL?
tol = 1.e-15;
[V, D] = eig (A + tol * randn (size(A)));
D = diag (feval (name, diag(D)));
B = V * D / V;
endif
endfunction
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