/usr/share/octave/packages/linear-algebra-2.2.0/funm.m is in octave-linear-algebra 2.2.0-1build1.
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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 | ## Copyright (C) 2000, 2011 P.R. Nienhuis <prnienhuis@users.sf.net>
## 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 3 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
## this program; 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
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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