/usr/share/octave/packages/linear-algebra-2.2.0/thfm.m is in octave-linear-algebra 2.2.0-1build1.
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 92 93 94 95 96 97 98 | ## Copyright (C) 2001 Rolf Fabian <fabian@tu-cottbus.de>
## Copyright (C) 2001 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2011 Philip Nienhuis <pr.nienhuis@hccnet.nl>
## Copyright (C) 2011 Carnë Draug <carandraug+dev@gmail.com>
##
## 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{y} =} thfm (@var{x}, @var{mode})
## Trigonometric/hyperbolic functions of square matrix @var{x}.
##
## @var{mode} must be the name of a function. Valid functions are 'sin', 'cos',
## 'tan', 'sec', 'csc', 'cot' and all their inverses and/or hyperbolic variants,
## and 'sqrt', 'log' and 'exp'.
##
## The code @code{thfm (x, 'cos')} calculates matrix cosinus @emph{even if} input
## matrix @var{x} is @emph{not} diagonalizable.
##
## @emph{Important note}:
## This algorithm does @emph{not} use an eigensystem similarity transformation. It
## maps the @var{mode} functions to functions of @code{expm}, @code{logm} and
## @code{sqrtm}, which are known to be robust with respect to non-diagonalizable
## ('defective') @var{x}.
##
## @seealso{funm}
## @end deftypefn
function y = thfm (x,M)
## minimal arg check only
if ( nargin != 2 || !ischar (M) || ischar (x) )
print_usage;
endif
## look for known functions of sqrt, log, exp
I = eye (size (x));
switch (M)
case {'cos'}
if (isreal(x)) y = real( expm( i*x ) );
else y = ( expm( i*x ) + expm( -i*x ) ) / 2;
endif
case {'sin'}
if (isreal(x)) y = imag( expm( i*x ) );
else y = ( expm( i*x ) - expm( -i*x ) ) / (2*i);
endif
case {'tan'}
if (isreal(x)) t = expm( i*x ); y = imag(t)/real(t);
else t = expm( -2*i*x ); y = -i*(I-t)/(I+t);
endif
case {'cot'}
if (isreal(x)) t = expm( i*x ); y = real(t)/imag(t);
else t = expm( -2*i*x ); y = i*(I+t)/(I-t);
endif
case {'sec'}
if (isreal(x)) y = inv( real(expm(i*x)) );
else y = inv( expm(i*x)+expm(-i*x) )*2 ;
endif
case {'csc'}
if (isreal(x)) y = inv( imag(expm(i*x)) );
else y = inv( expm(i*x)-expm(-i*x) )*2i;
endif
case {'log'} y = logm(x);
case {'exp'} y = expm(x);
case {'cosh'} y = ( expm(x)+expm(-x) )/2;
case {'sinh'} y = ( expm(x)-expm(-x) )/2;
case {'tanh'} t = expm( -2*x ); y = (I - t)/(I + t);
case {'coth'} t = expm( -2*x ); y = (I + t)/(I - t);
case {'sech'} y = 2 * inv( expm(x) + expm(-x) );
case {'csch'} y = 2 * inv( expm(x) - expm(-x) );
case {'asin'} y = -i * logm( i*x + sqrtm(I - x*x) );
case {'acos'} y = i * logm( x - i*sqrtm(I - x*x) );
case {'atan'} y = -i/2 * logm( (I + i*x)/(I - i*x) );
case {'acot'} y = i/2 * logm( (I + i*x)/(i*x - I) );
case {'asec'} y = i * logm( ( I - sqrtm(I - x*x) ) / x );
case {'acsc'} y = -i * logm( i*( I + sqrtm(I - x*x) ) / x );
case {'sqrt'} y = sqrtm(x);
case {'asinh'} y = logm( x + sqrtm (x*x + I) );
case {'acosh'} y = logm( x + sqrtm (x*x - I) );
case {'atanh'} y = logm( (I + x)/(I - x) ) / 2;
case {'acoth'} y = logm( (I + x)/(x - I) ) / 2;
case {'asech'} y = logm( (I + sqrtm (I - x*x)) / x );
case {'acsch'} y = logm( (I + sqrtm (I + x*x)) / x );
otherwise
error ("thfm doesn't support function %s - try to use funm instead.", M);
endswitch
endfunction
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