/usr/share/octave/packages/optim-1.3.0/cdiff.m is in octave-optim 1.3.0-1.
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 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 | ## Copyright (C) 2002 Etienne Grossmann <etienne@egdn.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/>.
## c = cdiff (func,wrt,N,dfunc,stack,dx) - Code for num. differentiation
## = "function df = dfunc (var1,..,dvar,..,varN) .. endfunction
##
## Returns a string of octave code that defines a function 'dfunc' that
## returns the derivative of 'func' with respect to it's 'wrt'th
## argument.
##
## The derivatives are obtained by symmetric finite difference.
##
## dfunc()'s return value is in the same format as that of ndiff()
##
## func : string : name of the function to differentiate
##
## wrt : int : position, in argument list, of the differentiation
## variable. Default:1
##
## N : int : total number of arguments taken by 'func'.
## If N=inf, dfunc will take variable argument list.
## Default:wrt
##
## dfunc : string : Name of the octave function that returns the
## derivatives. Default:['d',func]
##
## stack : string : Indicates whether 'func' accepts vertically
## (stack="rstack") or horizontally (stack="cstack")
## arguments. Any other string indicates that 'func'
## does not allow stacking. Default:''
##
## dx : real : Step used in the symmetric difference scheme.
## Default:10*sqrt(eps)
##
## See also : ndiff, eval, todisk
function c = cdiff (func,wrt,nargs,dfunc,stack,dx)
if nargin<2,
wrt = 1 ;
end
if nargin<3,
nargs = wrt ;
end
if nargin<4 || strcmp(dfunc,""),
dfunc = ["d",func] ;
if exist(dfunc)>=2,
printf(["cdiff : Warning : name of derivative not specified\n",...
" and canonic name '%s' is already taken\n"],...
dfunc);
## keyboard
end
end
if nargin<5, stack = "" ; end
if nargin<6, dx = 10*sqrt(eps) ; end
## verbose = 0 ;
## build argstr = "var1,..,dvar,...var_nargs"
if isfinite (nargs)
argstr = sprintf("var%i,",1:nargs);
else
argstr = [sprintf("var%i,",1:wrt),"...,"];
end
argstr = strrep(argstr,sprintf("var%i",wrt),"dvar") ;
argstr = argstr(1:length(argstr)-1) ;
if strcmp("cstack",stack) , # Horizontal stacking ################
calstr = "reshape (kron(ones(1,2*ps), dvar(:))+[-dx*eye(ps),dx*eye(ps)], sz.*[1,2*ps])";
calstr = strrep(argstr,"dvar",calstr) ;
calstr = sprintf("%s(%s)",func,calstr) ;
calstr = sprintf(strcat(" res = %s;\n",
" pr = prod (size(res)) / (2*ps);\n",
" res = reshape (res,pr,2*ps);\n",
" df = (res(:,ps+1:2*ps)-res(:,1:ps)) / (2*dx);\n"),
calstr) ;
elseif strcmp("rstack",stack), # Vertical stacking ##################
calstr = "kron(ones(2*ps,1),dvar)+dx*[-dv;dv]" ;
calstr = strrep(argstr,"dvar",calstr) ;
calstr = sprintf("%s(%s)",func,calstr) ;
calstr = sprintf(strcat(" dv = kron (eye(sz(2)), eye(sz(1))(:));\n",...
" res = %s;\n",...
" sr = size(res)./[2*ps,1];\n",...
" pr = prod (sr);\n",...
" df = (res(sr(1)*ps+1:2*sr(1)*ps,:)-res(1:sr(1)*ps,:))/(2*dx);\n",...
" scramble = reshape (1:pr,sr(2),sr(1))';\n",...
" df = reshape (df',pr,ps)(scramble(:),:);\n"),...
calstr) ;
## sayif(verbose,"cdiff : calstr='%s'\n",calstr) ;
else # No stacking ########################
calstr = sprintf("%s (%s)",func,argstr) ;
## "func(var1,dvar%sdv(:,%d:%d),...,varN),"
## calstr = strrep(calstr,"dvar","dvar%sdv(:,(i-1)*sz(2)+1:i*sz(2))")(:)';
calstr = strrep(calstr,"dvar","dvar%sdv")(:)';
## func(..,dvar+dv(:,1:sz(2)),..) - func(..)
calstr = strcat(calstr,"-",calstr) ; ## strcat(calstr,"-",calstr) ;
calstr = sprintf(calstr,"+","-") ;
tmp = calstr ;
## sayif(verbose,"cdiff : calstr='%s'\n",calstr) ;
calstr = sprintf(strcat(" dv = zeros (sz); dv(1) = dx;\n",...
" df0 = %s;\n",...
" sr = size (df0);\n",...
" df = zeros(prod (sr),ps); df(:,1) = df0(:);\n",...
" for i = 2:ps,\n",...
" dv(i) = dx; dv(i-1) = 0;\n",...
" df(:,i) = (%s)(:);\n",...
" end;\n",...
" df ./= 2*dx;\n"
),
calstr, tmp) ;
## sayif(verbose,"cdiff : calstr='%s'\n",calstr) ;
## "func(var1,reshape(dvar(1:NV,1),SZ1,SZ2),...,varN)," ,
## "func(var1,reshape(dvar(1:NV,2),SZ1,SZ2),...,varN)," , ...
## "func(var1,reshape(dvar(1:NV,NP),SZ1,SZ2),...,varN)"
## sayif(verbose,"cdiff : calstr='%s'\n",calstr) ;
end
argstr = strrep (argstr, "...", "varargin");
calstr = strrep (calstr, "...", "varargin{:}");
c = sprintf(strcat("function df = %s (%s)\n",...
" ## Numerical differentiation of '%s' wrt to it's %d'th argument\n",...
" ## This function has been written by 'cdiff()'\n",...
" dx = %e;\n",...
" sz = size (dvar);\n",...
" ps = prod (sz);\n",...
"%s",...
"endfunction\n"),...
dfunc,argstr,...
func,wrt,...
dx,...
calstr) ;
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