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%% Copyright (C) 2014-2016 Colin B. Macdonald | ||
%% | ||
%% This file is part of OctSymPy. | ||
%% | ||
%% OctSymPy 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 software 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 software; see the file COPYING. | ||
%% If not, see <http://www.gnu.org/licenses/>. | ||
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%% -*- texinfo -*- | ||
%% @documentencoding UTF-8 | ||
%% @defmethod @@sym diff (@var{f}) | ||
%% @defmethodx @@sym diff (@var{f}, @var{x}) | ||
%% @defmethodx @@sym diff (@var{f}, @var{x}, @dots{}) | ||
%% @defmethodx @@sym diff (@var{f}, @dots{}) | ||
%% Symbolic differentiation. | ||
%% | ||
%% Examples: | ||
%% @example | ||
%% @group | ||
%% syms x | ||
%% f = sin (cos (x)); | ||
%% diff (f) | ||
%% @result{} (sym) -sin(x)⋅cos(cos(x)) | ||
%% diff (f, x) | ||
%% @result{} (sym) -sin(x)⋅cos(cos(x)) | ||
%% simplify (diff (f, x, x)) | ||
%% @result{} (sym) | ||
%% 2 | ||
%% - sin (x)⋅sin(cos(x)) - cos(x)⋅cos(cos(x)) | ||
%% @end group | ||
%% @end example | ||
%% | ||
%% Partial differentiation: | ||
%% @example | ||
%% @group | ||
%% syms x y | ||
%% f = cos(2*x + 3*y); | ||
%% diff(f, x, y, x) | ||
%% @result{} (sym) 12⋅sin(2⋅x + 3⋅y) | ||
%% diff(f, x, 2, y, 3) | ||
%% @result{} (sym) -108⋅sin(2⋅x + 3⋅y) | ||
%% @end group | ||
%% @end example | ||
%% | ||
%% Other examples: | ||
%% @example | ||
%% @group | ||
%% diff(sym(1)) | ||
%% @result{} (sym) 0 | ||
%% @end group | ||
%% @end example | ||
%% | ||
%% @seealso{@@sym/int} | ||
%% @end defmethod | ||
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function z = diff(f, varargin) | ||
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cmd = { 'f = _ins[0]' | ||
'args = _ins[1:]' | ||
'd = list(f.free_symbols)' | ||
'if len(d) == 0:' | ||
' return sympy.S(0),' | ||
'if len(args) == 0:' | ||
' if len(d) > 1:' | ||
' return ("NO_DEV_VAR"),' | ||
'else:' | ||
' if args[0].is_integer:' | ||
' if len(d) > 1:' | ||
' return ("NO_DEV_VAR"),' | ||
' d = d*args[0]' | ||
' else:' | ||
' d = [args[0]]' | ||
' for i in xrange(1, len(args)):' | ||
' if args[i].is_integer:' | ||
' if args[i] >= 1:' | ||
' d = d + [d[-1]]*(args[i]-1)' | ||
' else:' | ||
' d = d + [args[i]]' | ||
'return f.diff(*d),' }; | ||
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varargin = sym(varargin); | ||
z = python_cmd (cmd, sym(f), varargin{:}); | ||
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if strcmp(z, 'NO_DEV_VAR') | ||
error('Please set a derive var, actually we do not support autodetect vars to chain rule'); | ||
end | ||
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end | ||
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%!shared x,y,z | ||
%! syms x y z | ||
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%!test | ||
%! % basic | ||
%! assert(logical( diff(sin(x)) - cos(x) == 0 )) | ||
%! assert(logical( diff(sin(x),x) - cos(x) == 0 )) | ||
%! assert(logical( diff(sin(x),x,x) + sin(x) == 0 )) | ||
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%!test | ||
%! % these fail when doubles are not converted to sym | ||
%! assert(logical( diff(sin(x),x,2) + sin(x) == 0 )) | ||
%! assert(logical( diff(sym(1),x) == 0 )) | ||
%! assert(logical( diff(1,x) == 0 )) | ||
%! assert(logical( diff(pi,x) == 0 )) | ||
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%!test | ||
%! % symbolic diff of const (w/o variable) fails in sympy, but we work around | ||
%! assert (isequal (diff(sym(1)), sym(0))) | ||
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%!test | ||
%! % nth symbolic diff of const | ||
%! assert (isequal (diff(sym(1), 2), sym(0))) | ||
%! assert (isequal (diff(sym(1), sym(1)), sym(0))) | ||
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%!test | ||
%! % octave's vector difference still works | ||
%! assert(isempty(diff(1))) | ||
%! assert((diff([2 6]) == 4)) | ||
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%!test | ||
%! % other forms | ||
%! f = sin(x); | ||
%! g = diff(f,x,2); | ||
%! assert (isequal (diff(f,2), g)) | ||
%! assert (isequal (diff(f,sym(2)), g)) | ||
%! assert (isequal (diff(f,sym(2),x), diff(g))) | ||
%! g = diff(f,x); | ||
%! assert (isequal (diff(f), g)) | ||
%! assert (isequal (diff(f,1), g)) | ||
%! assert (isequal (diff(f,1,x), diff(g))) | ||
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%!test | ||
%! % matrix | ||
%! A = [x sin(x); x*y 10]; | ||
%! B = [1 cos(x); y 0]; | ||
%! assert(isequal(diff(A,x),B)) | ||
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%!error | ||
%! % bug: use symvar | ||
%! a = x*y; | ||
%! b = diff(a); | ||
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%!test | ||
%! % bug: symvar should be used on the matrix, not comp-by-comp | ||
%! a = [x y x*x]; | ||
%! b = diff(a, x); | ||
%! assert (~isequal (b(2), 1)) | ||
%! assert (isequal (b, [1 0 2*x])) | ||
%! b = diff(a, x, 1); | ||
%! assert (~isequal (b(2), 1)) | ||
%! assert (isequal (b, [1 0 2*x])) |