[wip] New Diff2

inst/@sym/diff2.m

@@ -0,0 +1,162 @@
+%% 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/>.
+
+%% -*- texinfo -*-
+%% @documentencoding UTF-8
+%% @defmethod  @@sym diff2 (@var{f})
+%% @defmethodx @@sym diff2 (@var{f}, @var{x})
+%% @defmethodx @@sym diff2 (@var{f}, @var{x}, @dots{})
+%% @defmethodx @@sym diff2 (@var{f}, @dots{})
+%% Symbolic differentiation.
+%%
+%% Examples:
+%% @example
+%% @group
+%% syms x
+%% f = sin (cos (x));
+%% diff2 (f)
+%%   @result{} (sym) -sin(x)⋅cos(cos(x))
+%% diff2 (f, x)
+%%   @result{} (sym) -sin(x)⋅cos(cos(x))
+%% simplify (diff2 (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);
+%% diff2(f, x, y, x)
+%%   @result{} (sym) 12⋅sin(2⋅x + 3⋅y)
+%% diff2(f, x, 2, y, 3)
+%%   @result{} (sym) -108⋅sin(2⋅x + 3⋅y)
+%% @end group
+%% @end example
+%%
+%% Other examples:
+%% @example
+%% @group
+%% diff2(sym(1))
+%%   @result{} (sym) 0
+%% @end group
+%% @end example
+%%
+%% @seealso{@@sym/int}
+%% @end defmethod
+
+
+function z = diff2(f, varargin)
+
+  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:'
+          '        d = []'
+          '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),' };
+
+  varargin = sym(varargin);
+  z = python_cmd (cmd, sym(f), varargin{:});
+
+  if strcmp(z, 'NO_DEV_VAR')
+    error('Please set a derive var, actually we do not support autodetect vars to chain rule');
+  end
+
+end
+
+
+%!shared x,y,z
+%! syms x y z
+
+%!test
+%! % basic
+%! assert(logical( diff2(sin(x)) - cos(x) == 0 ))
+%! assert(logical( diff2(sin(x),x) - cos(x) == 0 ))
+%! assert(logical( diff2(sin(x),x,x) + sin(x) == 0 ))
+
+%!test
+%! % these fail when doubles are not converted to sym
+%! assert(logical( diff2(sin(x),x,2) + sin(x) == 0 ))
+%! assert(logical( diff2(sym(1),x) == 0 ))
+%! assert(logical( diff2(1,x) == 0 ))
+%! assert(logical( diff2(pi,x) == 0 ))
+
+%!test
+%! % symbolic diff of const (w/o variable) fails in sympy, but we work around
+%! assert (isequal (diff2(sym(1)), sym(0)))
+
+%!test
+%! % nth symbolic diff of const
+%! assert (isequal (diff2(sym(1), 2), sym(0)))
+%! assert (isequal (diff2(sym(1), sym(1)), sym(0)))
+
+%!test
+%! % octave's vector difference still works
+%! assert(isempty(diff2(1)))
+%! assert((diff2([2 6]) == 4))
+
+%!test
+%! % other forms
+%! f = sin(x);
+%! g = diff2(f,x,2);
+%! assert (isequal (diff2(f,2), g))
+%! assert (isequal (diff2(f,sym(2)), g))
+%! assert (isequal (diff2(f,sym(2),x), diff2(g)))
+%! g = diff2(f,x);
+%! assert (isequal (diff2(f), g))
+%! assert (isequal (diff2(f,1), g))
+%! assert (isequal (diff2(f,1,x), diff2(g)))
+
+%!test
+%! % matrix
+%! A = [x sin(x); x*y 10];
+%! B = [1 cos(x); y 0];
+%! assert(isequal(diff2(A,x),B))
+
+%!error
+%! a = x*y;
+%! b = diff2(a);
+
+%!test
+%! % bug: symvar should be used on the matrix, not comp-by-comp
+%! a = [x y x*x];
+%! b = diff2(a, x);
+%! assert (~isequal (b(2), 1))
+%! assert (isequal (b, [1 0 2*x]))
+%! b = diff2(a, x, 1);
+%! assert (~isequal (b(2), 1))
+%! assert (isequal (b, [1 0 2*x]))