Merge pull request #1214 from alexvong1995/add-piecewise

@sym/piecewise: Add new function.

Author: cbm755

INDEX

@@ -182,6 +182,7 @@ Mathematical methods for symbolic objects
  @sym/numden
  @sym/orth
  @sym/partfrac
+ @sym/piecewise
  @sym/pinv
  @sym/pochhammer
  @sym/polylog

NEWS

@@ -4,6 +4,7 @@ octsympy 3.0.1+
   * New symbolic commands:
 
           cart2pol
+          piecewise
 
 
 

inst/@sym/piecewise.m

@@ -0,0 +1,98 @@
+%% Copyright (C) 2022 Alex Vong
+%%
+%% 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 <https://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @documentencoding UTF-8
+%% @defmethod  @@sym piecewise (@var{cond1}, @var{val1}, @var{cond2}, @var{val2}, @dots{})
+%% @defmethodx @@sym piecewise (@var{cond1}, @var{val1}, @var{cond2}, @var{val2}, @dots{}, @var{else_val})
+%% Construct piecewise function.
+%%
+%% The returned piecewise function evaluates to @var{val1} if @var{cond1}
+%% holds, @var{val2} if @var{cond2} holds, @dots{} etc.  In the case where none
+%% of the conditions hold, it evaluates to @var{else_val} if provided.  If
+%% @var{else_val} is not provided, it evaluates to @code{nan}.
+%%
+%% Examples:
+%% @example
+%% @group
+%% syms x real
+%% f = piecewise (abs (x) < 1, exp (- 1 / (1 - x^2)), abs (x) >= 1, 0)
+%%   @result{} f = (sym)
+%%       ⎧  -1
+%%       ⎪ ──────
+%%       ⎪      2
+%%       ⎨ 1 - x
+%%       ⎪ℯ        for │x│ < 1
+%%       ⎪
+%%       ⎩   0      otherwise
+%% @end group
+%% @end example
+%%
+%% For this piecewise function, we can omit the redundant condition at the end:
+%% @example
+%% @group
+%% syms x real
+%% f = piecewise (abs (x) < 1, exp (- 1 / (1 - x^2)), 0)
+%%   @result{} f = (sym)
+%%       ⎧  -1
+%%       ⎪ ──────
+%%       ⎪      2
+%%       ⎨ 1 - x
+%%       ⎪ℯ        for │x│ < 1
+%%       ⎪
+%%       ⎩   0      otherwise
+%% @end group
+%% @end example
+%%
+%% @seealso{if}
+%% @end defmethod
+
+
+function f = piecewise (varargin)
+  if nargin < 1
+    print_usage ();
+  end
+
+  cmd = {'def chunks_of(ls, n):'
+         '    return itertools.zip_longest(*[ls[k::n] for k in range(n)])'
+         'args = [(val, cond) if val is not None else (cond, True)'
+         '        for cond, val in chunks_of(_ins, 2)]'
+         'return Piecewise(*args)'
+        };
+
+  args = cellfun (@sym, varargin, 'UniformOutput', false);
+  f = pycall_sympy__ (cmd, args{:});
+end
+
+
+%!test
+%! % basic
+%! syms x real
+%! f = piecewise (abs (x) < 1, 1);
+%! assert (isnan (subs (f, -1)));
+%! assert (isequal (subs (f, 0), 1));
+%! assert (isnan (subs (f, 1)));
+
+%!test
+%! % heaviside
+%! syms x real
+%! f = rewrite (heaviside (x, 1 / sym (2)), 'Piecewise');
+%! g = piecewise (x < 0, 0, x == 0, 1 / sym (2), x > 0, 1);
+%! assert (logical (simplify (f == g)));
+
+%% FIXME: expand test suite, add SMT compat tests, ...