bsxfun.cc

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/*

Copyright (C) 2007-2013 David Bateman
Copyright (C) 2009 VZLU Prague

This file is part of Octave.

Octave 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.

Octave 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 Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <string>
#include <vector>
#include <list>

#include "lo-mappers.h"

#include "oct-map.h"
#include "defun.h"
#include "parse.h"
#include "variables.h"
#include "ov-colon.h"
#include "unwind-prot.h"
#include "ov-fcn-handle.h"

// Optimized bsxfun operations
enum bsxfun_builtin_op
{
  bsxfun_builtin_plus = 0,
  bsxfun_builtin_minus,
  bsxfun_builtin_times,
  bsxfun_builtin_divide,
  bsxfun_builtin_max,
  bsxfun_builtin_min,
  bsxfun_builtin_eq,
  bsxfun_builtin_ne,
  bsxfun_builtin_lt,
  bsxfun_builtin_le,
  bsxfun_builtin_gt,
  bsxfun_builtin_ge,
  bsxfun_builtin_and,
  bsxfun_builtin_or,
  bsxfun_builtin_power,
  bsxfun_builtin_unknown,
  bsxfun_num_builtin_ops = bsxfun_builtin_unknown
};

const char *bsxfun_builtin_names[] =
{
  "plus",
  "minus",
  "times",
  "rdivide",
  "max",
  "min",
  "eq",
  "ne",
  "lt",
  "le",
  "gt",
  "ge",
  "and",
  "or",
  "power"
};

static bsxfun_builtin_op
bsxfun_builtin_lookup (const std::string& name)
{
  for (int i = 0; i < bsxfun_num_builtin_ops; i++)
    if (name == bsxfun_builtin_names[i])
      return static_cast<bsxfun_builtin_op> (i);
  return bsxfun_builtin_unknown;
}

typedef octave_value (*bsxfun_handler) (const octave_value&,
                                        const octave_value&);

// Static table of handlers.
bsxfun_handler bsxfun_handler_table[bsxfun_num_builtin_ops][btyp_num_types];

template <class NDA, NDA (bsxfun_op) (const NDA&, const NDA&)>
static octave_value
bsxfun_forward_op (const octave_value& x, const octave_value& y)
{
  NDA xa = octave_value_extract<NDA> (x);
  NDA ya = octave_value_extract<NDA> (y);
  return octave_value (bsxfun_op (xa, ya));
}

template <class NDA, boolNDArray (bsxfun_rel) (const NDA&, const NDA&)>
static octave_value
bsxfun_forward_rel (const octave_value& x, const octave_value& y)
{
  NDA xa = octave_value_extract<NDA> (x);
  NDA ya = octave_value_extract<NDA> (y);
  return octave_value (bsxfun_rel (xa, ya));
}

// pow() needs a special handler for reals
// because of the potentially complex result.
template <class NDA, class CNDA>
static octave_value
do_bsxfun_real_pow (const octave_value& x, const octave_value& y)
{
  NDA xa = octave_value_extract<NDA> (x);
  NDA ya = octave_value_extract<NDA> (y);
  if (! ya.all_integers () && xa.any_element_is_negative ())
    return octave_value (bsxfun_pow (CNDA (xa), ya));
  else
    return octave_value (bsxfun_pow (xa, ya));
}

static void maybe_fill_table (void)
{
  static bool filled = false;
  if (filled)
    return;

#define REGISTER_OP_HANDLER(OP, BTYP, NDA, FUNOP) \
  bsxfun_handler_table[OP][BTYP] = bsxfun_forward_op<NDA, FUNOP>
#define REGISTER_REL_HANDLER(REL, BTYP, NDA, FUNREL) \
  bsxfun_handler_table[REL][BTYP] = bsxfun_forward_rel<NDA, FUNREL>
#define REGISTER_STD_HANDLERS(BTYP, NDA) \
  REGISTER_OP_HANDLER (bsxfun_builtin_plus, BTYP, NDA, bsxfun_add); \
  REGISTER_OP_HANDLER (bsxfun_builtin_minus, BTYP, NDA, bsxfun_sub); \
  REGISTER_OP_HANDLER (bsxfun_builtin_times, BTYP, NDA, bsxfun_mul); \
  REGISTER_OP_HANDLER (bsxfun_builtin_divide, BTYP, NDA, bsxfun_div); \
  REGISTER_OP_HANDLER (bsxfun_builtin_max, BTYP, NDA, bsxfun_max); \
  REGISTER_OP_HANDLER (bsxfun_builtin_min, BTYP, NDA, bsxfun_min); \
  REGISTER_REL_HANDLER (bsxfun_builtin_eq, BTYP, NDA, bsxfun_eq); \
  REGISTER_REL_HANDLER (bsxfun_builtin_ne, BTYP, NDA, bsxfun_ne); \
  REGISTER_REL_HANDLER (bsxfun_builtin_lt, BTYP, NDA, bsxfun_lt); \
  REGISTER_REL_HANDLER (bsxfun_builtin_le, BTYP, NDA, bsxfun_le); \
  REGISTER_REL_HANDLER (bsxfun_builtin_gt, BTYP, NDA, bsxfun_gt); \
  REGISTER_REL_HANDLER (bsxfun_builtin_ge, BTYP, NDA, bsxfun_ge)

  REGISTER_STD_HANDLERS (btyp_double, NDArray);
  REGISTER_STD_HANDLERS (btyp_float, FloatNDArray);
  REGISTER_STD_HANDLERS (btyp_complex, ComplexNDArray);
  REGISTER_STD_HANDLERS (btyp_float_complex, FloatComplexNDArray);
  REGISTER_STD_HANDLERS (btyp_int8,  int8NDArray);
  REGISTER_STD_HANDLERS (btyp_int16, int16NDArray);
  REGISTER_STD_HANDLERS (btyp_int32, int32NDArray);
  REGISTER_STD_HANDLERS (btyp_int64, int64NDArray);
  REGISTER_STD_HANDLERS (btyp_uint8,  uint8NDArray);
  REGISTER_STD_HANDLERS (btyp_uint16, uint16NDArray);
  REGISTER_STD_HANDLERS (btyp_uint32, uint32NDArray);
  REGISTER_STD_HANDLERS (btyp_uint64, uint64NDArray);

  // For bools, we register and/or.
  REGISTER_OP_HANDLER (bsxfun_builtin_and, btyp_bool, boolNDArray, bsxfun_and);
  REGISTER_OP_HANDLER (bsxfun_builtin_or, btyp_bool, boolNDArray, bsxfun_or);

  // Register power handlers.
  bsxfun_handler_table[bsxfun_builtin_power][btyp_double] =
    do_bsxfun_real_pow<NDArray, ComplexNDArray>;
  bsxfun_handler_table[bsxfun_builtin_power][btyp_float] =
    do_bsxfun_real_pow<FloatNDArray, FloatComplexNDArray>;

  REGISTER_OP_HANDLER (bsxfun_builtin_power, btyp_complex, ComplexNDArray,
                       bsxfun_pow);
  REGISTER_OP_HANDLER (bsxfun_builtin_power, btyp_float_complex,
                       FloatComplexNDArray, bsxfun_pow);

  // For chars, we want just relational handlers.
  REGISTER_REL_HANDLER (bsxfun_builtin_eq, btyp_char, charNDArray, bsxfun_eq);
  REGISTER_REL_HANDLER (bsxfun_builtin_ne, btyp_char, charNDArray, bsxfun_ne);
  REGISTER_REL_HANDLER (bsxfun_builtin_lt, btyp_char, charNDArray, bsxfun_lt);
  REGISTER_REL_HANDLER (bsxfun_builtin_le, btyp_char, charNDArray, bsxfun_le);
  REGISTER_REL_HANDLER (bsxfun_builtin_gt, btyp_char, charNDArray, bsxfun_gt);
  REGISTER_REL_HANDLER (bsxfun_builtin_ge, btyp_char, charNDArray, bsxfun_ge);

  filled = true;
}

static octave_value
maybe_optimized_builtin (const std::string& name,
                         const octave_value& a, const octave_value& b)
{
  octave_value retval;

  maybe_fill_table ();

  bsxfun_builtin_op op = bsxfun_builtin_lookup (name);
  if (op != bsxfun_builtin_unknown)
    {
      builtin_type_t btyp_a = a.builtin_type (), btyp_b = b.builtin_type ();

      // Simplify single/double combinations.
      if (btyp_a == btyp_float && btyp_b == btyp_double)
        btyp_b = btyp_float;
      else if (btyp_a == btyp_double && btyp_b == btyp_float)
        btyp_a = btyp_float;
      else if (btyp_a == btyp_float_complex && btyp_b == btyp_complex)
        btyp_b = btyp_float_complex;
      else if (btyp_a == btyp_complex && btyp_b == btyp_float_complex)
        btyp_a = btyp_float_complex;

      if (btyp_a == btyp_b && btyp_a != btyp_unknown)
        {
          bsxfun_handler handler = bsxfun_handler_table[op][btyp_a];
          if (handler)
            retval = handler (a, b);
        }
    }

  return retval;
}

static bool
maybe_update_column (octave_value& Ac, const octave_value& A,
                     const dim_vector& dva, const dim_vector& dvc,
                     octave_idx_type i, octave_value_list &idx)
{
  octave_idx_type nd = dva.length ();

  if (i == 0)
    {
      idx(0) = octave_value (':');
      for (octave_idx_type j = 1; j < nd; j++)
        {
          if (dva (j) == 1)
            idx(j) = octave_value (1);
          else
            idx(j) = octave_value ((i % dvc(j)) + 1);

          i = i / dvc (j);
        }

      Ac = A;
      Ac = Ac.single_subsref ("(", idx);
      return true;
    }
  else
    {
      bool is_changed = false;
      octave_idx_type k = i;
      octave_idx_type k1 = i - 1;
      for (octave_idx_type j = 1; j < nd; j++)
        {
          if (dva(j) != 1 && k % dvc (j) != k1 % dvc (j))
            {
              idx (j) = octave_value ((k % dvc(j)) + 1);
              is_changed = true;
            }

          k = k / dvc (j);
          k1 = k1 / dvc (j);
        }

      if (is_changed)
        {
          Ac = A;
          Ac = Ac.single_subsref ("(", idx);
          return true;
        }
      else
        return false;
    }
}

#if 0
// FIXME: this function is not used; is it OK to delete it?
static void
update_index (octave_value_list& idx, const dim_vector& dv, octave_idx_type i)
{
  octave_idx_type nd = dv.length ();

  if (i == 0)
    {
      for (octave_idx_type j = nd - 1; j > 0; j--)
        idx(j) = octave_value (static_cast<double>(1));
      idx(0) = octave_value (':');
    }
  else
    {
      for (octave_idx_type j = 1; j < nd; j++)
        {
          idx (j) = octave_value (i % dv (j) + 1);
          i = i / dv (j);
        }
    }
}
#endif

static void
update_index (Array<int>& idx, const dim_vector& dv, octave_idx_type i)
{
  octave_idx_type nd = dv.length ();

  idx(0) = 0;
  for (octave_idx_type j = 1; j < nd; j++)
    {
      idx (j) = i % dv (j);
      i = i / dv (j);
    }
}

DEFUN (bsxfun, args, ,
       "-*- texinfo -*-\n\
@deftypefn {Built-in Function} {} bsxfun (@var{f}, @var{A}, @var{B})\n\
The binary singleton expansion function applier performs broadcasting,\n\
that is, applies a binary function @var{f} element-by-element to two\n\
array arguments @var{A} and @var{B}, and expands as necessary\n\
singleton dimensions in either input argument.  @var{f} is a function\n\
handle, inline function, or string containing the name of the function\n\
to evaluate.  The function @var{f} must be capable of accepting two\n\
column-vector arguments of equal length, or one column vector argument\n\
and a scalar.\n\
\n\
The dimensions of @var{A} and @var{B} must be equal or singleton.  The\n\
singleton dimensions of the arrays will be expanded to the same\n\
dimensionality as the other array.\n\
@seealso{arrayfun, cellfun}\n\
@end deftypefn")
{
  int nargin = args.length ();
  octave_value_list retval;

  if (nargin != 3)
    print_usage ();
  else
    {
      octave_value func = args(0);

      if (func.is_string ())
        {
          std::string name = func.string_value ();
          func = symbol_table::find_function (name);
          if (func.is_undefined ())
            error ("bsxfun: invalid function name: %s", name.c_str ());
        }
      else if (! (args(0).is_function_handle ()
               || args(0).is_inline_function ()))
        error ("bsxfun: F must be a string or function handle");

      const octave_value A = args (1);
      const octave_value B = args (2);

      if (func.is_builtin_function ()
          || (func.is_function_handle ()
              && ! A.is_object () && ! B.is_object ()))
        {
          // This may break if the default behavior is overriden.  But if you
          // override arithmetic operators for builtin classes, you should
          // expect mayhem anyway (constant folding etc).  Querying
          // is_overloaded() may not be exactly what we need here.
          octave_function *fcn_val = func.function_value ();
          if (fcn_val)
            {
              octave_value tmp = maybe_optimized_builtin (fcn_val->name (),
                                                          A, B);
              if (tmp.is_defined ())
                retval(0) = tmp;
            }
        }

      if (! error_state && retval.empty ())
        {
          dim_vector dva = A.dims ();
          octave_idx_type nda = dva.length ();
          dim_vector dvb = B.dims ();
          octave_idx_type ndb = dvb.length ();
          octave_idx_type nd = nda;

          if (nda > ndb)
            dvb.resize (nda, 1);
          else if (nda < ndb)
            {
              dva.resize (ndb, 1);
              nd = ndb;
            }

          for (octave_idx_type i = 0; i < nd; i++)
            if (dva (i) != dvb (i) && dva (i) != 1 && dvb (i) != 1)
              {
                error ("bsxfun: dimensions of A and B must match");
                break;
              }

          if (!error_state)
            {
              // Find the size of the output
              dim_vector dvc;
              dvc.resize (nd);

              for (octave_idx_type i = 0; i < nd; i++)
                dvc (i) = (dva (i) < 1 ? dva (i)
                                       : (dvb (i) < 1 ? dvb (i)
                                                      : (dva (i) > dvb (i)
                                                        ? dva (i) : dvb (i))));

              if (dva == dvb || dva.numel () == 1 || dvb.numel () == 1)
                {
                  octave_value_list inputs;
                  inputs (0) = A;
                  inputs (1) = B;
                  retval = func.do_multi_index_op (1, inputs);
                }
              else if (dvc.numel () < 1)
                {
                  octave_value_list inputs;
                  inputs (0) = A.resize (dvc);
                  inputs (1) = B.resize (dvc);
                  retval = func.do_multi_index_op (1, inputs);
                }
              else
                {
                  octave_idx_type ncount = 1;
                  for (octave_idx_type i = 1; i < nd; i++)
                    ncount *= dvc (i);

#define BSXDEF(T) \
                  T result_ ## T; \
                  bool have_ ## T = false;

                  BSXDEF(NDArray);
                  BSXDEF(ComplexNDArray);
                  BSXDEF(FloatNDArray);
                  BSXDEF(FloatComplexNDArray);
                  BSXDEF(boolNDArray);
                  BSXDEF(int8NDArray);
                  BSXDEF(int16NDArray);
                  BSXDEF(int32NDArray);
                  BSXDEF(int64NDArray);
                  BSXDEF(uint8NDArray);
                  BSXDEF(uint16NDArray);
                  BSXDEF(uint32NDArray);
                  BSXDEF(uint64NDArray);

                  octave_value Ac ;
                  octave_value_list idxA;
                  octave_value Bc;
                  octave_value_list idxB;
                  octave_value C;
                  octave_value_list inputs;
                  Array<int> ra_idx (dim_vector (dvc.length (), 1), 0);


                  for (octave_idx_type i = 0; i < ncount; i++)
                    {
                      if (maybe_update_column (Ac, A, dva, dvc, i, idxA))
                        inputs (0) = Ac;

                      if (maybe_update_column (Bc, B, dvb, dvc, i, idxB))
                        inputs (1) = Bc;

                      octave_value_list tmp = func.do_multi_index_op (1,
                                                                      inputs);

                      if (error_state)
                        break;

#define BSXINIT(T, CLS, EXTRACTOR) \
                      (result_type == CLS) \
                        { \
                            have_ ## T = true; \
                            result_ ## T = \
                                tmp (0). EXTRACTOR ## _array_value (); \
                            result_ ## T .resize (dvc); \
                        }

                      if (i == 0)
                        {
                          if (! tmp(0).is_sparse_type ())
                            {
                              std::string result_type = tmp(0).class_name ();
                              if (result_type == "double")
                                {
                                  if (tmp(0).is_real_type ())
                                    {
                                      have_NDArray = true;
                                      result_NDArray = tmp(0).array_value ();
                                      result_NDArray.resize (dvc);
                                    }
                                  else
                                    {
                                      have_ComplexNDArray = true;
                                      result_ComplexNDArray =
                                        tmp(0).complex_array_value ();
                                      result_ComplexNDArray.resize (dvc);
                                    }
                                }
                              else if (result_type == "single")
                                {
                                  if (tmp(0).is_real_type ())
                                    {
                                      have_FloatNDArray = true;
                                      result_FloatNDArray
                                        = tmp(0).float_array_value ();
                                      result_FloatNDArray.resize (dvc);
                                    }
                                  else
                                    {
                                      have_ComplexNDArray = true;
                                      result_ComplexNDArray =
                                        tmp(0).complex_array_value ();
                                      result_ComplexNDArray.resize (dvc);
                                    }
                                }
                              else if BSXINIT(boolNDArray, "logical", bool)
                              else if BSXINIT(int8NDArray, "int8", int8)
                              else if BSXINIT(int16NDArray, "int16", int16)
                              else if BSXINIT(int32NDArray, "int32", int32)
                              else if BSXINIT(int64NDArray, "int64", int64)
                              else if BSXINIT(uint8NDArray, "uint8", uint8)
                              else if BSXINIT(uint16NDArray, "uint16", uint16)
                              else if BSXINIT(uint32NDArray, "uint32", uint32)
                              else if BSXINIT(uint64NDArray, "uint64", uint64)
                              else
                                {
                                  C = tmp (0);
                                  C = C.resize (dvc);
                                }
                            }
                        }
                      else
                        {
                          update_index (ra_idx, dvc, i);

                          if (have_FloatNDArray ||
                              have_FloatComplexNDArray)
                            {
                              if (! tmp(0).is_float_type ())
                                {
                                  if (have_FloatNDArray)
                                    {
                                      have_FloatNDArray = false;
                                      C = result_FloatNDArray;
                                    }
                                  else
                                    {
                                      have_FloatComplexNDArray = false;
                                      C = result_FloatComplexNDArray;
                                    }
                                  C = do_cat_op (C, tmp(0), ra_idx);
                                }
                              else if (tmp(0).is_double_type ())
                                {
                                  if (tmp(0).is_complex_type () &&
                                      have_FloatNDArray)
                                    {
                                      result_ComplexNDArray =
                                        ComplexNDArray (result_FloatNDArray);
                                      result_ComplexNDArray.insert
                                        (tmp(0).complex_array_value (), ra_idx);
                                      have_FloatComplexNDArray = false;
                                      have_ComplexNDArray = true;
                                    }
                                  else
                                    {
                                      result_NDArray =
                                        NDArray (result_FloatNDArray);
                                      result_NDArray.insert
                                        (tmp(0).array_value (), ra_idx);
                                      have_FloatNDArray = false;
                                      have_NDArray = true;
                                    }
                                }
                              else if (tmp(0).is_real_type ())
                                result_FloatNDArray.insert
                                  (tmp(0).float_array_value (), ra_idx);
                              else
                                {
                                  result_FloatComplexNDArray =
                                    FloatComplexNDArray (result_FloatNDArray);
                                  result_FloatComplexNDArray.insert
                                    (tmp(0).float_complex_array_value (),
                                     ra_idx);
                                  have_FloatNDArray = false;
                                  have_FloatComplexNDArray = true;
                                }
                            }
                          else if (have_NDArray)
                            {
                              if (! tmp(0).is_float_type ())
                                {
                                  have_NDArray = false;
                                  C = result_NDArray;
                                  C = do_cat_op (C, tmp(0), ra_idx);
                                }
                              else if (tmp(0).is_real_type ())
                                result_NDArray.insert (tmp(0).array_value (),
                                                       ra_idx);
                              else
                                {
                                  result_ComplexNDArray =
                                    ComplexNDArray (result_NDArray);
                                  result_ComplexNDArray.insert
                                    (tmp(0).complex_array_value (), ra_idx);
                                  have_NDArray = false;
                                  have_ComplexNDArray = true;
                                }
                            }

#define BSXLOOP(T, CLS, EXTRACTOR) \
                        (have_ ## T) \
                          { \
                            if (tmp (0).class_name () != CLS) \
                              { \
                                have_ ## T = false; \
                                C = result_ ## T; \
                                C = do_cat_op (C, tmp (0), ra_idx); \
                              } \
                            else \
                              result_ ## T .insert \
                                (tmp(0). EXTRACTOR ## _array_value (), \
                                ra_idx); \
                          }

                          else if BSXLOOP(ComplexNDArray, "double", complex)
                          else if BSXLOOP(boolNDArray, "logical", bool)
                          else if BSXLOOP(int8NDArray, "int8", int8)
                          else if BSXLOOP(int16NDArray, "int16", int16)
                          else if BSXLOOP(int32NDArray, "int32", int32)
                          else if BSXLOOP(int64NDArray, "int64", int64)
                          else if BSXLOOP(uint8NDArray, "uint8", uint8)
                          else if BSXLOOP(uint16NDArray, "uint16", uint16)
                          else if BSXLOOP(uint32NDArray, "uint32", uint32)
                          else if BSXLOOP(uint64NDArray, "uint64", uint64)
                          else
                            C = do_cat_op (C, tmp(0), ra_idx);
                        }
                    }

#define BSXEND(T) \
                  (have_ ## T) \
                    retval(0) = result_ ## T;

                  if BSXEND(NDArray)
                  else if BSXEND(ComplexNDArray)
                  else if BSXEND(FloatNDArray)
                  else if BSXEND(FloatComplexNDArray)
                  else if BSXEND(boolNDArray)
                  else if BSXEND(int8NDArray)
                  else if BSXEND(int16NDArray)
                  else if BSXEND(int32NDArray)
                  else if BSXEND(int64NDArray)
                  else if BSXEND(uint8NDArray)
                  else if BSXEND(uint16NDArray)
                  else if BSXEND(uint32NDArray)
                  else if BSXEND(uint64NDArray)
                  else
                    retval(0) = C;
                }
            }
        }
    }

  return retval;
}

/*

%!shared a, b, c, f
%! a = randn (4, 4);
%! b = mean (a, 1);
%! c = mean (a, 2);
%! f = @minus;
%!error (bsxfun (f))
%!error (bsxfun (f, a))
%!error (bsxfun (a, b))
%!error (bsxfun (a, b, c))
%!error (bsxfun (f, a, b, c))
%!error (bsxfun (f, ones (4, 0), ones (4, 4)))
%!assert (bsxfun (f, ones (4, 0), ones (4, 1)), zeros (4, 0))
%!assert (bsxfun (f, ones (1, 4), ones (4, 1)), zeros (4, 4))
%!assert (bsxfun (f, a, b), a - repmat (b, 4, 1))
%!assert (bsxfun (f, a, c), a - repmat (c, 1, 4))
%!assert (bsxfun ("minus", ones (1, 4), ones (4, 1)), zeros (4, 4))

%!shared a, b, c, f
%! a = randn (4, 4);
%! a(1) *= 1i;
%! b = mean (a, 1);
%! c = mean (a, 2);
%! f = @minus;
%!error (bsxfun (f))
%!error (bsxfun (f, a))
%!error (bsxfun (a, b))
%!error (bsxfun (a, b, c))
%!error (bsxfun (f, a, b, c))
%!error (bsxfun (f, ones (4, 0), ones (4, 4)))
%!assert (bsxfun (f, ones (4, 0), ones (4, 1)), zeros (4, 0))
%!assert (bsxfun (f, ones (1, 4), ones (4, 1)), zeros (4, 4))
%!assert (bsxfun (f, a, b), a - repmat (b, 4, 1))
%!assert (bsxfun (f, a, c), a - repmat (c, 1, 4))
%!assert (bsxfun ("minus", ones (1, 4), ones (4, 1)), zeros (4, 4))

%!shared a, b, c, f
%! a = randn (4, 4);
%! a(end) *= 1i;
%! b = mean (a, 1);
%! c = mean (a, 2);
%! f = @minus;
%!error (bsxfun (f))
%!error (bsxfun (f, a))
%!error (bsxfun (a, b))
%!error (bsxfun (a, b, c))
%!error (bsxfun (f, a, b, c))
%!error (bsxfun (f, ones (4, 0), ones (4, 4)))
%!assert (bsxfun (f, ones (4, 0), ones (4, 1)), zeros (4, 0))
%!assert (bsxfun (f, ones (1, 4), ones (4, 1)), zeros (4, 4))
%!assert (bsxfun (f, a, b), a - repmat (b, 4, 1))
%!assert (bsxfun (f, a, c), a - repmat (c, 1, 4))
%!assert (bsxfun ("minus", ones (1, 4), ones (4, 1)), zeros (4, 4))

%!shared a, b, c, f
%! a = randn (4, 4);
%! b = a (1, :);
%! c = a (:, 1);
%! f = @(x, y) x == y;
%!error (bsxfun (f))
%!error (bsxfun (f, a))
%!error (bsxfun (a, b))
%!error (bsxfun (a, b, c))
%!error (bsxfun (f, a, b, c))
%!error (bsxfun (f, ones (4, 0), ones (4, 4)))
%!assert (bsxfun (f, ones (4, 0), ones (4, 1)), zeros (4, 0, "logical"))
%!assert (bsxfun (f, ones (1, 4), ones (4, 1)), ones (4, 4, "logical"))
%!assert (bsxfun (f, a, b), a == repmat (b, 4, 1))
%!assert (bsxfun (f, a, c), a == repmat (c, 1, 4))

%!shared a, b, c, d, f
%! a = randn (4, 4, 4);
%! b = mean (a, 1);
%! c = mean (a, 2);
%! d = mean (a, 3);
%! f = @minus;
%!error (bsxfun (f, ones ([4, 0, 4]), ones ([4, 4, 4])))
%!assert (bsxfun (f, ones ([4, 0, 4]), ones ([4, 1, 4])), zeros ([4, 0, 4]))
%!assert (bsxfun (f, ones ([4, 4, 0]), ones ([4, 1, 1])), zeros ([4, 4, 0]))
%!assert (bsxfun (f, ones ([1, 4, 4]), ones ([4, 1, 4])), zeros ([4, 4, 4]))
%!assert (bsxfun (f, ones ([4, 4, 1]), ones ([4, 1, 4])), zeros ([4, 4, 4]))
%!assert (bsxfun (f, ones ([4, 1, 4]), ones ([1, 4, 4])), zeros ([4, 4, 4]))
%!assert (bsxfun (f, ones ([4, 1, 4]), ones ([1, 4, 1])), zeros ([4, 4, 4]))
%!assert (bsxfun (f, a, b), a - repmat (b, [4, 1, 1]))
%!assert (bsxfun (f, a, c), a - repmat (c, [1, 4, 1]))
%!assert (bsxfun (f, a, d), a - repmat (d, [1, 1, 4]))
%!assert (bsxfun ("minus", ones ([4, 0, 4]), ones ([4, 1, 4])), zeros ([4, 0, 4]))

%% The test below is a very hard case to treat
%!assert (bsxfun (f, ones ([4, 1, 4, 1]), ones ([1, 4, 1, 4])), zeros ([4, 4, 4, 4]));

%!shared a, b, aa, bb
%! a = randn (3, 1, 3);
%! aa = a(:, ones (1, 3), :, ones (1, 3));
%! b = randn (1, 3, 3, 3);
%! bb = b(ones (1, 3), :, :, :);
%!assert (bsxfun (@plus, a, b), aa + bb)
%!assert (bsxfun (@minus, a, b), aa - bb)
%!assert (bsxfun (@times, a, b), aa .* bb)
%!assert (bsxfun (@rdivide, a, b), aa ./ bb)
%!assert (bsxfun (@ldivide, a, b), aa .\ bb)
%!assert (bsxfun (@power, a, b), aa .^ bb)
%!assert (bsxfun (@power, abs (a), b), abs (aa) .^ bb)
%!assert (bsxfun (@eq, round (a), round (b)), round (aa) == round (bb))
%!assert (bsxfun (@ne, round (a), round (b)), round (aa) != round (bb))
%!assert (bsxfun (@lt, a, b), aa < bb)
%!assert (bsxfun (@le, a, b), aa <= bb)
%!assert (bsxfun (@gt, a, b), aa > bb)
%!assert (bsxfun (@ge, a, b), aa >= bb)
%!assert (bsxfun (@min, a, b), min (aa, bb))
%!assert (bsxfun (@max, a, b), max (aa, bb))
%!assert (bsxfun (@and, a > 0, b > 0), (aa > 0) & (bb > 0))
%!assert (bsxfun (@or, a > 0, b > 0), (aa > 0) | (bb > 0))

%% Test automatic bsxfun
%
%!test
%! funs = {@plus, @minus, @times, @rdivide, @ldivide, @power, @max, @min, ...
%!         @rem, @mod, @atan2, @hypot, @eq, @ne, @lt, @le, @gt, @ge, ...
%!         @and, @or, @xor };
%!
%! float_types = {@single, @double};
%! int_types = {@int8, @int16, @int32, @int64, ...
%!              @uint8, @uint16, @uint32, @uint64};
%!
%! x = rand (3) * 10-5;
%! y = rand (3,1) * 10-5;
%!
%! for i=1:length (funs)
%!   for j = 1:length (float_types)
%!     for k = 1:length (int_types)
%!
%!       fun = funs{i};
%!       f_type = float_types{j};
%!       i_type = int_types{k};
%!
%!         assert (bsxfun (fun, f_type (x), i_type (y)), ...
%!                 fun (f_type(x), i_type (y)));
%!         assert (bsxfun (fun, f_type (y), i_type (x)), ...
%!                 fun (f_type(y), i_type (x)));
%!
%!         assert (bsxfun (fun, i_type (x), i_type (y)), ...
%!                 fun (i_type (x), i_type (y)));
%!         assert (bsxfun (fun, i_type (y), i_type (x)), ...
%!                 fun (i_type (y), i_type (x)));
%!
%!         assert (bsxfun (fun, f_type (x), f_type (y)), ...
%!                 fun (f_type (x), f_type (y)));
%!         assert (bsxfun (fun, f_type(y), f_type(x)), ...
%!                 fun (f_type (y), f_type (x)));
%!     endfor
%!   endfor
%! endfor
%!
*/