find.cc

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/*

Copyright (C) 1996-2018 John W. Eaton

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
<https://www.gnu.org/licenses/>.

*/

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "quit.h"

#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"

// Find at most N_TO_FIND nonzero elements in NDA.  Search forward if
// DIRECTION is 1, backward if it is -1.  NARGOUT is the number of
// output arguments.  If N_TO_FIND is -1, find all nonzero elements.

template <typename T>
octave_value_list
find_nonzero_elem_idx (const Array<T>& nda, int nargout,
                       octave_idx_type n_to_find, int direction)
{
  octave_value_list retval ((nargout == 0 ? 1 : nargout), Matrix ());

  Array<octave_idx_type> idx;
  if (n_to_find >= 0)
    idx = nda.find (n_to_find, direction == -1);
  else
    idx = nda.find ();

  // The maximum element is always at the end.
  octave_idx_type iext = (idx.isempty () ? 0 : idx.xelem (idx.numel () - 1) + 1);

  switch (nargout)
    {
    default:
    case 3:
      retval(2) = Array<T> (nda.index (idx_vector (idx)));
      OCTAVE_FALLTHROUGH;

    case 2:
      {
        Array<octave_idx_type> jdx (idx.dims ());
        octave_idx_type n = idx.numel ();
        octave_idx_type nr = nda.rows ();
        for (octave_idx_type i = 0; i < n; i++)
          {
            jdx.xelem (i) = idx.xelem (i) / nr;
            idx.xelem (i) %= nr;
          }
        iext = -1;
        retval(1) = idx_vector (jdx, -1);
      }
      OCTAVE_FALLTHROUGH;

    case 1:
    case 0:
      retval(0) = idx_vector (idx, iext);
      break;
    }

  return retval;
}

template <typename T>
octave_value_list
find_nonzero_elem_idx (const Sparse<T>& v, int nargout,
                       octave_idx_type n_to_find, int direction)
{
  nargout = std::min (nargout, 5);
  octave_value_list retval ((nargout == 0 ? 1 : nargout), Matrix ());

  octave_idx_type nr = v.rows ();
  octave_idx_type nc = v.cols ();
  octave_idx_type nz = v.nnz ();

  // Search in the default range.
  octave_idx_type start_nc = -1;
  octave_idx_type end_nc = -1;
  octave_idx_type count;

  // Search for the range to search
  if (n_to_find < 0)
    {
      start_nc = 0;
      end_nc = nc;
      n_to_find = nz;
      count = nz;
    }
  else if (direction > 0)
    {
      for (octave_idx_type j = 0; j < nc; j++)
        {
          octave_quit ();

          if (v.cidx (j) == 0 && v.cidx (j+1) != 0)
            start_nc = j;
          if (v.cidx (j+1) >= n_to_find)
            {
              end_nc = j + 1;
              break;
            }
        }
    }
  else
    {
      for (octave_idx_type j = nc; j > 0; j--)
        {
          octave_quit ();

          if (v.cidx (j) == nz && v.cidx (j-1) != nz)
            end_nc = j;
          if (nz - v.cidx (j-1) >= n_to_find)
            {
              start_nc = j - 1;
              break;
            }
        }
    }

  count = (n_to_find > v.cidx (end_nc) - v.cidx (start_nc) ?
           v.cidx (end_nc) - v.cidx (start_nc) : n_to_find);

  octave_idx_type result_nr;
  octave_idx_type result_nc;

  // Default case is to return a column vector, however, if the original
  // argument was a row vector, then force return of a row vector.
  if (nr == 1)
    {
      result_nr = 1;
      result_nc = count;
    }
  else
    {
      result_nr = count;
      result_nc = 1;
    }

  Matrix idx (result_nr, result_nc);

  Matrix i_idx (result_nr, result_nc);
  Matrix j_idx (result_nr, result_nc);

  Array<T> val (dim_vector (result_nr, result_nc));

  if (count > 0)
    {
      // Search for elements to return.  Only search the region where there
      // are elements to be found using the count that we want to find.
      for (octave_idx_type j = start_nc, cx = 0; j < end_nc; j++)
        for (octave_idx_type i = v.cidx (j); i < v.cidx (j+1); i++)
          {
            octave_quit ();

            if (direction < 0 && i < nz - count)
              continue;
            i_idx(cx) = static_cast<double> (v.ridx (i) + 1);
            j_idx(cx) = static_cast<double> (j + 1);
            idx(cx) = j * nr + v.ridx (i) + 1;
            val(cx) = v.data(i);
            cx++;
            if (cx == count)
              break;
          }
    }
  else
    {
      // No items found.  Fixup return dimensions for Matlab compatibility.
      // The behavior to match is documented in Array.cc (Array<T>::find).
      if ((nr == 0 && nc == 0) || (nr == 1 && nc == 1))
        {
          idx.resize (0, 0);

          i_idx.resize (0, 0);
          j_idx.resize (0, 0);

          val.resize (dim_vector (0, 0));
        }
    }

  switch (nargout)
    {
    case 0:
    case 1:
      retval(0) = idx;
      break;

    case 5:
      retval(4) = nc;
      OCTAVE_FALLTHROUGH;

    case 4:
      retval(3) = nr;
      OCTAVE_FALLTHROUGH;

    case 3:
      retval(2) = val;
      OCTAVE_FALLTHROUGH;

    case 2:
      retval(1) = j_idx;
      retval(0) = i_idx;
    }

  return retval;
}

octave_value_list
find_nonzero_elem_idx (const PermMatrix& v, int nargout,
                       octave_idx_type n_to_find, int direction)
{
  // There are far fewer special cases to handle for a PermMatrix.
  nargout = std::min (nargout, 5);
  octave_value_list retval ((nargout == 0 ? 1 : nargout), Matrix ());

  octave_idx_type nr = v.rows ();
  octave_idx_type nc = v.cols ();
  octave_idx_type start_nc, count;

  // Determine the range to search.
  if (n_to_find < 0 || n_to_find >= nc)
    {
      start_nc = 0;
      count = nc;
    }
  else if (direction > 0)
    {
      start_nc = 0;
      count = n_to_find;
    }
  else
    {
      start_nc = nc - n_to_find;
      count = n_to_find;
    }

  Matrix idx (count, 1);
  Matrix i_idx (count, 1);
  Matrix j_idx (count, 1);
  // Every value is 1.
  Array<double> val (dim_vector (count, 1), 1.0);

  if (count > 0)
    {
      const Array<octave_idx_type>& p = v.col_perm_vec ();
      for (octave_idx_type k = 0; k < count; k++)
        {
          octave_quit ();

          const octave_idx_type j = start_nc + k;
          const octave_idx_type i = p(j);
          i_idx(k) = static_cast<double> (1+i);
          j_idx(k) = static_cast<double> (1+j);
          idx(k) = j * nc + i + 1;
        }
    }
  else
    {
      // FIXME: Is this case even possible?  A scalar permutation matrix seems
      // to devolve to a scalar full matrix, at least from the Octave command
      // line.  Perhaps this function could be called internally from C++ with
      // such a matrix.
      // No items found.  Fixup return dimensions for Matlab compatibility.
      // The behavior to match is documented in Array.cc (Array<T>::find).
      if ((nr == 0 && nc == 0) || (nr == 1 && nc == 1))
        {
          idx.resize (0, 0);

          i_idx.resize (0, 0);
          j_idx.resize (0, 0);

          val.resize (dim_vector (0, 0));
        }
    }

  switch (nargout)
    {
    case 0:
    case 1:
      retval(0) = idx;
      break;

    case 5:
      retval(4) = nc;
      OCTAVE_FALLTHROUGH;

    case 4:
      retval(3) = nc;
      OCTAVE_FALLTHROUGH;

    case 3:
      retval(2) = val;
      OCTAVE_FALLTHROUGH;

    case 2:
      retval(1) = j_idx;
      retval(0) = i_idx;
    }

  return retval;
}

DEFUN (find, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{idx} =} find (@var{x})
@deftypefnx {} {@var{idx} =} find (@var{x}, @var{n})
@deftypefnx {} {@var{idx} =} find (@var{x}, @var{n}, @var{direction})
@deftypefnx {} {[i, j] =} find (@dots{})
@deftypefnx {} {[i, j, v] =} find (@dots{})
Return a vector of indices of nonzero elements of a matrix, as a row if
@var{x} is a row vector or as a column otherwise.

To obtain a single index for each matrix element, Octave pretends that the
columns of a matrix form one long vector (like Fortran arrays are stored).
For example:

@example
@group
find (eye (2))
  @result{} [ 1; 4 ]
@end group
@end example

If two inputs are given, @var{n} indicates the maximum number of elements to
find from the beginning of the matrix or vector.

If three inputs are given, @var{direction} should be one of
@qcode{"first"} or @qcode{"last"}, requesting only the first or last
@var{n} indices, respectively.  However, the indices are always returned in
ascending order.

If two outputs are requested, @code{find} returns the row and column
indices of nonzero elements of a matrix.  For example:

@example
@group
[i, j] = find (2 * eye (2))
    @result{} i = [ 1; 2 ]
    @result{} j = [ 1; 2 ]
@end group
@end example

If three outputs are requested, @code{find} also returns a vector
containing the nonzero values.  For example:

@example
@group
[i, j, v] = find (3 * eye (2))
       @result{} i = [ 1; 2 ]
       @result{} j = [ 1; 2 ]
       @result{} v = [ 3; 3 ]
@end group
@end example

Note that this function is particularly useful for sparse matrices, as
it extracts the nonzero elements as vectors, which can then be used to
create the original matrix.  For example:

@example
@group
sz = size (a);
[i, j, v] = find (a);
b = sparse (i, j, v, sz(1), sz(2));
@end group
@end example
@seealso{nonzeros}
@end deftypefn */)
{
  int nargin = args.length ();

  if (nargin < 1 || nargin > 3)
    print_usage ();

  // Setup the default options.
  octave_idx_type n_to_find = -1;
  if (nargin > 1)
    {
      double val = args(1).xscalar_value ("find: N must be an integer");

      if (val < 0 || (! octave::math::isinf (val)
                      && val != octave::math::round (val)))
        error ("find: N must be a non-negative integer");
      else if (! octave::math::isinf (val))
        n_to_find = val;
    }

  // Direction to do the searching (1 == forward, -1 == reverse).
  int direction = 1;
  if (nargin > 2)
    {
      direction = 0;

      std::string s_arg = args(2).string_value ();

      if (s_arg == "first")
        direction = 1;
      else if (s_arg == "last")
        direction = -1;
      else
        error (R"(find: DIRECTION must be "first" or "last")");
    }

  octave_value_list retval;

  octave_value arg = args(0);

  if (arg.islogical ())
    {
      if (arg.issparse ())
        {
          SparseBoolMatrix v = arg.sparse_bool_matrix_value ();

          retval = find_nonzero_elem_idx (v, nargout, n_to_find, direction);
        }
      else if (nargout <= 1 && n_to_find == -1 && direction == 1)
        {
          // This case is equivalent to extracting indices from a logical
          // matrix.  Try to reuse the possibly cached index vector.

          // No need to catch index_exception, since arg is bool.
          // Out-of-range errors have already set pos, and will be
          // caught later.

          octave_value result = arg.index_vector ().unmask ();

          dim_vector dv = result.dims ();

          retval(0) = (dv.all_zero () || dv.isvector ()
                       ? result : result.reshape (dv.as_column ()));
        }
      else
        {
          boolNDArray v = arg.bool_array_value ();

          retval = find_nonzero_elem_idx (v, nargout, n_to_find, direction);
        }
    }
  else if (arg.isinteger ())
    {
#define DO_INT_BRANCH(INTT)                                             \
      else if (arg.is_ ## INTT ## _type ())                             \
        {                                                               \
          INTT ## NDArray v = arg.INTT ## _array_value ();              \
                                                                        \
          retval = find_nonzero_elem_idx (v, nargout, n_to_find, direction); \
        }

      if (false)
        ;
      DO_INT_BRANCH (int8)
      DO_INT_BRANCH (int16)
      DO_INT_BRANCH (int32)
      DO_INT_BRANCH (int64)
      DO_INT_BRANCH (uint8)
      DO_INT_BRANCH (uint16)
      DO_INT_BRANCH (uint32)
      DO_INT_BRANCH (uint64)
      else
        panic_impossible ();
    }
  else if (arg.issparse ())
    {
      if (arg.isreal ())
        {
          SparseMatrix v = arg.sparse_matrix_value ();

          retval = find_nonzero_elem_idx (v, nargout, n_to_find, direction);
        }
      else if (arg.iscomplex ())
        {
          SparseComplexMatrix v = arg.sparse_complex_matrix_value ();

          retval = find_nonzero_elem_idx (v, nargout, n_to_find, direction);
        }
      else
        err_wrong_type_arg ("find", arg);
    }
  else if (arg.is_perm_matrix ())
    {
      PermMatrix P = arg.perm_matrix_value ();

      retval = find_nonzero_elem_idx (P, nargout, n_to_find, direction);
    }
  else if (arg.is_string ())
    {
      charNDArray chnda = arg.char_array_value ();

      retval = find_nonzero_elem_idx (chnda, nargout, n_to_find, direction);
    }
  else if (arg.is_single_type ())
    {
      if (arg.isreal ())
        {
          FloatNDArray nda = arg.float_array_value ();

          retval = find_nonzero_elem_idx (nda, nargout, n_to_find, direction);
        }
      else if (arg.iscomplex ())
        {
          FloatComplexNDArray cnda = arg.float_complex_array_value ();

          retval = find_nonzero_elem_idx (cnda, nargout, n_to_find, direction);
        }
    }
  else if (arg.isreal ())
    {
      NDArray nda = arg.array_value ();

      retval = find_nonzero_elem_idx (nda, nargout, n_to_find, direction);
    }
  else if (arg.iscomplex ())
    {
      ComplexNDArray cnda = arg.complex_array_value ();

      retval = find_nonzero_elem_idx (cnda, nargout, n_to_find, direction);
    }
  else
    err_wrong_type_arg ("find", arg);

  return retval;
}

/*
%!assert (find (char ([0, 97])), 2)
%!assert (find ([1, 0, 1, 0, 1]), [1, 3, 5])
%!assert (find ([1; 0; 3; 0; 1]), [1; 3; 5])
%!assert (find ([0, 0, 2; 0, 3, 0; -1, 0, 0]), [3; 5; 7])

%!assert <*53603> (find (ones (1,1,2) > 0), [1;2])
%!assert <*53603> (find (ones (1,1,1,3) > 0), [1;2;3])

%!test
%! [i, j, v] = find ([0, 0, 2; 0, 3, 0; -1, 0, 0]);
%!
%! assert (i, [3; 2; 1]);
%! assert (j, [1; 2; 3]);
%! assert (v, [-1; 3; 2]);

%!assert (find (single ([1, 0, 1, 0, 1])), [1, 3, 5])
%!assert (find (single ([1; 0; 3; 0; 1])), [1; 3; 5])
%!assert (find (single ([0, 0, 2; 0, 3, 0; -1, 0, 0])), [3; 5; 7])

%!test
%! [i, j, v] = find (single ([0, 0, 2; 0, 3, 0; -1, 0, 0]));
%!
%! assert (i, [3; 2; 1]);
%! assert (j, [1; 2; 3]);
%! assert (v, single ([-1; 3; 2]));

%!test
%! pcol = [5 1 4 3 2];
%! P = eye (5) (:, pcol);
%! [i, j, v] = find (P);
%! [ifull, jfull, vfull] = find (full (P));
%! assert (i, ifull);
%! assert (j, jfull);
%! assert (all (v == 1));

%!test
%! prow = [5 1 4 3 2];
%! P = eye (5) (prow, :);
%! [i, j, v] = find (P);
%! [ifull, jfull, vfull] = find (full (P));
%! assert (i, ifull);
%! assert (j, jfull);
%! assert (all (v == 1));

%!assert <*53655> (find (false), zeros (0, 0))
%!assert <*53655> (find ([false, false]), zeros (1, 0))
%!assert <*53655> (find ([false; false]), zeros (0, 1))
%!assert <*53655> (find ([false, false; false, false]), zeros (0, 1))

%!assert (find ([2 0 1 0 5 0], 1), 1)
%!assert (find ([2 0 1 0 5 0], 2, "last"), [3, 5])

%!assert (find ([2 0 1 0 5 0], Inf), [1, 3, 5])
%!assert (find ([2 0 1 0 5 0], Inf, "last"), [1, 3, 5])

%!error find ()
*/