kron.cc

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//
// Copyright (C) 2002-2021 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// 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.
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// 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/>.
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////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include "dMatrix.h"
#include "fMatrix.h"
#include "CMatrix.h"
#include "fCMatrix.h"
 
#include "dSparse.h"
#include "CSparse.h"
 
#include "dDiagMatrix.h"
#include "fDiagMatrix.h"
#include "CDiagMatrix.h"
#include "fCDiagMatrix.h"
 
#include "PermMatrix.h"
 
#include "mx-inlines.cc"
#include "quit.h"
 
#include "defun.h"
#include "error.h"
#include "ovl.h"
 
template <typename R, typename T>
static MArray<T>
kron (const MArray<R>& a, const MArray<T>& b)
{
  assert (a.ndims () == 2);
  assert (b.ndims () == 2);
 
  octave_idx_type nra = a.rows ();
  octave_idx_type nrb = b.rows ();
  octave_idx_type nca = a.cols ();
  octave_idx_type ncb = b.cols ();
 
  MArray<T> c (dim_vector (nra*nrb, nca*ncb));
  T *cv = c.fortran_vec ();
 
  for (octave_idx_type ja = 0; ja < nca; ja++)
    {
      octave_quit ();
      for (octave_idx_type jb = 0; jb < ncb; jb++)
        {
          for (octave_idx_type ia = 0; ia < nra; ia++)
            {
              mx_inline_mul (nrb, cv, a(ia, ja), b.data () + nrb*jb);
              cv += nrb;
            }
        }
    }
 
  return c;
}
 
template <typename R, typename T>
static MArray<T>
kron (const MDiagArray2<R>& a, const MArray<T>& b)
{
  assert (b.ndims () == 2);
 
  octave_idx_type nra = a.rows ();
  octave_idx_type nrb = b.rows ();
  octave_idx_type dla = a.diag_length ();
  octave_idx_type nca = a.cols ();
  octave_idx_type ncb = b.cols ();
 
  MArray<T> c (dim_vector (nra*nrb, nca*ncb), T ());
 
  for (octave_idx_type ja = 0; ja < dla; ja++)
    {
      octave_quit ();
      for (octave_idx_type jb = 0; jb < ncb; jb++)
        {
          mx_inline_mul (nrb, &c.xelem (ja*nrb, ja*ncb + jb), a.dgelem (ja),
                         b.data () + nrb*jb);
        }
    }
 
  return c;
}
 
template <typename T>
static MSparse<T>
kron (const MSparse<T>& A, const MSparse<T>& B)
{
  octave_idx_type idx = 0;
  MSparse<T> C (A.rows () * B.rows (), A.columns () * B.columns (),
                A.nnz () * B.nnz ());
 
  C.cidx (0) = 0;
 
  for (octave_idx_type Aj = 0; Aj < A.columns (); Aj++)
    {
      octave_quit ();
      for (octave_idx_type Bj = 0; Bj < B.columns (); Bj++)
        {
          for (octave_idx_type Ai = A.cidx (Aj); Ai < A.cidx (Aj+1); Ai++)
            {
              octave_idx_type Ci = A.ridx (Ai) * B.rows ();
              const T v = A.data (Ai);
 
              for (octave_idx_type Bi = B.cidx (Bj); Bi < B.cidx (Bj+1); Bi++)
                {
                  C.data (idx) = v * B.data (Bi);
                  C.ridx (idx++) = Ci + B.ridx (Bi);
                }
            }
          C.cidx (Aj * B.columns () + Bj + 1) = idx;
        }
    }
 
  return C;
}
 
static PermMatrix
kron (const PermMatrix& a, const PermMatrix& b)
{
  octave_idx_type na = a.rows ();
  octave_idx_type nb = b.rows ();
  const Array<octave_idx_type>& pa = a.col_perm_vec ();
  const Array<octave_idx_type>& pb = b.col_perm_vec ();
  Array<octave_idx_type> res_perm (dim_vector (na * nb, 1));
  octave_idx_type rescol = 0;
  for (octave_idx_type i = 0; i < na; i++)
    {
      octave_idx_type a_add = pa(i) * nb;
      for (octave_idx_type j = 0; j < nb; j++)
        res_perm.xelem (rescol++) = a_add + pb(j);
    }
 
  return PermMatrix (res_perm, true);
}
 
template <typename MTA, typename MTB>
octave_value
do_kron (const octave_value& a, const octave_value& b)
{
  MTA am = octave_value_extract<MTA> (a);
  MTB bm = octave_value_extract<MTB> (b);
 
  return octave_value (kron (am, bm));
}
 
octave_value
dispatch_kron (const octave_value& a, const octave_value& b)
{
  octave_value retval;
  if (a.is_perm_matrix () && b.is_perm_matrix ())
    retval = do_kron<PermMatrix, PermMatrix> (a, b);
  else if (a.issparse () || b.issparse ())
    {
      if (a.iscomplex () || b.iscomplex ())
        retval = do_kron<SparseComplexMatrix, SparseComplexMatrix> (a, b);
      else
        retval = do_kron<SparseMatrix, SparseMatrix> (a, b);
    }
  else if (a.is_diag_matrix ())
    {
      if (b.is_diag_matrix () && a.rows () == a.columns ()
          && b.rows () == b.columns ())
        {
          // We have two diagonal matrices, the product of those will be
          // another diagonal matrix.  To do that efficiently, extract
          // the diagonals as vectors and compute the product.  That
          // will be another vector, which we then use to construct a
          // diagonal matrix object.  Note that this will fail if our
          // digaonal matrix object is modified to allow the nonzero
          // values to be stored off of the principal diagonal (i.e., if
          // diag ([1,2], 3) is modified to return a diagonal matrix
          // object instead of a full matrix object).
 
          octave_value tmp = dispatch_kron (a.diag (), b.diag ());
          retval = tmp.diag ();
        }
      else if (a.is_single_type () || b.is_single_type ())
        {
          if (a.iscomplex ())
            retval = do_kron<FloatComplexDiagMatrix, FloatComplexMatrix> (a, b);
          else if (b.iscomplex ())
            retval = do_kron<FloatDiagMatrix, FloatComplexMatrix> (a, b);
          else
            retval = do_kron<FloatDiagMatrix, FloatMatrix> (a, b);
        }
      else
        {
          if (a.iscomplex ())
            retval = do_kron<ComplexDiagMatrix, ComplexMatrix> (a, b);
          else if (b.iscomplex ())
            retval = do_kron<DiagMatrix, ComplexMatrix> (a, b);
          else
            retval = do_kron<DiagMatrix, Matrix> (a, b);
        }
    }
  else if (a.is_single_type () || b.is_single_type ())
    {
      if (a.iscomplex ())
        retval = do_kron<FloatComplexMatrix, FloatComplexMatrix> (a, b);
      else if (b.iscomplex ())
        retval = do_kron<FloatMatrix, FloatComplexMatrix> (a, b);
      else
        retval = do_kron<FloatMatrix, FloatMatrix> (a, b);
    }
  else
    {
      if (a.iscomplex ())
        retval = do_kron<ComplexMatrix, ComplexMatrix> (a, b);
      else if (b.iscomplex ())
        retval = do_kron<Matrix, ComplexMatrix> (a, b);
      else
        retval = do_kron<Matrix, Matrix> (a, b);
    }
  return retval;
}
 
 
DEFUN (kron, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {} kron (@var{A}, @var{B})
@deftypefnx {} {} kron (@var{A1}, @var{A2}, @dots{})
Form the Kronecker product of two or more matrices.
 
This is defined block by block as
 
@example
x = [ a(i,j)*b ]
@end example
 
For example:
 
@example
@group
kron (1:4, ones (3, 1))
     @result{}  1  2  3  4
         1  2  3  4
         1  2  3  4
@end group
@end example
 
If there are more than two input arguments @var{A1}, @var{A2}, @dots{},
@var{An} the Kronecker product is computed as
 
@example
kron (kron (@var{A1}, @var{A2}), @dots{}, @var{An})
@end example
 
@noindent
Since the Kronecker product is associative, this is well-defined.
@end deftypefn */)
{
  int nargin = args.length ();
 
  if (nargin < 2)
    print_usage ();
 
  octave_value retval;
 
  octave_value a = args(0);
  octave_value b = args(1);
 
  retval = dispatch_kron (a, b);
 
  for (octave_idx_type i = 2; i < nargin; i++)
    retval = dispatch_kron (retval, args(i));
 
  return retval;
}
 
/*
%!test
%! x = ones (2);
%! assert (kron (x, x), ones (4));
 
%!shared x, y, z, p1, p2, d1, d2
%! x =  [1, 2];
%! y =  [-1, -2];
%! z =  [1,  2,  3,  4; 1,  2,  3,  4; 1,  2,  3,  4];
%! p1 = eye (3)([2, 3, 1], :);  ## Permutation matrix
%! p2 = [0 1 0; 0 0 1; 1 0 0];  ## Non-permutation equivalent
%! d1 = diag ([1 2 3]);         ## Diag type matrix
%! d2 = [1 0 0; 0 2 0; 0 0 3];  ## Non-diag equivalent
%!assert (kron (1:4, ones (3, 1)), z)
%!assert (kron (single (1:4), ones (3, 1)), single (z))
%!assert (kron (sparse (1:4), ones (3, 1)), sparse (z))
%!assert (kron (complex (1:4), ones (3, 1)), z)
%!assert (kron (complex (single(1:4)), ones (3, 1)), single(z))
%!assert (kron (x, y, z), kron (kron (x, y), z))
%!assert (kron (x, y, z), kron (x, kron (y, z)))
%!assert (kron (p1, p1), kron (p2, p2))
%!assert (kron (p1, p2), kron (p2, p1))
%!assert (kron (d1, d1), kron (d2, d2))
%!assert (kron (d1, d2), kron (d2, d1))
 
%!assert (kron (diag ([1, 2]), diag ([3, 4])), diag ([3, 4, 6, 8]))
 
## Test for two diag matrices.
## See the comments above in dispatch_kron for this case.
%!test
%! expected = zeros (16, 16);
%! expected (1, 11) = 3;
%! expected (2, 12) = 4;
%! expected (5, 15) = 6;
%! expected (6, 16) = 8;
%! assert (kron (diag ([1, 2], 2), diag ([3, 4], 2)), expected);
*/