inv.cc

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//
// Copyright (C) 1996-2021 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.
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// Octave is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
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////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
#include "ops.h"
#include "ov-re-diag.h"
#include "ov-cx-diag.h"
#include "ov-flt-re-diag.h"
#include "ov-flt-cx-diag.h"
#include "ov-perm.h"
 
DEFUN (inv, args, nargout,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} inv (@var{A})
@deftypefnx {} {[@var{x}, @var{rcond}] =} inv (@var{A})
@deftypefnx {} {[@dots{}] =} inverse (@dots{})
Compute the inverse of the square matrix @var{A}.
 
Return an estimate of the reciprocal condition number if requested,
otherwise warn of an ill-conditioned matrix if the reciprocal condition
number is small.
 
In general it is best to avoid calculating the inverse of a matrix directly.
For example, it is both faster and more accurate to solve systems of
equations (@var{A}*@math{x} = @math{b}) with
@code{@var{y} = @var{A} \ @math{b}}, rather than
@code{@var{y} = inv (@var{A}) * @math{b}}.
 
If called with a sparse matrix, then in general @var{x} will be a full
matrix requiring significantly more storage.  Avoid forming the inverse of a
sparse matrix if possible.
 
@code{inverse} is an alias and may be used identically in place of @code{inv}.
@seealso{ldivide, rdivide, pinv}
@end deftypefn */)
{
  if (args.length () != 1)
    print_usage ();
 
  octave_value arg = args(0);
 
  if (arg.isempty ())
    return ovl (Matrix ());
 
  if (arg.rows () != arg.columns ())
    err_square_matrix_required ("inverse", "A");
 
  octave_value result;
  octave_idx_type info;
  double rcond = 0.0;
  float frcond = 0.0;
  bool isfloat = arg.is_single_type ();
 
  if (arg.is_diag_matrix ())
    {
      rcond = 1.0;
      frcond = 1.0f;
      if (arg.iscomplex ())
        {
          if (isfloat)
            {
              result = arg.float_complex_diag_matrix_value ().inverse (info);
              if (info == -1)
                frcond = 0.0f;
              else if (nargout > 1)
                frcond = arg.float_complex_diag_matrix_value ().rcond ();
            }
          else
            {
              result = arg.complex_diag_matrix_value ().inverse (info);
              if (info == -1)
                rcond = 0.0;
              else if (nargout > 1)
                rcond = arg.complex_diag_matrix_value ().rcond ();
            }
        }
      else
        {
          if (isfloat)
            {
              result = arg.float_diag_matrix_value ().inverse (info);
              if (info == -1)
                frcond = 0.0f;
              else if (nargout > 1)
                frcond = arg.float_diag_matrix_value ().rcond ();
            }
          else
            {
              result = arg.diag_matrix_value ().inverse (info);
              if (info == -1)
                rcond = 0.0;
              else if (nargout > 1)
                rcond = arg.diag_matrix_value ().rcond ();
            }
        }
    }
  else if (arg.is_perm_matrix ())
    {
      rcond = 1.0;
      info = 0;
      result = arg.perm_matrix_value ().inverse ();
    }
  else if (isfloat)
    {
      if (arg.isreal ())
        {
          FloatMatrix m = arg.float_matrix_value ();
 
          MatrixType mattyp = args(0).matrix_type ();
          result = m.inverse (mattyp, info, frcond, 1);
          args(0).matrix_type (mattyp);
        }
      else if (arg.iscomplex ())
        {
          FloatComplexMatrix m = arg.float_complex_matrix_value ();
 
          MatrixType mattyp = args(0).matrix_type ();
          result = m.inverse (mattyp, info, frcond, 1);
          args(0).matrix_type (mattyp);
        }
    }
  else
    {
      if (arg.isreal ())
        {
          if (arg.issparse ())
            {
              SparseMatrix m = arg.sparse_matrix_value ();
 
              MatrixType mattyp = args(0).matrix_type ();
              result = m.inverse (mattyp, info, rcond, 1);
              args(0).matrix_type (mattyp);
            }
          else
            {
              Matrix m = arg.matrix_value ();
 
              MatrixType mattyp = args(0).matrix_type ();
              result = m.inverse (mattyp, info, rcond, 1);
              args(0).matrix_type (mattyp);
            }
        }
      else if (arg.iscomplex ())
        {
          if (arg.issparse ())
            {
              SparseComplexMatrix m = arg.sparse_complex_matrix_value ();
 
              MatrixType mattyp = args(0).matrix_type ();
              result = m.inverse (mattyp, info, rcond, 1);
              args(0).matrix_type (mattyp);
            }
          else
            {
              ComplexMatrix m = arg.complex_matrix_value ();
 
              MatrixType mattyp = args(0).matrix_type ();
              result = m.inverse (mattyp, info, rcond, 1);
              args(0).matrix_type (mattyp);
            }
        }
      else
        err_wrong_type_arg ("inv", arg);
    }
 
  octave_value_list retval (nargout > 1 ? 2 : 1);
 
  retval(0) = result;
  if (nargout > 1)
    retval(1) = (isfloat ? octave_value (frcond) : octave_value (rcond));
 
  bool rcond_plus_one_eq_one = false;
 
  if (isfloat)
    {
      volatile float xrcond = frcond;
      rcond_plus_one_eq_one = xrcond + 1.0f == 1.0f;
    }
  else
    {
      volatile double xrcond = rcond;
      rcond_plus_one_eq_one = xrcond + 1.0 == 1.0;
    }
 
  if (nargout < 2 && (info == -1 || rcond_plus_one_eq_one))
    octave::warn_singular_matrix (isfloat ? frcond : rcond);
 
  return retval;
}
 
/*
%!assert (inv ([1, 2; 3, 4]), [-2, 1; 1.5, -0.5], sqrt (eps))
%!assert (inv (single ([1, 2; 3, 4])), single ([-2, 1; 1.5, -0.5]), sqrt (eps ("single")))
 
## Test special inputs
%!assert (inv (zeros (2,0)), [])
%!warning <matrix singular> assert (inv (Inf), 0)
%!warning <matrix singular> assert (inv (-Inf), -0)
%!warning <matrix singular> assert (inv (single (Inf)), single (0))
%!warning <matrix singular> assert (inv (complex (1, Inf)), 0)
%!warning <matrix singular> assert (inv (single (complex (1,Inf))), single (0))
 
%!test
%! [xinv, rcond] = inv (single ([1,2;3,4]));
%! assert (isa (xinv, "single"));
%! assert (isa (rcond, "single"));
 
%!test
%! [xinv, rcond] = inv ([1,2;3,4]);
%! assert (isa (xinv, "double"));
%! assert (isa (rcond, "double"));
 
%!testif HAVE_UMFPACK <*56232>
%! fail ("A = inv (sparse ([1, 2;0 ,0]))", "warning", "matrix singular");
%! assert (A, sparse ([Inf, Inf; 0, 0]));
 
%!testif HAVE_UMFPACK <*56232>
%! fail ("A = inv (sparse ([1i, 2;0 ,0]))", "warning", "matrix singular");
%! assert (A, sparse ([Inf, Inf; 0, 0]));
 
%!test
%! fail ("A = inv (diag ([1, 0, 1]))", "warning", "matrix singular");
%! assert (A, diag ([Inf, Inf, Inf]));
 
%!error <inverse of the null matrix not defined> inv (diag ([0, 0]))
%!error <inverse of the null matrix not defined> inv (diag (complex ([0, 0])))
 
%!testif HAVE_UMFPACK <*56232>
%! fail ("A = inv (sparse ([1, 0, 0; 0, 0, 0; 0, 0, 1]))", "warning", "matrix singular");
%! assert (A, sparse ([Inf, 0, 0; 0, 0, 0; 0, 0, Inf]));
 
%!error inv ()
%!error inv ([1, 2; 3, 4], 2)
%!error <must be a square matrix> inv ([1, 2; 3, 4; 5, 6])
%!error <inverse of the null matrix not defined> inv (sparse (2, 2, 0))
*/
 
DEFALIAS (inverse, inv);