### Copyright (C) 1996 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 2, 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, write to the Free
### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
### 02111-1307, USA.

## usage: norm (x, p)
##
## Compute the p-norm of x.
##
## If x is a matrix:
##
##   value of p     norm returns
##   ----------     ------------
##       1          1-norm, the largest column sum of x
##       2          largest singular value of x
##      Inf         infinity norm, the largest row sum of x
##     "inf"        same as Inf
##     "fro"        Frobenius norm of x, sqrt (sum (diag (x' * x)))
##
## If x is a vector or a scalar:
##
##   value of p     norm returns
##   ----------     ------------
##      Inf         max (abs (x))
##     -Inf         min (abs (x))
##     other        p-norm of x, sum (abs (x) .^ p) ^ (1/p)
##
## If the second argument is missing, p = 2 is assumed.
##
## See also: cond, svd

function retval = norm (x, p)

  if (nargin < 1 || nargin > 2)
    error ("usage: norm (x [, p])");
  endif

  if (isempty (x))
    retval = [];
    return;
  endif

  ## Do we have a vector or matrix as the first argument?

  if (rows (x) == 1 || columns (x) == 1)

    if (nargin == 2)
      if (isstr (p))
        if (strcmp (p, "fro"))
          retval = sqrt (sum (diag (x' * x)));
        elseif (strcmp (p, "inf"))
          retval = max (abs (x));
        else
          error ("norm: unrecognized norm");
        endif
      else
	if (p == Inf)
	  retval = max (abs (x));
	elseif (p == -Inf)
	  retval = min (abs (x));
	else
	  retval = sum (abs (x) .^ p) ^ (1/p);
	endif
      endif
    elseif (nargin == 1)
      retval = sum (abs (x) .^ 2) ^ 0.5;
    endif

  else

    if (nargin == 2)
      if (isstr (p))
        if (strcmp (p, "fro"))
          retval = sqrt (sum (diag (x' * x)));
        elseif (strcmp (p, "inf"))
          xp = x';
          retval = max (sum (abs (real (xp)) + abs (imag (xp))));
        else
          error ("norm: unrecognized norm");
        endif
      else
        if (p == 1)
          retval = max (sum (abs (real (x)) + abs (imag (x))));
        elseif (p == 2)
          s = svd (x);
          retval = s (1);
        elseif (p == Inf)
          xp = x';
          retval = max (sum (abs (real (xp)) + abs (imag (xp))));
        endif
      endif
    elseif (nargin == 1)
      s = svd (x);
      retval = s (1);
    endif

  endif

endfunction