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## 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
## Author: jwe
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
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