Mercurial > hg > octave-nkf
diff scripts/linear-algebra/norm.m @ 3372:f16c2ce14886
[project @ 1999-11-23 19:07:09 by jwe]
author | jwe |
---|---|
date | Tue, 23 Nov 1999 19:07:18 +0000 |
parents | 041ea33fbbf4 |
children | 5e0a0b1cba43 |
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--- a/scripts/linear-algebra/norm.m +++ b/scripts/linear-algebra/norm.m @@ -17,30 +17,43 @@ ## 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. -## +## -*- texinfo -*- +## @deftypefn {Function File} {} norm (@var{a}, @var{p}) +## Compute the p-norm of the matrix @var{a}. If the second argument is +## missing, @code{p = 2} is assumed. +## +## If @var{a} is a matrix: +## +## @table @asis +## @item @var{p} = @code{1} +## 1-norm, the largest column sum of @var{a}. +## +## @item @var{p} = @code{2} +## Largest singular value of @var{a}. +## +## @item @var{p} = @code{Inf} +## @cindex infinity norm +## Infinity norm, the largest row sum of @var{a}. +## +## @item @var{p} = @code{"fro"} +## @cindex Frobenius norm +## Frobenius norm of @var{a}, @code{sqrt (sum (diag (@var{a}' * @var{a})))}. +## @end table +## +## If @var{a} is a vector or a scalar: +## +## @table @asis +## @item @var{p} = @code{Inf} +## @code{max (abs (@var{a}))}. +## +## @item @var{p} = @code{-Inf} +## @code{min (abs (@var{a}))}. +## +## @item other +## p-norm of @var{a}, @code{(sum (abs (@var{a}) .^ @var{p})) ^ (1/@var{p})}. +## @end table +## @end deftypefn + ## See also: cond, svd ## Author: jwe