\HeaderA{norm}{Matrix Norms}{norm}
\aliasA{norm,ANY,missing-method}{norm}{norm,ANY,missing.Rdash.method}
\aliasA{norm,Matrix,character-method}{norm}{norm,Matrix,character.Rdash.method}
\aliasA{norm,matrix,character-method}{norm}{norm,matrix,character.Rdash.method}
\keyword{algebra}{norm}
\begin{Description}\relax
Computes a matrix norm of \code{x} using Lapack.  The norm can be
the one norm, the infinity norm, the Frobenius norm, or the maximum
modulus among elements of a matrix, as determined by the value of
\code{type}.
\end{Description}
\begin{Usage}
\begin{verbatim}
norm(x, type, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a real or complex matrix.

\item[\code{type}] A character indicating the type of norm desired.
\describe{
\item[\code{"O"}, \code{"o"} or \code{"1"}] specifies the one norm,
(maximum absolute column sum);
\item[\code{"I"} or \code{"i"}] specifies the infinity norm (maximum
absolute row sum);
\item[\code{"F"} or \code{"f"}] specifies the Frobenius norm (the
Euclidean norm of \code{x} treated as if it were a vector); and
\item[\code{"M"} or \code{"m"}] specifies the maximum modulus of
all the elements in \code{x}.
}
The default is \code{"O"}.  Only the first character of
\code{type[1]} is used.

\item[\code{...}] further arguments passed to or from other methods.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
For dense matrices, the methods eventually call the Lapack functions
\code{dlange}, \code{dlansy}, \code{dlantr}, \code{zlange},
\code{zlansy}, and \code{zlantr}.
\end{Details}
\begin{Value}
A numeric value of class \code{"norm"}, representing the quantity
chosen according to \code{type}.
\end{Value}
\begin{References}\relax
Anderson, E., et al. (1994).
\emph{LAPACK User's Guide,}
2nd edition, SIAM, Philadelphia.
\end{References}
\begin{Examples}
\begin{ExampleCode}
x <- Hilbert(9)
norm(x, "1")
norm(x, "I")
norm(x, "F")
norm(x, "M")
\end{ExampleCode}
\end{Examples}

