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[matrix] View of /pkg/man/norm.Rd
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# View of /pkg/man/norm.Rd

Wed Jul 18 14:46:20 2007 UTC (12 years, 1 month ago) by maechler
File size: 1688 byte(s)
norm() for sparse; systematic checking of norm() and all "Summary" methods
\name{norm}
\title{Matrix Norms}
\alias{norm}
\alias{norm,ANY,missing-method}
\alias{norm,matrix,character-method}
\alias{norm,Matrix,character-method}
\usage{
norm(x, type, \dots)
}
\description{
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}.
}
\arguments{
\item{x}{
a real or complex matrix.
}
\item{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{\dots}{further arguments passed to or from other methods.}
}
\value{
A numeric value of class \code{"norm"}, representing the quantity
chosen according to \code{type}.
}
\details{
For dense matrices, the methods eventually call the Lapack functions
\code{dlange}, \code{dlansy}, \code{dlantr}, \code{zlange},
\code{zlansy}, and \code{zlantr}.
}
\references{
Anderson, E., et al. (1994).
\emph{LAPACK User's Guide,}