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\name{trapz}
\alias{trapz}
\title{Trapezoid Rule Numerical Integration}
\description{Computes the integral of Y with respect to X using trapezoid rule
integration.}
\usage{trapz(x, y)}
\arguments{
\item{x}{ Sorted vector of x-axis values. }
\item{y}{ Vector of y-axis values. }
}
\details{
The function has only two lines:
\preformatted{
idx = 2:length(x)
return (as.double( (x[idx] - x[idx-1]) \%*\% (y[idx] + y[idx-1])) / 2)
}
}
\value{Integral of Y with respect to X or area under the Y curve.}
\note{
Trapezoid rule is not the most accurate way of calculating integrals (it is
exact for linear functions), for example Simpson's rule (exact for linear and
quadratic functions) is more accurate.
}
\author{Jarek Tuszynski (SAIC) \email{jaroslaw.w.tuszynski@saic.com}}
\references{ D. Kincaid & W. Chaney (1991), \emph{Numerical Analysis}, p.445 }
\seealso{
\itemize{
\item \code{\link[PROcess]{intg}} from \pkg{PROcess} package
\item \code{\link[ROC]{trapezint}} from \pkg{ROC} package
\item \code{\link{integrate}}
\item Matlab's \code{trapz} function (\url{
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/trapz.html})
}
}
\examples{
# integral of sine function in [0, pi] range suppose to be exactly 2.
# lets calculate it using 10 samples:
x = (1:10)*pi/10
trapz(x, sin(x))
# now lets calculate it using 1000 samples:
x = (1:1000)*pi/1000
trapz(x, sin(x))
}
\keyword{math}
\concept{integration}
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