integrate {base}

R Documentation

Integration of One-Dimensional Functions

Description

Adaptive quadrature of functions of one variable over a finite or infinite interval.

Usage

integrate(f, lower, upper, subdivisions=100,
          rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
          stop.on.error = TRUE, keep.xy = FALSE, aux = NULL, ...)

Arguments

f	An R function taking a numeric first argument and returning a numeric vector the same length. Returning a non-finite element will generate an error.
lower, upper	The limits of integration. Can be infinite.
subdivisions	the maximum number of subintervals.
rel.tol	relative accuracy requested.
abs.tol	absolute accuracy requested.
stop.on.error	logical. If true (the default) an error stops the function. If false some errors will give a result with a warning in the message component.
keep.xy	unused. For compatibility with S.
aux	unused. For compatibility with S.
...	additional arguments to be passes to f.

Details

If one or both limits are infinite, the infinite range is mapped onto a finite interval.

For a finite interval, globally adaptive interval subdivision is used in connection with extrapolation by the Epsilon algorithm.

rel.tol cannot be less than max(50*.Machine$double.eps, 0.5e-28) if abs.tol <= 0.

Value

A list of class "integrate" with components

value	the final estimate of the integral.
abs.error	estimate of the modulus of the absolute error.
subdivisions	the number of subintervals produced in the subdivision process.
message	"OK" or a character string giving the error message.
call	the matched call.

References

Based on QUADPACK routines dqags and dqagi by R. Piessens and E. deDoncker-Kapenga, available from Netlib.

See
R. Piessens, E. deDoncker-Kapenga, C. Uberhuber, D. Kahaner (1983) Quadpack: a Subroutine Package for Automatic Integration; Springer Verlag.

See Also

The function adapt in the adapt package on CRAN, for multivariate integration.

Examples

integrate(dnorm, -1.96, 1.96)
integrate(dnorm, -Inf, Inf)


## a slowly-convergent integral
integrand <- function(x) {1/((x+1)*sqrt(x))}
integrate(integrand, lower = 0, upper = Inf)

integrate(integrand, lower = 0, upper = 10)
integrate(integrand, lower = 0, upper = 100000)
integrate(integrand, lower = 0, upper = 1000000, stop.on.error = FALSE)

try(integrate(function(x) 2, 0, 1))  ## no vectorizable function
integrate(function(x) rep(2, length(x)), 0, 1)  ## correct

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