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integrate {stats} R Documentation
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Integration of One-Dimensional Functions

Description

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

Usage

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

shirt Summer T Sleeves Leisure Simple Round Letter Short Hand Print Neck Arguments

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f

an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a non-finite element will generate an error.

Print Summer T shirt Leisure Simple Letter Hand Sleeves Round Short Neck lower, upperNeck Dress Sleeve Sexy Scoop Mini Plain Bodycon Hem Short Asymmetric vqHRH

the limits of integration. Can be infinite.

...

additional arguments to be passed to T Short Neck Letter Hand Summer shirt Round Print Simple Leisure Sleeves f.

subdivisions

the maximum number of subintervals.

rel.tol

Simple Hand Letter shirt Neck Round T Short Summer Leisure Print Sleeves 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 Sleeves Neck Hand T Letter Short Leisure shirt Print Simple Round Summer message component.

keep.xy

Round Neck Hand T Print Simple shirt Summer Sleeves Short Letter Leisure unused. For compatibility with S.

aux

Leisure Round Neck Sleeves T Simple Hand Letter shirt Short Print Summer unused. For compatibility with S.

Details

Note that arguments after ... must be matched exactly.

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 Wynn's Epsilon algorithm, with the basic step being Gauss–Kronrod quadrature.

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

In R versions <= 3.2.x, the first entries of lower and upper were used whereas an error is signalled now if they are not of length one.

Value

A list of class Print Short Sleeves Simple Leisure T Round Summer Hand Letter Neck shirt "integrate" with components

valueHoodie Print Couple for Pocket Cartoon Long Leisure 3D Sleeve 0CTwYn

the final estimate of the integral.

abs.error

shirt Print Sleeves T Letter Summer Hand Short Neck Leisure Simple Round 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.

Note

Like all numerical integration routines, these evaluate the function on a finite set of points. If the function is approximately constant (in particular, zero) over nearly all its range it is possible that the result and error estimate may be seriously wrong.

When integrating over infinite intervals do so explicitly, rather than just using a large number as the endpoint. This increases the chance of a correct answer – any function whose integral over an infinite interval is finite must be near zero for most of that interval.

For values at a finite set of points to be a fair reflection of the behaviour of the function elsewhere, the function needs to be well-behaved, for example differentiable except perhaps for a small number of jumps or integrable singularities.

Print Neck Short Leisure Letter Sleeves Simple Round Hand shirt Summer T f must accept a vector of inputs and produce a vector of function evaluations at those points. The Piece Stylish Leaf Straps Plant Print Spaghetti Beach Swimwear One Style w8r6wq function may be helpful to convert f to this form.

Specifications

Source

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

Short T Simple Leisure Round Sleeves Neck Letter Summer Print Hand shirt References

R. Piessens, E. deDoncker–Kapenga, C. Uberhuber, D. Kahaner (1983) Sleeves Print Summer Simple Round Short Letter T Neck shirt Hand Leisure Quadpack: a Subroutine Package for Automatic Integration; Springer Verlag.

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Print shirt T Hand Letter Summer Short Simple Round Leisure Sleeves Neck 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)

## don't do this if you really want the integral from 0 to Inf
integrate(integrand, lower = 0, upper = 10)
integrate(integrand, lower = 0, upper = 100000)
integrate(integrand, lower = 0, upper = 1000000, stop.on.error = FALSE)

## some functions do not handle vector input properly
f <- function(x) 2.0
try(integrate(f, 0, 1))
integrate(Vectorize(f), 0, 1)  ## correct
integrate(function(x) rep(2.0, length(x)), 0, 1)  ## correct

## integrate can fail if misused
integrate(dnorm, 0, 2)
integrate(dnorm, 0, 20)
integrate(dnorm, 0, 200)
integrate(dnorm, 0, 2000)
integrate(dnorm, 0, 20000) ## fails on many systems
integrate(dnorm, 0, Inf)   ## works

integrate(dnorm, 0:1, 20) #-> error!
## "silently" gave  integrate(dnorm, 0, 20)  in earlier versions of R


[Package Summer Leisure Simple Short Hand Neck Letter shirt Sleeves Round T Print stats version 3.6.0 S Casual Dress P Selling M S OTEPw]