| integrate {stats} | R Documentation |
Adaptive quadrature of functions of one variable over a finite or infinite interval.
integrate(f, lower, upper, subdivisions=100,
rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
stop.on.error = TRUE, keep.xy = FALSE, aux = NULL, ...)
f |
an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a non-finite element will generate an error. |
lower, upper |
the limits of integration. Can be infinite. |
subdivisions |
the maximum number of subintervals. |
rel.tol |
relative accuracy requested. |
abs.tol |
absolute accuracy requested. |
stop.on.error |
logical. If true (the default) an error stops the
function. If false some errors will give a result with a warning in
the message component. |
keep.xy |
unused. For compatibility with S. |
aux |
unused. For compatibility with S. |
... |
additional arguments to be passed to f. Remember
to use argument names not matching those of integrate(.)! |
If one or both limits are infinite, the infinite range is mapped onto a finite interval.
For a finite interval, globally adaptive interval subdivision is used in connection with extrapolation by the Epsilon algorithm.
rel.tol cannot be less than max(50*.Machine$double.eps,
0.5e-28) if abs.tol <= 0.
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. |
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.
f must accept a vector of inputs and produce a vector of function
evaluations at those points. The Vectorize function
may be helpful to convert f to this form.
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.
The function adapt in the adapt package on
CRAN, for multivariate integration.
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
try(integrate(f, 0, 1))
integrate(Vectorize(f), 0, 1) ## correct
integrate(function(x) rep(2, 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