safeIntegrate: Safe Integration of One-Dimensional Functions

Description

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

Usage

safeIntegrate(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, ...)

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.

Arguments

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 safeIntegrate(.)!

Details

This function is just a wrapper around integrate to check for equality of upper and lower. A check is made using all.equal. When numerical equality is detected, if lower (and hence upper) is infinite, the value of the integral and the absolute error are both set to 0. When lower is finite, the value of the integral is set to 0, and the absolute error to the average of the function values at upper and lower times the difference between upper and lower.

When upper and lower are determined to be different, the result is exactly as given by integrate.

Examples

Run this code

integrate(dnorm, -1.96, 1.96)
safeIntegrate(dnorm, -1.96, 1.96)  # Same as for integrate()
integrate(dnorm, -Inf, Inf)
safeIntegrate(dnorm, -Inf, Inf)    # Same as for integrate()
integrate(dnorm, 1.96, 1.96)       # OK here but can give an error
safeIntegrate(dnorm, 1.96, 1.96)
integrate(dnorm, -Inf, -Inf)
safeIntegrate(dnorm, -Inf, -Inf)   # Avoids nonsense answer
integrate(dnorm, Inf, Inf)
safeIntegrate(dnorm, Inf, Inf)     # Avoids nonsense answer