quad: Adaptive Simpson Quadrature

In pracma: Practical Numerical Math Functions

Adaptive Simpson Quadrature

Description

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

Usage

quad(f, xa, xb, tol = .Machine$double.eps^0.5, trace = FALSE, ...)

Arguments

f	a one-dimensional function; needs to be vectorized.
xa	lower limit of integration; must be finite
xb	upper limit of integration; must be finite
tol	accuracy requested.
trace	logical; shall a trace be printed?
...	additional arguments to be passed to f.

Details

Realizes adaptive Simpson quadrature in R through recursive calls.

The function f needs to be vectorized though this could be changed easily. quad is not suitable for functions with singularities in the interval or at end points.

Value

A single numeric value, the computed integral.

Note

More modern adaptive methods based on Gauss-Kronrod or Clenshaw-Curtis quadrature are now generally preferred.

Author(s)

Copyright (c) 1998 Walter Gautschi for the Matlab version published as part of the referenced article. R implementation by Hans W Borchers 2011.

References

Gander, W. and W. Gautschi (2000). “Adaptive Quadrature — Revisited”. BIT, Vol. 40, 2000, pp. 84-101.

See Also

integrate, quadl

Examples

# options(digits=15)
f <- function(x) x * cos(0.1*exp(x)) * sin(0.1*pi*exp(x))
quad(f, 0, 4)              # 1.2821290747821
quad(f, 0, 4, tol=10^-15)  # 1.2821290743501
integrate(f, 0, 4)
# 1.28212907435010 with absolute error < 4.1e-06

## Not run: 
xx <- seq(0, 4, length.out = 200)
yy <- f(xx)
plot(xx, yy, type = 'l')
grid()
## End(Not run)

pracma documentation built on Nov. 10, 2023, 1:14 a.m.