int {rmutil} | R Documentation |
int
performs numerical integration of a given function using
either Romberg integration or algorithm 614 of the collected
algorithms from ACM. Only the former is vectorized. The latter
appeared in ACM-Trans. Math. Software, Vol.10, No. 2, Jun., 1984,
p. 152-160 and uses formulae optimal in certain Hardy spaces h(p,d);
see Sikorski,K., Optimal quadrature algorithms in HP spaces,
Num. Math., 39, 405-410 (1982).
Functions may have singularities at one or both end-points of the interval (a,b).
int(f, a="-infty", b="infty", type="Romberg", eps=1.0e-6, max, d, p=0)
f |
The function (of one variable) to integrate, returning either a scalar or a vector. |
a |
A scalar or vector giving the lower bound. If non-numeric, taken to be -infty, in which case it must be the same for the whole vector. |
b |
A scalar or vector giving the upper bound. If non-numeric, taken to be infty, in which case it must be the same for the whole vector. |
type |
The algorithm to be used, by default Romberg integration. Otherwise, it uses the TOMS614 algorithm. |
eps |
Precision. |
max |
For Romberg, the maximum number of steps, by default set to 16. For TOMS614, the maximum number of function evaluations, by default set to 100. |
d |
For Romberg, the number of extrapolation points so that 2k is the order of integration, by default set to 5; d=2 is Simpson's rule. For TOMS614, heuristic termination = any real number; deterministic termination = a number in the range 0 < d < pi/2 by default, set to 1. |
p |
For TOMS614, p = 0: heuristic termination, p = 1: deterministic termination with the infinity norm, p > 1: deterministic termination with the p-th norm. |
J.K. Lindsey
f <- function(x) sin(x)+cos(x)-x^2 int(f, a=0, b=2) # f <- function(x) exp(-(x-2)^2/2)/sqrt(2*pi) int(f, a=0:3) 1-pnorm(0:3, 2)