indefinteg: Indefinite Integral

In spatstat.random: Random Generation Functionality for the 'spatstat' Family

Indefinite Integral

Description

Computes the indefinite integral of the given function.

Usage

  indefinteg(f, x, ...,
             method=c("trapezoid", "quadrature"),
             lower=min(x), nfine=8192) 

Arguments

f	an R function taking a numeric first argument and returning a numeric vector of the same length.
x	Vector of values of the argument for which the indefinite integral should be evaluated.
...	additional arguments to be passed to f.
method	String (partially matched) specifying how to compute the integrals.
lower	Lower limit of integration. A single number.
nfine	Number of sub-intervals to use for computation if method='trapezoid'.

Details

The indefinite integral of the given function f is computed numerically at each of the desired values x. The lower limit of integration is taken to be min(x).

The result is a numeric vector y of the same length as x, with entries

y_i = \int_{\mbox{lower}}^{x_i} f(t) dt

If method='trapezoid' (the default), the integrals are computed rapidly using the trapezoid rule. If method='quadrature' the integrals are computed accurately but much more slowly, using the numerical quadrature routine integrate.

If method='trapezoid' the function f is first evaluated on a finer grid of values of the function argument. The fine grid contains nfine sample points. The values of the indefinite integral on the fine grid are computed using the trapezoidal approximation. Finally the values of the indefinite integral are extracted at the desired argument values x.

Value

Numeric vector of the same length as x.

Author(s)

\adrian

.

See Also

integrate

Examples

  curve(indefinteg(sin, x), to=pi)

spatstat.random documentation built on Oct. 22, 2023, 1:17 a.m.