pracma (version 1.4.5)

dblquad: Double and Triple Integration

Description

Numerically evaluate double integral over rectangle.

Usage

dblquad(f, xa, xb, ya, yb, dim = 2, ..., 
        subdivs = 300, tol = .Machine$double.eps^0.5)
triplequad(f, xa, xb, ya, yb, za, zb, 
            subdivs = 300, tol = .Machine$double.eps^0.5, ...)

Arguments

f

function of two variables, the integrand.

xa, xb

left and right endpoint for first variable.

ya, yb

left and right endpoint for second variable.

za, zb

left and right endpoint for third variable.

dim

which variable to integrate first.

subdivs

number of subdivisions to use.

tol

relative tolerance to use in integrate.

...

additional parameters to be passed to the integrand.

Value

• Numerical scalar, the value of the integral.

Details

Function dblquad applies the internal single variable integration function integrate two times, once for each variable.

Function triplequad reduces the problem to dblquad by first integrating over the innermost variable.

See Also

integrate, quad2d, simpson2d

Examples

f1 <- function(x, y) x^2 + y^2
dblquad(f1, -1, 1, -1, 1)       #   2.666666667 , i.e. 8/3 . err = 0

f2 <- function(x, y) y*sin(x)+x*cos(y)
dblquad(f2, pi, 2*pi, 0, pi)    #  -9.869604401 , i.e. -pi^2, err = 0

# f3 <- function(x, y) sqrt((1 - (x^2 + y^2)) * (x^2 + y^2 <= 1))
f3 <- function(x, y) sqrt(pmax(0, 1 - (x^2 + y^2)))
dblquad(f3, -1, 1, -1, 1)       #   2.094395124 , i.e. 2/3*pi , err = 2e-8

f4 <- function(x, y, z) y*sin(x)+z*cos(x)
triplequad(f4, 0,pi, 0,1, -1,1) # - 2.0 => -2.220446e-16