quadv

Syntax

area=quadv(@func,a,b)

area=quadv(@func,a,b,abstol)

[area,count]=quadv(...)

Inputs

func

The function to integrate.

The input is a scalar and the output is a scalar.

A function handle or anonymous function is also supported.

a

Lower integration limit.

Type: double

Dimension: scalar | vector | matrix

b

Upper integration limit.

Type: double

Dimension: scalar | vector | matrix

abstol

Absolute tolerance (default: sqrt(eps) or about 1.0e-8).

Type: double

Dimension: scalar

Outputs

area

The estimated area.

Dimension: scalar | matrix

count

Number of function evaluations.

Dimension: scalar | matrix

Examples

function y = Integrand(x)
    y = 13 * (x - x^2) * exp(-3*x/2);
end

[area,count] = quadv(@Integrand, 0, 4, 1.0e-5)

area = -1.54878858
count = 69

Multiple intervals with an anonymous function:

[area,count] = quadv(@(x) sqrt(x), [0, 1], [1, 2])

area = [Matrix] 1 x 2
0.66667  1.21895
count = [Matrix] 1 x 2
309  29

Comments

quadv recursively bisects each interval until the improvement from the bisections falls below the absolute tolerance. Intervals are assumed to have finite bounds.

The maximum number of function evaluations is 10,000, and the minimum interval is 1.0e-12.

To pass additional parameters to a function argument, use an anonymous function.

quadv does not yet support func returning a matrix to support multiple simultaneous integrands.