`quadv`

Adaptive Simpson quadrature of a vector-valued function of one variable.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

Q = quadv(fun, a, b)

Integrates fun from a to b, where fun(x) returns an array for a scalar x.

Q = quadv(fun, a, b, tol)

Uses the absolute tolerance tol.

Description

All components are integrated together on a shared subdivision of the interval, which is faster than calling quad once per component. The function is evaluated one point at a time, so it does not need to be vectorized in x.

The modern equivalent is integral(fun, a, b, 'ArrayValued', true).

Input arguments

fun: Handle called with a scalar x that returns a scalar, vector or array.
a, b: Finite limits.
tol: Absolute tolerance. Default 1e-6.

Output arguments

Q: Array of the same size as fun(x), holding the integrals of every component.

Example

Two integrals at once

Q = quadv(@(x) [x, x.^2], 0, 1)

Output

Q = 1×2

    0.5000    0.3333

quadv