• All Implemented Interfaces:
Integrator<Double,​Double,​Function<Double,​Double>>

Gauss-Jacobi quadrature approximates the value of integrals of the form \begin{align*} \int_{-1}^{1} (1 - x)^\alpha (1 + x)^\beta f(x) dx \end{align*} The weights and abscissas are generated by GaussJacobiWeightAndAbscissaFunction.

In this integrator, $\alpha = 0$ and $\beta = 0$, which means that no adjustment to the function must be performed. However, the function is scaled in such a way as to allow any values for the limits of the integrals.

• ### Constructor Detail

Parameters:
n - The number of sample points to be used in the integration, not negative or zero
• ### Method Detail

• #### getIntegralFunction

public Function<Double,​Double> getIntegralFunction​(Function<Double,​Double> function,
Double lower,
Double upper)
Returns a function that is valid for both the type of quadrature and the limits of integration. To evaluate an integral over $[a, b]$, a change of interval must be performed: \begin{align*} \int_a^b f(x)dx &= \frac{b - a}{2}\int_{-1}^1 f(\frac{b - a}{2} x + \frac{a + b}{2})dx\\ &\approx \frac{b - a}{2}\sum_{i=1}^n w_i f(\frac{b - a}{2} x + \frac{a + b}{2}) \end{align*}
Specified by: