Struct rgsl::types::integration::IntegrationQawsTable

pub struct IntegrationQawsTable { /* private fields */ }

The QAWS algorithm is designed for integrands with algebraic-logarithmic singularities at the end-points of an integration region. In order to work efficiently the algorithm requires a precomputed table of Chebyshev moments.

Implementations

impl IntegrationQawsTable

pub fn new(
    alpha: f64,
    beta: f64,
    mu: i32,
    nu: i32
) -> Option<IntegrationQawsTable>

This function allocates space for a gsl_integration_qaws_table struct describing a singular weight function W(x) with the parameters alpha, beta, mu and nu,

W(x) = (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x)

where alpha > -1f64, beta > -1f64, and mu = 0, 1, nu = 0, 1. The weight function can take four different forms depending on the values of mu and nu,

W(x) = (x-a)^alpha (b-x)^beta                   (mu = 0, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(x-a)          (mu = 1, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(b-x)          (mu = 0, nu = 1)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)

The singular points (a,b) do not have to be specified until the integral is computed, where they are the endpoints of the integration range.

The function returns a pointer to the newly allocated table gsl_integration_qaws_table if no errors were detected, and 0 in the case of error.

pub fn set(&mut self, alpha: f64, beta: f64, mu: i32, nu: i32) -> Value

This function modifies the parameters (\alpha, \beta, \mu, \nu)

pub fn qaws<F: Fn(f64) -> f64>(
    &mut self,
    f: F,
    a: f64,
    b: f64,
    epsabs: f64,
    epsrel: f64,
    limit: usize,
    workspace: &mut IntegrationWorkspace
) -> (Value, f64, f64)

This function computes the integral of the function f(x) over the interval (a,b) with the singular weight function (x-a)^\alpha (b-x)^\beta \log^\mu (x-a) \log^\nu (b-x). The parameters of the weight function (\alpha, \beta, \mu, \nu) are taken from the table self. The integral is,

I = \int_a^b dx f(x) (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x).

The adaptive bisection algorithm of QAG is used. When a subinterval contains one of the endpoints then a special 25-point modified Clenshaw-Curtis rule is used to control the singularities. For subintervals which do not include the endpoints an ordinary 15-point Gauss-Kronrod integration rule is used.

Returns (result, abs_err)

Trait Implementations

impl Drop for IntegrationQawsTable

fn drop(&mut self)

Executes the destructor for this type.