Struct rgsl::types::monte_carlo::PlainMonteCarlo

pub struct PlainMonteCarlo { /* fields omitted */ }

The plain Monte Carlo algorithm samples points randomly from the integration region to estimate the integral and its error. Using this algorithm the estimate of the integral E(f; N) for N randomly distributed points x_i is given by,

E(f; N) = = V = (V / N) \sum_i^N f(x_i) where V is the volume of the integration region. The error on this estimate \sigma(E;N) is calculated from the estimated variance of the mean,

\sigma² (E; N) = (V² / N²⁾ \sum_i^N (f(x_i) - )^2.

For large N this variance decreases asymptotically as \Var(f)/N, where \Var(f) is the true variance of the function over the integration region. The error estimate itself should decrease as \sigma(f)/\sqrt{N}. The familiar law of errors decreasing as 1/\sqrt{N} applies—to reduce the error by a factor of 10 requires a 100-fold increase in the number of sample points.

Methods

impl PlainMonteCarlo

fn new(dim: usize) -> Option<PlainMonteCarlo>

This function allocates and initializes a workspace for Monte Carlo integration in dim dimensions.

fn init(&mut self) -> Value

This function initializes a previously allocated integration state. This allows an existing workspace to be reused for different integrations.

fn integrate<F: FnMut(&[f64]) -> f64>(
    &mut self,
    dim: usize,
    f: F,
    xl: &[f64],
    xu: &[f64],
    t_calls: usize,
    r: &mut Rng
) -> Result<(f64, f64), Value>

This routines uses the plain Monte Carlo algorithm to integrate the function f over the dim-dimensional hypercubic region defined by the lower and upper limits in the arrays xl and xu, each of the same size. The integration uses a fixed number of function calls calls, and obtains random sampling points using the random number generator r. A previously allocated workspace s must be supplied. The result of the integration is returned in result, with an estimated absolute error abserr.

In C, the function takes a gsl_monte_function as first argument. In here, you have to pass the dim argument and the function pointer (which became a closure) directly to the function.

It returns either Ok((result, abserr)) or Err(enums::Value).

Trait Implementations

impl Drop for PlainMonteCarlo

fn drop(&mut self)

A method called when the value goes out of scope.