Struct rgsl::types::monte_carlo::PlainMonteCarlo
source · pub struct PlainMonteCarlo { /* private fields */ }Expand description
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
\sigma^2 (E; N) = (V^2 / N^2) \sum_i^N (f(x_i) -
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.
Implementations§
source§impl PlainMonteCarlo
impl PlainMonteCarlo
sourcepub fn new(dim: usize) -> Option<PlainMonteCarlo>
pub fn new(dim: usize) -> Option<PlainMonteCarlo>
This function allocates and initializes a workspace for Monte Carlo integration in dim dimensions.
sourcepub fn init(&mut self) -> Value
pub fn init(&mut self) -> Value
This function initializes a previously allocated integration state. This allows an existing workspace to be reused for different integrations.
sourcepub 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>
pub 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).