ComputePi (Apache Commons RNG Quadrature Example 1.6 API)

java.lang.Object
- org.apache.commons.rng.examples.quadrature.MonteCarloIntegration
- - org.apache.commons.rng.examples.quadrature.ComputePi

```
public class ComputePi
extends MonteCarloIntegration
```
Computation of \( \pi \) using Monte-Carlo integration. The computation estimates the value by computing the probability that a point \( p = (x, y) \) will lie in the circle of radius \( r = 1 \) inscribed in the square of side \( r = 1 \). The probability could be computed by \[ area_{circle} / area_{square} \], where \( area_{circle} = \pi * r^2 \) and \( area_{square} = 4 r^2 \). Hence, the probability is \( \frac{\pi}{4} \). The Monte Carlo simulation will produce \( N \) points. Defining \( N_c \) as the number of point that satisfy \( x^2 + y^2 \le 1 \), we will have \( \frac{N_c}{N} \approx \frac{\pi}{4} \).

Constructor Summary

Constructors
Constructor Description

ComputePi(org.apache.commons.rng.UniformRandomProvider rng)
Create an instance.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`compute(long numPoints)`	Compute the value of pi.
`protected boolean`	`isInside(double... rand)`	Indicates whether the given points is inside the region whose integral is computed.
`static void`	`main(String[] args)`	Program entry point.

Methods inherited from class org.apache.commons.rng.examples.quadrature.MonteCarloIntegration
integrate

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - ComputePi
```
public ComputePi(org.apache.commons.rng.UniformRandomProvider rng)
```
    Create an instance.
    
    Parameters:
    
    rng - RNG.
- Method Detail
  - main
```
public static void main(String[] args)
```
    Program entry point.
    Parameters:
    
    args - Arguments. The order is as follows:
    
    Number of random 2-dimensional points to generate.
    
    Random source identifier.
  - compute
```
public double compute(long numPoints)
```
    Compute the value of pi.
    
    Parameters:
    
    numPoints - Number of random points to generate.
    
    Returns:
    
    the approximate value of pi.
  - isInside
```
protected boolean isInside(double... rand)
```
    Indicates whether the given points is inside the region whose integral is computed.
    
    Specified by:
    
    isInside in class MonteCarloIntegration
    
    Parameters:
    
    rand - Point whose coordinates are random numbers uniformly distributed in the unit interval.
    
    Returns:
    
    true if the point is inside.