## math.numerics Class Integral

```java.lang.Object
math.numerics.Integral
```

`public final class Integralextends java.lang.Object`

Class Integral defines various integration algorithms. This class cannot be subclassed or instantiated because all methods are static.

Author:
Wolfgang Christian

Method Summary
`static double[][]` ```fillArray(Function f, double start, double stop, double tol, double[][] data)```
Fills the given data array with the intgral of the given function.
`static double[][]` ```fillArray(Function f, double start, double stop, double tol, int n)```
Fills a data array with the integral of the given function.
`static double` ```ode(Function f, double start, double stop, double tol)```

`static double` ```romberg(Function f, double a, double b, int n, double tol)```
Integrates the function using Romberg's algorithm based on Richardson's deferred approach.
`static double` ```simpson(Function f, double start, double stop, int n)```
Numerical integration using Simpson's rule.
`static double` ```simpson(Function f, double start, double stop, int n, double tol)```
Numerical integration using Simpson's rule.
`static double` ```trapezoidal(Function f, double start, double stop, int n, double tol)```
Integrates the function using the trapezoidal method.

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

Method Detail

### trapezoidal

```public static double trapezoidal(Function f,
double start,
double stop,
int n,
double tol)```
Integrates the function using the trapezoidal method.

Parameters:
`f` - the function
`start` - the first ordinate.
`stop` - the last ordinate.
`n` - the number of partitions
`tol` - relative tolerance
Returns:

### simpson

```public static double simpson(Function f,
double start,
double stop,
int n)
throws java.lang.IllegalArgumentException```
Numerical integration using Simpson's rule.

Parameters:
`f` - a function.
`start` - the first ordinate.
`stop` - the last ordinate.
`n` - the number of partitions
`the` - integral
Throws:
`java.lang.IllegalArgumentException`

### simpson

```public static double simpson(Function f,
double start,
double stop,
int n,
double tol)```
Numerical integration using Simpson's rule.

Parameters:
`f` - the function
`start` - the first ordinate.
`stop` - the last ordinate.
`n` - minimum number of partitions
`tol` - relative tolerance
Returns:
the integral

### romberg

```public static double romberg(Function f,
double a,
double b,
int n,
double tol)```
Integrates the function using Romberg's algorithm based on Richardson's deferred approach.

Parameters:
`f` - the function
`start` -
`stop` -
`tol` - tolerance
Returns:
the integral

### ode

```public static double ode(Function f,
double start,
double stop,
double tol)```

### fillArray

```public static double[][] fillArray(Function f,
double start,
double stop,
double tol,
int n)```
Fills a data array with the integral of the given function.

Parameters:
`f` - Function to be integrated
`start` - double start of integral
`stop` - double end of integral
`tol` - double computation tolerance
`n` - int number of data points
Returns:
double[][]

### fillArray

```public static double[][] fillArray(Function f,
double start,
double stop,
double tol,
double[][] data)```
Fills the given data array with the intgral of the given function.

Parameters:
`f` - Function to be integrated
`start` - double start of integral
`stop` - double end of integral
`tol` - double computation tolerance
`data` - double[][]
Returns:
double[][]