org.opensourcephysics.numerics
Class Util

java.lang.Object
  org.opensourcephysics.numerics.Util

public final class Util
extends java.lang.Object

A utility class for numerical analysis. This class cannot be subclassed or instantiated because all methods are static.

Version:

1.0

Author:

Wolfgang Christian

Field Summary

static double	defaultNumericalPrecision The default precision for numerical analysis.
static double	LOG10
static double	SQRT2PI

Method Summary

static int	checkSorting(double[] array) Checks if an array is sorted.
static double	computeAverage(double[] array, int start, int num) Computes the average value of a subset of an array.
static Function	constantFunction(double c) Creates a function having a constant value.
static double	evalMath(java.lang.String str) Evalautes a mathematical expression without variables.
static java.lang.String	f2(double d) Convert a double to a string, printing two decimal places.
static java.lang.String	f3(double d) Convert a double to a string, printing three decimal places.
static java.lang.String	f4(double d) Convert a double to a string, printing four decimal places.
static double[]	functionFill(Function f, double start, double stop, double[] data) Fills the given double[n] array with f(x) on the interval [start, stop].
static double[][]	functionFill(Function f, double start, double stop, double[][] data) Fills the given double[2][n] array with x and f(x) values on interval [start, stop].
static Function	gaussian(double x0, double sigma) Creates a Guassian (normal) distribution function.
static double[]	getRange(Function f, double a, double b, int n) Gets the approximate range of a function within the given domain.
static Function	linearFunction(double m, double b) Creates a linear function with the given slope and intercept.
static double	relativePrecision(double epsilon, double result) Computes the relativePrecision except near zero where the absolute precision is returned.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

SQRT2PI

public static final double SQRT2PI

LOG10

public static final double LOG10

defaultNumericalPrecision

public static final double defaultNumericalPrecision

The default precision for numerical analysis.

Method Detail

f2

public static java.lang.String f2(double d)

Convert a double to a string, printing two decimal places.

Parameters:

d - Input double

f3

public static java.lang.String f3(double d)

Convert a double to a string, printing three decimal places.

Parameters:

d - Input double

f4

public static java.lang.String f4(double d)

Convert a double to a string, printing four decimal places.

Parameters:

d - Input double

relativePrecision

public static double relativePrecision(double epsilon,
                                       double result)

Computes the relativePrecision except near zero where the absolute precision is returned.

Parameters:

epsilon - the absolute error

result - the result

Returns:

the relative error

checkSorting

public static int checkSorting(double[] array)

Checks if an array is sorted. Returns: Positive integer if array is sorted in increasing value. Negative integer if array is sorted in decreasing value. Zero if array is not sorted.

Parameters:

array - double[]

Returns:

int 1,0,-1 based on sorting

getRange

public static double[] getRange(Function f,
                                double a,
                                double b,
                                int n)

Gets the approximate range of a function within the given domain. The range is deterermiend by evaluating the function at n points and finding the minimum and maximum values.

Parameters:

f - Function

a - double

b - double

n - int

Returns:

double[]

functionFill

public static double[][] functionFill(Function f,
                                      double start,
                                      double stop,
                                      double[][] data)

Fills the given double[2][n] array with x and f(x) values on interval [start, stop].

Parameters:

f - Function

start - double

stop - double

data - double[][]

Returns:

double[][]

functionFill

public static double[] functionFill(Function f,
                                    double start,
                                    double stop,
                                    double[] data)

Fills the given double[n] array with f(x) on the interval [start, stop].

Parameters:

f - Function

start - double starting value of x

stop - double stopping value of x

data - double[]

Returns:

double[]

computeAverage

public static double computeAverage(double[] array,
                                    int start,
                                    int num)

Computes the average value of a subset of an array.

Parameters:

array - the data to be averaged

start - the index of the first point to be averaged

num - the total number of points to be averaged

Returns:

constantFunction

public static Function constantFunction(double c)

Creates a function having a constant value.

Parameters:

c -

Returns:

linearFunction

public static Function linearFunction(double m,
                                      double b)

Creates a linear function with the given slope and intercept.

Parameters:

m - double slope

b - double intercept

Returns:

Function

gaussian

public static Function gaussian(double x0,
                                double sigma)

Creates a Guassian (normal) distribution function. The distribution is normalized. The full width at half maximum is 2*sigma*Math.sqrt(2 Math.log(2)) ~ 2.3548*sigma

Parameters:

x0 - double center of the distribution

sigma - double width of the distributuon

Returns:

Function

evalMath

public static double evalMath(java.lang.String str)

Evalautes a mathematical expression without variables.

Parameters:

str - String

Returns:

double