Package org.hortonmachine.gears.utils.math

Class NumericsUtilities

java.lang.Object

org.hortonmachine.gears.utils.math.NumericsUtilities

public class NumericsUtilities
extends Object

Class to help out with numeric issues, mostly due to floating point usage.

Since the floating point representation keeps a constant relative precision, comparison is done using relative error.

Be aware of the fact that the methods

• dEq(double, double)
• fEq(float, float)

can be used in the case of "simple" numerical comparison, while in the case of particular values that are generated through iterations the user/developer should consider to supply an epsilon value derived from the knowledge of the domain of the current problem and use the methods

• dEq(double, double, double)
• fEq(float, float, float)

Author:

Andrea Antonello (www.hydrologis.com)

Field Summary

Fields

Modifier and Type	Field	Description
static double	D_TOLERANCE	The double tolerance used for comparisons.
static float	F_TOLERANCE	The float tolerance used for comparisons.
static double	RADTODEG	Radiants to degrees conversion factor.

Constructor Summary

Constructors

Constructor	Description
NumericsUtilities()

Method Summary

Modifier and Type	Method	Description
static boolean	dEq(double a, double b)	Returns true if two doubles are considered equal based on a tolerance of .
static boolean	dEq(double a, double b, double epsilon)	Returns true if two doubles are considered equal based on an supplied epsilon.
static boolean	fEq(float a, float b)	Returns true if two floats are considered equal based on a tolerance of .
static boolean	fEq(float a, float b, float epsilon)	Returns true if two floats are considered equal based on an supplied epsilon.
static double	gamma(double x)
static double	getMachineDEpsilon()	Getter for the calculated machine double epsilon.
static List<int[]>	getNegativeRanges(double[] x)	Get the range index for which x is negative.
static boolean	isBetween(double value, double... ranges)	Check if value is inside a ND interval (bounds included).
static <T extends Number> T	isNumber(String value, Class<T> adaptee)	Checks if a string is a number (currently Double, Float, Integer).
static double	logGamma(double x)	Gamma function ported from the apache math package.
static float	machineFEpsilon()	Getter for the calculated machine float epsilon.
static double	normalize(double max, double min, double value, double normMax)	Normalizes a value for a given normalization max (assuming the lower is 0).
static double	pythagoras(double d1, double d2)	Calculates the hypothenuse as of the Pythagorean theorem.
static double[]	range2Bins(double min, double max, double step, boolean doLastEqual)	Creates an array of bins from a range and a step to use.
static double[]	range2Bins(double min, double max, int binsNum)	Creates an array of equal bin from a range and the number of bins.

Methods inherited from class java.lang.Object

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

Field Detail

D_TOLERANCE

public static final double D_TOLERANCE

The double tolerance used for comparisons.

F_TOLERANCE

public static final float F_TOLERANCE

The float tolerance used for comparisons.

RADTODEG

public static final double RADTODEG

Radiants to degrees conversion factor.

See Also:

Constant Field Values

Constructor Detail

NumericsUtilities

public NumericsUtilities()

Method Detail

getMachineDEpsilon

public static double getMachineDEpsilon()

Getter for the calculated machine double epsilon.

Returns:

the machine epsilon for double values.

machineFEpsilon

public static float machineFEpsilon()

Getter for the calculated machine float epsilon.

Returns:

the machine epsilon for float values.

dEq

public static boolean dEq(double a,
                          double b)

Returns true if two doubles are considered equal based on a tolerance of .

Note that two Double.NaN are seen as equal and return true.

Parameters:

a - double to compare.

b - double to compare.

Returns:

true if two doubles are considered equal.

dEq

public static boolean dEq(double a,
                          double b,
                          double epsilon)

Returns true if two doubles are considered equal based on an supplied epsilon.

Note that two Double.NaN are seen as equal and return true.

Parameters:

a - double to compare.

b - double to compare.

Returns:

true if two doubles are considered equal.

fEq

public static boolean fEq(float a,
                          float b)

Returns true if two floats are considered equal based on a tolerance of .

Note that two Float.NaN are seen as equal and return true.

Parameters:

a - float to compare.

b - float to compare.

Returns:

true if two floats are considered equal.

fEq

public static boolean fEq(float a,
                          float b,
                          float epsilon)

Returns true if two floats are considered equal based on an supplied epsilon.

Note that two Float.NaN are seen as equal and return true.

Parameters:

a - float to compare.

b - float to compare.

Returns:

true if two float are considered equal.

isNumber

public static <T extends Number> T isNumber(String value,
                                            Class<T> adaptee)

Checks if a string is a number (currently Double, Float, Integer).

Type Parameters:

T -

Parameters:

value - the string to check.

adaptee - the class to check against. If null, the more permissive Double will be used.

Returns:

the number or null, if the parsing fails.

pythagoras

public static double pythagoras(double d1,
                                double d2)

Calculates the hypothenuse as of the Pythagorean theorem.

Parameters:

d1 - the length of the first leg.

d2 - the length of the second leg.

Returns:

the length of the hypothenuse.

isBetween

public static boolean isBetween(double value,
                                double... ranges)

Check if value is inside a ND interval (bounds included).

Parameters:

value - the value to check.

ranges - the bounds (low1, high1, low2, high2, ...)

Returns:

true if value lies inside the interval.

logGamma

public static double logGamma(double x)

Gamma function ported from the apache math package. This should be removed if the apache math lib gets in use by HortonMachine.

Returns the natural logarithm of the gamma function Γ(x). The implementation of this method is based on:

• Gamma Function, equation (28).
• Lanczos Approximation, equations (1) through (5).
• Paul Godfrey, A note on the computation of the convergent Lanczos complex Gamma approximation

Parameters:

x - Value.

Returns:

log(Γ(x))

gamma

public static double gamma(double x)

normalize

public static double normalize(double max,
                               double min,
                               double value,
                               double normMax)

Normalizes a value for a given normalization max (assuming the lower is 0).

Parameters:

max - the max of the sampling values.

min - the min of the sampling values.

value - the current value from the sampling values to be normalized.

normMax - the normalization maximum to use.

Returns:

the normalized value.

getNegativeRanges

public static List<int[]> getNegativeRanges(double[] x)

Get the range index for which x is negative.

Parameters:

x -

Returns:

range2Bins

public static double[] range2Bins(double min,
                                  double max,
                                  int binsNum)

Creates an array of equal bin from a range and the number of bins.

Parameters:

min - the min value.

max - the max value.

binsNum - the number of wanted bins.

Returns:

the array of bin bounds of size [binNum+1], since it contains the min and max.

range2Bins

public static double[] range2Bins(double min,
                                  double max,
                                  double step,
                                  boolean doLastEqual)

Creates an array of bins from a range and a step to use.

Note that if the step doesn't split the range exactly, the last bin will be smaller if doLastEqual is set to false.

Parameters:

min - the min value.

max - the max value.

step - the wanted size of the bins.

doLastEqual - make also the last bin of equal step size.

Returns:

the array of bin bounds.