de.erichseifert.gral.util

Class MathUtils

java.lang.Object

de.erichseifert.gral.util.MathUtils

public abstract class MathUtils
extends java.lang.Object

Abstract class that provides utility functions which are useful for mathematical calculations.

Method Summary

Modifier and Type	Method and Description
static boolean	almostEqual(double a, double b, double delta) Check whether two floating point values match with a given precision.
static int	binarySearch(double[] a, double key) Perform a binary search on a sorted array a to find the element with the nearest element to key.
static int	binarySearchCeil(double[] a, double key) Perform a binary search on a sorted array a to find the element with the smallest distance to key.
static int	binarySearchFloor(double[] a, double key) Perform a binary search on a sorted array a to find the element with the smallest distance to key.
static double	ceil(double a, double precision) Returns a rounded number larger than a with a defined precision.
static double	floor(double a, double precision) Returns a rounded number smaller than a with a defined precision.
static boolean	isCalculatable(double n) Returns whether a specified double can be used for calculations.
static boolean	isCalculatable(java.lang.Number n) Returns whether a specified java.lang.Number object can be used for calculations.
static double	limit(double value, double min, double max) Clamps a double number to specified limits: if value is greater than max then max will be returned.
static float	limit(float value, float min, float max) Clamps a float number to specified limits: if value is greater than max then max will be returned.
static int	limit(int value, int min, int max) Clamps a integer number to specified limits: if value is greater than max then max will be returned.
static <T extends java.lang.Number> T	limit(T value, T min, T max) Clamps a number object to specified limits: if value is greater than max then max will be returned.
static double	magnitude(double base, double n) Returns the magnitude of the specified number.
static double	normalizeDegrees(double angle) Converts an angle in degrees so that it lies between 0.0 and 360.0.
static double	quantile(java.util.List<java.lang.Double> values, double q) Utility method used to calculate arbitrary quantiles from a sorted list of values.
static <T extends java.lang.Comparable<T>> int	randomizedSelect(java.util.List<T> a, int lower, int upper, int i) Perform a randomized search on an unsorted array a to find the ith smallest element.
static double	round(double a, double precision) Mathematically rounds a number with a defined precision.

Methods inherited from class java.lang.Object

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

Method Detail

almostEqual

public static boolean almostEqual(double a,
                                  double b,
                                  double delta)

Check whether two floating point values match with a given precision.

Parameters:

a - First value

b - Second value

delta - Precision

Returns:

true if the difference of a and b is smaller or equal than delta, otherwise false

round

public static double round(double a,
                           double precision)

Mathematically rounds a number with a defined precision.

Parameters:

a - Value

precision - Precision

Returns:

Rounded value

floor

public static double floor(double a,
                           double precision)

Returns a rounded number smaller than a with a defined precision.

Parameters:

a - Value

precision - Precision

Returns:

Rounded value

ceil

public static double ceil(double a,
                          double precision)

Returns a rounded number larger than a with a defined precision.

Parameters:

a - Value

precision - Precision

Returns:

Rounded value

binarySearch

public static int binarySearch(double[] a,
                               double key)

Perform a binary search on a sorted array a to find the element with the nearest element to key.

Parameters:

a - Array with ascending values

key - Pivot value

Returns:

Index of the array element whose value is nearly or exactly key

binarySearchFloor

public static int binarySearchFloor(double[] a,
                                    double key)

Perform a binary search on a sorted array a to find the element with the smallest distance to key. The returned element's value is always less than or equal to key.

Parameters:

a - Array with ascending values

key - Pivot value

Returns:

Index of the array element whose value is less than or equal to key

binarySearchCeil

public static int binarySearchCeil(double[] a,
                                   double key)

Perform a binary search on a sorted array a to find the element with the smallest distance to key. The returned element's value is always greater than or equal to key.

Parameters:

a - Array with ascending values

key - Pivot value

Returns:

Index of the array element whose value is greater than or equal to key

limit

public static <T extends java.lang.Number> T limit(T value,
                                                   T min,
                                                   T max)

Clamps a number object to specified limits: if value is greater than max then max will be returned. If value is greater than min then min will be returned.

Type Parameters:

T - Numeric data type

Parameters:

value - Double value to be clamped

min - Minimum

max - Maximum

Returns:

Clamped value

limit

public static double limit(double value,
                           double min,
                           double max)

Clamps a double number to specified limits: if value is greater than max then max will be returned. If value is greater than min then min will be returned.

Parameters:

value - Double value to be clamped

min - Minimum

max - Maximum

Returns:

Clamped value

limit

public static float limit(float value,
                          float min,
                          float max)

Clamps a float number to specified limits: if value is greater than max then max will be returned. If value is greater than min then min will be returned.

Parameters:

value - Float value to be clamped

min - Minimum

max - Maximum

Returns:

Clamped value

limit

public static int limit(int value,
                        int min,
                        int max)

Clamps a integer number to specified limits: if value is greater than max then max will be returned. If value is greater than min then min will be returned.

Parameters:

value - Integer value to be clamped

min - Minimum

max - Maximum

Returns:

Clamped value

randomizedSelect

public static <T extends java.lang.Comparable<T>> int randomizedSelect(java.util.List<T> a,
                                                                       int lower,
                                                                       int upper,
                                                                       int i)

Perform a randomized search on an unsorted array a to find the ith smallest element. The array contents are be modified during the operation!

See Cormen et al. (2001): Introduction to Algorithms. 2nd edition. p. 186

Type Parameters:

T - Data type of the array

Parameters:

a - Unsorted array

lower - Starting index

upper - End index

i - Smallness rank of value to search starting at 1

Returns:

Index of the element that is the ith smallest in array a

magnitude

public static double magnitude(double base,
                               double n)

Returns the magnitude of the specified number. Example for magnitude base 10:

-0.05	-0.01
0.05	0.01
3.14	1.00
54.32	10.00
123.45	100.00

Parameters:

base - Base.

n - Number.

Returns:

Magnitude.

quantile

public static double quantile(java.util.List<java.lang.Double> values,
                              double q)

Utility method used to calculate arbitrary quantiles from a sorted list of values. Currently only one method is implemented: the default method that is used by R (method 7). The list must be sorted.

For more information see:

• Statistics: computing quantiles with Python
• Wikipedia article on quantile calculation
• Source code of quantile calculation in R language
• Stackoverflow thread on quantile calculation in R

Parameters:

values - Data values.

q - Quantile in range [0, 1]

Returns:

Quantile value

isCalculatable

public static boolean isCalculatable(java.lang.Number n)

Returns whether a specified java.lang.Number object can be used for calculations. null values, NaN values or infinite values are considered as non-calculatable.

Parameters:

n - Number object.

Returns:

whether n can be used for calculations.

isCalculatable

public static boolean isCalculatable(double n)

Returns whether a specified double can be used for calculations. NaN values or infinite values are considered non-calculatable.

Parameters:

n - double value

Returns:

whether n can be used for calculations.

normalizeDegrees

public static double normalizeDegrees(double angle)

Converts an angle in degrees so that it lies between 0.0 and 360.0.

Parameters:

angle - Arbitrary angle in degrees.

Returns:

Angle between 0.0 and 360.0.