Class MathUtils

java.lang.Object

org.episteme.core.mathematics.util.MathUtils

public final class MathUtils
extends Object

The extra math library. Provides extra functions not in java.lang.Math class. This class cannot be subclassed or instantiated because all methods are static.

Version:

1.2

Author:

Mark Hale

Method Summary

Modifier and Type	Method	Description
static double	acosh(double x)	Returns the inverse hyperbolic cosine of a double.
static double	asinh(double x)	Returns the inverse hyperbolic sine of a double.
static double	atanh(double x)	Returns the inverse hyperbolic tangent of a double.
static double	binomial(double n, double k)	Returns the binomial coefficient (n k).
static int	binomial(int n, int k)	Returns the binomial coefficient (n k).
static double	cosh(double x)	Returns the hyperbolic cosine of a double.
static double	factorial(double x)	Returns the factorial.
static int	GCD(int a, int b)	Returns the Greatest Common Divisor (GCD).
static double	hypot(double x, double y)	Returns sqrt(x2+y2).
static int	LCM(int a, int b)	Returns the Least Common Multiple (LCM).
static double	log10(double x)	Returns the base 10 logarithm of a double.
static double	log2(double d)	Returns the base 2 logarithm of a double.
static double	logB(double d, double d1)	Returns the logarithm of a double in a given base.
static double	logFactorial(double x)	Returns the natural logarithm of the factorial.
static double	maxOf3(double a, double b, double c)	Returns the maximum of three double values.
static double	midOf3(double a, double b, double c)	Returns the middle of three double values.
static double	minOf3(double a, double b, double c)	Returns the minimum of three double values.
static double[]	pascalTriangle(int n)	Returns the n-th row of Pascal's triangle.
static double	polynomialExpansion(double n, double[] k)	Returns the multinomial coefficient (n k[]).
static int	pow(int a, int b)	Returns ab.
static int	pow2(int a)	Returns 2a.
static double	round(double x, int significant)	Rounds a number to so many significant figures.
static double	sigmoid(double x)	Produces a double between 0 and 1 using the sigmoid function.
static double	sigmoid(double x, double flatteningFactor)	Produces a double between 0 and 1 using a flattened sigmoid function.
static int	sign(double x)	Returns the signum of a double.
static double	sinh(double x)	Returns the hyperbolic sine of a double.
static int	sumOfDigits(long number)	Returns the sum of all individual digits of a number.
static double	tanh(double x)	Returns the hyperbolic tangent of a double.

Methods inherited from class Object

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

Method Details

round

public static double round(double x,
 int significant)

Rounds a number to so many significant figures.

Parameters:

x - a number to be rounded.

significant - number of significant figures to round to.

Returns:

the rounded number

hypot

public static double hypot(double x,
 double y)

Returns sqrt(x²+y²).

Parameters:

x - a double

y - a double

Returns:

the hypotenuse

See Also:

• Math.hypot(double, double)

pow

public static int pow(int a,
 int b)

Returns a^b.

Parameters:

a - an integer.

b - a positive integer.

Returns:

a^b

pow2

public static int pow2(int a)

Returns 2^a.

Parameters:

a - a positive integer.

Returns:

2^a

factorial

public static double factorial(double x)

Returns the factorial. (Wrapper for the gamma function).

Parameters:

x - a double.

Returns:

x!

See Also:

• SpecialMathUtils.gamma(double)

logFactorial

public static double logFactorial(double x)

Returns the natural logarithm of the factorial. (Wrapper for the log gamma function).

Parameters:

x - a double.

Returns:

ln(x!)

See Also:

• SpecialMathUtils.logGamma(double)

binomial

public static int binomial(int n,
 int k)

Returns the binomial coefficient (n k). Uses Pascal's recursion formula.

Parameters:

n - an integer.

k - an integer.

Returns:

(n k)

binomial

public static double binomial(double n,
 double k)

Returns the binomial coefficient (n k). Uses gamma functions.

Parameters:

n - a double.

k - a double between 0 and n.

Returns:

(n k)

polynomialExpansion

public static double polynomialExpansion(double n,
 double[] k)

Returns the multinomial coefficient (n k[]). Uses gamma functions.

Parameters:

n - a double.

k - a double array such that k1 + k2 + k3 + ... + km = n (unchecked).

Returns:

the multinomial coefficient

GCD

public static int GCD(int a,
 int b)

Returns the Greatest Common Divisor (GCD).

Parameters:

a - the first integer.

b - the second integer.

Returns:

the GCD.

LCM

public static int LCM(int a,
 int b)

Returns the Least Common Multiple (LCM).

Parameters:

a - the first integer.

b - the second integer.

Returns:

the LCM.

log10

public static double log10(double x)

Returns the base 10 logarithm of a double.

Parameters:

x - a double.

Returns:

log10(x)

logB

public static double logB(double d,
 double d1)

Returns the logarithm of a double in a given base.

Parameters:

d - the value

d1 - the base

Returns:

log_d1(d)

log2

public static double log2(double d)

Returns the base 2 logarithm of a double.

Parameters:

d - the value

Returns:

log2(d)

sinh

public static double sinh(double x)

Returns the hyperbolic sine of a double.

Parameters:

x - a double.

Returns:

sinh(x)

See Also:

• Math.sinh(double)

cosh

public static double cosh(double x)

Returns the hyperbolic cosine of a double.

Parameters:

x - a double.

Returns:

cosh(x)

See Also:

• Math.cosh(double)

tanh

public static double tanh(double x)

Returns the hyperbolic tangent of a double.

Parameters:

x - a double.

Returns:

tanh(x)

See Also:

• Math.tanh(double)

asinh

public static double asinh(double x)

Returns the inverse hyperbolic sine of a double.

Parameters:

x - a double.

Returns:

asinh(x)

acosh

public static double acosh(double x)

Returns the inverse hyperbolic cosine of a double.

Parameters:

x - a double.

Returns:

acosh(x)

atanh

public static double atanh(double x)

Returns the inverse hyperbolic tangent of a double.

Parameters:

x - a double.

Returns:

atanh(x)

sign

public static int sign(double x)

Returns the signum of a double.

Parameters:

x - the double

Returns:

the signum

maxOf3

public static double maxOf3(double a,
 double b,
 double c)

Returns the maximum of three double values.

Parameters:

a - first value

b - second value

c - third value

Returns:

max(a, b, c)

midOf3

public static double midOf3(double a,
 double b,
 double c)

Returns the middle of three double values.

Parameters:

a - first value

b - second value

c - third value

Returns:

the middle value

minOf3

public static double minOf3(double a,
 double b,
 double c)

Returns the minimum of three double values.

Parameters:

a - first value

b - second value

c - third value

Returns:

min(a, b, c)

sigmoid

public static double sigmoid(double x)

Produces a double between 0 and 1 using the sigmoid function.

Parameters:

x - the value

Returns:

sigmoid(x)

sigmoid

public static double sigmoid(double x,
 double flatteningFactor)

Produces a double between 0 and 1 using a flattened sigmoid function.

Parameters:

x - the value

flatteningFactor - the factor

Returns:

flattened sigmoid

sumOfDigits

public static int sumOfDigits(long number)

Returns the sum of all individual digits of a number.

Parameters:

number - the number

Returns:

the sum of digits

pascalTriangle

public static double[] pascalTriangle(int n)

Returns the n-th row of Pascal's triangle.

Parameters:

n - the row index (number of elements in the row)

Returns:

the row as an array of doubles.