ch.obermuhlner.math.big

Class BigComplexMath

java.lang.Object

ch.obermuhlner.math.big.BigComplexMath

public class BigComplexMath
extends java.lang.Object

Provides advanced functions operating on BigComplexs.

Constructor Summary

Constructors

Constructor and Description
BigComplexMath()

Method Summary

Modifier and Type	Method and Description
static java.math.BigDecimal	abs(BigComplex x, java.math.MathContext mathContext) Calculates the absolute value (also known as magnitude, length or radius) of the given complex number using the specified MathContext.
static java.math.BigDecimal	absSquare(BigComplex x, java.math.MathContext mathContext) Calculates the square of the absolute value (also known as magnitude, length or radius) of the given complex number using the specified MathContext.
static BigComplex	acos(BigComplex x, java.math.MathContext mathContext) Calculates the arc cosine (inverted cosine) of BigComplex x in the complex domain.
static BigComplex	acot(BigComplex x, java.math.MathContext mathContext) Calculates the arc cotangens (inverted cotangens) of BigComplex x in the complex domain.
static java.math.BigDecimal	angle(BigComplex x, java.math.MathContext mathContext) Calculates the angle in radians of the given complex number using the specified MathContext.
static BigComplex	asin(BigComplex x, java.math.MathContext mathContext) Calculates the arc sine (inverted sine) of BigComplex x in the complex domain.
static BigComplex	atan(BigComplex x, java.math.MathContext mathContext) Calculates the arc tangens (inverted tangens) of BigComplex x in the complex domain.
static BigComplex	conjugate(BigComplex x) Calculates the conjugate of the given complex number using the specified MathContext.
static BigComplex	cos(BigComplex x, java.math.MathContext mathContext) Calculates the cosine (cosinus) of BigComplex x in the complex domain.
static BigComplex	exp(BigComplex x, java.math.MathContext mathContext) Calculates the natural exponent of BigComplex x (ex) in the complex domain.
static BigComplex	factorial(BigComplex x, java.math.MathContext mathContext) Calculates the factorial of the specified BigComplex.
static BigComplex	gamma(BigComplex x, java.math.MathContext mathContext) Calculates the gamma function of the specified BigComplex.
static BigComplex	log(BigComplex x, java.math.MathContext mathContext) Calculates the natural logarithm of BigComplex x in the complex domain.
static BigComplex	pow(BigComplex x, BigComplex y, java.math.MathContext mathContext) Calculates BigComplex x to the power of BigComplex y (xy).
static BigComplex	pow(BigComplex x, java.math.BigDecimal y, java.math.MathContext mathContext) Calculates BigComplex x to the power of BigDecimal y (xy).
static BigComplex	pow(BigComplex x, long y, java.math.MathContext mathContext) Calculates BigComplex x to the power of long y (xy).
static BigComplex	reciprocal(BigComplex x, java.math.MathContext mathContext) Calculates the reciprocal of the given complex number using the specified MathContext.
static BigComplex	root(BigComplex x, BigComplex n, java.math.MathContext mathContext) Calculates the BigComplex n'th root of BigComplex x (n√x).
static BigComplex	root(BigComplex x, java.math.BigDecimal n, java.math.MathContext mathContext) Calculates the BigDecimal n'th root of BigComplex x (n√x).
static BigComplex	sin(BigComplex x, java.math.MathContext mathContext) Calculates the sine (sinus) of BigComplex x in the complex domain.
static BigComplex	sqrt(BigComplex x, java.math.MathContext mathContext) Calculates the square root of BigComplex x in the complex domain (√x).
static BigComplex	tan(BigComplex x, java.math.MathContext mathContext) Calculates the tangens of BigComplex x in the complex domain.

Methods inherited from class java.lang.Object

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

Constructor Detail

BigComplexMath

public BigComplexMath()

Method Detail

reciprocal

public static BigComplex reciprocal(BigComplex x,
                                    java.math.MathContext mathContext)

Calculates the reciprocal of the given complex number using the specified MathContext.

Parameters:

x - the complex number to calculate the reciprocal

mathContext - the MathContext used to calculate the result

Returns:

the calculated BigComplex result

See Also:

BigComplex.reciprocal(MathContext)

conjugate

public static BigComplex conjugate(BigComplex x)

Calculates the conjugate of the given complex number using the specified MathContext.

Parameters:

x - the complex number to calculate the conjugate

Returns:

the calculated BigComplex result

See Also:

BigComplex.conjugate()

abs

public static java.math.BigDecimal abs(BigComplex x,
                                       java.math.MathContext mathContext)

Calculates the absolute value (also known as magnitude, length or radius) of the given complex number using the specified MathContext.

Parameters:

x - the complex number to calculate the absolute value

mathContext - the MathContext used to calculate the result

Returns:

the calculated BigComplex result

See Also:

BigComplex.abs(MathContext)

absSquare

public static java.math.BigDecimal absSquare(BigComplex x,
                                             java.math.MathContext mathContext)

Calculates the square of the absolute value (also known as magnitude, length or radius) of the given complex number using the specified MathContext.

Parameters:

x - the complex number to calculate the square of the absolute value

mathContext - the MathContext used to calculate the result

Returns:

the calculated BigComplex result

See Also:

BigComplex.absSquare(MathContext)

angle

public static java.math.BigDecimal angle(BigComplex x,
                                         java.math.MathContext mathContext)

Calculates the angle in radians of the given complex number using the specified MathContext.

Parameters:

x - the complex number to calculate the angle

mathContext - the MathContext used to calculate the result

Returns:

the calculated BigComplex angle in radians

See Also:

BigComplex.angle(MathContext)

factorial

public static BigComplex factorial(BigComplex x,
                                   java.math.MathContext mathContext)

Calculates the factorial of the specified BigComplex.

This implementation uses Spouge's approximation to calculate the factorial for non-integer values.

This involves calculating a series of constants that depend on the desired precision. Since this constant calculation is quite expensive (especially for higher precisions), the constants for a specific precision will be cached and subsequent calls to this method with the same precision will be much faster.

It is therefore recommended to do one call to this method with the standard precision of your application during the startup phase and to avoid calling it with many different precisions.

See: Wikipedia: Factorial - Extension of factorial to non-integer values of argument

Parameters:

x - the BigComplex

mathContext - the MathContext used for the result

Returns:

the factorial BigComplex

Throws:

java.lang.ArithmeticException - if x is a negative integer value (-1, -2, -3, ...)

See Also:

BigDecimalMath.factorial(BigDecimal, MathContext), gamma(BigComplex, MathContext)

gamma

public static BigComplex gamma(BigComplex x,
                               java.math.MathContext mathContext)

Calculates the gamma function of the specified BigComplex.

This implementation uses factorial(BigComplex, MathContext) internally, therefore the performance implications described there apply also for this method.

See: Wikipedia: Gamma function

Parameters:

x - the BigComplex

mathContext - the MathContext used for the result

Returns:

the gamma BigComplex

Throws:

java.lang.ArithmeticException - if x-1 is a negative integer value (-1, -2, -3, ...)

See Also:

BigDecimalMath.gamma(BigDecimal, MathContext), factorial(BigComplex, MathContext)

exp

public static BigComplex exp(BigComplex x,
                             java.math.MathContext mathContext)

Calculates the natural exponent of BigComplex x (e^x) in the complex domain.

See: Wikipedia: Exponent (Complex plane)

Parameters:

x - the BigComplex to calculate the exponent for

mathContext - the MathContext used for the result

Returns:

the calculated exponent BigComplex with the precision specified in the mathContext

sin

public static BigComplex sin(BigComplex x,
                             java.math.MathContext mathContext)

Calculates the sine (sinus) of BigComplex x in the complex domain.

See: Wikipedia: Sine (Sine with a complex argument)

Parameters:

x - the BigComplex to calculate the sine for

mathContext - the MathContext used for the result

Returns:

the calculated sine BigComplex with the precision specified in the mathContext

cos

public static BigComplex cos(BigComplex x,
                             java.math.MathContext mathContext)

Calculates the cosine (cosinus) of BigComplex x in the complex domain.

Parameters:

x - the BigComplex to calculate the cosine for

mathContext - the MathContext used for the result

Returns:

the calculated cosine BigComplex with the precision specified in the mathContext

tan

public static BigComplex tan(BigComplex x,
                             java.math.MathContext mathContext)

Calculates the tangens of BigComplex x in the complex domain.

Parameters:

x - the BigComplex to calculate the tangens for

mathContext - the MathContext used for the result

Returns:

the calculated tangens BigComplex with the precision specified in the mathContext

atan

public static BigComplex atan(BigComplex x,
                              java.math.MathContext mathContext)

Calculates the arc tangens (inverted tangens) of BigComplex x in the complex domain.

See: Wikipedia: Inverse trigonometric functions (Extension to complex plane)

Parameters:

x - the BigComplex to calculate the arc tangens for

mathContext - the MathContext used for the result

Returns:

the calculated arc tangens BigComplex with the precision specified in the mathContext

acot

public static BigComplex acot(BigComplex x,
                              java.math.MathContext mathContext)

Calculates the arc cotangens (inverted cotangens) of BigComplex x in the complex domain.

See: Wikipedia: Inverse trigonometric functions (Extension to complex plane)

Parameters:

x - the BigComplex to calculate the arc cotangens for

mathContext - the MathContext used for the result

Returns:

the calculated arc cotangens BigComplex with the precision specified in the mathContext

asin

public static BigComplex asin(BigComplex x,
                              java.math.MathContext mathContext)

Calculates the arc sine (inverted sine) of BigComplex x in the complex domain.

See: Wikipedia: Inverse trigonometric functions (Extension to complex plane)

Parameters:

x - the BigComplex to calculate the arc sine for

mathContext - the MathContext used for the result

Returns:

the calculated arc sine BigComplex with the precision specified in the mathContext

acos

public static BigComplex acos(BigComplex x,
                              java.math.MathContext mathContext)

Calculates the arc cosine (inverted cosine) of BigComplex x in the complex domain.

See: Wikipedia: Inverse trigonometric functions (Extension to complex plane)

Parameters:

x - the BigComplex to calculate the arc cosine for

mathContext - the MathContext used for the result

Returns:

the calculated arc cosine BigComplex with the precision specified in the mathContext

sqrt

public static BigComplex sqrt(BigComplex x,
                              java.math.MathContext mathContext)

Calculates the square root of BigComplex x in the complex domain (√x).

See Wikipedia: Square root (Square root of an imaginary number)

Parameters:

x - the BigComplex to calculate the square root for

mathContext - the MathContext used for the result

Returns:

the calculated square root BigComplex with the precision specified in the mathContext

log

public static BigComplex log(BigComplex x,
                             java.math.MathContext mathContext)

Calculates the natural logarithm of BigComplex x in the complex domain.

See: Wikipedia: Complex logarithm

Parameters:

x - the BigComplex to calculate the natural logarithm for

mathContext - the MathContext used for the result

Returns:

the calculated natural logarithm BigComplex with the precision specified in the mathContext

pow

public static BigComplex pow(BigComplex x,
                             long y,
                             java.math.MathContext mathContext)

Calculates BigComplex x to the power of long y (x^y).

The implementation tries to minimize the number of multiplications of x (using squares whenever possible).

See: Wikipedia: Exponentiation - efficient computation

Parameters:

x - the BigComplex value to take to the power

y - the long value to serve as exponent

mathContext - the MathContext used for the result

Returns:

the calculated x to the power of y with the precision specified in the mathContext

pow

public static BigComplex pow(BigComplex x,
                             java.math.BigDecimal y,
                             java.math.MathContext mathContext)

Calculates BigComplex x to the power of BigDecimal y (x^y).

Parameters:

x - the BigComplex value to take to the power

y - the BigDecimal value to serve as exponent

mathContext - the MathContext used for the result

Returns:

the calculated x to the power of y with the precision specified in the mathContext

pow

public static BigComplex pow(BigComplex x,
                             BigComplex y,
                             java.math.MathContext mathContext)

Calculates BigComplex x to the power of BigComplex y (x^y).

Parameters:

x - the BigComplex value to take to the power

y - the BigComplex value to serve as exponent

mathContext - the MathContext used for the result

Returns:

the calculated x to the power of y with the precision specified in the mathContext

root

public static BigComplex root(BigComplex x,
                              java.math.BigDecimal n,
                              java.math.MathContext mathContext)

Calculates the BigDecimal n'th root of BigComplex x (ⁿ√x).

See Wikipedia: Square root

Parameters:

x - the BigComplex value to calculate the n'th root

n - the BigDecimal defining the root

mathContext - the MathContext used for the result

Returns:

the calculated n'th root of x with the precision specified in the mathContext

root

public static BigComplex root(BigComplex x,
                              BigComplex n,
                              java.math.MathContext mathContext)

Calculates the BigComplex n'th root of BigComplex x (ⁿ√x).

See Wikipedia: Square root

Parameters:

x - the BigComplex value to calculate the n'th root

n - the BigComplex defining the root

mathContext - the MathContext used for the result

Returns:

the calculated n'th root of x with the precision specified in the mathContext