Package org.flag4j.complex_numbers

Class CNumber

java.lang.Object

java.lang.Number

org.flag4j.complex_numbers.CNumber

All Implemented Interfaces:

Serializable

public class CNumber
extends Number

A complex number stored in rectangular form with both the real and imaginary components stored as a 64-bit floats.

A CNumber is immutable.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final CNumber	E	The real double value closer to the mathematical constant e than any other.
final double	im	Imaginary component of the complex number.
static final CNumber	IMAGINARY_UNIT	The imaginary unit i.
static final CNumber	INV_IMAGINARY_UNIT	The additive inverse of the imaginary unit, -i.
static final CNumber	MAX_REAL	The maximum real double value 1.7976931348623157E308.
static final CNumber	MIN_REAL	The minimum real double value 4.9E-324
static final CNumber	MIN_REAL_NORMAL	The smallest possible real normal double 2.2250738585072014E-308.
static final CNumber	NaN	Complex number with real and imaginary parts equal to Double.NaN.
static final CNumber	NEGATIVE_INFINITY	Complex number with real part equal to Double.NEGATIVE_INFINITY.
static final CNumber	NEGATIVE_ONE	The complex number with zero imaginary part and negative one real part.
static final CNumber	ONE	The complex number with zero imaginary part and one real part.
static final CNumber	PI	The real double value closer to pi than any other.
static final CNumber	POSITIVE_INFINITY	Complex number with real part equal to Double.POSITIVE_INFINITY.
final double	re	Real component of the complex number.
static final CNumber	ROOT_THREE	The double value closer than any other to the square root of 3
static final CNumber	ROOT_TWO	The double value closer than any other to the square root of 2
static final CNumber	TWO	The complex number with zero imaginary part and two real part.
static final CNumber	ZERO	The complex number with zero imaginary and real parts.

Constructor Summary

Constructors

Constructor	Description
CNumber(double re)	Constructs a complex number with specified real component and zero imaginary component.
CNumber(double re, double im)	Constructs a complex number with specified complex and real components.
CNumber(String num)	Constructs a complex number from a string of the form "a +/- bi" where a and {b} are real values and either may be omitted.

Method Summary

Modifier and Type	Method	Description
double	abs()	Computes the absolute value / magnitude of a complex number.
static CNumber	acos(double num)	Computes the inverse cosine of a value.
static CNumber	acos(CNumber num)	Computes the inverse cosine of a complex value.
CNumber	add(double b)	Adds a double to a complex number.
CNumber	add(CNumber b)	Adds two complex numbers.
CNumber	addInv()	Computes the additive inverse of this complex number.
static double	arg(CNumber num)	Computes the complex argument function for a complex number.
static CNumber	argAsCNumber(CNumber num)	Computes the complex argument function for a complex number.
static int	argMax(CNumber... values)	Computes the index of the maximum magnitude from an array of complex numbers.
static int	argMaxReal(CNumber... values)	Computes the index of the minimum real component from an array of complex numbers.
static int	argMin(CNumber... values)	Computes the index of the minimum magnitude from an array of complex numbers.
static int	argMinReal(CNumber... values)	Computes the index of the minimum real component from an array of complex numbers.
static CNumber	asin(double num)	Computes the inverse sine of a value.
static CNumber	asin(CNumber num)	Computes the inverse sine of a complex value.
static CNumber	atan(double num)	Computes the inverse tangent of a value.
static CNumber	atan(CNumber num)	Computes the inverse tangent of a complex value.
static double	atan2(CNumber num)	Computes the 2 argument arc-tangent function for a complex number.
static CNumber	atan2AsCNumber(CNumber num)	Computes the 2 argument arc-tangent function for a complex number.
int	compareTo(CNumber b)	Compares the size of two complex numbers (magnitudes).
int	compareToReal(double b)	Compares the real value of two numbers.
int	compareToReal(CNumber b)	Compares the real value of two numbers.
CNumber	conj()	Computes the complex conjugate of this complex number.
static CNumber	cos(double num)	Computes the trigonometric cosine of a value.
static CNumber	cos(CNumber num)	Computes the trigonometric cosine value of a complex value.
static CNumber	cosh(double num)	Computes the hyperbolic cosine of a value.
static CNumber	cosh(CNumber num)	Computes the hyperbolic cosine of a complex value.
CNumber	div(double b)	Computes the division of a complex numbers with a double value.
CNumber	div(CNumber b)	Computes the division of two complex numbers.
double	doubleImaginaryValue()	Gets the double value of the imaginary component of this complex number.
double	doubleValue()	Gets the value of the specified number as a double.
boolean	equals(double b)	Checks if a complex number is numerically equal to some double value.
boolean	equals(Object b)	Checks if two complex numbers are equal.
boolean	equalsNumber(Number b)	Checks if a Number is numerically equal to this complex number.
static CNumber	exp(double exponent)	Computes the exponential function with the given input.
static CNumber	exp(CNumber exponent)	Computes the exponential function with the given input.
float	floatImaginaryValue()	Note: This method may result in loss of accuracy
float	floatValue()	Gets the value of the specified number as a float.
static CNumber	fromPolar(double r, double theta)	Converts a complex number expressed in polar from to the rectangular form.
int	hashCode()	Generates the hashcode for this CNumber.
double	im()	Gets the imaginary component of this complex number.
int	intImaginaryValue()	Note: This method may result in loss of accuracy
int	intValue()	Gets the value of the specified number as an int.
boolean	isComplex()	Checks if this complex number has non-zero imaginary part.
boolean	isDouble()	Checks if this complex number is a real valued double.
boolean	isFinite()	Checks that both components of this complex number are finite valued.
boolean	isImaginary()	Checks if this complex number has zero real part.
boolean	isInfinite()	Checks if either component of this complex number is infinitely large in absolute value.
boolean	isInt()	Checks if this complex number is a real valued integer.
boolean	isNaN()	Checks if either component of this complex number is NaN.
boolean	isReal()	Checks if this complex number has zero imaginary part.
static int	length(CNumber a)	Gets the length of the string representation of this complex number.
static CNumber	ln(double num)	Computes the natural logarithm of a double.
static CNumber	ln(CNumber num)	Computes the complex natural logarithm of a complex number.
static CNumber	log(double num)	Computes the complex logarithm base 10 of a complex number.
static CNumber	log(double base, double num)	Computes the complex logarithm, with specified base, of a complex number.
static CNumber	log(double base, CNumber num)	Computes the complex logarithm, with specified base, of a complex number.
static CNumber	log(CNumber num)	Computes the complex logarithm base 10 of a complex number.
static CNumber	log(CNumber base, CNumber num)	Computes the complex logarithm, with specified base, of a complex number.
long	longImaginaryValue()	Note: This method may result in loss of accuracy
long	longValue()	Gets the value of the specified number as a long.
double	mag()	Computes the magnitude value of a complex number as a double.
double	magSquared()	Squares this magnitude of this complex number.
static CNumber	max(CNumber... values)	Computes the maximum magnitude from an array of complex numbers.
static CNumber	maxRe(CNumber... values)	Computes the minimum real component from an array of complex numbers.
static CNumber	min(CNumber... values)	Computes the minimum magnitude from an array of complex numbers.
static CNumber	minRe(CNumber... values)	Computes the minimum real component from an array of complex numbers.
CNumber	mult(double b)	Computes the multiplication of a complex number and a double.
CNumber	mult(CNumber b)	Computes the multiplication of two complex numbers.
CNumber	multInv()	Computes the multiplicative inverse of this complex number.
static boolean	nearZero(CNumber n, double tol)	Checks if a number is near zero in magnitude.
static CNumber	pow(double a, double b)	Compute a raised to the power of b.
static CNumber	pow(double a, CNumber b)	Compute a raised to the power of b.
static CNumber	pow(CNumber a, double b)	Computes a raised to the power of b.
static CNumber	pow(CNumber a, CNumber b)	Compute a raised to the power of b.
double	re()	Gets the real component of this complex number.
static CNumber	round(CNumber n)	Rounds both components of a complex number to the nearest respective integer.
static CNumber	round(CNumber n, int decimals)	Rounds number to specified number of decimal places.
static CNumber	roundToZero(CNumber n, double tol)	Rounds a complex numbers to zero if its magnitude within the specified tolerance from zero.
static CNumber	sgn(CNumber value)	The complex signum function.
static CNumber	sin(double num)	Computes the trigonometric sine of a value.
static CNumber	sin(CNumber num)	Computes the trigonometric sine of a complex value.
static CNumber	sinh(double num)	Computes the hyperbolic sine of a value.
static CNumber	sinh(CNumber num)	Computes the hyperbolic sine of a complex value.
static CNumber	sqrt(double num)	Computes the principle square root of a number.
static CNumber	sqrt(CNumber num)	Computes the principle square root of a number.
CNumber	sub(double b)	subtracts a double from a complex number.
CNumber	sub(CNumber b)	Subtracting two complex numbers.
static CNumber	sum(CNumber... numbers)	Sums an array of complex numbers.
static CNumber	tan(double num)	Computes the trigonometric tangent of a value.
static CNumber	tan(CNumber num)	Computes the trigonometric tangent value of a complex value.
static CNumber	tanh(double num)	Computes the hyperbolic tangent of a value.
static CNumber	tanh(CNumber num)	Computes the hyperbolic tangent of a complex value.
double[]	toPolar()	Converts a complex number to an equivalent polar from.
String	toString()	Converts the complex number to a string representation.

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Details

ZERO

public static final CNumber ZERO

The complex number with zero imaginary and real parts.

ONE

public static final CNumber ONE

The complex number with zero imaginary part and one real part.

TWO

public static final CNumber TWO

The complex number with zero imaginary part and two real part.

NEGATIVE_ONE

public static final CNumber NEGATIVE_ONE

The complex number with zero imaginary part and negative one real part.

PI

public static final CNumber PI

The real double value closer to pi than any other.

E

public static final CNumber E

The real double value closer to the mathematical constant e than any other.

ROOT_TWO

public static final CNumber ROOT_TWO

The double value closer than any other to the square root of 2

ROOT_THREE

public static final CNumber ROOT_THREE

The double value closer than any other to the square root of 3

IMAGINARY_UNIT

public static final CNumber IMAGINARY_UNIT

The imaginary unit i.

INV_IMAGINARY_UNIT

public static final CNumber INV_IMAGINARY_UNIT

The additive inverse of the imaginary unit, -i.

MAX_REAL

public static final CNumber MAX_REAL

The maximum real double value 1.7976931348623157E308.

MIN_REAL

public static final CNumber MIN_REAL

The minimum real double value 4.9E-324

MIN_REAL_NORMAL

public static final CNumber MIN_REAL_NORMAL

The smallest possible real normal double 2.2250738585072014E-308.

POSITIVE_INFINITY

public static final CNumber POSITIVE_INFINITY

Complex number with real part equal to Double.POSITIVE_INFINITY.

NEGATIVE_INFINITY

public static final CNumber NEGATIVE_INFINITY

Complex number with real part equal to Double.NEGATIVE_INFINITY.

NaN

public static final CNumber NaN

Complex number with real and imaginary parts equal to Double.NaN.

re

public final double re

Real component of the complex number.

im

public final double im

Imaginary component of the complex number.

Constructor Details

CNumber

public CNumber(double re)

Constructs a complex number with specified real component and zero imaginary component.

Parameters:

re - Real component of complex number.

CNumber

public CNumber(double re,
 double im)

Constructs a complex number with specified complex and real components.

Parameters:

re - Real component of complex number.

im - Imaginary component of complex number.

CNumber

public CNumber(String num)

Constructs a complex number from a string of the form "a +/- bi" where a and {b} are real values and either may be omitted. i.e. "a", "bi", "a +/- i", and "i" are all also valid.

Parameters:

num - The string representation of a complex number.

Method Details

equals

public boolean equals(Object b)

Checks if two complex numbers are equal. That is, if both numbers have equivalent real and complex parts.

Overrides:

equals in class Object

Parameters:

b - The object to compare.

Returns:

True if b has real and imaginary components equal to that of this

equalsNumber

public boolean equalsNumber(Number b)

Checks if a Number is numerically equal to this complex number.

Parameters:

b - Number to compare to this complex number.

Returns:

True if this complex number has zero imaginary component and the real component is equal to b.doubleValue().

equals

public boolean equals(double b)

Checks if a complex number is numerically equal to some double value. That is, if the real component of this complex number is zero and the real component is equivalent to the double parameter.

Parameters:

b - The double to compare.

Returns:

True if b is a complex number and is equivalent to this complex number in both the real and imaginary components. False, otherwise.

hashCode

public int hashCode()

Generates the hashcode for this CNumber.

Overrides:

hashCode in class Object

Returns:

An integer hash for this CNumber.

intValue

public int intValue()

Gets the value of the specified number as an int. This will be calculated only with the real component of this CNumber.

Specified by:

intValue in class Number

Returns:

the numeric value represented by this object after conversion to type int.

longValue

public long longValue()

Gets the value of the specified number as a long. This will be calculated only with the real component of this CNumber.

Specified by:

longValue in class Number

Returns:

the numeric value represented by this object after conversion to type long.

floatValue

public float floatValue()

Gets the value of the specified number as a float. This will be calculated only with the real component of this CNumber.

Specified by:

floatValue in class Number

Returns:

the numeric value represented by this object after conversion to type float.

doubleValue

public double doubleValue()

Gets the value of the specified number as a double. This will be calculated only with the real component of this CNumber.

Specified by:

doubleValue in class Number

Returns:

the numeric value represented by this object after conversion to type double.

doubleImaginaryValue

public double doubleImaginaryValue()

Gets the double value of the imaginary component of this complex number.

Returns:

imaginary part of given Number as double

floatImaginaryValue

public float floatImaginaryValue()

Note: This method may result in loss of accuracy

Returns:

imaginary part of given Number as float

intImaginaryValue

public int intImaginaryValue()

Note: This method may result in loss of accuracy

Returns:

imaginary part of given Number as int

longImaginaryValue

public long longImaginaryValue()

Note: This method may result in loss of accuracy

Returns:

imaginary part of given Number as long

add

public CNumber add(CNumber b)

Adds two complex numbers.

Parameters:

b - The number to add to this complex number.

Returns:

The result of adding this complex number with b.

add

public CNumber add(double b)

Adds a double to a complex number.

Parameters:

b - The double value to add to this complex number.

Returns:

The result of adding b to this complex number.

sub

public CNumber sub(CNumber b)

Subtracting two complex numbers.

Parameters:

b - The number to subtract from complex number.

Returns:

The result of subtracting b from this complex number.

sub

public CNumber sub(double b)

subtracts a double from a complex number.

Parameters:

b - The double value to subtract from this complex number.

Returns:

The result of subtracting b from this complex number.

sum

public static CNumber sum(CNumber... numbers)

Sums an array of complex numbers.

Parameters:

numbers - Numbers to sum.

Returns:

The sum of all values in numbers.

mult

public CNumber mult(CNumber b)

Computes the multiplication of two complex numbers.

Parameters:

b - Second complex number in the product.

Returns:

Product of this complex number with b.

mult

public CNumber mult(double b)

Computes the multiplication of a complex number and a double.

Parameters:

b - Second complex number in the product.

Returns:

Product of this complex number with b.

div

public CNumber div(CNumber b)

Computes the division of two complex numbers.

Parameters:

b - The divisor for the complex division.

Returns:

The quotient of this complex number with b. If b is equivalent to ZERO then NaN is returned.

div

public CNumber div(double b)

Computes the division of a complex numbers with a double value.

Parameters:

b - The divisor for the complex division.

Returns:

The quotient of this complex number with b. If b is zero then NaN is returned.

abs

public double abs()

Computes the absolute value / magnitude of a complex number.
Note: This method is the same as mag().

Returns:

The absolute value/magnitude of this complex number.

mag

public double mag()

Computes the magnitude value of a complex number as a double.

Returns:

The absolute value/magnitude of this complex number as a double.

addInv

public CNumber addInv()

Computes the additive inverse of this complex number.

Returns:

The additive inverse of this complex number.

multInv

public CNumber multInv()

Computes the multiplicative inverse of this complex number.

Returns:

The multiplicative inverse of this complex number.

conj

public CNumber conj()

Computes the complex conjugate of this complex number.

Returns:

The complex conjugate of this complex number.

pow

public static CNumber pow(double a,
 double b)

Compute a raised to the power of b. This method wraps Math.pow(double, double) and returns a CNumber.

Parameters:

a - The base.

b - The exponent.

Returns:

a raised to the power of b.

pow

public static CNumber pow(double a,
 CNumber b)

Compute a raised to the power of b. and returns a CNumber.

Parameters:

a - The base.

b - The exponent.

Returns:

a to the power of b.

pow

public static CNumber pow(CNumber a,
 CNumber b)

Compute a raised to the power of b. and returns a CNumber.

Parameters:

a - The base.

b - The exponent.

Returns:

a to the power of b.

pow

public static CNumber pow(CNumber a,
 double b)

Computes a raised to the power of b.

Parameters:

a - The base.

b - The exponent.

Returns:

a raised to the power of b.

magSquared

public double magSquared()

Squares this magnitude of this complex number.

Returns:

The square of the magnitude of this complex number as a real value.

exp

public static CNumber exp(double exponent)

Computes the exponential function with the given input. This method simply wraps the Math.exp(double) method and returns a CNumber.

Parameters:

exponent - Input to the exponential function.

Returns:

The output of the exponential function.

exp

public static CNumber exp(CNumber exponent)

Computes the exponential function with the given input.

Parameters:

exponent - Input to the exponential function.

Returns:

The output of the exponential function.

ln

public static CNumber ln(double num)

Computes the natural logarithm of a double. For non-negative values this function is equivalent to Math.log(double). If the number is negative, then it is passed on as a complex value to ln(CNumber).

Parameters:

num - Input to the complex natural logarithm function.

Returns:

The principle value of the complex natural logarithm for the given input.

ln

public static CNumber ln(CNumber num)

Computes the complex natural logarithm of a complex number. This function is the analytic continuation of the natural logarithm, that is the log base e.

Parameters:

num - Input to the complex natural logarithm function.

Returns:

The principle value of the complex natural logarithm for the given input.

log

public static CNumber log(double num)

Computes the complex logarithm base 10 of a complex number. Please note, this is NOT the natural logarithm. If the complex natural logarithm is desired see ln(double). To specify a base, see log(double, CNumber) or log(CNumber, CNumber). If the argument is non-negative, then this function is equivalent to Math.log(double).

Parameters:

num - Input to the complex logarithm base 10 function.

Returns:

The principle value of the complex logarithm base 10 for the given input.

log

public static CNumber log(CNumber num)

Computes the complex logarithm base 10 of a complex number. Please note, this is NOT the complex natural logarithm. If the complex natural logarithm is desired see ln(CNumber). To specify a base, see log(double, CNumber) or log(CNumber, CNumber).

Parameters:

num - Input to the complex logarithm base 10 function.

Returns:

The principle value of the complex logarithm base 10 for the given input.

log

public static CNumber log(double base,
 double num)

Computes the complex logarithm, with specified base, of a complex number.

Parameters:

base - Base of the logarithm.

num - Input to the complex logarithm function with specified base.

Returns:

The principle value of the complex logarithm, with specified base, for the given input.

log

public static CNumber log(double base,
 CNumber num)

Computes the complex logarithm, with specified base, of a complex number.

Parameters:

base - Base of the logarithm.

num - Input to the complex logarithm function with specified base.

Returns:

The principle value of the complex logarithm, with specified base, for the given input.

log

public static CNumber log(CNumber base,
 CNumber num)

Computes the complex logarithm, with specified base, of a complex number.

Parameters:

base - Base of the logarithm.

num - Input to the complex logarithm function with specified base.

Returns:

The principle value of the complex logarithm, with specified base, for the given input.

sqrt

public static CNumber sqrt(double num)

Computes the principle square root of a number. This method wraps Math.sqrt(double) and returns a CNumber.

Parameters:

num - Input to square root.

Returns:

The principle square root of num.

sqrt

public static CNumber sqrt(CNumber num)

Computes the principle square root of a number.

Parameters:

num - Input to square root.

Returns:

The principle square root of num. That is, the square root of num with positive real part.

sgn

public static CNumber sgn(CNumber value)

The complex signum function. Please note, if the value passed to this method is zero, the function will return zero.

Parameters:

value - Value to evaluate the signum function at.

Returns:

If the number is zero then this function returns zero. Otherwise, returns the number divided by its magnitude.

toPolar

public double[] toPolar()

Converts a complex number to an equivalent polar from.

Returns:

An array of length 2 containing in order, the radius and angle (in radians) if the complex number.

fromPolar

public static CNumber fromPolar(double r,
 double theta)

Converts a complex number expressed in polar from to the rectangular form.

Parameters:

r - Radius of complex number.

theta - Angle of the complex number in radians.

Returns:

An equivalent complex number in rectangular form.

atan2

public static double atan2(CNumber num)

Computes the 2 argument arc-tangent function for a complex number. That is, for a complex number a+bi, atan2(b, a) is computed. This method wraps Math.atan2(double, double).
To get the result as an CNumber see atan2AsCNumber(CNumber).

Parameters:

num - The input to the atan2 function.

Returns:

The output of the atan2 function given the specified input. If the complex number is zero, then Double.NaN is returned.

arg

public static double arg(CNumber num)

Computes the complex argument function for a complex number. is computed. This method is equivalent to atan2(CNumber).
To get the result as an CNumber see argAsCNumber(CNumber).

Parameters:

num - The input to the atan2 function.

Returns:

The output of the atan2 function given the specified input. If the complex number is zero, then Double.NaN is returned.

argAsCNumber

public static CNumber argAsCNumber(CNumber num)

Computes the complex argument function for a complex number. is computed. This method wraps is equivalent to CNumber.
To get the result as a double see arg(CNumber).

Parameters:

num - The input to the atan2 function.

Returns:

The output of the atan2 function given the specified input. If the complex number is zero, then Double.NaN is returned.

atan2AsCNumber

public static CNumber atan2AsCNumber(CNumber num)

Computes the 2 argument arc-tangent function for a complex number. That is, for a complex number a+bi, atan2(b, a) is computed. This method wraps Math.atan2(double, double).
To get the result as a double see atan2(CNumber).

Parameters:

num - The input to the atan2 function.

Returns:

The output of the atan2 function given the specified input. If the complex number is zero, then Double.NaN is returned.

sin

public static CNumber sin(double num)

Computes the trigonometric sine of a value.
Note, this method wraps Math.sin(double) and returns a CNumber.

Parameters:

num - Input angle in radians.

Returns:

The trigonometric sine function evaluated at the specified value.

sin

public static CNumber sin(CNumber num)

Computes the trigonometric sine of a complex value.

Parameters:

num - Complex valued input to the sine function. If num is real, then this is an angle in radians.

Returns:

The trigonometric sine function evaluated at the specified value.

asin

public static CNumber asin(double num)

Computes the inverse sine of a value.
Note, this method wraps Math.asin(double) and returns CNumber.

Parameters:

num - Input to the inverse sine function.

Returns:

The inverse sine of the input value. That is, the angle whose sine value is num.

asin

public static CNumber asin(CNumber num)

Computes the inverse sine of a complex value.

Parameters:

num - Input to the inverse sine function.

Returns:

The inverse sine of the input value.

sinh

public static CNumber sinh(double num)

Computes the hyperbolic sine of a value.
Note, this method wraps Math.sinh(double) and returns a CNumber.

Parameters:

num - Input to the hyperbolic sine function.

Returns:

The hyperbolic sine of the input value.

sinh

public static CNumber sinh(CNumber num)

Computes the hyperbolic sine of a complex value.

Parameters:

num - Input to the hyperbolic sine function.

Returns:

The hyperbolic sine of the input value.

cos

public static CNumber cos(double num)

Computes the trigonometric cosine of a value.
Note, this method wraps Math.cos(double) and returns a CNumber.

Parameters:

num - Input angle in radians.

Returns:

The trigonometric cosine function evaluated at the specified value.

cos

public static CNumber cos(CNumber num)

Computes the trigonometric cosine value of a complex value.

Parameters:

num - Complex valued input to the cosine function. If num is real, then this is an angle in radians.

Returns:

The trigonometric cosine function evaluated at the specified value.

acos

public static CNumber acos(double num)

Computes the inverse cosine of a value.
Note, this method wraps Math.acos(double) and returns CNumber.

Parameters:

num - Input to the inverse cosine function.

Returns:

The inverse cosine of the input value. That is, the angle whose cosine value is num.

acos

public static CNumber acos(CNumber num)

Computes the inverse cosine of a complex value.

Parameters:

num - Input to the inverse cosine function.

Returns:

The inverse cosine of the input value.

cosh

public static CNumber cosh(double num)

Computes the hyperbolic cosine of a value.
Note, this method wraps Math.cosh(double) and returns a CNumber.

Parameters:

num - Input to the hyperbolic cosine function.

Returns:

The hyperbolic cosine of the input value.

cosh

public static CNumber cosh(CNumber num)

Computes the hyperbolic cosine of a complex value.

Parameters:

num - Input to the hyperbolic cosine function.

Returns:

The hyperbolic cosine of the input value.

tan

public static CNumber tan(double num)

Computes the trigonometric tangent of a value.
Note, this method wraps Math.tan(double) and returns a CNumber.

Parameters:

num - Input angle in radians.

Returns:

The trigonometric tangent function evaluated at the specified value.

tan

public static CNumber tan(CNumber num)

Computes the trigonometric tangent value of a complex value.

Parameters:

num - Complex valued input to the tangent function. If num is real, then this is an angle in radians.

Returns:

The trigonometric tangent function evaluated at the specified value.

atan

public static CNumber atan(double num)

Computes the inverse tangent of a value.
Note, this method wraps Math.atan(double) and returns CNumber.

Parameters:

num - Input to the inverse tangent function.

Returns:

The inverse tangent of the input value. That is, the angle whose tangent value is num.

atan

public static CNumber atan(CNumber num)

Computes the inverse tangent of a complex value.

Parameters:

num - Input to the inverse tangent function.

Returns:

The inverse tangent of the input value.

tanh

public static CNumber tanh(double num)

Computes the hyperbolic tangent of a value.
Note, this method wraps Math.tanh(double) and returns a CNumber.

Parameters:

num - Input to the hyperbolic tangent function.

Returns:

The hyperbolic tangent of the input value.

tanh

public static CNumber tanh(CNumber num)

Computes the hyperbolic tangent of a complex value.

Parameters:

num - Input to the hyperbolic tangent function.

Returns:

The hyperbolic tangent of the input value.

isReal

public boolean isReal()

Checks if this complex number has zero imaginary part.

Returns:

True if this complex number has zero imaginary part. False otherwise.

See Also:

• isComplex()
• isImaginary()

isImaginary

public boolean isImaginary()

Checks if this complex number has zero real part.

Returns:

True if this complex number has zero real part. False otherwise.

See Also:

• isComplex()
• isReal()

isComplex

public boolean isComplex()

Checks if this complex number has non-zero imaginary part.

Returns:

True if this complex number has non-zero imaginary part. False otherwise.

See Also:

• isReal()
• isImaginary()

round

public static CNumber round(CNumber n)

Rounds both components of a complex number to the nearest respective integer.

Parameters:

n - The complex number to round.

Returns:

A complex number with integer real and imaginary components closest to the real and imaginary components of the parameter n

Throws:

NumberFormatException - If n is Double.NaN, Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY

See Also:

• round(CNumber, int)

round

public static CNumber round(CNumber n,
 int decimals)

Rounds number to specified number of decimal places. If the number is complex, both the real and imaginary parts will be rounded.

Parameters:

n - Number to round.

decimals - Number of decimals to round to.

Returns:

The number n rounded to the specified number of decimals.

Throws:

IllegalArgumentException - If decimals is less than zero.

NumberFormatException - If n is Double.NaN, Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY

See Also:

• round(CNumber)

roundToZero

public static CNumber roundToZero(CNumber n,
 double tol)

Rounds a complex numbers to zero if its magnitude within the specified tolerance from zero.

Parameters:

n - Number to round.

tol - Max distances in complex plane for which number should be rounded to zero.

Returns:

The

nearZero

public static boolean nearZero(CNumber n,
 double tol)

Checks if a number is near zero in magnitude.

Parameters:

n - Number to round.

tol - Tolerance of how close to zero is considered "near".

Returns:

Returns true if magnitude of number is less than or equal to tol. Otherwise, returns false.

Throws:

IllegalArgumentException - If tol is less than 0.

compareTo

public int compareTo(CNumber b)

Compares the size of two complex numbers (magnitudes).

Parameters:

b - Number to compare to this number.

Returns:

- If the magnitude of this number is equal to that of b, then this method will return 0.
- If the magnitude of this number is less than that of b, then this method will return a negative number.
- If the magnitude of this number is greater than that of b, then this method will return a positive number.

compareToReal

public int compareToReal(CNumber b)

Compares the real value of two numbers.

Parameters:

b - Number to compare to this number.

Returns:

- If the real value of this number is equal to that of b, then this method will return 0.
- If the real value of this number is less than that of b, then this method will return a negative number.
- If the real value of this number is greater than that of b, then this method will return a positive number.

compareToReal

public int compareToReal(double b)

Compares the real value of two numbers. This method wraps Double.compareTo(Double) which is computed with the real component of this complex number.

Parameters:

b - Number to compare to this number.

Returns:

- If the real value of this number is equal to that of b, then this method will return 0.
- If the real value of this number is less than that of b, then this method will return a negative number.
- If the real value of this number is greater than that of b, then this method will return a positive number.

min

public static CNumber min(CNumber... values)

Computes the minimum magnitude from an array of complex numbers.

Parameters:

values - Array of values to compute the minimum magnitude from.

Returns:

The minimum magnitude from the values array. If the array has zero length, then -1 is returned.

minRe

public static CNumber minRe(CNumber... values)

Computes the minimum real component from an array of complex numbers. All imaginary components are ignored.

Parameters:

values - Array of values to compute the minimum real component from.

Returns:

The minimum magnitude from the values array. If the array has zero length, Double.NaN is returned.

max

public static CNumber max(CNumber... values)

Computes the maximum magnitude from an array of complex numbers.

Parameters:

values - Array of values to compute the maximum magnitude from.

Returns:

The minimum magnitude from the values array. If the array has zero length, then -1 is returned.

maxRe

public static CNumber maxRe(CNumber... values)

Computes the minimum real component from an array of complex numbers. All imaginary components are ignored.

Parameters:

values - Array of values to compute the minimum real component from.

Returns:

The minimum magnitude from the values array. If the array has zero length, Double.NaN is returned.

argMin

public static int argMin(CNumber... values)

Computes the index of the minimum magnitude from an array of complex numbers.

Parameters:

values - Array of values to compute the index of the minimum magnitude from.

Returns:

The index of the minimum magnitude from the values array. If the array has zero length, then -1 is returned.

argMinReal

public static int argMinReal(CNumber... values)

Computes the index of the minimum real component from an array of complex numbers. All imaginary components are ignored.

Parameters:

values - Array of values to compute the index of the minimum real component from.

Returns:

The index of the minimum magnitude from the values array. If the array has zero length, -1 is returned.

argMax

public static int argMax(CNumber... values)

Computes the index of the maximum magnitude from an array of complex numbers.

Parameters:

values - Array of values to compute the index of the maximum magnitude from.

Returns:

The index of the minimum magnitude from the values array. If the array has zero length, then -1 is returned.

argMaxReal

public static int argMaxReal(CNumber... values)

Computes the index of the minimum real component from an array of complex numbers. All imaginary components are ignored.

Parameters:

values - Array of values to compute the index of the minimum real component from.

Returns:

The index of the minimum magnitude from the values array. If the array has zero length, -1 is returned.

isInt

public boolean isInt()

Checks if this complex number is a real valued integer.

Returns:

True if the real component of this number is an integer and the complex component is zero. Otherwise, returns false.

isDouble

public boolean isDouble()

Checks if this complex number is a real valued double.

Returns:

True if the complex component is zero. Otherwise, returns false.

isNaN

public boolean isNaN()

Checks if either component of this complex number is NaN.

Returns:

True if either component is NaN. Otherwise, returns false.

isFinite

public boolean isFinite()

Checks that both components of this complex number are finite valued.

Returns:

True if both components are finite. Otherwise, returns false (including NaN).

isInfinite

public boolean isInfinite()

Checks if either component of this complex number is infinitely large in absolute value.

Returns:

True if either components are infinite. Otherwise, returns false.

re

public double re()

Gets the real component of this complex number.

Returns:

The real component of this complex number.

im

public double im()

Gets the imaginary component of this complex number.

Returns:

The imaginary component of this complex number.

length

public static int length(CNumber a)

Gets the length of the string representation of this complex number.

Parameters:

a - Complex number.

Returns:

The length of the string representation of the number.

toString

public String toString()

Converts the complex number to a string representation.

Overrides:

toString in class Object

Returns:

A string representation of the complex number.