Package linalg.complex_number

Class CNumber

java.lang.Object

linalg.complex_number.CNumber

public class CNumber
extends Object

This class allows for the creation of complex and real numbers and provides methods for computation with those numbers.

Field Summary

Fields

Modifier and Type	Field	Description
static CNumber	E	The double value closer than any other to Euler's Constant e = 2.71828...
double	im	re is real portion of complex number.
static CNumber	IMAGINARY_UNIT	The imaginary unit Defined as i^2=-1 => i=(-1)^(1/2).
static CNumber	MAX_VALUE	A real number holding the largest positive finite value of type double, (2-2^(-52))^21023
static CNumber	MIN_VALUE	A real number holding the smallest possible double value, 2^(-1074)
static CNumber	NEGATIVE_ONE	The number -1.
static CNumber	ONE	The number 1.
static CNumber	PI	The double value closer than any other to the mathmatical constant pi = 3.14159...
double	re	re is real portion of complex number.
static CNumber	ZERO	The number 0.

Constructor Summary

Constructors

Constructor	Description
CNumber()
CNumber(double real)
CNumber(double real, double imaginary)
CNumber(String num)
CNumber(CNumber n)

Method Summary

Modifier and Type	Method	Description
static CNumber	abs(CNumber value)	Computes absolute value of a number.
static CNumber	add(CNumber a, CNumber b)	Performs complex addition of two numbers.
static CNumber	add(CNumber a, CNumber b, CNumber... values)	Performs complex addition of two or more numbers.
static CNumber	addInv(CNumber value)	Computes the additive inverse of a Number.
static CNumber[]	allSqrt(CNumber value)	Computes all possible square roots of a 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.
static CNumber	conjugate(CNumber a)	Computes and returns complex conjugate of a complex number.
static CNumber	divide(CNumber a, CNumber b)	Performs complex division of two numbers.
double	doubleImaginaryValue()
double	doubleValue()
boolean	equals(double b)	Checks for equivalence between two complex numbers Also see equals(Object)
boolean	equals(Object b)	Checks for equivalence between two complex numbers
static CNumber	exp(double x)
static CNumber	exp(CNumber x)
float	floatImaginaryValue()	Note: This method may result in loss of accuracy
float	floatValue()	Note: This method may result in loss of accuracy
double	getImaginary()
double	getReal()
int	intImaginaryValue()	Note: This method may result in loss of accuracy
int	intValue()	Note: This method may result in loss of accuracy
static CNumber	inv(CNumber value)	Computes the multiplicative inverse of a Number.
boolean	isComplex()	Checks if given number has non-zero imaginary part.
boolean	isImaginary()	Checks if given number has no real part.
boolean	isInt()	Checks if a give number is a real integer.
boolean	isReal()	Checks if given number has no imaginary part.
static int	length(CNumber a)
long	longImaginaryValue()	Note: This method may result in loss of accuracy
long	longValue()	Note: This method may result in loss of accuracy
double	mag()	Computes the magnitude of a complex number (The numbers distance from the origin in the complex plane).
static CNumber	max(CNumber... values)	Computes value with greatest magnitude amongst all passed values.
static CNumber	min(CNumber... values)	Computes value with smallest magnitude amongst all passed values.
static CNumber	multiply(CNumber a, CNumber b)	Performs complex multiplication of two numbers.
boolean	nearZero(double tol)	Checks if a number is near zero.
static CNumber	pow(CNumber base, int exponenent)	Performs complex exponentiation of two numbers.
static CNumber	pow(CNumber base, CNumber exponent)	Performs complex exponentiation of two numbers.
static CNumber	randn()	Generates a random real a where a is a normaly distributed psedorandom number with a mean of zero and standard deviation of one.
static CNumber	randn(boolean complex)	Generates a random real or complex number a, or a+bi where a and b are normaly distributed psedorandom numbers with a mean of zero and standard deviation of one.
static CNumber	random()	Generates a random real number.
static CNumber	random(double mag)	Generates a random complex number with given magnitude.
static CNumber	random(double min, double max, boolean... magnitude_flag)	Generates a random number between min and max.
static CNumber	round(CNumber n, int decimals)	Rounds number to specified number of decimal places.
static CNumber	sign(CNumber value)	The complex signum function.
static CNumber	sqrt(CNumber value)	Computes the square root of a number. Note: This method only returns the principle square root (the positive square root or square root with positive real part).
static CNumber	subtract(CNumber a, CNumber b)	Performs complex subtraction of two numbers.
String	toString()

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Details

re

public double re

re is real portion of complex number. im is imaginary portion of complex number.

im

public double im

re is real portion of complex number. im is imaginary portion of complex number.

ONE

public static final CNumber ONE

The number 1.

NEGATIVE_ONE

public static final CNumber NEGATIVE_ONE

The number -1.

ZERO

public static final CNumber ZERO

The number 0.

IMAGINARY_UNIT

public static final CNumber IMAGINARY_UNIT

The imaginary unit Defined as i^2=-1 => i=(-1)^(1/2).

PI

public static final CNumber PI

The double value closer than any other to the mathmatical constant pi = 3.14159...

E

public static final CNumber E

The double value closer than any other to Euler's Constant e = 2.71828...

MAX_VALUE

public static final CNumber MAX_VALUE

A real number holding the largest positive finite value of type double, (2-2^(-52))^21023

MIN_VALUE

public static final CNumber MIN_VALUE

A real number holding the smallest possible double value, 2^(-1074)

Constructor Details

CNumber

public CNumber()

CNumber

public CNumber(double real)

CNumber

public CNumber(double real,
 double imaginary)

CNumber

public CNumber(String num)

CNumber

public CNumber(CNumber n)

Method Details

randn

public static CNumber randn(boolean complex)

Generates a random real or complex number a, or a+bi where a and b are normaly distributed psedorandom numbers with a mean of zero and standard deviation of one.

Parameters:

complex - - selects if a real or complex number should be selected..

Returns:

If complex false, a random real number is returned. If complex true, a random real and imaginary component are chosen and a complex number is returned.

randn

public static CNumber randn()

Generates a random real a where a is a normaly distributed psedorandom number with a mean of zero and standard deviation of one.

Returns:

A random real number from a standard normal distribution.

random

public static CNumber random()

Generates a random real number.

Returns:

random real number

random

public static CNumber random(double mag)

Generates a random complex number with given magnitude. Note: the magnitude must be a non-negative real number.

Parameters:

mag - - magnitude

Returns:

random complex number with specified magnitude.

random

public static CNumber random(double min,
 double max,
 boolean... magnitude_flag)

Generates a random number between min and max. If magnitude_flag is passed a true, then a random complex number with magnitude between min and max (where min and max are non-negative values) is generated. If magnitude_flag is passed a false, then a random real value between min and max is generated. If no magnitude_flag is passed, then it is treated as false.

Parameters:

min - - minimum value for random number

max - - maximum value for random number

magnitude_flag - - optional flag to indicate if the Number should be real or complex.

Returns:

random real or complex number between min and max.

conjugate

public static CNumber conjugate(CNumber a)

Computes and returns complex conjugate of a complex number. For example the complex conjugate of a+bi is a-bi.

Parameters:

a - - complex number

Returns:

complex conjugate of a

add

public static CNumber add(CNumber a,
 CNumber b)

Performs complex addition of two numbers.

Parameters:

a - - complex number

b - - complex number

Returns:

sum of a and b. e.g. a+b

add

public static CNumber add(CNumber a,
 CNumber b,
 CNumber... values)

Performs complex addition of two or more numbers.

Parameters:

a - - complex number

b - - complex number

values - - Optional list of additional values to sum

Returns:

Sum of complex numbers.

subtract

public static CNumber subtract(CNumber a,
 CNumber b)

Performs complex subtraction of two numbers.

Parameters:

a - - complex number

b - - complex number

Returns:

difference of a and b. e.g. a-b

multiply

public static CNumber multiply(CNumber a,
 CNumber b)

Performs complex multiplication of two numbers.

Parameters:

a - - complex number

b - - complex number

Returns:

product of a and b. e.g. a*b

divide

public static CNumber divide(CNumber a,
 CNumber b)

Performs complex division of two numbers.

Parameters:

a - - complex number

b - - complex number

Returns:

Quotient of a and b. e.g. a/b

abs

public static CNumber abs(CNumber value)

Computes absolute value of a number. Note: this will Always result in a non-negative real number.
This method is the same as mag()

Parameters:

value - - value to take absolute value of.

Returns:

The absolute value of the number.

inv

public static CNumber inv(CNumber value)

Computes the multiplicative inverse of a Number. For example, given a number n, the inverse is 1/n. This is equivalent to Number.divide(Number.ONE, value);

Parameters:

value - - Number to take inverse of

Returns:

- Inverse of value

addInv

public static CNumber addInv(CNumber value)

Computes the additive inverse of a Number. For example, given a number n, the inverse is -n. This is equivalent to Number.subtract(Number.ZERO, value);

Parameters:

value - - Number to take inverse of

Returns:

- Inverse of value

pow

public static CNumber pow(CNumber base,
 int exponenent)

Performs complex exponentiation of two numbers. Note: base can be any complex number. TODO: Extend this using to complex numbers using Talyor series expansion of e^x. (May need a new method exponenent())

Parameters:

base - - base of exponential expression

exponenent - - exponent of exponential expression

Returns:

Result of the exponential expression base^exponenent

pow

public static CNumber pow(CNumber base,
 CNumber exponent)

Performs complex exponentiation of two numbers. Note: The exponent, must be a real integer. TODO: Extend this using to complex numbers using Talyor series expansion of e^x. (May need a new method exp())

Parameters:

base - - base of exponential expression

exponent - - exponent of exponential expression

Returns:

Result of the exponential expression base^exp

exp

public static CNumber exp(double x)

Parameters:

x - - exponent

Returns:

e^x

exp

public static CNumber exp(CNumber x)

Parameters:

x - - exponent

Returns:

e^x

sqrt

public static CNumber sqrt(CNumber value)

Computes the square root of a number.

Note: This method only returns the principle square root (the positive square root or square root with positive real part).
If you wish to see all square roots, see allSqrt(CNumber value)

Parameters:

value - - value to take square root of.

Returns:

Returns the square root of value.

allSqrt

public static CNumber[] allSqrt(CNumber value)

Computes all possible square roots of a number. If you would only like the principle square root then see sqrt(CNumber value)

Parameters:

value - - value to take square root of.

Returns:

Returns all square roots of value (both positive and negative) in an array.

sign

public static CNumber sign(CNumber value)

The complex signum function.

Parameters:

value - - Value to evaluet in sign function.

Returns:

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

equals

public boolean equals(Object b)

Checks for equivalence between two complex numbers

Overrides:

equals in class Object

Parameters:

b - - Number to check equivalence to

Returns:

True if the two numbers are equivalent. Otherwise, returns false.

equals

public boolean equals(double b)

Checks for equivalence between two complex numbers

Also see equals(Object)

Parameters:

b - - Number to check equivalence to

Returns:

True if the two numbers are equivalent. Otherwise, returns false.

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.

nearZero

public boolean nearZero(double tol)

Checks if a number is near zero.

Parameters:

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

Returns:

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

compareTo

public int compareTo(CNumber b)

Compares the size of two complex numbers (magnitudes).

Parameters:

b - - Number to compare

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

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 greator 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.

Parameters:

b - - Number to compare

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.

mag

public double mag()

Computes the magnitude of a complex number (The numbers distance from the origin in the complex plane).
This method is the same as abs(CNumber)

Returns:

magnitude of complex number

max

public static CNumber max(CNumber... values)

Computes value with greatest magnitude amongst all passed values.

Parameters:

values - - a set of values of which to compute the maximum. Each item may be passed as its own variable or as an array. For example, given the CNumbers a, b, c and an array of CNumbers vals, this method may be called in either of the following ways.
- CNumber.max(a, b, c)
- CNumber.max(vals)

Returns:

Returns value with maximum magnitude amongst values. If two values tie for largest, the first encountered will be returned.

min

public static CNumber min(CNumber... values)

Computes value with smallest magnitude amongst all passed values.

Parameters:

values - - a set of values of which to compute the minimum. Each item may be passed as its own variable or as an array. For example, given the CNumbers a, b, c and an array of CNumbers vals, this method may be called in either of the following ways.
- CNumber.max(a, b, c)
- CNumber.max(vals)

Returns:

Returns value with minimum magnitude amounts values. If two values tie for smallest, the first encountered will be returned.

getReal

public double getReal()

Returns:

Real part of number

getImaginary

public double getImaginary()

Returns:

Complex part of number

isReal

public boolean isReal()

Checks if given number has no imaginary part.

Returns:

true if given Number has no imaginary part. Otherwise, returns false.

isComplex

public boolean isComplex()

Checks if given number has non-zero imaginary part.

Returns:

true if given Number has non-zero imaginary part. Otherwise, returns false.

isImaginary

public boolean isImaginary()

Checks if given number has no real part.

Returns:

true if given Number has no real part and non-zero imaginary part. Otherwise, returns false.

isInt

public boolean isInt()

Checks if a give number is a real integer.

Returns:

true if number is a real integer. Otherwise, returns false.

doubleValue

public double doubleValue()

Returns:

real part of given Number as double

floatValue

public float floatValue()

Note: This method may result in loss of accuracy

Returns:

real part of given Number as float

intValue

public int intValue()

Note: This method may result in loss of accuracy

Returns:

real part of given Number as int

longValue

public long longValue()

Note: This method may result in loss of accuracy

Returns:

real part of given Number as double

doubleImaginaryValue

public double doubleImaginaryValue()

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

length

public static int length(CNumber a)

Parameters:

a - - a number

Returns:

The length of the string representation of the number

toString

public String toString()

Overrides:

toString in class Object