org.flag4j.algebraic_structures.Complex64

All Implemented Interfaces:: Serializable, Comparable<Complex64>, Field<Complex64>, Ring<Complex64>, Semiring<Complex64>

public class Complex64 extends Object implements Field<Complex64>

Represents an immutable complex number with single-precision floating point components.

This class models a complex number in rectangular (Cartesian) form, defined by its real and imaginary parts, each stored as a 32-bit floating-point number (float). Instances of Complex64 are immutable and thread-safe.

The class provides various operations for complex arithmetic, including addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric and hyperbolic functions, as well as utilities for comparing and rounding complex numbers.

Usage Example:


 Complex64 a = new Complex64(2.5f, 3.2f);  // Creates a complex number 2.5 + 3.2i.
 Complex64 b = new Complex64(1, -4);       // Creates a complex number 1 - 4i.
 Complex64 sum = a.add(b);                 // Sum of a and b.
 Complex64 product = a.mult(b);            // Product of a and b.

Special Values:

The class defines several constants for common complex numbers:

ZERO - Complex number representing zero (0 + 0i).
ONE - Complex number representing one (1 + 0i).
TWO - Complex number representing two (2 + 0i).
THREE - Complex number representing three (3 + 0i).
IMAGINARY_UNIT - The imaginary unit (0 + 1i).
INV_IMAGINARY_UNIT - Negative imaginary unit (0 - 1i).
NaN - Complex number representing a Not-a-Number value.
POSITIVE_INFINITY - Complex number with infinite real part.
NEGATIVE_INFINITY - Complex number with negative infinite real part.

Mathematical Functions:

The class provides methods for several mathematical functions:

sqrt() - Computes the square root.
ln(Complex64) - Computes the natural logarithm.
exp(Complex64) - Computes the exponential function.
pow(Complex64, Complex64) - Computes the power function.
sin(Complex64) - Computes the sine function.
cos(Complex64) - Computes the cosine function.
tan(Complex64) - Computes the tangent function.
sinh(Complex64) - Computes the hyperbolic sine function.
cosh(Complex64) - Computes the hyperbolic cosine function.
tanh(Complex64) - Computes the hyperbolic tangent function.

See Also:

Field Summary

Fields

Modifier and Type

Field

Description

final float

im

Imaginary component of the complex number.

static final Complex64

IMAGINARY_UNIT

The imaginary unit i.

static final Complex64

INV_IMAGINARY_UNIT

The additive inverse of the imaginary unit, -i.

static final Complex64

NaN

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

static final Complex64

NEGATIVE_INFINITY

Complex number with real part equal to Float.NEGATIVE_INFINITY.

static final Complex64

ONE

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

static final Complex64

POSITIVE_INFINITY

Complex number with real part equal to Float.POSITIVE_INFINITY.

final float

re

Real component of the complex number.

static final Complex64

ROOT_THREE

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

static final Complex64

ROOT_TWO

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

static final Complex64

THREE

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

static final Complex64

TWO

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

static final Complex64

ZERO

The complex number with zero imaginary and real parts.
Constructor Summary

Constructors

Constructor

Description

Complex64(float re)

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

Complex64(float re, float im)

Constructs a complex number with specified complex and real components.

Complex64(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.
Method Summary

Modifier and Type

Method

Description

static Complex64

acos(Complex64 num)

Computes the inverse cosine of a complex value.

Complex64

add(float b)

Sums an elements of this field with a real number.

Complex64

add(Complex64 b)

Sums two elements of this field (associative and commutative).

Complex64

addInv()

Computes the additive inverse for an element of this field.

static float

arg(Complex64 num)

Computes the complex argument function for a complex number.

static int

argmax(Complex64... values)

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

static int

argmaxReal(Complex64... values)

Computes the index of the minimum real component from an array of complex numbers.

static int

argmin(Complex64... values)

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

static int

argminReal(Complex64... values)

Computes the index of the minimum real component from an array of complex numbers.

static Complex64

asin(Complex64 num)

Computes the inverse sine of a complex value.

static Complex64

atan(Complex64 num)

Computes the inverse tangent of a complex value.

static float

atan2(Complex64 num)

Computes the 2 argument arc-tangent function for a complex number.

int

compareTo(Complex64 b)

Compares this element of the field with b.

Complex64

conj()

Computes the conjugate of this field element.

static Complex64

cos(Complex64 num)

Computes the trigonometric cosine value of a complex value.

static Complex64

cosh(Complex64 num)

Computes the hyperbolic cosine of a complex value.

Complex64

div(float b)

Computes the quotient of an elements of this field and a real number.

Complex64

div(Complex64 b)

Computes the quotient of two elements of this field.

double

doubleValue()

Converts this complex number to an equivalent double.

boolean

equals(float b)

Checks if this complex has zero imaginary part and real part equal to a double.

boolean

equals(Object b)

Checks if an object is equal to this Field element.

static Complex64

exp(Complex64 exponent)

Computes the exponential function with the given input.

static Complex64

fromPolar(float r, float theta)

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

Complex64

getOne()

Gets the multiplicative identity for this semiring.

Complex64

getZero()

Gets the additive identity for this semiring.

int

hashCode()

Generates the hashcode for this complex number.

float

im()

Gets the imaginary component of this complex number.

boolean

isComplex()

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

boolean

isFinite()

Checks if this field element is finite in magnitude.

boolean

isFloat()

Checks if this complex number is a real valued float.

boolean

isImaginary()

Checks if this complex number has zero real part.

boolean

isInfinite()

Checks if this field element is infinite in magnitude.

boolean

isInt()

Checks if this complex number is a real valued integer.

boolean

isNaN()

Checks if this field element is NaN in magnitude.

boolean

isOne()

Checks if this value is a multiplicative identity for this semiring.

boolean

isReal()

Checks if this complex number has zero imaginary part.

boolean

isZero()

Checks if this value is an additive identity for this semiring.

static int

length(Complex64 a)

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

static Complex64

ln(float num)

Computes the natural logarithm of a float.

static Complex64

ln(Complex64 num)

Computes the complex natural logarithm of a complex number.

static Complex64

log(float num)

Computes the complex logarithm base 10 of a complex number.

static Complex64

log(float base, float num)

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

static Complex64

log(float base, Complex64 num)

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

static Complex64

log(Complex64 num)

Computes the complex logarithm base 10 of a complex number.

static Complex64

log(Complex64 base, Complex64 num)

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

double

mag()

Computes the magnitude of this field element.

float

magSquared()

Squares this magnitude of this complex number.

static Complex64

max(Complex64... values)

Computes the maximum magnitude from an array of complex numbers.

static Complex64

maxRe(Complex64... values)

Computes the minimum real component from an array of complex numbers.

static Complex64

min(Complex64... values)

Computes the minimum magnitude from an array of complex numbers.

static Complex64

minRe(Complex64... values)

Computes the minimum real component from an array of complex numbers.

Complex64

mult(float b)

Multiplies an element of this field and a real number (associative and commutative).

Complex64

mult(Complex64 b)

Multiplies two elements of this field (associative and commutative).

Complex64

multInv()

Computes the multiplicative inverse of this complex number.

static boolean

nearZero(Complex64 n, float tol)

Checks if a number is near zero in magnitude.

static Complex64

pow(float a, Complex64 b)

Compute a raised to the power of b.

static Complex64

pow(Complex64 a, float b)

Computes a raised to the power of b.

static Complex64

pow(Complex64 a, Complex64 b)

Computes a raised to the power of b.

float

re()

Gets the real component of this complex number.

static Complex64

round(Complex64 n)

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

static Complex64

round(Complex64 n, int decimals)

Rounds number to specified number of decimal places.

static Complex64

roundToZero(Complex64 n, float tol)

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

static Complex64

sgn(Complex64 value)

The complex signum function.

static Complex64

sin(Complex64 num)

Computes the trigonometric sine of a complex value.

static Complex64

sinh(Complex64 num)

Computes the hyperbolic sine of a complex value.

Complex64

sqrt()

Computes the square root of this field element.

static Complex64

sqrt(float num)

Computes the principle square root of a number.

Complex64

sub(float b)

Computes difference of an element of this field and a real number.

Complex64

sub(Complex64 b)

Computes difference of two elements of this field.

static Complex64

sum(Complex64... numbers)

Computes the sum of all data of specified array.

static Complex64

tan(Complex64 num)

Computes the trigonometric tangent value of a complex value.

static Complex64

tanh(Complex64 num)

Computes the hyperbolic tangent of a complex value.

float[]

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.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.flag4j.algebraic_structures.Field
add, div, mult, sub

Methods inherited from interface org.flag4j.algebraic_structures.Ring
abs

Field Details
- ZERO
  
  public static final Complex64 ZERO
  
  The complex number with zero imaginary and real parts.
- ONE
  
  public static final Complex64 ONE
  
  The complex number with zero imaginary part and one real part.
- TWO
  
  public static final Complex64 TWO
  
  The complex number with zero imaginary part and two real part.
- THREE
  
  public static final Complex64 THREE
  
  The complex number with zero imaginary part and three real part.
- ROOT_TWO
  
  public static final Complex64 ROOT_TWO
  
  The float value closer than any other to the square root of 2
- ROOT_THREE
  
  public static final Complex64 ROOT_THREE
  
  The float value closer than any other to the square root of 3
- IMAGINARY_UNIT
  
  public static final Complex64 IMAGINARY_UNIT
  
  The imaginary unit i.
- INV_IMAGINARY_UNIT
  
  public static final Complex64 INV_IMAGINARY_UNIT
  
  The additive inverse of the imaginary unit, -i.
- POSITIVE_INFINITY
  
  public static final Complex64 POSITIVE_INFINITY
  
  Complex number with real part equal to Float.POSITIVE_INFINITY.
- NEGATIVE_INFINITY
  
  public static final Complex64 NEGATIVE_INFINITY
  
  Complex number with real part equal to Float.NEGATIVE_INFINITY.
- NaN
  
  public static final Complex64 NaN
  
  Complex number with real and imaginary parts equal to Float.NaN.
- re
  
  public final float re
  
  Real component of the complex number.
- im
  
  public final float im
  
  Imaginary component of the complex number.
Constructor Details
- Complex64
  
  public Complex64(float re)
  
  Constructs a complex number with specified real component and zero imaginary component.
  
  Parameters:
  
  re - Real component of complex number.
- Complex64
  
  public Complex64(float re, float im)
  
  Constructs a complex number with specified complex and real components.
  
  Parameters:
  
  re - Real component of complex number.
  
  im - Imaginary component of complex number.
- Complex64
  
  public Complex64(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(float b)
  
  Checks if this complex has zero imaginary part and real part equal to a double.
  
  Returns:
  
  True if this.re == b && this.im == 0. False otherwise.
- equals
  
  public boolean equals(Object b)
  
  Checks if an object is equal to this Field element.
  
  Overrides:
  
  equals in class Object
  
  Parameters:
  
  b - Object to compare to this Field element.
  
  Returns:
  
  True if the objects are the same or are both Complex64's and have equal real and imaginary parts.
- hashCode
  
  public int hashCode()
  
  Generates the hashcode for this complex number.
  
  Overrides:
  
  hashCode in class Object
  
  Returns:
  
  An integer hash for this complex number.
- 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()
- add
  
  public Complex64 add(Complex64 b)
  
  Sums two elements of this field (associative and commutative).
  
  Specified by:
  
  add in interface Semiring<Complex64>
  
  Parameters:
  
  b - Second field element in sum.
  
  Returns:
  
  The sum of this element and b.
- add
  
  public Complex64 add(float b)
  
  Sums an elements of this field with a real number.
  
  Parameters:
  
  b - Second element in sum.
  
  Returns:
  
  The sum of this element and b.
- sub
  
  public Complex64 sub(Complex64 b)
  
  Computes difference of two elements of this field.
  
  Specified by:
  
  sub in interface Ring<Complex64>
  
  Parameters:
  
  b - Second field element in difference.
  
  Returns:
  
  The difference of this field element and b.
- sub
  
  public Complex64 sub(float b)
  
  Computes difference of an element of this field and a real number.
  
  Parameters:
  
  b - Second element in difference.
  
  Returns:
  
  The difference of this field element and b.
- sum
  
  public static Complex64 sum(Complex64... numbers)
  
  Computes the sum of all data of specified array.
  
  Parameters:
  
  values - Values to compute product of.
  
  Returns:
  
  The sum of all values in values.
- mult
  
  public Complex64 mult(Complex64 b)
  
  Multiplies two elements of this field (associative and commutative).
  
  Specified by:
  
  mult in interface Semiring<Complex64>
  
  Parameters:
  
  b - Second field element in product.
  
  Returns:
  
  The product of this field element and b.
- isZero
  
  public boolean isZero()
  
  Checks if this value is an additive identity for this semiring.
  An element 0 is an additive identity if a + 0 = a for any a in the semiring.
  
  Specified by:
  
  isZero in interface Semiring<Complex64>
  
  Returns:
  
  True if this value is an additive identity for this semiring. Otherwise, false.
- isOne
  
  public boolean isOne()
  
  Checks if this value is a multiplicative identity for this semiring.
  An element 1 is a multiplicative identity if a * 1 = a for any a in the semiring.
  
  Specified by:
  
  isOne in interface Semiring<Complex64>
  
  Returns:
  
  True if this value is a multiplicative identity for this semiring. Otherwise, false.
- getZero
  
  public Complex64 getZero()
  
  Gets the additive identity for this semiring.
  An element 0 is an additive identity if a + 0 = a for any a in the semiring.
  
  Specified by:
  
  getZero in interface Semiring<Complex64>
  
  Returns:
  
  The additive identity for this semiring.
- getOne
  
  public Complex64 getOne()
  
  Gets the multiplicative identity for this semiring.
  An element 1 is a multiplicative identity if a * 1 = a for any a in the semiring.
  
  Specified by:
  
  getOne in interface Semiring<Complex64>
  
  Returns:
  
  The multiplicative identity for this semiring.
- mult
  
  public Complex64 mult(float b)
  
  Multiplies an element of this field and a real number (associative and commutative).
  
  Parameters:
  
  b - Real number product.
  
  Returns:
  
  The product of this field element and b.
- div
  
  public Complex64 div(Complex64 b)
  
  Computes the quotient of two elements of this field.
  
  Specified by:
  
  div in interface Field<Complex64>
  
  Parameters:
  
  b - Second field element in quotient.
  
  Returns:
  
  The quotient of this field element and b.
- div
  
  public Complex64 div(float b)
  
  Computes the quotient of an elements of this field and a real number.
  
  Parameters:
  
  b - Second element in quotient.
  
  Returns:
  
  The quotient of this field element and b.
- mag
  
  public double mag()
  
  Computes the magnitude of this field element.
  
  Specified by:
  
  mag in interface Ring<Complex64>
  
  Returns:
  
  The magnitude of this field element.
- sqrt
  
  public Complex64 sqrt()
  
  Computes the square root of this field element.
  
  Specified by:
  
  sqrt in interface Field<Complex64>
  
  Returns:
  
  The square root of this field element.
- magSquared
  
  public float magSquared()
  
  Squares this magnitude of this complex number.
  
  Returns:
  
  The square of the magnitude of this complex number as a real value.
- addInv
  
  public Complex64 addInv()
  
  Computes the additive inverse for an element of this field.
  An element -x is an additive inverse for a field element x if -x + x = 0 where 0 is the additive identity.
  
  Specified by:
  
  addInv in interface Ring<Complex64>
  
  Returns:
  
  The additive inverse for this field element.
- multInv
  
  public Complex64 multInv()
  
  Computes the multiplicative inverse of this complex number.
  
  Specified by:
  
  multInv in interface Field<Complex64>
  
  Returns:
  
  The multiplicative inverse of this complex number.
- conj
  
  public Complex64 conj()
  
  Computes the conjugate of this field element.
  
  Specified by:
  
  conj in interface Ring<Complex64>
  
  Returns:
  
  The conjugate of this field element.
- pow
  
  public static Complex64 pow(float a, Complex64 b)
  
  Compute a raised to the power of b. and returns a Complex64.
  
  Parameters:
  
  a - The base.
  
  b - The exponent.
  
  Returns:
  
  a to the power of b.
- pow
  
  public static Complex64 pow(Complex64 a, Complex64 b)
  
  Computes a raised to the power of b.
  
  Parameters:
  
  a - The base.
  
  b - The exponent.
  
  Returns:
  
  a raised to the power of b.
- pow
  
  public static Complex64 pow(Complex64 a, float b)
  
  Computes a raised to the power of b.
  
  Parameters:
  
  a - The base.
  
  b - The exponent.
  
  Returns:
  
  a raised to the power of b.
- exp
  
  public static Complex64 exp(Complex64 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 Complex64 ln(float num)
  
  Computes the natural logarithm of a float. 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(Complex64).
  
  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 Complex64 ln(Complex64 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 Complex64 log(float 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(float). To specify a base, see log(float, Complex64) or log(Complex64, Complex64). 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 Complex64 log(Complex64 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(Complex64). To specify a base, see log(float, Complex64) or log(Complex64, Complex64).
  
  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 Complex64 log(float base, float 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 Complex64 log(float base, Complex64 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 Complex64 log(Complex64 base, Complex64 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 Complex64 sqrt(float num)
  
  Computes the principle square root of a number. This method wraps Math.sqrt(double) and returns a Complex64.
  
  Parameters:
  
  num - Input to square root.
  
  Returns:
  
  The principle square root of num.
- toPolar
  
  public float[] 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 Complex64 fromPolar(float r, float 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 float atan2(Complex64 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).
  
  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 Float.NaN is returned.
- arg
  
  public static float arg(Complex64 num)
  
  Computes the complex argument function for a complex number. is computed. This method is equivalent to atan2(Complex64).
  
  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 Float.NaN is returned.
- sin
  
  public static Complex64 sin(Complex64 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 Complex64 asin(Complex64 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 Complex64 sinh(Complex64 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 Complex64 cos(Complex64 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 Complex64 acos(Complex64 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 Complex64 cosh(Complex64 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 Complex64 tan(Complex64 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 Complex64 atan(Complex64 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 Complex64 tanh(Complex64 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.
- sgn
  
  public static Complex64 sgn(Complex64 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.
- round
  public static Complex64 round(Complex64 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 Float.NaN, Float.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY
  
  See Also:
  
  round(Complex64, int)
- round
  public static Complex64 round(Complex64 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 rounded to the specified number of decimals.
  
  Throws:
  
  IllegalArgumentException - If decimals is less than zero.
  
  See Also:
  
  round(Complex64)
- roundToZero
  
  public static Complex64 roundToZero(Complex64 n, float 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(Complex64 n, float 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; false otherwise.
  
  Throws:
  
  IllegalArgumentException - If tol is less than 0.
- compareTo
  public int compareTo(Complex64 b)
  
  Compares this element of the field with b.
  
  Specified by:
  
  compareTo in interface Comparable<Complex64>
  
  Specified by:
  
  compareTo in interface Semiring<Complex64>
  
  Parameters:
  
  b - Second element of the field.
  
  Returns:
  
  An int value:
  
  0 if this field element is equal to b in magnitude.
  
  invalid input: '<' 0 if this field element is less than b in magnitude.
  
  > 0 if this field element is greater than b in magnitude.
  Hence, this method returns zero if and only if the two field elements are equal in magnitude, a negative value if and only the field element it was called on is less than b in magnitude and positive if and only if the field element it was called on is greater than b in magnitude.
- doubleValue
  
  public double doubleValue()
  
  Converts this complex number to an equivalent double. This will be the magnitude of the complex number.
  
  Specified by:
  
  doubleValue in interface Semiring<Complex64>
  
  Returns:
  
  A double value equivalent to this complex number. This will be the magnitude of the complex number.
- min
  
  public static Complex64 min(Complex64... 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 null is returned.
- minRe
  
  public static Complex64 minRe(Complex64... 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, Float.NaN is returned.
- max
  
  public static Complex64 max(Complex64... 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 null is returned.
- maxRe
  
  public static Complex64 maxRe(Complex64... 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, Float.NaN is returned.
- argmin
  
  public static int argmin(Complex64... 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(Complex64... 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(Complex64... 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(Complex64... 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; false otherwise.
- isFloat
  
  public boolean isFloat()
  
  Checks if this complex number is a real valued float.
  
  Returns:
  
  true if the complex component is zero; false otherwise.
- isFinite
  
  public boolean isFinite()
  
  Checks if this field element is finite in magnitude.
  NOTE: It may be possible for this method to return true and mag() to return Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY, or Float.NaN if both components are finite but computing the magnitude explicitly results in an overflow.
  
  Specified by:
  
  isFinite in interface Field<Complex64>
  
  Returns:
  
  True if this field element is finite in magnitude. False otherwise (i.e. infinite, NaN etc.).
- isInfinite
  
  public boolean isInfinite()
  
  Checks if this field element is infinite in magnitude.
  
  Specified by:
  
  isInfinite in interface Field<Complex64>
  
  Returns:
  
  True if this field element is infinite in magnitude. False otherwise (i.e. finite, NaN, etc.).
- isNaN
  
  public boolean isNaN()
  
  Checks if this field element is NaN in magnitude.
  
  Specified by:
  
  isNaN in interface Field<Complex64>
  
  Returns:
  
  True if this field element is NaN in magnitude. False otherwise (i.e. finite, NaN, etc.).
- re
  
  public float re()
  
  Gets the real component of this complex number.
  
  Returns:
  
  The real component of this complex number.
- im
  
  public float im()
  
  Gets the imaginary component of this complex number.
  
  Returns:
  
  The imaginary component of this complex number.
- length
  
  public static int length(Complex64 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.

Class Complex64

Usage Example:

Special Values:

Mathematical Functions:

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.flag4j.algebraic_structures.Field

Methods inherited from interface org.flag4j.algebraic_structures.Ring

Field Details

ZERO

ONE

TWO

THREE

ROOT_TWO

ROOT_THREE

IMAGINARY_UNIT

INV_IMAGINARY_UNIT

POSITIVE_INFINITY

NEGATIVE_INFINITY

NaN

re

im

Constructor Details

Complex64

Complex64

Complex64

Method Details

equals

equals

hashCode

isReal

isImaginary

isComplex

add

add

sub

sub

sum

mult

isZero

isOne

getZero

getOne

mult

div

div

mag

sqrt

magSquared

addInv

multInv

conj

pow

pow

pow

exp

ln

ln

log

log

log

log

log

sqrt

toPolar

fromPolar

atan2

arg

sin

asin

sinh

cos

acos

cosh

tan

atan

tanh

sgn