Package org.hipparchus.complex

Class FieldComplex<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.complex.FieldComplex<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

CalculusFieldElement<FieldComplex<T>>, FieldElement<FieldComplex<T>>

public class FieldComplex<T extends CalculusFieldElement<T>>
extends Object
implements CalculusFieldElement<FieldComplex<T>>

Representation of a Complex number, i.e. a number which has both a real and imaginary part.

Implementations of arithmetic operations handle NaN and infinite values according to the rules for Double, i.e. equals(java.lang.Object) is an equivalence relation for all instances that have a NaN in either real or imaginary part, e.g. the following are considered equal:

• 1 + NaNi
• NaN + i
• NaN + NaNi

Note that this contradicts the IEEE-754 standard for floating point numbers (according to which the test x == x must fail if x is NaN). The method equals for primitive double in Precision conforms with IEEE-754 while this class conforms with the standard behavior for Java object types.

Since:

2.0

Constructor Summary

Constructors

Constructor	Description
FieldComplex(T real)	Create a complex number given only the real part.
FieldComplex(T real, T imaginary)	Create a complex number given the real and imaginary parts.

Method Summary

Modifier and Type	Method	Description
FieldComplex<T>	abs()	Return the absolute value of this complex number.
FieldComplex<T>	acos()	Compute the inverse cosine of this complex number.
FieldComplex<T>	acosh()	Inverse hyperbolic cosine operation.
FieldComplex<T>	add(double addend)	Returns a Complex whose value is (this + addend), with addend interpreted as a real number.
FieldComplex<T>	add(FieldComplex<T> addend)	Returns a Complex whose value is (this + addend).
FieldComplex<T>	add(T addend)	Returns a Complex whose value is (this + addend), with addend interpreted as a real number.
FieldComplex<T>	asin()	Compute the inverse sine of this complex number.
FieldComplex<T>	asinh()	Inverse hyperbolic sine operation.
FieldComplex<T>	atan()	Compute the inverse tangent of this complex number.
FieldComplex<T>	atan2(FieldComplex<T> x)	Two arguments arc tangent operation.
FieldComplex<T>	atanh()	Inverse hyperbolic tangent operation.
FieldComplex<T>	cbrt()	Cubic root.
FieldComplex<T>	ceil()	Get the smallest whole number larger than instance.
FieldComplex<T>	conjugate()	Returns the conjugate of this complex number.
FieldComplex<T>	copySign(double r)	Returns the instance with the sign of the argument.
FieldComplex<T>	copySign(FieldComplex<T> z)	Returns the instance with the sign of the argument.
FieldComplex<T>	cos()	Compute the cosine of this complex number.
FieldComplex<T>	cosh()	Compute the hyperbolic cosine of this complex number.
protected FieldComplex<T>	createComplex(T realPart, T imaginaryPart)	Create a complex number given the real and imaginary parts.
FieldComplex<T>	divide(double divisor)	Returns a Complex whose value is (this / divisor), with divisor interpreted as a real number.
FieldComplex<T>	divide(FieldComplex<T> divisor)	Returns a Complex whose value is (this / divisor).
FieldComplex<T>	divide(T divisor)	Returns a Complex whose value is (this / divisor), with divisor interpreted as a real number.
boolean	equals(Object other)	Test for equality with another object.
static <T extends CalculusFieldElement<T>> boolean	equals(FieldComplex<T> x, FieldComplex<T> y)	Returns true iff the values are equal as defined by equals(x, y, 1).
static <T extends CalculusFieldElement<T>> boolean	equals(FieldComplex<T> x, FieldComplex<T> y, double eps)	Returns true if, both for the real part and for the imaginary part, there is no T value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
static <T extends CalculusFieldElement<T>> boolean	equals(FieldComplex<T> x, FieldComplex<T> y, int maxUlps)	Test for the floating-point equality between Complex objects.
static <T extends CalculusFieldElement<T>> boolean	equalsWithRelativeTolerance(FieldComplex<T> x, FieldComplex<T> y, double eps)	Returns true if, both for the real part and for the imaginary part, there is no T value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance.
FieldComplex<T>	exp()	Compute the exponential function of this complex number.
FieldComplex<T>	expm1()	Exponential minus 1.
FieldComplex<T>	floor()	Get the largest whole number smaller than instance.
FieldComplex<T>	getAddendum()	Get the addendum to the real value of the number.
T	getArgument()	Compute the argument of this complex number.
FieldComplexField<T>	getField()	Get the Field to which the instance belongs.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getI(Field<T> field)	Get the square root of -1.
T	getImaginary()	Access the imaginary part.
T	getImaginaryPart()	Access the imaginary part.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getInf(Field<T> field)	Get a complex number representing "+INF + INFi".
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getMinusI(Field<T> field)	Get the square root of -1.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getMinusOne(Field<T> field)	Get a complex number representing "-1.0 + 0.0i".
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getNaN(Field<T> field)	Get a complex number representing "NaN + NaNi".
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getOne(Field<T> field)	Get a complex number representing "1.0 + 0.0i".
Field<T>	getPartsField()	Get the Field the real and imaginary parts belong to.
FieldComplex<T>	getPi()	Get the Archimedes constant π.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getPi(Field<T> field)	Get a complex number representing "π + 0.0i".
double	getReal()	Access the real part.
T	getRealPart()	Access the real part.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	getZero(Field<T> field)	Get a complex number representing "0.0 + 0.0i".
int	hashCode()	Get a hashCode for the complex number.
FieldComplex<T>	hypot(FieldComplex<T> y)	Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
boolean	isInfinite()	Checks whether either the real or imaginary part of this complex number takes an infinite value (either Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY) and neither part is NaN.
boolean	isMathematicalInteger()	Check whether the instance is an integer (i.e. imaginary part is zero and real part has no fractional part).
boolean	isNaN()	Checks whether either or both parts of this complex number is NaN.
boolean	isReal()	Check whether the instance is real (i.e. imaginary part is zero).
boolean	isZero()	Check if an element is semantically equal to zero.
FieldComplex<T>	linearCombination(double[] a, FieldComplex<T>[] b)	Compute a linear combination.
FieldComplex<T>	linearCombination(double a1, FieldComplex<T> b1, double a2, FieldComplex<T> b2)	Compute a linear combination.
FieldComplex<T>	linearCombination(double a1, FieldComplex<T> b1, double a2, FieldComplex<T> b2, double a3, FieldComplex<T> b3)	Compute a linear combination.
FieldComplex<T>	linearCombination(double a1, FieldComplex<T> b1, double a2, FieldComplex<T> b2, double a3, FieldComplex<T> b3, double a4, FieldComplex<T> b4)	Compute a linear combination.
FieldComplex<T>	linearCombination(FieldComplex<T>[] a, FieldComplex<T>[] b)	Compute a linear combination.
FieldComplex<T>	linearCombination(FieldComplex<T> a1, FieldComplex<T> b1, FieldComplex<T> a2, FieldComplex<T> b2)	Compute a linear combination.
FieldComplex<T>	linearCombination(FieldComplex<T> a1, FieldComplex<T> b1, FieldComplex<T> a2, FieldComplex<T> b2, FieldComplex<T> a3, FieldComplex<T> b3)	Compute a linear combination.
FieldComplex<T>	linearCombination(FieldComplex<T> a1, FieldComplex<T> b1, FieldComplex<T> a2, FieldComplex<T> b2, FieldComplex<T> a3, FieldComplex<T> b3, FieldComplex<T> a4, FieldComplex<T> b4)	Compute a linear combination.
FieldComplex<T>	log()	Compute the natural logarithm of this complex number.
FieldComplex<T>	log10()	Base 10 logarithm.
FieldComplex<T>	log1p()	Shifted natural logarithm.
FieldComplex<T>	multiply(double factor)	Returns a Complex whose value is this * factor, with factor interpreted as a real number.
FieldComplex<T>	multiply(int factor)	Returns a Complex whose value is this * factor, with factor interpreted as a integer number.
FieldComplex<T>	multiply(FieldComplex<T> factor)	Returns a Complex whose value is this * factor.
FieldComplex<T>	multiply(T factor)	Returns a Complex whose value is this * factor, with factor interpreted as a real number.
FieldComplex<T>	multiplyMinusI()	Compute this *- -i.
FieldComplex<T>	multiplyPlusI()	Compute this * i.
FieldComplex<T>	negate()	Returns a Complex whose value is (-this).
FieldComplex<T>	newInstance(double realPart)	Create an instance corresponding to a constant real value.
List<FieldComplex<T>>	nthRoot(int n)	Computes the n-th roots of this complex number.
FieldComplex<T>	pow(double x)	Returns of value of this complex number raised to the power of x.
FieldComplex<T>	pow(int n)	Integer power operation.
FieldComplex<T>	pow(FieldComplex<T> x)	Returns of value of this complex number raised to the power of x.
FieldComplex<T>	pow(T x)	Returns of value of this complex number raised to the power of x.
FieldComplex<T>	reciprocal()	Returns the multiplicative inverse of this element.
FieldComplex<T>	remainder(double a)	IEEE remainder operator.
FieldComplex<T>	remainder(FieldComplex<T> a)	IEEE remainder operator.
FieldComplex<T>	rint()	Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
FieldComplex<T>	rootN(int n)	Nth root.
FieldComplex<T>	scalb(int n)	Multiply the instance by a power of 2.
FieldComplex<T>	sign()	Compute the sign of the instance.
FieldComplex<T>	sin()	Compute the sine of this complex number.
FieldSinCos<FieldComplex<T>>	sinCos()	Combined Sine and Cosine operation.
FieldComplex<T>	sinh()	Compute the hyperbolic sine of this complex number.
FieldSinhCosh<FieldComplex<T>>	sinhCosh()	Combined hyperbolic sine and cosine operation.
FieldComplex<T>	sqrt()	Compute the square root of this complex number.
FieldComplex<T>	sqrt1z()	Compute the square root of 1 - this2 for this complex number.
FieldComplex<T>	square()	Compute this × this.
FieldComplex<T>	subtract(double subtrahend)	Returns a Complex whose value is (this - subtrahend).
FieldComplex<T>	subtract(FieldComplex<T> subtrahend)	Returns a Complex whose value is (this - subtrahend).
FieldComplex<T>	subtract(T subtrahend)	Returns a Complex whose value is (this - subtrahend).
FieldComplex<T>	tan()	Compute the tangent of this complex number.
FieldComplex<T>	tanh()	Compute the hyperbolic tangent of this complex number.
FieldComplex<T>	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP
FieldComplex<T>	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP
String	toString()
FieldComplex<T>	ulp()	Compute least significant bit (Unit in Last Position) for a number.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	valueOf(T realPart)	Create a complex number given only the real part.
static <T extends CalculusFieldElement<T>> FieldComplex<T>	valueOf(T realPart, T imaginaryPart)	Create a complex number given the real and imaginary parts.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.hipparchus.CalculusFieldElement

getExponent, isFinite, norm, round

Constructor Details

FieldComplex

public FieldComplex(T real)

Create a complex number given only the real part.

Parameters:

real - Real part.

FieldComplex

public FieldComplex(T real,
 T imaginary)

Create a complex number given the real and imaginary parts.

Parameters:

real - Real part.

imaginary - Imaginary part.

Method Details

getI

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getI(Field<T> field)

Get the square root of -1.

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

number representing "0.0 + 1.0i"

getMinusI

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getMinusI(Field<T> field)

Get the square root of -1.

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

number representing "0.0 _ 1.0i"

getNaN

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getNaN(Field<T> field)

Get a complex number representing "NaN + NaNi".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "NaN + NaNi"

getInf

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getInf(Field<T> field)

Get a complex number representing "+INF + INFi".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "+INF + INFi"

getOne

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getOne(Field<T> field)

Get a complex number representing "1.0 + 0.0i".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "1.0 + 0.0i"

getMinusOne

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getMinusOne(Field<T> field)

Get a complex number representing "-1.0 + 0.0i".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "-1.0 + 0.0i"

getZero

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getZero(Field<T> field)

Get a complex number representing "0.0 + 0.0i".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "0.0 + 0.0i

getPi

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> getPi(Field<T> field)

Get a complex number representing "π + 0.0i".

Type Parameters:

T - the type of the field elements

Parameters:

field - field the complex components belong to

Returns:

complex number representing "π + 0.0i

abs

public FieldComplex<T> abs()

Return the absolute value of this complex number. Returns NaN if either real or imaginary part is NaN and Double.POSITIVE_INFINITY if neither part is NaN, but at least one part is infinite.

Specified by:

abs in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the absolute value.

add

public FieldComplex<T> add(FieldComplex<T> addend)
                    throws NullArgumentException

Returns a Complex whose value is (this + addend). Uses the definitional formula

(a + bi) + (c + di) = (a+c) + (b+d)i

If either this or addend has a NaN value in either part, getNaN(Field) is returned; otherwise Infinite and NaN values are returned in the parts of the result according to the rules for Double arithmetic.

Specified by:

add in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

addend - Value to be added to this Complex.

Returns:

this + addend.

Throws:

NullArgumentException - if addend is null.

add

public FieldComplex<T> add(T addend)

Returns a Complex whose value is (this + addend), with addend interpreted as a real number.

Parameters:

addend - Value to be added to this Complex.

Returns:

this + addend.

See Also:

• add(FieldComplex)

add

public FieldComplex<T> add(double addend)

Returns a Complex whose value is (this + addend), with addend interpreted as a real number.

Specified by:

add in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

addend - Value to be added to this Complex.

Returns:

this + addend.

See Also:

• add(FieldComplex)

conjugate

public FieldComplex<T> conjugate()

Returns the conjugate of this complex number. The conjugate of a + bi is a - bi.

getNaN(Field) is returned if either the real or imaginary part of this Complex number equals Double.NaN.

If the imaginary part is infinite, and the real part is not NaN, the returned value has infinite imaginary part of the opposite sign, e.g. the conjugate of 1 + POSITIVE_INFINITY i is 1 - NEGATIVE_INFINITY i.

Returns:

the conjugate of this Complex object.

divide

public FieldComplex<T> divide(FieldComplex<T> divisor)
                       throws NullArgumentException

Returns a Complex whose value is (this / divisor). Implements the definitional formula

  
    a + bi          ac + bd + (bc - ad)i
    ----------- = -------------------------
    c + di         c2 + d2
  
 

but uses prescaling of operands to limit the effects of overflows and underflows in the computation.

Infinite and NaN values are handled according to the following rules, applied in the order presented:

• If either this or divisor has a NaN value in either part, getNaN(Field) is returned.
• If divisor equals getZero(Field), getNaN(Field) is returned.
• If this and divisor are both infinite, getNaN(Field) is returned.
• If this is finite (i.e., has no Infinite or NaN parts) and divisor is infinite (one or both parts infinite), getZero(Field) is returned.
• If this is infinite and divisor is finite, NaN values are returned in the parts of the result if the Double rules applied to the definitional formula force NaN results.

Specified by:

divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

divide in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

divisor - Value by which this Complex is to be divided.

Returns:

this / divisor.

Throws:

NullArgumentException - if divisor is null.

divide

public FieldComplex<T> divide(T divisor)

Returns a Complex whose value is (this / divisor), with divisor interpreted as a real number.

Parameters:

divisor - Value by which this Complex is to be divided.

Returns:

this / divisor.

See Also:

• divide(FieldComplex)

divide

public FieldComplex<T> divide(double divisor)

Returns a Complex whose value is (this / divisor), with divisor interpreted as a real number.

Specified by:

divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

divisor - Value by which this Complex is to be divided.

Returns:

this / divisor.

See Also:

• divide(FieldComplex)

reciprocal

public FieldComplex<T> reciprocal()

Returns the multiplicative inverse of this element.

Specified by:

reciprocal in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

the inverse of this.

equals

public boolean equals(Object other)

Test for equality with another object. If both the real and imaginary parts of two complex numbers are exactly the same, and neither is Double.NaN, the two Complex objects are considered to be equal. The behavior is the same as for JDK's Double:

• All NaN values are considered to be equal, i.e, if either (or both) real and imaginary parts of the complex number are equal to Double.NaN, the complex number is equal to NaN.
• Instances constructed with different representations of zero (i.e. either "0" or "-0") are not considered to be equal.

Overrides:

equals in class Object

Parameters:

other - Object to test for equality with this instance.

Returns:

true if the objects are equal, false if object is null, not an instance of Complex, or not equal to this instance.

equals

public static <T extends CalculusFieldElement<T>>
boolean equals(FieldComplex<T> x,
 FieldComplex<T> y,
 int maxUlps)

Test for the floating-point equality between Complex objects. It returns true if both arguments are equal or within the range of allowed error (inclusive).

Type Parameters:

T - the type of the field elements

Parameters:

x - First value (cannot be null).

y - Second value (cannot be null).

maxUlps - (maxUlps - 1) is the number of floating point values between the real (resp. imaginary) parts of x and y.

Returns:

true if there are fewer than maxUlps floating point values between the real (resp. imaginary) parts of x and y.

See Also:

• Precision.equals(double,double,int)

equals

public static <T extends CalculusFieldElement<T>>
boolean equals(FieldComplex<T> x,
 FieldComplex<T> y)

Returns true iff the values are equal as defined by equals(x, y, 1).

Type Parameters:

T - the type of the field elements

Parameters:

x - First value (cannot be null).

y - Second value (cannot be null).

Returns:

true if the values are equal.

equals

public static <T extends CalculusFieldElement<T>>
boolean equals(FieldComplex<T> x,
 FieldComplex<T> y,
 double eps)

Returns true if, both for the real part and for the imaginary part, there is no T value strictly between the arguments or the difference between them is within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.

Type Parameters:

T - the type of the field elements

Parameters:

x - First value (cannot be null).

y - Second value (cannot be null).

eps - Amount of allowed absolute error.

Returns:

true if the values are two adjacent floating point numbers or they are within range of each other.

See Also:

• Precision.equals(double,double,double)

equalsWithRelativeTolerance

public static <T extends CalculusFieldElement<T>>
boolean equalsWithRelativeTolerance(FieldComplex<T> x,
 FieldComplex<T> y,
 double eps)

Returns true if, both for the real part and for the imaginary part, there is no T value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance. Returns false if either of the arguments is NaN.

Type Parameters:

T - the type of the field elements

Parameters:

x - First value (cannot be null).

y - Second value (cannot be null).

eps - Amount of allowed relative error.

Returns:

true if the values are two adjacent floating point numbers or they are within range of each other.

See Also:

• Precision.equalsWithRelativeTolerance(double,double,double)

hashCode

public int hashCode()

Get a hashCode for the complex number. Any Double.NaN value in real or imaginary part produces the same hash code 7.

Overrides:

hashCode in class Object

Returns:

a hash code value for this object.

isZero

public boolean isZero()

Check if an element is semantically equal to zero.

The default implementation simply calls equals(getField().getZero()). However, this may need to be overridden in some cases as due to compatibility with hashCode() some classes implements equals(Object) in such a way that -0.0 and +0.0 are different, which may be a problem. It prevents for example identifying a diagonal element is zero and should be avoided when doing partial pivoting in LU decomposition.

This implementation considers +0.0 and -0.0 to be equal for both real and imaginary components.

Specified by:

isZero in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

true if the element is semantically equal to zero

getImaginary

public T getImaginary()

Access the imaginary part.

Returns:

the imaginary part.

getImaginaryPart

public T getImaginaryPart()

Access the imaginary part.

Returns:

the imaginary part.

getReal

public double getReal()

Access the real part.

Specified by:

getReal in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

the real part.

getAddendum

public FieldComplex<T> getAddendum()

Get the addendum to the real value of the number.

The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.

Specified by:

getAddendum in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

real value

getRealPart

public T getRealPart()

Access the real part.

Returns:

the real part.

isNaN

public boolean isNaN()

Checks whether either or both parts of this complex number is NaN.

Specified by:

isNaN in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

true if either or both parts of this complex number is NaN; false otherwise.

isReal

public boolean isReal()

Check whether the instance is real (i.e. imaginary part is zero).

Returns:

true if imaginary part is zero

isMathematicalInteger

public boolean isMathematicalInteger()

Check whether the instance is an integer (i.e. imaginary part is zero and real part has no fractional part).

Returns:

true if imaginary part is zero and real part has no fractional part

isInfinite

public boolean isInfinite()

Checks whether either the real or imaginary part of this complex number takes an infinite value (either Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY) and neither part is NaN.

Specified by:

isInfinite in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

true if one or both parts of this complex number are infinite and neither part is NaN.

multiply

public FieldComplex<T> multiply(FieldComplex<T> factor)
                         throws NullArgumentException

Returns a Complex whose value is this * factor. Implements preliminary checks for NaN and infinity followed by the definitional formula:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Returns getNaN(Field) if either this or factor has one or more NaN parts.

Returns getInf(Field) if neither this nor factor has one or more NaN parts and if either this or factor has one or more infinite parts (same result is returned regardless of the sign of the components).

Returns finite values in components of the result per the definitional formula in all remaining cases.

Specified by:

multiply in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

factor - value to be multiplied by this Complex.

Returns:

this * factor.

Throws:

NullArgumentException - if factor is null.

multiply

public FieldComplex<T> multiply(int factor)

Returns a Complex whose value is this * factor, with factor interpreted as a integer number.

Specified by:

multiply in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

multiply in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

factor - value to be multiplied by this Complex.

Returns:

this * factor.

See Also:

• multiply(FieldComplex)

multiply

public FieldComplex<T> multiply(double factor)

Returns a Complex whose value is this * factor, with factor interpreted as a real number.

Specified by:

multiply in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

factor - value to be multiplied by this Complex.

Returns:

this * factor.

See Also:

• multiply(FieldComplex)

multiply

public FieldComplex<T> multiply(T factor)

Returns a Complex whose value is this * factor, with factor interpreted as a real number.

Parameters:

factor - value to be multiplied by this Complex.

Returns:

this * factor.

See Also:

• multiply(FieldComplex)

multiplyPlusI

public FieldComplex<T> multiplyPlusI()

Compute this * i.

Returns:

this * i

Since:

2.0

multiplyMinusI

public FieldComplex<T> multiplyMinusI()

Compute this *- -i.

Returns:

this * i

Since:

2.0

square

public FieldComplex<T> square()

Description copied from interface: CalculusFieldElement

Compute this × this.

Specified by:

square in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

a new element representing this × this

negate

public FieldComplex<T> negate()

Returns a Complex whose value is (-this). Returns NaN if either real or imaginary part of this Complex number is Double.NaN.

Specified by:

negate in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

-this.

subtract

public FieldComplex<T> subtract(FieldComplex<T> subtrahend)
                         throws NullArgumentException

Returns a Complex whose value is (this - subtrahend). Uses the definitional formula

(a + bi) - (c + di) = (a-c) + (b-d)i

If either this or subtrahend has a NaN] value in either part, getNaN(Field) is returned; otherwise infinite and NaN values are returned in the parts of the result according to the rules for Double arithmetic.

Specified by:

subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

subtract in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

subtrahend - value to be subtracted from this Complex.

Returns:

this - subtrahend.

Throws:

NullArgumentException - if subtrahend is null.

subtract

public FieldComplex<T> subtract(double subtrahend)

Returns a Complex whose value is (this - subtrahend).

Specified by:

subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

subtrahend - value to be subtracted from this Complex.

Returns:

this - subtrahend.

See Also:

• subtract(FieldComplex)

subtract

public FieldComplex<T> subtract(T subtrahend)

Returns a Complex whose value is (this - subtrahend).

Parameters:

subtrahend - value to be subtracted from this Complex.

Returns:

this - subtrahend.

See Also:

• subtract(FieldComplex)

acos

public FieldComplex<T> acos()

Compute the inverse cosine of this complex number. Implements the formula:

acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN or infinite.

Specified by:

acos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the inverse cosine of this complex number.

asin

public FieldComplex<T> asin()

Compute the inverse sine of this complex number. Implements the formula:

asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN or infinite.

Specified by:

asin in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the inverse sine of this complex number.

atan

public FieldComplex<T> atan()

Compute the inverse tangent of this complex number. Implements the formula:

atan(z) = (i/2) log((1 - iz)/(1 + iz))

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN or infinite.

Specified by:

atan in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the inverse tangent of this complex number

cos

public FieldComplex<T> cos()

Compute the cosine of this complex number. Implements the formula:

cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   cos(1 ± INFINITY i) = 1 ∓ INFINITY i
   cos(±INFINITY + i) = NaN + NaN i
   cos(±INFINITY ± INFINITY i) = NaN + NaN i
  
 

Specified by:

cos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the cosine of this complex number.

cosh

public FieldComplex<T> cosh()

Compute the hyperbolic cosine of this complex number. Implements the formula:

  
   cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
  
 

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   cosh(1 ± INFINITY i) = NaN + NaN i
   cosh(±INFINITY + i) = INFINITY ± INFINITY i
   cosh(±INFINITY ± INFINITY i) = NaN + NaN i
  
 

Specified by:

cosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the hyperbolic cosine of this complex number.

exp

public FieldComplex<T> exp()

Compute the exponential function of this complex number. Implements the formula:

  
   exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
  
 

where the (real) functions on the right-hand side are FastMath.exp(CalculusFieldElement) p}, FastMath.cos(CalculusFieldElement), and FastMath.sin(CalculusFieldElement).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   exp(1 ± INFINITY i) = NaN + NaN i
   exp(INFINITY + i) = INFINITY + INFINITY i
   exp(-INFINITY + i) = 0 + 0i
   exp(±INFINITY ± INFINITY i) = NaN + NaN i
  
 

Specified by:

exp in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

ethis.

expm1

public FieldComplex<T> expm1()

Exponential minus 1.

Specified by:

expm1 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

exponential minus one of the instance

log

public FieldComplex<T> log()

Compute the natural logarithm of this complex number. Implements the formula:

  
   log(a + bi) = ln(|a + bi|) + arg(a + bi)i
  
 

where ln on the right hand side is FastMath.log(CalculusFieldElement), |a + bi| is the modulus, abs(), and arg(a + bi) = FastMath.atan2(double, double)(b, a).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite (or critical) values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   log(1 ± INFINITY i) = INFINITY ± (π/2)i
   log(INFINITY + i) = INFINITY + 0i
   log(-INFINITY + i) = INFINITY + πi
   log(INFINITY ± INFINITY i) = INFINITY ± (π/4)i
   log(-INFINITY ± INFINITY i) = INFINITY ± (3π/4)i
   log(0 + 0i) = -INFINITY + 0i
  
 

Specified by:

log in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the value ln this, the natural logarithm of this.

log1p

public FieldComplex<T> log1p()

Shifted natural logarithm.

Specified by:

log1p in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

logarithm of one plus the instance

log10

public FieldComplex<T> log10()

Base 10 logarithm.

Specified by:

log10 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

base 10 logarithm of the instance

pow

public FieldComplex<T> pow(FieldComplex<T> x)
                    throws NullArgumentException

Returns of value of this complex number raised to the power of x.

If x is a real number whose real part has an integer value, returns pow(int), if both this and x are real and FastMath.pow(double, double) with the corresponding real arguments would return a finite number (neither NaN nor infinite), then returns the same value converted to Complex, with the same special cases. In all other cases real cases, implements y^x = exp(x·log(y)).

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

x - exponent to which this Complex is to be raised.

Returns:

thisx.

Throws:

NullArgumentException - if x is null.

pow

public FieldComplex<T> pow(T x)

Returns of value of this complex number raised to the power of x.

If x has an integer value, returns pow(int), if this is real and FastMath.pow(double, double) with the corresponding real arguments would return a finite number (neither NaN nor infinite), then returns the same value converted to Complex, with the same special cases. In all other cases real cases, implements y^x = exp(x·log(y)).

Parameters:

x - exponent to which this Complex is to be raised.

Returns:

thisx.

pow

public FieldComplex<T> pow(double x)

Returns of value of this complex number raised to the power of x.

If x has an integer value, returns pow(int), if this is real and FastMath.pow(double, double) with the corresponding real arguments would return a finite number (neither NaN nor infinite), then returns the same value converted to Complex, with the same special cases. In all other cases real cases, implements y^x = exp(x·log(y)).

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

x - exponent to which this Complex is to be raised.

Returns:

thisx.

pow

public FieldComplex<T> pow(int n)

Integer power operation.

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - power to apply

Returns:

thisⁿ

sin

public FieldComplex<T> sin()

Compute the sine of this complex number. Implements the formula:

  
   sin(a + bi) = sin(a)cosh(b) + cos(a)sinh(b)i
  
 

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   sin(1 ± INFINITY i) = 1 ± INFINITY i
   sin(±INFINITY + i) = NaN + NaN i
   sin(±INFINITY ± INFINITY i) = NaN + NaN i
  
 

Specified by:

sin in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the sine of this complex number.

sinCos

public FieldSinCos<FieldComplex<T>> sinCos()

Combined Sine and Cosine operation.

Specified by:

sinCos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

[sin(this), cos(this)]

atan2

public FieldComplex<T> atan2(FieldComplex<T> x)

Two arguments arc tangent operation.

Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.

Specified by:

atan2 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

acosh

public FieldComplex<T> acosh()

Inverse hyperbolic cosine operation.

Branch cuts are on the real axis, below +1.

Specified by:

acosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

acosh(this)

asinh

public FieldComplex<T> asinh()

Inverse hyperbolic sine operation.

Branch cuts are on the imaginary axis, above +i and below -i.

Specified by:

asinh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

asin(this)

atanh

public FieldComplex<T> atanh()

Inverse hyperbolic tangent operation.

Branch cuts are on the real axis, above +1 and below -1.

Specified by:

atanh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

atanh(this)

sinh

public FieldComplex<T> sinh()

Compute the hyperbolic sine of this complex number. Implements the formula:

  
   sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
  
 

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   sinh(1 ± INFINITY i) = NaN + NaN i
   sinh(±INFINITY + i) = ± INFINITY + INFINITY i
   sinh(±INFINITY ± INFINITY i) = NaN + NaN i
  
 

Specified by:

sinh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the hyperbolic sine of this.

sinhCosh

public FieldSinhCosh<FieldComplex<T>> sinhCosh()

Combined hyperbolic sine and cosine operation.

Specified by:

sinhCosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

[sinh(this), cosh(this)]

sqrt

public FieldComplex<T> sqrt()

Compute the square root of this complex number. Implements the following algorithm to compute sqrt(a + bi):

1. Let t = sqrt((|a| + |a + bi|) / 2)

2. if  a ≥ 0 return t + (b/2t)i
     else return |b|/2t + sign(b)t i 

where

• |a| = abs(a)
• |a + bi| = hypot(a, b)
• sign(b) = copySign(1, b)

The real part is therefore always nonnegative.

Returns NaN if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   sqrt(1 ± ∞ i) = ∞ + NaN i
   sqrt(∞ + i) = ∞ + 0i
   sqrt(-∞ + i) = 0 + ∞ i
   sqrt(∞ ± ∞ i) = ∞ + NaN i
   sqrt(-∞ ± ∞ i) = NaN ± ∞ i
  
 

Specified by:

sqrt in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the square root of this with nonnegative real part.

sqrt1z

public FieldComplex<T> sqrt1z()

Compute the square root of 1 - this2 for this complex number. Computes the result directly as sqrt(ONE.subtract(z.square())).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

Returns:

the square root of 1 - this2.

cbrt

public FieldComplex<T> cbrt()

Cubic root.

This implementation compute the principal cube root by using a branch cut along real negative axis.

Specified by:

cbrt in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

cubic root of the instance

rootN

public FieldComplex<T> rootN(int n)

N^th root.

This implementation compute the principal n^th root by using a branch cut along real negative axis.

Specified by:

rootN in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - order of the root

Returns:

n^th root of the instance

tan

public FieldComplex<T> tan()

Compute the tangent of this complex number. Implements the formula:

  
   tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i
  
 

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite (or critical) values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   tan(a ± INFINITY i) = 0 ± i
   tan(±INFINITY + bi) = NaN + NaN i
   tan(±INFINITY ± INFINITY i) = NaN + NaN i
   tan(±π/2 + 0 i) = ±INFINITY + NaN i
  
 

Specified by:

tan in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the tangent of this.

tanh

public FieldComplex<T> tanh()

Compute the hyperbolic tangent of this complex number. Implements the formula:

  
   tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
  
 

where the (real) functions on the right-hand side are FastMath.sin(double), FastMath.cos(double), FastMath.cosh(double) and FastMath.sinh(double).

Returns getNaN(Field) if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

  Examples:
  
   tanh(a ± INFINITY i) = NaN + NaN i
   tanh(±INFINITY + bi) = ±1 + 0 i
   tanh(±INFINITY ± INFINITY i) = NaN + NaN i
   tanh(0 + (π/2)i) = NaN + INFINITY i
  
 

Specified by:

tanh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

the hyperbolic tangent of this.

getArgument

public T getArgument()

Compute the argument of this complex number. The argument is the angle phi between the positive real axis and the point representing this number in the complex plane. The value returned is between -PI (not inclusive) and PI (inclusive), with negative values returned for numbers with negative imaginary parts.

If either real or imaginary part (or both) is NaN, NaN is returned. Infinite parts are handled as Math.atan2 handles them, essentially treating finite parts as zero in the presence of an infinite coordinate and returning a multiple of pi/4 depending on the signs of the infinite parts. See the javadoc for Math.atan2 for full details.

Returns:

the argument of this.

nthRoot

public List<FieldComplex<T>> nthRoot(int n)
                              throws MathIllegalArgumentException

Computes the n-th roots of this complex number. The nth roots are defined by the formula:

  
   zk = abs1/n (cos(phi + 2πk/n) + i (sin(phi + 2πk/n))
  
 

for k=0, 1, ..., n-1, where abs and phi are respectively the modulus and argument of this complex number.

If one or both parts of this complex number is NaN, a list with just one element, getNaN(Field) is returned. if neither part is NaN, but at least one part is infinite, the result is a one-element list containing getInf(Field).

Parameters:

n - Degree of root.

Returns:

a List of all n-th roots of this.

Throws:

MathIllegalArgumentException - if n <= 0.

createComplex

protected FieldComplex<T> createComplex(T realPart,
 T imaginaryPart)

Create a complex number given the real and imaginary parts.

Parameters:

realPart - Real part.

imaginaryPart - Imaginary part.

Returns:

a new complex number instance.

See Also:

• valueOf(CalculusFieldElement, CalculusFieldElement)

valueOf

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> valueOf(T realPart,
 T imaginaryPart)

Create a complex number given the real and imaginary parts.

Type Parameters:

T - the type of the field elements

Parameters:

realPart - Real part.

imaginaryPart - Imaginary part.

Returns:

a Complex instance.

valueOf

public static <T extends CalculusFieldElement<T>>
FieldComplex<T> valueOf(T realPart)

Create a complex number given only the real part.

Type Parameters:

T - the type of the field elements

Parameters:

realPart - Real part.

Returns:

a Complex instance.

newInstance

public FieldComplex<T> newInstance(double realPart)

Create an instance corresponding to a constant real value.

Specified by:

newInstance in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

realPart - constant real value

Returns:

instance corresponding to a constant real value

getField

public FieldComplexField<T> getField()

Get the Field to which the instance belongs.

Specified by:

getField in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

Field to which the instance belongs

getPartsField

public Field<T> getPartsField()

Get the Field the real and imaginary parts belong to.

Returns:

Field the real and imaginary parts belong to

toString

public String toString()

Overrides:

toString in class Object

scalb

public FieldComplex<T> scalb(int n)

Multiply the instance by a power of 2.

Specified by:

scalb in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - power of 2

Returns:

this × 2ⁿ

ulp

public FieldComplex<T> ulp()

Compute least significant bit (Unit in Last Position) for a number.

Specified by:

ulp in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

ulp(this)

hypot

public FieldComplex<T> hypot(FieldComplex<T> y)

Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Specified by:

hypot in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

y - a value

Returns:

sqrt(this² +y²)

linearCombination

public FieldComplex<T> linearCombination(FieldComplex<T>[] a,
 FieldComplex<T>[] b)
                                  throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public FieldComplex<T> linearCombination(double[] a,
 FieldComplex<T>[] b)
                                  throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public FieldComplex<T> linearCombination(FieldComplex<T> a1,
 FieldComplex<T> b1,
 FieldComplex<T> a2,
 FieldComplex<T> b2)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldComplex<T> linearCombination(double a1,
 FieldComplex<T> b1,
 double a2,
 FieldComplex<T> b2)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

public FieldComplex<T> linearCombination(FieldComplex<T> a1,
 FieldComplex<T> b1,
 FieldComplex<T> a2,
 FieldComplex<T> b2,
 FieldComplex<T> a3,
 FieldComplex<T> b3)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldComplex<T> linearCombination(double a1,
 FieldComplex<T> b1,
 double a2,
 FieldComplex<T> b2,
 double a3,
 FieldComplex<T> b3)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

public FieldComplex<T> linearCombination(FieldComplex<T> a1,
 FieldComplex<T> b1,
 FieldComplex<T> a2,
 FieldComplex<T> b2,
 FieldComplex<T> a3,
 FieldComplex<T> b3,
 FieldComplex<T> a4,
 FieldComplex<T> b4)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldComplex<T> linearCombination(double a1,
 FieldComplex<T> b1,
 double a2,
 FieldComplex<T> b2,
 double a3,
 FieldComplex<T> b3,
 double a4,
 FieldComplex<T> b4)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)

ceil

public FieldComplex<T> ceil()

Get the smallest whole number larger than instance.

Specified by:

ceil in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

ceil(this)

floor

public FieldComplex<T> floor()

Get the largest whole number smaller than instance.

Specified by:

floor in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

floor(this)

rint

public FieldComplex<T> rint()

Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.

Specified by:

rint in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5

remainder

public FieldComplex<T> remainder(double a)

IEEE remainder operator.

for complex numbers, the integer n corresponding to this.subtract(remainder(a)).divide(a) is a Wikipedia - Gaussian integer.

Specified by:

remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

remainder

public FieldComplex<T> remainder(FieldComplex<T> a)

IEEE remainder operator.

for complex numbers, the integer n corresponding to this.subtract(remainder(a)).divide(a) is a Wikipedia - Gaussian integer.

Specified by:

remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

sign

public FieldComplex<T> sign()

Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)

Specified by:

sign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

copySign

public FieldComplex<T> copySign(FieldComplex<T> z)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

The signs of real and imaginary parts are copied independently.

Specified by:

copySign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

z - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

copySign

public FieldComplex<T> copySign(double r)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Specified by:

copySign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

r - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

toDegrees

public FieldComplex<T> toDegrees()

Convert radians to degrees, with error of less than 0.5 ULP

Specified by:

toDegrees in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

instance converted into degrees

toRadians

public FieldComplex<T> toRadians()

Convert degrees to radians, with error of less than 0.5 ULP

Specified by:

toRadians in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

instance converted into radians

getPi

public FieldComplex<T> getPi()

Get the Archimedes constant π.

Archimedes constant is the ratio of a circle's circumference to its diameter.

Specified by:

getPi in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

Archimedes constant π