java.lang.Object
- com.singularsys.jep.standard.Complex
- - com.singularsys.jep.standard.Complex.NonPropagatingImmutableComplex
  - - com.singularsys.jep.standard.ImmutableComplex

All Implemented Interfaces:

java.io.Serializable
```
public class ImmutableComplex
extends Complex.NonPropagatingImmutableComplex
```
An Immutable version of the Complex numbers. In this class the values of complex numbers can never be changed, further any operation like conj() or add(Complex) will also return an ImmutableComplex.

Since:

Jep 4.0

See Also:

Serialized Form

Nested Class Summary
- Nested classes/interfaces inherited from class com.singularsys.jep.standard.Complex
  Complex.NonPropagatingImmutableComplex

Field Summary

Fields
Modifier and Type	Field	Description
`static Complex`	`U_I`	Unmodifiable constant 0+1 i
`static Complex`	`U_MINUS_I`	Unmodifiable constant 0-1 i
`static Complex`	`U_MINUS_ONE`	Unmodifiable constant -1+0 i
`static Complex`	`U_ONE`	Unmodifiable constant 1+0 i
`static Complex`	`U_ZERO`	Unmodifiable constant 0+0 i

Fields inherited from class com.singularsys.jep.standard.Complex
I, MINUS_I, MINUS_ONE, ONE, ZERO

Constructor Summary

Constructors
Constructor	Description
`ImmutableComplex()`
`ImmutableComplex(double x)`
`ImmutableComplex(double x, double y)`
`ImmutableComplex(Complex z)`
`ImmutableComplex(java.lang.Number x)`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`ImmutableComplex`	`acos()`	Returns the arccos of this complex number.
`ImmutableComplex`	`acosh()`	Returns the inverse hyperbolic cosine of this complex number.
`ImmutableComplex`	`add(Complex z)`	Adds the complex number with another complex value.
`ImmutableComplex`	`asin()`	Returns the arcsin of this complex number.
`ImmutableComplex`	`asinh()`	Returns the inverse hyperbolic sine of this complex number.
`ImmutableComplex`	`atan()`	Returns the arc tangent of this complex number.
`ImmutableComplex`	`atanh()`	Returns the inverse hyperbolic tangent of this complex number.
`ImmutableComplex`	`conj()`	Returns the complex conjugate.
`ImmutableComplex`	`cos()`	Returns the cosine of this complex number.
`ImmutableComplex`	`cosh()`	Returns the hyperbolic cosine of this complex number.
`ImmutableComplex`	`div(Complex z)`	Returns the result of dividing this complex number by the parameter.
`ImmutableComplex`	`fastPower(int n)`	Calculate integer powers by repeated multiplications.
`ImmutableComplex`	`log()`	Returns the logarithm of this complex number.
`ImmutableComplex`	`mul(double b)`	Multiply the complex number with a double value.
`ImmutableComplex`	`mul(Complex z)`	Multiply the complex number with another complex value.
`ImmutableComplex`	`neg()`	Returns the negative value of this complex number.
`static ImmutableComplex`	`polarValueOf(java.lang.Number r, java.lang.Number theta)`
`ImmutableComplex`	`power(double exponent)`	Returns this complex number raised to a double argument.
`ImmutableComplex`	`power(int n)`	Raise this complex to an integer power.
`ImmutableComplex`	`power(Complex exponent)`	Returns the value of this complex number raised to the power of a complex exponent If the this is zero return this.
`ImmutableComplex`	`powerD(double exponent)`	Returns the value of this complex number raised to the power of a real component (in double precision).
`ImmutableComplex`	`powerI(int n)`	Raise a complex number to an integer power.
`ImmutableComplex`	`reciprocal()`	Returns the reciprocal of a complex number 1/z.
`ImmutableComplex`	`sin()`	Returns the sine of this complex number.
`ImmutableComplex`	`sinh()`	Returns the hyperbolic sine of this complex number.
`ImmutableComplex`	`sqrt()`	Calculates the square root of this object.
`ImmutableComplex`	`sub(Complex z)`	Subtracts a complex number from this
`ImmutableComplex`	`tan()`	Returns the tangent of this complex number.
`ImmutableComplex`	`tanh()`	Returns the hyperbolic tangent of this complex number.

Methods inherited from class com.singularsys.jep.standard.Complex.NonPropagatingImmutableComplex
set, set, setIm, setRe

Methods inherited from class com.singularsys.jep.standard.Complex
abs, abs2, arg, doubleValue, eq, equals, equals, floatValue, hashCode, im, intValue, isInfinite, isNaN, longValue, re, toString, toString, toString, toString

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - U_ZERO
```
public static final Complex U_ZERO
```
    Unmodifiable constant 0+0 i
  - U_ONE
```
public static final Complex U_ONE
```
    Unmodifiable constant 1+0 i
  - U_MINUS_ONE
```
public static final Complex U_MINUS_ONE
```
    Unmodifiable constant -1+0 i
  - U_I
```
public static final Complex U_I
```
    Unmodifiable constant 0+1 i
  - U_MINUS_I
```
public static final Complex U_MINUS_I
```
    Unmodifiable constant 0-1 i
- Constructor Detail
  - ImmutableComplex
```
public ImmutableComplex()
```
  - ImmutableComplex
```
public ImmutableComplex(Complex z)
```
  - ImmutableComplex
```
public ImmutableComplex(double x,
                        double y)
```
  - ImmutableComplex
```
public ImmutableComplex(double x)
```
  - ImmutableComplex
```
public ImmutableComplex(java.lang.Number x)
```
- Method Detail
  - polarValueOf
```
public static ImmutableComplex polarValueOf(java.lang.Number r,
                                            java.lang.Number theta)
```
  - neg
```
public ImmutableComplex neg()
```
    Description copied from class: Complex
    
    Returns the negative value of this complex number.
    
    Overrides:
    
    neg in class Complex
    
    Returns:
    
    -(x+i y)
  - mul
```
public ImmutableComplex mul(double b)
```
    Description copied from class: Complex
    
    Multiply the complex number with a double value.
    
    Overrides:
    
    mul in class Complex
    
    Parameters:
    
    b - real number to multiply by
    
    Returns:
    
    The result of the multiplication
  - add
```
public ImmutableComplex add(Complex z)
```
    Description copied from class: Complex
    
    Adds the complex number with another complex value.
    
    Overrides:
    
    add in class Complex
    
    Parameters:
    
    z - complex number to add
    
    Returns:
    
    The result of the addition
  - sub
```
public ImmutableComplex sub(Complex z)
```
    Description copied from class: Complex
    
    Subtracts a complex number from this
    
    Overrides:
    
    sub in class Complex
    
    Parameters:
    
    z - complex number to subtract
    
    Returns:
    
    (this) - z
  - mul
```
public ImmutableComplex mul(Complex z)
```
    Description copied from class: Complex
    
    Multiply the complex number with another complex value.
    
    Overrides:
    
    mul in class Complex
    
    Parameters:
    
    z - complex number to multiply
    
    Returns:
    
    The result of the multiplication
  - div
```
public ImmutableComplex div(Complex z)
```
    Description copied from class: Complex
    
    Returns the result of dividing this complex number by the parameter. Algorithm adapted from Numerical Recipes in C - The Art of Scientific Computing ISBN 0-521-43108-5
    
    Overrides:
    
    div in class Complex
    
    Parameters:
    
    z - complex number to divide by
    
    Returns:
    
    (this)/z
  - reciprocal
```
public ImmutableComplex reciprocal()
```
    Description copied from class: Complex
    
    Returns the reciprocal of a complex number 1/z. This was broken in version < 4.0.
    
    Overrides:
    
    reciprocal in class Complex
    
    Returns:
    
    1/(this)
  - power
```
public ImmutableComplex power(int n)
```
    Description copied from class: Complex
    
    Raise this complex to an integer power. For small power use the Complex.fastPower(int) method which does repeated multiplication and is generally faster. For larger power use Complex.powerI(int) which can be more accurate.
    
    Overrides:
    
    power in class Complex
    
    Parameters:
    
    n - the power
    
    Returns:
    
    (this)^n
  - powerI
```
public ImmutableComplex powerI(int n)
```
    Description copied from class: Complex
    
    Raise a complex number to an integer power. Uses the polar form [r;th]^n -> [r^n;n th] and the efficient power method from Power.power(double, int) Slower than
    
    Overrides:
    
    powerI in class Complex
    
    Returns:
  - fastPower
```
public ImmutableComplex fastPower(int n)
```
    Description copied from class: Complex
    
    Calculate integer powers by repeated multiplications. So z^5 = z*(z*z)*(z*z). This routine is generally faster but can accumulate errors for large exponents.
    
    Overrides:
    
    fastPower in class Complex
    
    Returns:
  - powerD
```
public ImmutableComplex powerD(double exponent)
```
    Description copied from class: Complex
    
    Returns the value of this complex number raised to the power of a real component (in double precision).
    This method considers special cases where a simpler algorithm would return "ugly" results.
    For example when the expression (-1e40)^0.5 is evaluated without considering the special case, the argument of the base is the double number closest to pi. When sin and cos are used for the final evaluation of the result, the slight difference of the argument from pi causes a non-zero value for the real component of the result. Because the value of the base is so high, the error is magnified. Although the error is normal for floating point calculations, the consideration of commonly occurring special cases improves the accuracy and aesthetics of the results.
    If you know a more elegant way to solve this problem, please let me know at [email protected] .
    Testing with roots of unity show errors are typically within 128 * ulp, so |actual-result|/|actual| < 1e-13.
    
    Overrides:
    
    powerD in class Complex
    
    Parameters:
    
    exponent - exponent
    
    Returns:
    
    (this)^exponent
  - power
```
public ImmutableComplex power(double exponent)
```
    Description copied from class: Complex
    
    Returns this complex number raised to a double argument. If the exponent is an integer returns Complex.power(int) otherwise calls Complex.powerD(double).
    
    Overrides:
    
    power in class Complex
    
    Returns:
    
    this^exponent
  - power
```
public ImmutableComplex power(Complex exponent)
```
    Description copied from class: Complex
    
    Returns the value of this complex number raised to the power of a complex exponent If the this is zero return this. If the exponent has zero imaginary part use
    
    Overrides:
    
    power in class Complex
    
    Parameters:
    
    exponent - exponent
    
    Returns:
    
    (this)^exponent
  - conj
```
public ImmutableComplex conj()
```
    Description copied from class: Complex
    
    Returns the complex conjugate.
    
    Overrides:
    
    conj in class Complex
    
    Returns:
    
    (x-i y)
  - log
```
public ImmutableComplex log()
```
    Description copied from class: Complex
    
    Returns the logarithm of this complex number. The real part is Math.log(this.abs()) and the complex part is this.arg(), in the range -pi .. pi.
    
    Overrides:
    
    log in class Complex
    
    Returns:
    
    ln(z) = ln(r) + i th
  - sqrt
```
public ImmutableComplex sqrt()
```
    Description copied from class: Complex
    
    Calculates the square root of this object. Adapted from Numerical Recipes in C - The Art of Scientific Computing (ISBN 0-521-43108-5)
    
    Overrides:
    
    sqrt in class Complex
    
    Returns:
    
    sqrt(z)
  - sin
```
public ImmutableComplex sin()
```
    Description copied from class: Complex
    
    Returns the sine of this complex number.
    
    Overrides:
    
    sin in class Complex
    
    Returns:
    
    sin(this)
  - cos
```
public ImmutableComplex cos()
```
    Description copied from class: Complex
    
    Returns the cosine of this complex number.
    
    Overrides:
    
    cos in class Complex
    
    Returns:
    
    cos(this)
  - tan
```
public ImmutableComplex tan()
```
    Description copied from class: Complex
    
    Returns the tangent of this complex number.
    
    Overrides:
    
    tan in class Complex
    
    Returns:
    
    tan(this)
  - asin
```
public ImmutableComplex asin()
```
    Description copied from class: Complex
    
    Returns the arcsin of this complex number.
    
    Overrides:
    
    asin in class Complex
    
    Returns:
    
    asin(this)
  - acos
```
public ImmutableComplex acos()
```
    Description copied from class: Complex
    
    Returns the arccos of this complex number.
    
    Overrides:
    
    acos in class Complex
    
    Returns:
    
    acos(this)
  - atan
```
public ImmutableComplex atan()
```
    Description copied from class: Complex
    
    Returns the arc tangent of this complex number.
    
    Overrides:
    
    atan in class Complex
    
    Returns:
    
    atan(this)
  - sinh
```
public ImmutableComplex sinh()
```
    Description copied from class: Complex
    
    Returns the hyperbolic sine of this complex number.
    
    Overrides:
    
    sinh in class Complex
    
    Returns:
    
    sinh(this)
  - cosh
```
public ImmutableComplex cosh()
```
    Description copied from class: Complex
    
    Returns the hyperbolic cosine of this complex number.
    
    Overrides:
    
    cosh in class Complex
    
    Returns:
    
    cosh(this)
  - tanh
```
public ImmutableComplex tanh()
```
    Description copied from class: Complex
    
    Returns the hyperbolic tangent of this complex number.
    
    Overrides:
    
    tanh in class Complex
    
    Returns:
    
    tanh(this)
  - asinh
```
public ImmutableComplex asinh()
```
    Description copied from class: Complex
    
    Returns the inverse hyperbolic sine of this complex number.
    
    Overrides:
    
    asinh in class Complex
    
    Returns:
    
    asinh(this)
  - acosh
```
public ImmutableComplex acosh()
```
    Description copied from class: Complex
    
    Returns the inverse hyperbolic cosine of this complex number.
    
    Overrides:
    
    acosh in class Complex
    
    Returns:
    
    acosh(this)
  - atanh
```
public ImmutableComplex atanh()
```
    Description copied from class: Complex
    
    Returns the inverse hyperbolic tangent of this complex number.
    
    Overrides:
    
    atanh in class Complex
    
    Returns:
    
    atanh(this)

Class ImmutableComplex

Nested Class Summary

Nested classes/interfaces inherited from class com.singularsys.jep.standard.Complex

Field Summary

Fields inherited from class com.singularsys.jep.standard.Complex

Constructor Summary

Method Summary

Methods inherited from class com.singularsys.jep.standard.Complex.NonPropagatingImmutableComplex

Methods inherited from class com.singularsys.jep.standard.Complex

Methods inherited from class java.lang.Object

Field Detail

U_ZERO

U_ONE

U_MINUS_ONE

U_I

U_MINUS_I

Constructor Detail

ImmutableComplex

ImmutableComplex

ImmutableComplex

ImmutableComplex

ImmutableComplex

Method Detail

polarValueOf

neg

mul

add

sub

mul

div

reciprocal

power

powerI

fastPower

powerD

power

power

conj

log

sqrt

sin

cos

tan

asin

acos

atan

sinh

cosh

tanh

asinh

acosh

atanh