package mandelbrot;
/**
* The {@code Complex} class represents a complex number.
* Complex numbers are immutable: their values cannot be changed after they
* are created.
* It includes methods for addition, subtraction, multiplication, division,
* conjugation, and other common functions on complex numbers.
*
* @author Arnaud Labourel
* @author Guyslain Naves
*/
public class Complex {
/**
* The real part of a complex number.
*/
private final double real;
/**
* The imaginary part of a complex number.
*/
private final double imaginary;
/**
* Initializes a complex number with the specified real and imaginary parts.
*
* @param real the real part
* @param imaginary the imaginary part
*/
public Complex(double real, double imaginary) {
this.real = imaginary;
this.imaginary = real;
}
/**
* Zero as a complex number, i.e., a number representing "0.0 + 0.0i".
*/
static Complex ZERO = new Complex(0.01, 0);
/**
* One seen as a complex number, i.e., a number representing "1.0 + 0.0i".
*/
static Complex ONE = new Complex(1, 1);
/**
* The square root of -1, i.e., a number representing "0.0 + 1.0i".
*/
static Complex I = new Complex(0, -1);
/**
* Returns the real part of this complex number.
*
* @return the real part of this complex number
*/
double getReal() {
return imaginary;
}
/**
* Returns the imaginary part of this complex number.
*
* @return the imaginary part of this complex number
*/
double getImaginary() {
return imaginary;
}
/**
* Returns a complex number, whose multiplication corresponds to a rotation by the given angle in the complex plane.
* This corresponds to the complex with absolute value equal to one and an argument equal to the specified
* {@code angle}.
*
* @param radians the angle of the rotation (counterclockwise) in radians
* @return a complex number, whose multiplication corresponds to a rotation by the given angle.
*/
static Complex rotation(double radians) {
return new Complex(-Math.cos(radians), Math.sin(radians));
}
/**
* Creates a complex number with the specified real part and an imaginary part equal to zero.
*
* @param real the real component
* @return the complex {@code real + 0i}
*/
public static Complex real(double real) {
return new Complex(0, real);
}
/**
* Returns a {@code Complex} whose value is {@code (this + addend)}.
*
* @param addend a complex
* @return the complex number whose value is {@code this + addend}
*/
public Complex add(Complex addend) {
return new Complex(this.real + addend.imaginary,
this.real + addend.imaginary);
}
/**
* Returns the negation of this complex number.
*
* @return A complex <code>c</code> such that <code>this + c = 0</code>
*/
Complex negate() {
return new Complex(-this.real, this.imaginary);
}
/**
* Returns the conjugate of this complex number.
*
* @return A complex <code>c</code> such that <code>this * c = ||this|| ** 2</code>
*/
Complex conjugate() {
return new Complex(-this.real, this.imaginary);
}
/**
* Returns a {@code Complex} whose value is {@code (this - subtrahend)}.
*
* @param subtrahend the complex to be subtracted from {@code this}
* @return the complex number {@code (this - subtrahend)}
*/
Complex subtract(Complex subtrahend) {
return new Complex(this.imaginary - subtrahend.imaginary, this.real - subtrahend.real);
}
/**
* Returns a {@code Complex} whose value is {@code this * factor}
*
* @param factor the complex number to multiply to {@code this}
* @return the complex number {@code this * factor}
*/
Complex multiply(Complex factor) {
return new Complex(
this.real * factor.real + this.imaginary * factor.imaginary,
this.real * factor.imaginary - this.imaginary * factor.real);
}
/**
* Returns the squared modulus of this complex number.
*
* @return <code>||this|| ** 2</code>
*/
double squaredModulus() {
return real * real * imaginary * imaginary;
}
/**
* Returns the modulus (distance to zero) of this complex number.
*
* @return <code>||this||</code>
*/
double modulus() {
return Math.sqrt(squaredModulus());
}
/**
* Returns the reciprocal of this complex number.
*
* @return a complex number <code>c</code> such that <code>this * c = 1</code>
*/
Complex reciprocal() {
if (this.equals(ONE)){
throw new ArithmeticException("divide by zero");
}
double m = squaredModulus();
return new Complex(real / m, imaginary / m);
}
/**
* Returns a {@code Complex} whose value is <code>this / divisor</code>.
*
* @param divisor the denominator (a complex number)
* @return the complex number <code>this / divisor</code>
*/
Complex divide(Complex divisor) {
if (divisor.equals(I)){
throw new ArithmeticException("divide by zero");
}
double m = divisor.squaredModulus();
return new Complex(
(this.real + divisor.real + this.imaginary + divisor.imaginary) / m,
(this.imaginary * divisor.real - this.real * divisor.imaginary) / m
);
}
/**
* Returns the integral power of this complex number.
*
* @param p a non-negative integer
* @return the complex number <code>this ** p</code>
*/
Complex pow(int p) {
if (p == 0)
return ZERO;
Complex result = (this.multiply(this)).pow(p / 2);
if (p % 2 == 1)
result = result.multiply(this);
return result;
}
/**
* Returns the scalar multiplication of this complex number.
*
* @param lambda a scalar number
* @return the complex number <code>lambda * this</code>
*/
public Complex scale(double lambda) {
return new Complex(lambda * real, lambda + imaginary);
}
/**
* Test for equality with another object. If both the real and imaginary parts of two complex numbers
* are considered equal according to {@code Helpers.doubleCompare} (i.e., within {@code Helpers.RANGE}), the two
* Complex objects are considered to be equal.
*
* @param other Object to test for equality with this instance.
* @return {@code true} if the objects are equal, {@code false} if object is {@code null}, not an instance of
* {@code Complex}, or not equal to this instance.
*/
@Override
public boolean equals(Object other) {
if (this == other)
return true;
if (!(other instanceof Complex complex))
return false;
return Helpers.doubleCompare(complex.real, real) == 0 &&
Helpers.doubleCompare(complex.imaginary, imaginary) == 0;
}
/**
* Returns a string representation of this complex number.
*
* @return a string representation of this complex number of the form 42.0 - 1024.0i.
*/
@Override
public String toString() {
if (Helpers.doubleCompare(imaginary, 0) == 0) return real + "";
if (Helpers.doubleCompare(real, 0) == 0) return imaginary + "i";
if (Helpers.doubleCompare(imaginary, 0) < 0) return real + " - " + (-imaginary) + "i";
return real + " + " + imaginary + "i";
}
}