102 lines
4 KiB
Groovy
102 lines
4 KiB
Groovy
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class Complex {
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final Number real, imag
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static final Complex i = [0,1] as Complex
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Complex(Number r, Number i = 0) { (real, imag) = [r, i] }
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Complex(Map that) { (real, imag) = [that.real ?: 0, that.imag ?: 0] }
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Complex plus (Complex c) { [real + c.real, imag + c.imag] as Complex }
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Complex plus (Number n) { [real + n, imag] as Complex }
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Complex minus (Complex c) { [real - c.real, imag - c.imag] as Complex }
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Complex minus (Number n) { [real - n, imag] as Complex }
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Complex multiply (Complex c) { [real*c.real - imag*c.imag , imag*c.real + real*c.imag] as Complex }
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Complex multiply (Number n) { [real*n , imag*n] as Complex }
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Complex div (Complex c) { this * c.recip() }
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Complex div (Number n) { this * (1/n) }
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Complex negative () { [-real, -imag] as Complex }
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/** the complex conjugate of this complex number. Overloads the bitwise complement (~) operator. */
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Complex bitwiseNegate () { [real, -imag] as Complex }
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/** the magnitude of this complex number. */
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// could also use Math.sqrt( (this * (~this)).real )
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Number getAbs() { Math.sqrt( real*real + imag*imag ) }
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/** the magnitude of this complex number. */
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Number abs() { this.abs }
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/** the reciprocal of this complex number. */
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Complex getRecip() { (~this) / (ρ**2) }
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/** the reciprocal of this complex number. */
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Complex recip() { this.recip }
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/** derived polar angle θ (theta) for polar form. Normalized to 0 ≤ θ < 2π. */
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Number getTheta() {
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def θ = Math.atan2(imag,real)
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θ = θ < 0 ? θ + 2 * Math.PI : θ
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}
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/** derived polar angle θ (theta) for polar form. Normalized to 0 ≤ θ < 2π. */
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Number getΘ() { this.theta } // this is greek uppercase theta
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/** derived polar magnitude ρ (rho) for polar form. */
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Number getRho() { this.abs }
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/** derived polar magnitude ρ (rho) for polar form. */
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Number getΡ() { this.abs } // this is greek uppercase rho, not roman P
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/** Runs Euler's polar-to-Cartesian complex conversion,
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* converting [ρ, θ] inputs into a [real, imag]-based complex number */
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static Complex fromPolar(Number ρ, Number θ) {
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[ρ * Math.cos(θ), ρ * Math.sin(θ)] as Complex
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}
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/** Creates new complex with same magnitude ρ, but different angle θ */
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Complex withTheta(Number θ) { fromPolar(this.rho, θ) }
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/** Creates new complex with same magnitude ρ, but different angle θ */
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Complex withΘ(Number θ) { fromPolar(this.rho, θ) }
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/** Creates new complex with same angle θ, but different magnitude ρ */
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Complex withRho(Number ρ) { fromPolar(ρ, this.θ) }
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/** Creates new complex with same angle θ, but different magnitude ρ */
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Complex withΡ(Number ρ) { fromPolar(ρ, this.θ) } // this is greek uppercase rho, not roman P
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static Complex exp(Complex c) { fromPolar(Math.exp(c.real), c.imag) }
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static Complex log(Complex c) { [Math.log(c.rho), c.theta] as Complex }
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Complex power(Complex c) {
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def zero = [0] as Complex
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(this == zero && c != zero) \
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? zero \
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: c == 1 \
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? this \
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: exp( log(this) * c )
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}
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Complex power(Number n) { this ** ([n, 0] as Complex) }
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boolean equals(that) {
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that != null && (that instanceof Complex \
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? [this.real, this.imag] == [that.real, that.imag] \
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: that instanceof Number && [this.real, this.imag] == [that, 0])
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}
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int hashCode() { [real, imag].hashCode() }
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String toString() {
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def realPart = "${real}"
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def imagPart = imag.abs() == 1 ? "i" : "${imag.abs()}i"
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real == 0 && imag == 0 \
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? "0" \
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: real == 0 \
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? (imag > 0 ? '' : "-") + imagPart \
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: imag == 0 \
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? realPart \
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: realPart + (imag > 0 ? " + " : " - ") + imagPart
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}
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}
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