77 lines
2.1 KiB
Scala
77 lines
2.1 KiB
Scala
object ConjugateTranspose {
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case class Complex(re: Double, im: Double) {
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def conjugate(): Complex = Complex(re, -im)
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def +(other: Complex) = Complex(re + other.re, im + other.im)
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def *(other: Complex) = Complex(re * other.re - im * other.im, re * other.im + im * other.re)
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override def toString(): String = {
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if (im < 0) {
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s"${re}${im}i"
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} else {
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s"${re}+${im}i"
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}
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}
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}
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case class Matrix(val entries: Vector[Vector[Complex]]) {
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def *(other: Matrix): Matrix = {
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new Matrix(
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Vector.tabulate(entries.size, other.entries(0).size)((r, c) => {
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val rightRow = entries(r)
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val leftCol = other.entries.map(_(c))
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rightRow.zip(leftCol)
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.map{ case (x, y) => x * y } // multiply pair-wise
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.foldLeft(new Complex(0,0)){ case (x, y) => x + y } // sum over all
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})
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)
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}
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def conjugateTranspose(): Matrix = {
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new Matrix(
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Vector.tabulate(entries(0).size, entries.size)((r, c) => entries(c)(r).conjugate)
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)
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}
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def isHermitian(): Boolean = {
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this == conjugateTranspose()
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}
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def isNormal(): Boolean = {
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val ct = conjugateTranspose()
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this * ct == ct * this
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}
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def isIdentity(): Boolean = {
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val entriesWithIndexes = for (r <- 0 until entries.size; c <- 0 until entries(r).size) yield (r, c, entries(r)(c))
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entriesWithIndexes.forall { case (r, c, x) =>
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if (r == c) {
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x == Complex(1.0, 0.0)
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} else {
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x == Complex(0.0, 0.0)
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}
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}
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}
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def isUnitary(): Boolean = {
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(this * conjugateTranspose()).isIdentity()
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}
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override def toString(): String = {
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entries.map(" " + _.mkString("[", ",", "]")).mkString("[\n", "\n", "\n]")
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}
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}
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def main(args: Array[String]): Unit = {
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val m = new Matrix(
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Vector.fill(3, 3)(new Complex(Math.random() * 2 - 1.0, Math.random() * 2 - 1.0))
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)
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println("Matrix: " + m)
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println("Conjugate Transpose: " + m.conjugateTranspose())
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println("Hermitian: " + m.isHermitian())
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println("Normal: " + m.isNormal())
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println("Unitary: " + m.isUnitary())
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}
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}
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