Data commit

Task/Conjugate-transpose/Scala/conjugate-transpose.scala

@@ -0,0 +1,77 @@
+object ConjugateTranspose {
+
+  case class Complex(re: Double, im: Double) {
+    def conjugate(): Complex = Complex(re, -im)
+    def +(other: Complex) = Complex(re + other.re, im + other.im)
+    def *(other: Complex) = Complex(re * other.re - im * other.im, re * other.im + im * other.re)
+    override def toString(): String = {
+      if (im < 0) {
+        s"${re}${im}i"
+      } else {
+        s"${re}+${im}i"
+      }
+    }
+  }
+
+  case class Matrix(val entries: Vector[Vector[Complex]]) {
+
+    def *(other: Matrix): Matrix = {
+      new Matrix(
+        Vector.tabulate(entries.size, other.entries(0).size)((r, c) => {
+          val rightRow = entries(r)
+          val leftCol = other.entries.map(_(c))
+          rightRow.zip(leftCol)
+            .map{ case (x, y) => x * y } // multiply pair-wise
+            .foldLeft(new Complex(0,0)){ case (x, y) => x + y } // sum over all
+        })
+      )
+    }
+
+    def conjugateTranspose(): Matrix = {
+      new Matrix(
+        Vector.tabulate(entries(0).size, entries.size)((r, c) => entries(c)(r).conjugate)
+      )
+    }
+
+    def isHermitian(): Boolean = {
+      this == conjugateTranspose()
+    }
+
+    def isNormal(): Boolean = {
+      val ct = conjugateTranspose()
+      this * ct == ct * this
+    }
+
+    def isIdentity(): Boolean = {
+      val entriesWithIndexes = for (r <- 0 until entries.size; c <- 0 until entries(r).size) yield (r, c, entries(r)(c))
+      entriesWithIndexes.forall { case (r, c, x) =>
+        if (r == c) {
+          x == Complex(1.0, 0.0)
+        } else {
+          x == Complex(0.0, 0.0)
+        }
+      }
+    }
+
+    def isUnitary(): Boolean = {
+      (this * conjugateTranspose()).isIdentity()
+    }
+
+    override def toString(): String = {
+      entries.map("  " + _.mkString("[", ",", "]")).mkString("[\n", "\n", "\n]")
+    }
+
+  }
+
+  def main(args: Array[String]): Unit = {
+    val m = new Matrix(
+      Vector.fill(3, 3)(new Complex(Math.random() * 2 - 1.0, Math.random() * 2 - 1.0))
+    )
+    println("Matrix: " + m)
+    println("Conjugate Transpose: " + m.conjugateTranspose())
+    println("Hermitian: " + m.isHermitian())
+    println("Normal: " + m.isNormal())
+    println("Unitary: " + m.isUnitary())
+  }
+
+}