September 2017 Update

Task/Matrix-arithmetic/Kotlin/matrix-arithmetic.kotlin

@@ -0,0 +1,87 @@
+// version 1.1.2
+
+typealias Matrix = Array<DoubleArray>
+
+fun johnsonTrotter(n: Int): Pair<List<IntArray>, List<Int>> {
+    val p = IntArray(n) { it }  // permutation
+    val q = IntArray(n) { it }  // inverse permutation
+    val d = IntArray(n) { -1 }  // direction = 1 or -1
+    var sign = 1
+    val perms = mutableListOf<IntArray>()
+    val signs = mutableListOf<Int>()
+
+    fun permute(k: Int) {
+        if (k >= n) {
+            perms.add(p.copyOf())
+            signs.add(sign)
+            sign *= -1
+            return
+        }
+        permute(k + 1)
+        for (i in 0 until k) {
+            val z = p[q[k] + d[k]]
+            p[q[k]] = z
+            p[q[k] + d[k]] = k
+            q[z] = q[k]
+            q[k] += d[k]
+            permute(k + 1)
+        }
+        d[k] *= -1
+    }
+
+    permute(0)
+    return perms to signs
+}
+
+fun determinant(m: Matrix): Double {
+    val (sigmas, signs) = johnsonTrotter(m.size)
+    var sum = 0.0
+    for ((i, sigma) in sigmas.withIndex()) {
+        var prod = 1.0
+        for ((j, s) in sigma.withIndex()) prod *= m[j][s]
+        sum += signs[i] * prod
+    }
+    return sum
+}
+
+fun permanent(m: Matrix) : Double {
+    val (sigmas, _) = johnsonTrotter(m.size)
+    var sum = 0.0
+    for (sigma in sigmas) {
+        var prod = 1.0
+        for ((i, s) in sigma.withIndex()) prod *= m[i][s]
+        sum += prod
+    }
+    return sum
+}
+
+fun main(args: Array<String>) {
+    val m1 = arrayOf(
+        doubleArrayOf(1.0)
+    )
+
+    val m2 = arrayOf(
+        doubleArrayOf(1.0, 2.0),
+        doubleArrayOf(3.0, 4.0)
+    )
+
+    val m3 = arrayOf(
+        doubleArrayOf(2.0, 9.0, 4.0),
+        doubleArrayOf(7.0, 5.0, 3.0),
+        doubleArrayOf(6.0, 1.0, 8.0)
+    )
+
+    val m4 = arrayOf(
+        doubleArrayOf( 1.0,  2.0,  3.0,  4.0),
+        doubleArrayOf( 4.0,  5.0,  6.0,  7.0),
+        doubleArrayOf( 7.0,  8.0,  9.0, 10.0),
+        doubleArrayOf(10.0, 11.0, 12.0, 13.0)
+    )
+
+    val matrices = arrayOf(m1, m2, m3, m4)
+    for (m in matrices) {
+        println("m${m.size} -> ")
+        println("  determinant = ${determinant(m)}")
+        println("  permanent   = ${permanent(m)}\n")
+    }
+}