June 2018 Update

Task/LU-decomposition/Kotlin/lu-decomposition.kotlin

@@ -0,0 +1,102 @@
+// version 1.1.4-3
+
+typealias Vector = DoubleArray
+typealias Matrix = Array<Vector>
+
+operator fun Matrix.times(other: Matrix): Matrix {
+    val rows1 = this.size
+    val cols1 = this[0].size
+    val rows2 = other.size
+    val cols2 = other[0].size
+    require(cols1 == rows2)
+    val result = Matrix(rows1) { Vector(cols2) }
+    for (i in 0 until rows1) {
+        for (j in 0 until cols2) {
+            for (k in 0 until rows2) {
+                result[i][j] += this[i][k] * other[k][j]
+            }
+        }
+    }
+    return result
+}
+
+fun pivotize(m: Matrix): Matrix {
+    val n = m.size
+    val im = Array(n) { Vector(n) }
+    for (i in 0 until n) im[i][i] = 1.0
+    for (i in 0 until n) {
+        var max = m[i][i]
+        var row = i
+        for (j in i until n) {
+            if (m[j][i] > max) {
+                max = m[j][i]
+                row = j
+            }
+        }
+        if (i != row) {
+            val t = im[i]
+            im[i] = im[row]
+            im[row] = t
+        }
+    }
+    return im
+}
+
+fun lu(a: Matrix): Array<Matrix> {
+    val n = a.size
+    val l = Array(n) { Vector(n) }
+    val u = Array(n) { Vector(n) }
+    val p = pivotize(a)
+    val a2 = p * a
+
+    for (j in 0 until n) {
+        l[j][j] = 1.0
+        for (i in 0 until j + 1) {
+            var sum = 0.0
+            for (k in 0 until i) sum += u[k][j] * l[i][k]
+            u[i][j] = a2[i][j] - sum
+        }
+        for (i in j until n) {
+            var sum2 = 0.0
+            for(k in 0 until j) sum2 += u[k][j] * l[i][k]
+            l[i][j] = (a2[i][j] - sum2) / u[j][j]
+        }
+    }
+    return arrayOf(l, u, p)
+}
+
+fun printMatrix(title: String, m: Matrix, f: String) {
+    val n = m.size
+    println("\n$title\n")
+    for (i in 0 until n) {
+        for (j in 0 until n) print("${f.format(m[i][j])}  ")
+        println()
+    }
+}
+
+fun main(args: Array<String>) {
+    val a1 = arrayOf(
+        doubleArrayOf( 1.0,  3.0,  5.0),
+        doubleArrayOf( 2.0,  4.0,  7.0),
+        doubleArrayOf( 1.0,  1.0,  0.0)
+    )
+    val (l1, u1, p1) = lu(a1)
+    println("EXAMPLE 1:-")
+    printMatrix("A:", a1, "%1.0f")
+    printMatrix("L:", l1, "% 7.5f")
+    printMatrix("U:", u1, "% 8.5f")
+    printMatrix("P:", p1, "%1.0f")
+
+    val a2 = arrayOf(
+        doubleArrayOf(11.0,  9.0, 24.0,  2.0),
+        doubleArrayOf( 1.0,  5.0,  2.0,  6.0),
+        doubleArrayOf( 3.0, 17.0, 18.0,  1.0),
+        doubleArrayOf( 2.0,  5.0,  7.0,  1.0)
+    )
+    val (l2, u2, p2) = lu(a2)
+    println("\nEXAMPLE 2:-")
+    printMatrix("A:", a2, "%2.0f")
+    printMatrix("L:", l2, "%7.5f")
+    printMatrix("U:", u2, "%8.5f")
+    printMatrix("P:", p2, "%1.0f")
+}