June 2018 Update

Task/Multiple-regression/Kotlin/multiple-regression.kotlin

@@ -0,0 +1,121 @@
+// Version 1.2.31
+
+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 Matrix.transpose(): Matrix {
+    val rows = this.size
+    val cols = this[0].size
+    val trans = Matrix(cols) { Vector(rows) }
+    for (i in 0 until cols) {
+        for (j in 0 until rows) trans[i][j] = this[j][i]
+    }
+    return trans
+}
+
+fun Matrix.inverse(): Matrix {
+    val len = this.size
+    require(this.all { it.size == len }) { "Not a square matrix" }
+    val aug = Array(len) { DoubleArray(2 * len) }
+    for (i in 0 until len) {
+        for (j in 0 until len) aug[i][j] = this[i][j]
+        // augment by identity matrix to right
+        aug[i][i + len] = 1.0
+    }
+    aug.toReducedRowEchelonForm()
+    val inv = Array(len) { DoubleArray(len) }
+    // remove identity matrix to left
+    for (i in 0 until len) {
+        for (j in len until 2 * len) inv[i][j - len] = aug[i][j]
+    }
+    return inv
+}
+
+fun Matrix.toReducedRowEchelonForm() {
+    var lead = 0
+    val rowCount = this.size
+    val colCount = this[0].size
+    for (r in 0 until rowCount) {
+        if (colCount <= lead) return
+        var i = r
+
+        while (this[i][lead] == 0.0) {
+            i++
+            if (rowCount == i) {
+                i = r
+                lead++
+                if (colCount == lead) return
+            }
+        }
+
+        val temp = this[i]
+        this[i] = this[r]
+        this[r] = temp
+
+        if (this[r][lead] != 0.0) {
+           val div = this[r][lead]
+           for (j in 0 until colCount) this[r][j] /= div
+        }
+
+        for (k in 0 until rowCount) {
+            if (k != r) {
+                val mult = this[k][lead]
+                for (j in 0 until colCount) this[k][j] -= this[r][j] * mult
+            }
+        }
+
+        lead++
+    }
+}
+
+fun printVector(v: Vector) {
+    println(v.asList())
+    println()
+}
+
+fun multipleRegression(y: Vector, x: Matrix): Vector {
+    val cy = (arrayOf(y)).transpose()  // convert 'y' to column vector
+    val cx = x.transpose()             // convert 'x' to column vector array
+    return ((x * cx).inverse() * x * cy).transpose()[0]
+}
+
+fun main(args: Array<String>) {
+    var y = doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0)
+    var x = arrayOf(doubleArrayOf(2.0, 1.0, 3.0, 4.0, 5.0))
+    var v = multipleRegression(y, x)
+    printVector(v)
+
+    y = doubleArrayOf(3.0, 4.0, 5.0)
+    x = arrayOf(
+        doubleArrayOf(1.0, 2.0, 1.0),
+        doubleArrayOf(1.0, 1.0, 2.0)
+    )
+    v = multipleRegression(y, x)
+    printVector(v)
+
+    y = doubleArrayOf(52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29,
+                      63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46)
+
+    val a = doubleArrayOf(1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70,
+                          1.73, 1.75, 1.78, 1.80, 1.83)
+    x = arrayOf(DoubleArray(a.size) { 1.0 }, a, a.map { it * it }.toDoubleArray())
+    v = multipleRegression(y, x)
+    printVector(v)
+}