Initial data commit

Task/LU-decomposition/Java/lu-decomposition.java

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+import static java.util.Arrays.stream;
+import java.util.Locale;
+import static java.util.stream.IntStream.range;
+
+public class Test {
+
+    static double dotProduct(double[] a, double[] b) {
+        return range(0, a.length).mapToDouble(i -> a[i] * b[i]).sum();
+    }
+
+    static double[][] matrixMul(double[][] A, double[][] B) {
+        double[][] result = new double[A.length][B[0].length];
+        double[] aux = new double[B.length];
+
+        for (int j = 0; j < B[0].length; j++) {
+
+            for (int k = 0; k < B.length; k++)
+                aux[k] = B[k][j];
+
+            for (int i = 0; i < A.length; i++)
+                result[i][j] = dotProduct(A[i], aux);
+        }
+        return result;
+    }
+
+    static double[][] pivotize(double[][] m) {
+        int n = m.length;
+        double[][] id = range(0, n).mapToObj(j -> range(0, n)
+                .mapToDouble(i -> i == j ? 1 : 0).toArray())
+                .toArray(double[][]::new);
+
+        for (int i = 0; i < n; i++) {
+            double maxm = m[i][i];
+            int row = i;
+            for (int j = i; j < n; j++)
+                if (m[j][i] > maxm) {
+                    maxm = m[j][i];
+                    row = j;
+                }
+
+            if (i != row) {
+                double[] tmp = id[i];
+                id[i] = id[row];
+                id[row] = tmp;
+            }
+        }
+        return id;
+    }
+
+    static double[][][] lu(double[][] A) {
+        int n = A.length;
+        double[][] L = new double[n][n];
+        double[][] U = new double[n][n];
+        double[][] P = pivotize(A);
+        double[][] A2 = matrixMul(P, A);
+
+        for (int j = 0; j < n; j++) {
+            L[j][j] = 1;
+            for (int i = 0; i < j + 1; i++) {
+                double s1 = 0;
+                for (int k = 0; k < i; k++)
+                    s1 += U[k][j] * L[i][k];
+                U[i][j] = A2[i][j] - s1;
+            }
+            for (int i = j; i < n; i++) {
+                double s2 = 0;
+                for (int k = 0; k < j; k++)
+                    s2 += U[k][j] * L[i][k];
+                L[i][j] = (A2[i][j] - s2) / U[j][j];
+            }
+        }
+        return new double[][][]{L, U, P};
+    }
+
+    static void print(double[][] m) {
+        stream(m).forEach(a -> {
+            stream(a).forEach(n -> System.out.printf(Locale.US, "%5.1f ", n));
+            System.out.println();
+        });
+        System.out.println();
+    }
+
+    public static void main(String[] args) {
+        double[][] a = {{1.0, 3, 5}, {2.0, 4, 7}, {1.0, 1, 0}};
+
+        double[][] b = {{11.0, 9, 24, 2}, {1.0, 5, 2, 6}, {3.0, 17, 18, 1},
+        {2.0, 5, 7, 1}};
+
+        for (double[][] m : lu(a))
+            print(m);
+
+        System.out.println();
+
+        for (double[][] m : lu(b))
+            print(m);
+    }
+}