Data commit

Task/Gaussian-elimination/Java/gaussian-elimination.java

@@ -0,0 +1,95 @@
+import java.util.Locale;
+
+public class GaussianElimination {
+    public static double solve(double[][] a, double[][] b) {
+        if (a == null || b == null || a.length == 0 || b.length == 0) {
+            throw new IllegalArgumentException("Invalid dimensions");
+        }
+
+        int n = b.length, p = b[0].length;
+        if (a.length != n || a[0].length != n) {
+            throw new IllegalArgumentException("Invalid dimensions");
+        }
+
+        double det = 1.0;
+
+        for (int i = 0; i < n - 1; i++) {
+            int k = i;
+            for (int j = i + 1; j < n; j++) {
+                if (Math.abs(a[j][i]) > Math.abs(a[k][i])) {
+                    k = j;
+                }
+            }
+
+            if (k != i) {
+                det = -det;
+
+                for (int j = i; j < n; j++) {
+                    double s = a[i][j];
+                    a[i][j] = a[k][j];
+                    a[k][j] = s;
+                }
+
+                for (int j = 0; j < p; j++) {
+                    double s = b[i][j];
+                    b[i][j] = b[k][j];
+                    b[k][j] = s;
+                }
+            }
+
+            for (int j = i + 1; j < n; j++) {
+                double s = a[j][i] / a[i][i];
+                for (k = i + 1; k < n; k++) {
+                    a[j][k] -= s * a[i][k];
+                }
+
+                for (k = 0; k < p; k++) {
+                    b[j][k] -= s * b[i][k];
+                }
+            }
+        }
+
+        for (int i = n - 1; i >= 0; i--) {
+            for (int j = i + 1; j < n; j++) {
+                double s = a[i][j];
+                for (int k = 0; k < p; k++) {
+                    b[i][k] -= s * b[j][k];
+                }
+            }
+            double s = a[i][i];
+            det *= s;
+            for (int k = 0; k < p; k++) {
+                b[i][k] /= s;
+            }
+        }
+
+        return det;
+    }
+
+    public static void main(String[] args) {
+        double[][] a = new double[][] {{4.0, 1.0, 0.0, 0.0, 0.0},
+                                       {1.0, 4.0, 1.0, 0.0, 0.0},
+                                       {0.0, 1.0, 4.0, 1.0, 0.0},
+                                       {0.0, 0.0, 1.0, 4.0, 1.0},
+                                       {0.0, 0.0, 0.0, 1.0, 4.0}};
+
+        double[][] b = new double[][] {{1.0 / 2.0},
+                                       {2.0 / 3.0},
+                                       {3.0 / 4.0},
+                                       {4.0 / 5.0},
+                                       {5.0 / 6.0}};
+
+        double[] x = {39.0 / 400.0,
+                      11.0 / 100.0,
+                      31.0 / 240.0,
+                      37.0 / 300.0,
+                      71.0 / 400.0};
+
+        System.out.println("det: " + solve(a, b));
+
+
+        for (int i = 0; i < 5; i++) {
+            System.out.printf(Locale.US, "%12.8f %12.4e\n", b[i][0], b[i][0] - x[i]);
+        }
+    }
+}