chore: Refactor algorithm to run until error < delta

Author: Samya-S

Diff for: OT Lab - 1 (26-07-24)/gauss-seidel.cpp

@@ -46,6 +46,7 @@ int main() {
     }
 
     vector<double> x(n, 0), y(n, 0);
+
     // cout << "Enter initial values of x" << endl;
     for (int i = 0; i < n; i++) {
         // cout << "x:[" << i << "] = ";
@@ -58,25 +59,44 @@ int main() {
     // cout << endl;
 
     // cout << endl << "Enter the allowed error: ";
-    // int delta; cin >> delta;
+    int delta;
+    cin >> delta;
     // cout << endl;
 
-    int error = 1e9;
-    while (iter--) {
-        // do {
+    // int count = 0;
+    double maxError = 0;
+    do {
         for (int i = 0; i < n; i++) {
-            y[i] = (b[i] / a[i][i]);
+            // y[i] = (b[i] / a[i][i]);
+            y[i] = b[i];
             for (int j = 0; j < n; j++) {
-                if (j == i)
-                    continue;
-                y[i] = y[i] - ((a[i][j] / a[i][i]) * x[j]);
-                x[i] = y[i];
+            //     if (j == i)
+            //         continue;
+            //     y[i] = y[i] - ((a[i][j] / a[i][i]) * x[j]);
+            //     // x[i] = y[i];
+            // }
+
+                if (i != j) {
+                    y[i] -= a[i][j] * x[j];
+                }
             }
-            // error = max(error, )
+            y[i] /= a[i][i];
+        }
+
+        maxError = 0;
+        for (int i = 0; i < n; i++) {
+            maxError = max(maxError, abs(x[i] - y[i]));
+            x[i] = y[i];
+            // cout << "x" << i + 1 << " = " << y[i] << " ";
             cout << "x" << i + 1 << " = " << fixed << setprecision(6) << y[i] << " ";
         }
         cout << endl;
-        // } while(error > delta);
+        // count++;
+    } while (maxError > delta);
+
+    cout << "The final solution is:" << endl;
+    for (int i = 0; i < n; i++) {
+        cout << "x[" << i << "] = " << x[i] << endl;
     }
 
     return 0;

Diff for: input.txt

@@ -1,14 +1,10 @@
-7
-10 2 -1 1 2 -1 1
-1 8 1 0 1 -1 0
-1 1 9 2 0 0 1
-0 -1 5 1 11 -1 1
-0 0 2 -1 10 0 0
-2 1 - 1 -2 10 1
-1 1 -1 -1 1 -1 9
-14 10 14 16 11 11 9
+3
+-7 3 1 
+2 8 -3 
+-5 -1 9 
+4 10 -6
 0
 0
 0
 5
-0.001
+0.01

Diff for: output.txt

@@ -1,2 +1,52 @@
-The matrix is not diagonally dominant.
-The Gauss-Seidel method may not converge.
+x1 = -0.571429 x2 = 1.25 x3 = -0.666667 
+x1 = -0.130952 x2 = 1.14286 x3 = -0.845238 
+x1 = -0.202381 x2 = 0.965774 x3 = -0.612434 
+x1 = -0.245016 x2 = 1.07093 x3 = -0.671792 
+x1 = -0.208428 x2 = 1.05933 x3 = -0.683794 
+x1 = -0.215114 x2 = 1.04568 x3 = -0.664756 
+x1 = -0.218243 x2 = 1.05449 x3 = -0.669987 
+x1 = -0.215215 x2 = 1.05332 x3 = -0.670747 
+x1 = -0.215829 x2 = 1.05227 x3 = -0.669195 
+x1 = -0.216054 x2 = 1.05301 x3 = -0.669652 
+x1 = -0.215804 x2 = 1.05289 x3 = -0.669695 
+x1 = -0.215859 x2 = 1.05282 x3 = -0.669569 
+x1 = -0.215875 x2 = 1.05288 x3 = -0.669609 
+x1 = -0.215854 x2 = 1.05287 x3 = -0.669611 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669601 
+x1 = -0.21586 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669603 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+x1 = -0.215859 x2 = 1.05286 x3 = -0.669604 
+The final solution is:
+x[0] = -0.215859
+x[1] = 1.05286
+x[2] = -0.669604