Feat: hw2 done

HW2_111550013/HW2_111550013_code/problem2.cpp

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+// Problem 2: Scaled partial pivoting
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+#include <vector>
+using namespace std;
+
+double roundSig(double val, int sig) {
+    if (val == 0) return 0;
+    double d = ceil(log10(fabs(val)));
+    double p = pow(10, sig - d);
+    return round(val * p) / p;
+}
+
+void solve(vector<vector<double>> A, int n, int sig) {
+    cout << "\n" << sig << " significant digits:\n";
+
+    vector<double> s(n);
+    for (int i = 0; i < n; i++)
+        for (int j = 0; j < n; j++) s[i] = max(s[i], fabs(A[i][j]));
+
+    vector<int> idx(n);
+    for (int i = 0; i < n; i++) idx[i] = i;
+
+    for (int k = 0; k < n - 1; k++) {
+        int maxRow = k;
+        double maxRatio = fabs(A[idx[k]][k]) / s[idx[k]];
+        for (int i = k + 1; i < n; i++) {
+            double ratio = fabs(A[idx[i]][k]) / s[idx[i]];
+            if (ratio > maxRatio) { maxRatio = ratio; maxRow = i; }
+        }
+        swap(idx[k], idx[maxRow]);
+
+        for (int i = k + 1; i < n; i++) {
+            double m = roundSig(A[idx[i]][k] / A[idx[k]][k], sig);
+            for (int j = k; j <= n; j++)
+                A[idx[i]][j] = roundSig(A[idx[i]][j] - m * A[idx[k]][j], sig);
+        }
+    }
+
+    vector<double> x(n);
+    for (int i = n - 1; i >= 0; i--) {
+        x[i] = A[idx[i]][n];
+        for (int j = i + 1; j < n; j++)
+            x[i] = roundSig(x[i] - A[idx[i]][j] * x[j], sig);
+        x[i] = roundSig(x[i] / A[idx[i]][i], sig);
+    }
+
+    for (int i = 0; i < n; i++)
+        cout << "x" << (i+1) << " = " << fixed << setprecision(6) << x[i] << "\n";
+}
+
+int main() {
+    vector<vector<double>> A = {
+        {4.13, -2.20, 0.95, 3.02},
+        {6.14, 4.45, -1.45, -4.02},
+        {1.03, 1.86, 0.44, 5.22}
+    };
+    solve(A, 3, 6);
+    solve(A, 3, 3);
+    return 0;
+}