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ex1G_dense_matrices_access/main.cpp

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+#include "../utils/timing.h"
+#include "DenseMatrix.h"
+#include "ProductMatrix.h"
+#include <algorithm>
+
+int main()
+{
+    // b) ------------------------------------------------------------------------------------------------------
+    DenseMatrix const M(5,3);
+    vector<double> const u{{1, 2, 3}};
+    vector<double> f1 = M.Mult(u);
+    vector<double> const v{{-1, 2, -3, 4, -5}};
+    vector<double> f2 = M.MultT(v);
+
+    M.Print();
+
+    for(size_t i = 0; i < f1.size(); ++i)
+        cout << f1[i] << endl;
+    cout << endl;
+
+
+    for(size_t j = 0; j < f2.size(); ++j)
+        cout << f2[j] << "  ";
+    cout << endl << "-------------------------------------------------" << endl;
+
+    // c) ------------------------------------------------------------------------------------------------------
+    size_t n = pow(10,3);
+    DenseMatrix const M_1(n,n);
+    vector<double> x(n, 1.0);
+
+    size_t n_loops = 100;
+    vector<double> y_1;
+    vector<double> y_2;
+
+    double time_1 = 0;
+    double time_2 = 0;
+
+    tic();
+    for(int l = 0; l < n_loops; ++l)
+        y_1 = M_1.Mult(x);
+    time_1 += toc();
+
+    tic();
+    for(int l = 0; l < n_loops; ++l)
+        y_2 = M_1.MultT(x);
+    time_2 += toc();
+
+    vector<double> error_vec(n,0);
+    for(int i = 0; i < n; ++i)
+        error_vec[i] = abs(y_1[i] - y_2[i]);
+    double sup_error = *max_element(error_vec.begin(), error_vec.end());
+
+
+    cout << "n = " << n << endl;
+    cout << "Average duration for Mult: " << time_1/n_loops << endl;
+    cout << "Average duration for MultT: " << time_2/n_loops << endl;
+    cout << "sup-error: " << sup_error << endl;
+    cout << "-------------------------------------------------" << endl;
+
+    // d) ------------------------------------------------------------------------------------------------------
+    vector<double> u_M(n,0);
+    for(int i = 0; i < n; ++i)
+        u_M[i] = sigmoid(x_entry(i, n));
+
+    ProductMatrix const M_2(u_M, u_M);
+
+    time_1 = 0;
+    time_2 = 0;
+
+    tic();
+    for(int l = 0; l < n_loops; ++l)
+        y_1 = M_2.Mult(x);
+    time_1 += toc();
+
+    tic();
+    for(int l = 0; l < n_loops; ++l)
+        y_2 = M_2.MultT(x);
+    time_2 += toc();
+
+    for(int i = 0; i < n; ++i)
+        error_vec[i] = abs(y_1[i] - y_2[i]);
+    sup_error = *max_element(error_vec.begin(), error_vec.end());
+
+
+    cout << "n = " << n << endl;
+    cout << "Average duration for Mult: " << time_1/n_loops << endl;
+    cout << "Average duration for MultT: " << time_2/n_loops << endl;
+    cout << "sup-error: " << sup_error << endl;
+    cout << "-------------------------------------------------" << endl;
+
+
+    return 0;
+}