Compute loss and gradient

main.cpp

@@ -45,11 +45,18 @@ Matrix compute_dct_matrix(uint32_t n_samples) {
 }
 
 //--------------------------------------------------------------------------------------------------
-int main() {
-    //Vector x = Vector::Random(5);
-    //std::cout << x << '\n';
-
+// Selects certain columns of a matrix.
+Matrix matrix_subset(Matrix const& matrix, std::vector<uint32_t> const& subset_indices) {
+    Matrix subset(matrix.rows(), subset_indices.size());
+    for (uint32_t i = 0; i < subset_indices.size(); ++i) {
+        auto const index = subset_indices[i];
+        subset.col(i) = matrix.col(index);
+    }
+    return subset;
+}
 
+//--------------------------------------------------------------------------------------------------
+int main() {
     constexpr Scalar f1 = 697;
     constexpr Scalar f2 = 1209;
 
@@ -67,7 +74,7 @@ int main() {
     python_print("dct", dct);
 
     // Part (c)
-    Vector const recovered_sample_values = dct_matrix.transpose() * dct;
+    Vector recovered_sample_values = dct_matrix.transpose() * dct;
     python_print("recovered_sample_values", recovered_sample_values);
 
     // Part (d)
@@ -93,5 +100,21 @@ int main() {
     python_print("subset_sample_times", subset_sample_times);
     python_print("subset_sample_values", subset_sample_values);
 
+    // Part (e)
+    Matrix const subset_dct_matrix = matrix_subset(dct_matrix, subset_indices);
+    Vector recovered_dct = Vector::Random(n_samples);
+    recovered_sample_values = dct_matrix.transpose() * recovered_dct;
+    Vector subset_recovered_sample_values(n_subsamples);
+    for (uint32_t i = 0; i < n_subsamples; ++i) {
+        auto const index = subset_indices[i];
+        subset_recovered_sample_values[i] = recovered_sample_values[index];
+    }
+    Vector subset_differences = subset_sample_values - subset_recovered_sample_values;
+    Scalar loss = subset_differences.squaredNorm();
+    Vector gradient = -2 * subset_dct_matrix * subset_differences;
+
+    std::cout << loss << '\n';
+    std::cout << gradient << '\n';
+
     return 0;
 }