Added QR Decomp.

MLPP/LinAlg/LinAlg.cpp

@@ -611,6 +611,38 @@ namespace MLPP{
         return {left_eigenvecs, sigma, right_eigenvecs};
     }
 
+    std::vector<double> LinAlg::vectorProjection(std::vector<double> a, std::vector<double> b){
+        double product = dot(a, b)/dot(a, a);
+        return scalarMultiply(product, a); // Projection of vector a onto b. Denotated as proj_a(b).
+    }
+
+    std::vector<std::vector<double>> LinAlg::gramSchmidtProcess(std::vector<std::vector<double>> A){
+        A = transpose(A); // C++ vectors lack a mechanism to directly index columns. So, we transpose *a copy* of A for this purpose for ease of use.
+        std::vector<std::vector<double>> B;
+        B.resize(A.size());
+        for(int i = 0; i < B.size(); i++){
+            B[i].resize(A[0].size());
+        }
+
+        B[0] = A[0]; // We set a_1 = b_1 as an initial condition.
+        B[0] = scalarMultiply(1/norm_2(B[0]), B[0]);
+        for(int i = 1; i < B.size(); i++){
+            B[i] = A[i];
+            for(int j = i-1; j >= 0; j--){
+                B[i] = subtraction(B[i], vectorProjection(B[j], A[i]));
+            }
+            B[i] = scalarMultiply(1/norm_2(B[i]), B[i]); // Very simply multiply all elements of vec B[i] by 1/||B[i]||_2
+        }
+        return transpose(B); // We re-transpose the marix. 
+    }
+
+    std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>> LinAlg::QRD(std::vector<std::vector<double>> A){
+        std::vector<std::vector<double>> Q = gramSchmidtProcess(A);
+        std::vector<std::vector<double>> R = matmult(transpose(Q), A);
+        return {Q, R};
+
+    }
+
     double LinAlg::sum_elements(std::vector<std::vector<double>> A){
         double sum = 0;
         for(int i = 0; i < A.size(); i++){
@@ -866,6 +898,10 @@ namespace MLPP{
         return std::sqrt(dist);
     }
 
+    double LinAlg::norm_2(std::vector<double> a){
+        return std::sqrt(norm_sq(a));
+    }
+
     double LinAlg::norm_sq(std::vector<double> a){
         double n_sq = 0;
         for(int i = 0; i < a.size(); i++){
@@ -883,7 +919,7 @@ namespace MLPP{
     }
 
     double LinAlg::cosineSimilarity(std::vector<double> a, std::vector<double> b){
-        return dot(a, b) / (std::sqrt(norm_sq(a)) * std::sqrt(norm_sq(b)));
+        return dot(a, b) / (norm_2(a) * norm_2(b));
     }
 
     void LinAlg::printVector(std::vector<double> a){

MLPP/LinAlg/LinAlg.hpp

@@ -88,6 +88,12 @@ namespace MLPP{
 
         std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>, std::vector<std::vector<double>>> SVD(std::vector<std::vector<double>> A);
 
+        std::vector<double> vectorProjection(std::vector<double> a, std::vector<double> b);
+
+        std::vector<std::vector<double>> gramSchmidtProcess(std::vector<std::vector<double>> A);
+
+        std::tuple<std::vector<std::vector<double>>, std::vector<std::vector<double>>> QRD(std::vector<std::vector<double>> A);
+
         double sum_elements(std::vector<std::vector<double>> A);
 
         std::vector<double> flatten(std::vector<std::vector<double>> A);
@@ -152,6 +158,8 @@ namespace MLPP{
 
         double euclideanDistance(std::vector<double> a, std::vector<double> b);
         
+        double norm_2(std::vector<double> a);
+
         double norm_sq(std::vector<double> a);
         
         double sum_elements(std::vector<double> a);

main.cpp

@@ -433,5 +433,18 @@ int main() {
     // data.getImage("../../Data/apple.jpeg", chicken);
     // alg.printVector(chicken);
 
+    // TESTING QR DECOMP. EXAMPLE VIA WIKIPEDIA. SEE https://en.wikipedia.org/wiki/QR_decomposition.
+
+    std::vector<std::vector<double>> P = {{12, -51, 4}, {6, 167, -68}, {-4, 24, -41}};
+    alg.printMatrix(P);
+
+    alg.printMatrix(alg.gramSchmidtProcess(P));
+
+    auto [Q, R] = alg.QRD(P); // It works! 
+    
+     alg.printMatrix(Q);
+
+     alg.printMatrix(R); 
+
     return 0;
 }