added QR decomposition algorithm

Signed-off-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>

numerical_methods/qr_decomposition.cpp

@@ -0,0 +1,58 @@
+/**
+ * @file
+ * \brief Program to compute the [QR
+ * decomposition](https://en.wikipedia.org/wiki/QR_decomposition) of a given
+ * matrix.
+ * \author [Krishna Vedala](https://github.com/kvedala)
+ */
+
+#include <array>
+#include <cmath>
+#include <cstdlib>
+#include <ctime>
+#include <iostream>
+
+#include "./qr_decompose.h"
+
+using qr_algorithm::qr_decompose;
+using qr_algorithm::operator<<;
+
+/**
+ * main function
+ */
+int main(void) {
+    unsigned int ROWS, COLUMNS;
+
+    std::cout << "Enter the number of rows and columns: ";
+    std::cin >> ROWS >> COLUMNS;
+
+    std::cout << "Enter matrix elements row-wise:\n";
+
+    std::valarray<std::valarray<double>> A(ROWS);
+    std::valarray<std::valarray<double>> Q(ROWS);
+    std::valarray<std::valarray<double>> R(COLUMNS);
+    for (int i = 0; i < std::max(ROWS, COLUMNS); i++) {
+        if (i < ROWS) {
+            A[i] = std::valarray<double>(COLUMNS);
+            Q[i] = std::valarray<double>(COLUMNS);
+        }
+        if (i < COLUMNS) {
+            R[i] = std::valarray<double>(COLUMNS);
+        }
+    }
+
+    for (int i = 0; i < ROWS; i++)
+        for (int j = 0; j < COLUMNS; j++) std::cin >> A[i][j];
+
+    std::cout << A << "\n";
+
+    clock_t t1 = clock();
+    qr_decompose(A, &Q, &R);
+    double dtime = static_cast<double>(clock() - t1) / CLOCKS_PER_SEC;
+
+    std::cout << Q << "\n";
+    std::cout << R << "\n";
+    std::cout << "Time taken to compute: " << dtime << " sec\n ";
+
+    return 0;
+}