added LU decomposition algorithm

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

numerical_methods/lu_decompose.cpp

@@ -0,0 +1,126 @@
+/**
+ * \file
+ * \brief [LU decomposition](https://en.wikipedia.org/wiki/LU_decompositon) of a
+ * square matrix
+ * \author [Krishna Vedala](https://github.com/kvedala)
+ */
+#include <ctime>
+#include <iomanip>
+#include <iostream>
+#include <vector>
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+
+/** Perform LU decomposition on matrix
+ * \param[in] A matrix to decompose
+ * \param[out] L output L matrix
+ * \param[out] U output U matrix
+ * \returns 0 if no errors
+ * \returns negative if error occurred
+ */
+int lu_decomposition(const std::vector<std::vector<double>> &A,
+                     std::vector<std::vector<double>> *L,
+                     std::vector<std::vector<double>> *U) {
+    int row, col, j;
+    int mat_size = A.size();
+
+    if (mat_size != A[0].size()) {
+        // check matrix is a square matrix
+        std::cerr << "Not a square matrix!\n";
+        return -1;
+    }
+
+    // regularize each row
+    for (row = 0; row < mat_size; row++) {
+        // Upper triangular matrix
+#ifdef _OPENMP
+#pragma omp for
+#endif
+        for (col = row; col < mat_size; col++) {
+            // Summation of L[i,j] * U[j,k]
+            double lu_sum = 0.;
+            for (j = 0; j < row; j++) lu_sum += L[0][row][j] * U[0][j][col];
+
+            // Evaluate U[i,k]
+            U[0][row][col] = A[row][col] - lu_sum;
+        }
+
+        // Lower triangular matrix
+#ifdef _OPENMP
+#pragma omp for
+#endif
+        for (col = row; col < mat_size; col++) {
+            if (row == col) {
+                L[0][row][col] = 1.;
+                continue;
+            }
+
+            // Summation of L[i,j] * U[j,k]
+            double lu_sum = 0.;
+            for (j = 0; j < row; j++) lu_sum += L[0][col][j] * U[0][j][row];
+
+            // Evaluate U[i,k]
+            L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];
+        }
+    }
+
+    return 0;
+}
+
+/**
+ * operator to print a matrix
+ */
+template <typename T>
+std::ostream &operator<<(std::ostream &out,
+                         std::vector<std::vector<T>> const &v) {
+    const int width = 10;
+    const char separator = ' ';
+
+    for (size_t row = 0; row < v.size(); row++) {
+        for (size_t col = 0; col < v[row].size(); col++)
+            out << std::left << std::setw(width) << std::setfill(separator)
+                << v[row][col];
+        out << std::endl;
+    }
+
+    return out;
+}
+
+/** Main function */
+int main(int argc, char **argv) {
+    int mat_size = 3;  // default matrix size
+    const int range = 50;
+    const int range2 = range >> 1;
+
+    if (argc == 2)
+        mat_size = atoi(argv[1]);
+
+    std::srand(std::time(NULL));  // random number initializer
+
+    /* Create a square matrix with random values */
+    std::vector<std::vector<double>> A(mat_size);
+    std::vector<std::vector<double>> L(mat_size);  // output
+    std::vector<std::vector<double>> U(mat_size);  // output
+    for (int i = 0; i < mat_size; i++) {
+        // calloc so that all valeus are '0' by default
+        A[i] = std::vector<double>(mat_size);
+        L[i] = std::vector<double>(mat_size);
+        U[i] = std::vector<double>(mat_size);
+        for (int j = 0; j < mat_size; j++)
+            /* create random values in the limits [-range2, range-1] */
+            A[i][j] = static_cast<double>(rand() % range - range2);
+    }
+
+    std::clock_t start_t = std::clock();
+    lu_decomposition(A, &L, &U);
+    std::clock_t end_t = std::clock();
+    std::cout << "Time taken: "
+              << static_cast<double>(end_t - start_t) / CLOCKS_PER_SEC << "\n";
+
+    std::cout << "A = \n" << A << "\n";
+    std::cout << "L = \n" << L << "\n";
+    std::cout << "U = \n" << U << "\n";
+
+    return 0;
+}