added QR and LU decomposition

test.c

@@ -0,0 +1,58 @@
+#include <stdio.h>
+#include "src/lina.h"
+
+void print_square_matrix(double *M, int n, FILE *stream)
+{
+    for (int i = 0; i < n; i++)
+        {
+            fprintf(stream, "| ");
+            for (int j = 0; j < n; j++)
+                {
+                    fprintf(stderr, "%2.2f ", M[i * n + j]);
+                }
+            fprintf(stream, "|\n");
+        }
+    fprintf(stream, "\n");
+}
+
+void print_vector(double *V, int n, FILE *stream)
+{
+    fprintf(stream, "[ ");
+    for (int i = 0; i < n; i++)
+        fprintf(stderr, "%2.2f ", V[i]);
+    fprintf(stream, "]\n");
+}
+
+int main(void)
+{
+    double A[4] = {1, 2, 3, 4};
+    
+    double L[4];
+    double U[4];
+    double LU[4];
+    lina_decompLU(A, L, U, 2);
+    lina_dot(L, U, LU, 2, 2, 2);
+    print_square_matrix(A,  2, stderr);
+    print_square_matrix(L,  2, stderr);
+    print_square_matrix(U,  2, stderr);
+    print_square_matrix(LU, 2, stderr);
+
+    double det;
+    lina_det(A, 2, &det);
+    fprintf(stderr, "det=%2.2f\n", det);
+
+    double Q[4];
+    double R[4];
+    double QR[4];
+    lina_decompQR(A, Q, R, 2);
+    lina_dot(Q, R, QR, 2, 2, 2);
+    print_square_matrix(Q,  2, stderr);
+    print_square_matrix(R,  2, stderr);
+    print_square_matrix(QR, 2, stderr);
+
+    double E[4];
+    lina_eig(A, E, 2);
+    print_vector(E, 2, stderr);
+
+    return 0;
+}