diff --git a/Makefile b/Makefile
index b7182d2..cf37720 100644
--- a/Makefile
+++ b/Makefile
@@ -7,24 +7,33 @@ FFLAGS=-O0 -debug full -traceback
 ## Deps & objs for the C++ stuff
 cppDEPS = cppmain.cpp SM_MaponiA3.cpp SM_MaponiA3.hpp Helpers.hpp
 cppOBJ = cppmain.o SM_MaponiA3.o
+
 ## Deps & objs for the Fortran stuff
 fDEPS = fmain.f90 SM_MaponiA3_mod.f90
-fOBJ = SM_MaponiA3_mod.o fmain.o
+fOBJ = SM_MaponiA3.o SM_MaponiA3_mod.o fmain.o
 
+## Compile recipes for C++ stuff
 %.o: %.cpp $(cppDEPS)
 	$(CXX) $(ARCH) $(CXXFLAGS) -c -o $@ $<
 
+## Compile recepies for Fortran stuff
 %.o: %.f90 $(fDEPS)
 	$(FC) $(ARCH) $(FFLAGS) -c -o $@ $<
 
+.PHONY: all clean distclean
+
 all: cppSherman-Morrison fSherman-Morrison
 
-cppSherman-Morrison: $(cppOBJ)
-	$(CXX) $(ARCH) $(CXXFLAGS) -o $@ $^
-
-fSherman-Morrison: $(fOBJ)
-	$(FC) $(ARCH) $(FFLAGS) -o $@ $^
-
 clean:
 	@rm -vf *.o *.mod
-	
\ No newline at end of file
+	
+distclean: clean
+	@rm -vf cppSherman-Morrison fSherman-Morrison
+
+## Linking the C++ example program
+cppSherman-Morrison: $(cppOBJ)
+	$(CXX) $(ARCH) $(CXXFLAGS) -o $@ $^
+
+## Linking Fortran example program calling the C++ function 'Sherman_Morrison()'
+fSherman-Morrison: $(fOBJ)
+	$(FC) $(ARCH) $(FFLAGS) -o $@ $^
diff --git a/SM_MaponiA3.cpp b/SM_MaponiA3.cpp
index a652fe2..9fc477c 100644
--- a/SM_MaponiA3.cpp
+++ b/SM_MaponiA3.cpp
@@ -4,7 +4,7 @@
 #include "SM_MaponiA3.hpp"
 #include "Helpers.hpp"
 
-void Sherman_Morrison_(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) {
+void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index) {
     unsigned int k, l, lbar, i, j, tmp, M = *Dim;
     unsigned int *p = new unsigned int[M+1];
     unsigned int **Id = new unsigned int*[M];
diff --git a/SM_MaponiA3.hpp b/SM_MaponiA3.hpp
index 065d662..0a53741 100644
--- a/SM_MaponiA3.hpp
+++ b/SM_MaponiA3.hpp
@@ -1,5 +1,5 @@
 // SM-MaponiA3.hpp
-
 extern "C" {
-    void Sherman_Morrison_(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index);    
-}
\ No newline at end of file
+    void Sherman_Morrison(int **Slater0, double **Slater_inv, unsigned int *Dim, unsigned int *N_updates, int **Updates, unsigned int *Updates_index);    
+}
+
diff --git a/cppmain.cpp b/cppmain.cpp
index 79671a5..2592370 100644
--- a/cppmain.cpp
+++ b/cppmain.cpp
@@ -65,7 +65,7 @@ int main() {
     // Define pointers dim and n_updates to use in Sherman-Morrison(...) function call
     unsigned int *dim = new unsigned int(M);
     unsigned int *n_updates = new unsigned int(M);
-    Sherman_Morrison_(A0, A0_inv, dim, n_updates, Ar, Ar_index);
+    Sherman_Morrison(A0, A0_inv, dim, n_updates, Ar, Ar_index);
     showMatrix(A0_inv, M, "A0_inv");
     
     // Deallocate all vectors and matrices 
diff --git a/fmain.f90 b/fmain.f90
index 44a2a53..fe6447f 100644
--- a/fmain.f90
+++ b/fmain.f90
@@ -24,12 +24,29 @@ program Interface_test
     A(3,2) = 0
     A(3,3) = -1
 
-    do i=1,3
-        do j=1,3
-            write(*,"(I)", advance="no") A(i,j)
+    !! Prepare the diagonal matrix A0 and the update matrix Ar
+    do i=1,dim
+        Ar_index(i) = i
+        do j=1,dim
+            if (i == j) then
+                A0(i,j) = A(i,j)
+                A0_inv(i,j) = 1.0d0 / A0(i,j)
+            else
+                A0(i,j) = 0
+                A0_inv(i,j) = 0.0d0
+            end if
+            Ar(i,j) = A(i,j) - A0(i,j)
         end do
-        write(*,*)
     end do
 
+    ! do i=1,dim
+    !     do j=1,dim
+    !         write(*,"(I)", advance="no") Ar_index(i)
+    !     end do
+    !     write(*,*)
+    ! end do
+  
+    call MYSUBROUTINE(A0, A0_inv, dim, n_updates, Ar, Ar_index)
+
     deallocate(Ar_index, A, A0, Ar, A0_inv)
 end program