diff --git a/code/Compact.f90 b/code/Compact.f90
index 46b292b..0fd1a9e 100644
--- a/code/Compact.f90
+++ b/code/Compact.f90
@@ -155,6 +155,51 @@
 
      END SUBROUTINE ludcmp_calculate
 
+
+     SUBROUTINE test_nonp_lud1(xx, coef)
+      INTEGER :: xx
+      REAL(KIND=8), DIMENSION(xx) :: aa
+      REAL(KIND=8), DIMENSION(xx), INTENT(OUT) :: coef
+       aa=3.
+       aa(1)=0.5 ; aa(2)=4.
+       aa(xx-1)=4. ; aa(xx)=0.5
+
+       CALL stdlu(aa,xx,coef)
+     END SUBROUTINE test_nonp_lud1
+
+
+     SUBROUTINE test_nonp_lud2(xx, coef)
+      INTEGER :: xx
+      REAL(KIND=8), DIMENSION(xx) :: aa
+      REAL(KIND=8), DIMENSION(xx), INTENT(OUT) :: coef
+       aa=5.5
+       aa(1)=2./11. ; aa(2)=10.
+       aa(xx-1)=10. ; aa(xx)=2./11.
+
+       CALL stdlu(aa,xx,coef)
+     END SUBROUTINE test_nonp_lud2
+
+
+     SUBROUTINE test_p_lud1(xx, coef1, coef2)
+      INTEGER :: xx
+      REAL(KIND=8) :: a
+      REAL(KIND=8), DIMENSION(xx), INTENT(OUT) :: coef1, coef2
+      a=3. ! first derivative
+
+      CALL ptdlu(a,xx,coef1,coef2) ! x-direction
+     END SUBROUTINE test_p_lud1
+
+
+     SUBROUTINE test_p_lud2(xx, coef1, coef2)
+      INTEGER :: xx
+      REAL(KIND=8) :: a
+      REAL(KIND=8), DIMENSION(xx), INTENT(OUT) :: coef1, coef2
+      a=11./2. ! second derivative
+
+      CALL ptdlu(a,xx,coef1,coef2) ! x-direction
+     END SUBROUTINE test_p_lud2
+
+
      SUBROUTINE nonp_lud(xyz,xx)
       INTEGER :: i,xyz,xx
       REAL(KIND=8), DIMENSION(xx) :: aa
@@ -313,7 +358,7 @@
      SUBROUTINE ptdslv(r,n,l,w,nd)
       INTEGER,INTENT(IN) :: n,nd
       REAL(KIND=8),INTENT(INOUT),DIMENSION(nd,n) :: r
-      REAL(KIND=8),INTENT(IN),DIMENSION(:) :: l,w
+      REAL(KIND=8),INTENT(IN),DIMENSION(n) :: l,w
       INTEGER i,j
       REAL(KIND=8), DIMENSION(nd) :: sum
       DO j=1,nd
@@ -406,7 +451,7 @@
      SUBROUTINE tdslv(r,n,l,nd)
       INTEGER,INTENT(IN) :: n,nd
       REAL(KIND=8),INTENT(INOUT),DIMENSION(nd,n) :: r
-      REAL(KIND=8),INTENT(IN),DIMENSION(:) :: l
+      REAL(KIND=8),INTENT(IN),DIMENSION(n) :: l
       INTEGER i,j
       REAL(KIND=8) t1
       DO j=1,nd
diff --git a/code/pycompact/pycompact.py b/code/pycompact/pycompact.py
index dd553a2..064f0b9 100644
--- a/code/pycompact/pycompact.py
+++ b/code/pycompact/pycompact.py
@@ -67,7 +67,7 @@ class CompactScheme:
         # dst = np.zeros((nx, ny, nz,), order="F")
         dst = np.zeros((nz, ny, nx,), dtype=np.float64,)
 
-        if self.px:
+        if self.px: # Periodic BC
             for i in range(nz):
                 xsrc[:] = src[i]
                 dst[i] = compact.dfp(self.hx, xsrc, 1)
@@ -221,16 +221,18 @@ def validate_trigonometric():
 
     pi8 = np.arccos(-1.)
 
-    print (pi8)
+    print ("calculated pi value = ", pi8)
 
     l_0 = 2.0
     hyp=l_0*pi8/ny
     hxp=hyp
     hzp=hyp
 
-    Y1 = np.zeros(shape)
 
-    dY = np.zeros(shape)
+    cs = CompactScheme(nx, ny, nz, False, True, True, 4., 2., 2.)
+
+
+    Y1 = np.zeros(shape)
 
     true = np.zeros(shape)
 
@@ -244,8 +246,6 @@ def validate_trigonometric():
     Y1[:] = np.sin(1.1 * xx) * np.sin(3.0 * yy) * np.sin(2.0 * zz)[:]
     true[:] = (1.1 * np.cos(1.1 * xx) * np.sin(3.0 * yy) * np.sin(2.0 * zz))[:]
 
-    cs = CompactScheme(nx, ny, nz, False, True, True, 4., 2., 2.)
-
     y = np.memmap("phi", dtype=np.float64, mode="w+", shape=cs.shape)
     y[:] = Y1[:]