Resolved third round of requested changes

src/misc.f90

@@ -1657,39 +1657,35 @@ end subroutine subtitle
   subroutine Hilbert_transform(fx, Hfx)
      !! Does Hilbert tranform for a given function
      !! Ref - EQ (4)3, R. Balito et. al.
-     !! "An algorithm for fast Hilbert transform of real
-     !! functions"
+     !! "An algorithm for fast Hilbert transform of real functions"
 
      real(r64), intent(in) :: fx(:)
      real(r64), allocatable, intent(out) :: Hfx(:)
-
      ! Local variables
      integer :: n, k, nfx
      real(r64) :: term2, term3, b
 
      nfx = size(fx)
      allocate(Hfx(nfx))
-
      ! Hilbert function is zero at the edges
      Hfx(1) = 0.0_r64
      Hfx(nfx) = 0.0_r64
      ! Note: In the reference, we have N + 1 points and indexing is 0-based
      ! whereas here we have N points and indexing is 1-based
-     do k = 1, nfx - 2      ! Run over the internal points
-        term2 = 0.0_r64  ! 2nd term in Bilato Eq. 4
-        term3 = 0.0_r64  ! 3rd term in Bilato Eq. 4
+     do k = 1, nfx - 2 ! Run over the internal points
+        term2 = 0.0_r64 ! 2nd term in Bilato Eq. 4
+        term3 = 0.0_r64 ! 3rd term in Bilato Eq. 4
 
-        do n = 1, nfx - 2 - k  ! Partial sum over internal points
+        do n = 1, nfx - 2 - k ! Partial sum over internal points
            b = log((n + 1.0_r64)/n)
            term2 = term2 - (1.0_r64 - (n + 1.0_r64)*b)*fx(k + n + 1) + &
                           (1.0_r64 - n*b)*fx(k + n + 2)
         end do
-        do n = 1, k - 1      ! Partial sum over internal points
+        do n = 1, k - 1 ! Partial sum over internal points
            b = log((n + 1.0_r64)/n)
            term3 = term3 + (1.0_r64 - (n + 1.0_r64)*b)*fx(k - n + 1) - &
                          (1.0_r64 - n*b)*fx(k - n)
         end do
-
         Hfx(k + 1) = -(fx(k + 2) - fx(k) + term2 + term3)/pi
      end do
   end subroutine Hilbert_transform

test/test_misc.f90

@@ -409,6 +409,6 @@ end function fx2
      ! Hfx2 is actual hilbert transform of fx2, is an even function
      pure elemental real(r64) function hfx2(x)
         real(r64), intent(in) :: x
-        hfx2 = (1/exp(1.0_r64) - cos(x))/(1.0_r64 + x**2)
+        hfx2 = (exp(-1.0_r64) - cos(x))/(1.0_r64 + x**2)
      end function hfx2
 end program test_misc