Add example of the transform of a closed-form real function

example/CMakeLists.txt

@@ -1,2 +1,11 @@
-add_executable(bench1 bench1.f90)
-target_link_libraries(bench1 fftpack)
+add_executable(bench1 bench01_zfft.f90)
+target_link_libraries(bench1 fftpack)
+
+add_executable(bench2 bench02_zfft.f90)
+target_link_libraries(bench2 fftpack)
+
+add_executable(bench3 bench03_dfft.f90)
+target_link_libraries(bench3 fftpack)
+
+add_executable(rfft_example)
+target_link_libraries(rfft_example fftpack)

example/real-forward-transform.f90

@@ -1,41 +1,51 @@
 program forward_transform_of_real_function
-  !! This program computes the forward transform of a real function and constructs
-  !! the complex result (re)organized to match the array subscripting to the common
-  !! analytical form [1].  Which form one uses in practice requires balancing the
-  !! need for speed versus clarity. 
+  !! This program invokes fftpack's rrft function to compute the forward transform of a real function
+  !! and constructs the resulting complex Fourier coefficients by (re)organizing and normalizing the
+  !! rfft result according to array element layout described at [1].  The program also demonstrates
+  !! the inverse transform of the raw rrft result to recover the original function.
   !!
   !! [1] https://docs.scipy.org/doc/scipy/reference/generated/scipy.fftpack.rfft.html#scipy.fftpack.rfft
   use fftpack, only: rfft, irfft
   implicit none
   integer j, k
   integer, parameter :: N = 8
   double precision, parameter :: two_pi = 2.D0*acos(-1.D0), tolerance = 1.0D-06, f_avg = 3.D0, zero=0.D0
-  double precision, parameter :: f(0:N-1) = f_avg + [(cos(two_pi*dble(j)/dble(N)), j=0,N-1)]
+  double precision, parameter :: x(0:N-1) = [(two_pi*dble(j)/dble(N), j=0,N-1)]
+  double precision, parameter :: f(0:N-1) = f_avg + cos(x)
+    !! sample f(x) = 3 + cos(x) uniformly on [0,2*pi)
+    !!             = 3 + (exp(i*x) - exp(-i*x))/2  
+    !! which yields the Fourier coefficients
+    !!                { 3, k = 0
+    !!       f_hat =  { 1/2, k = 1
+    !!                { 0, otherwise
   double precision, dimension(0:N-1) :: f_round_trip, rfft_f
   integer, parameter :: rk = kind(two_pi)
   complex(rk) f_hat(0:N/2)
+  character(len=*), parameter :: real_format = "(a,*(g10.4,:,1x))" !! space-separated values
+  character(len=*), parameter :: complex_format= "(a,*('(',g10.4,',',g10.4,')',:,1x)))" !! space-separated complex values
 
   call assert(mod(N,2)==0, "the algorithm below requires even N")
 
   rfft_f(:) = rfft(f)/dble(N)
-  f_hat(:) = [ cmplx(rfft_f(0),zero), [( cmplx(k,k+1),  k=lbound(rfft_f,1)+1,ubound(rfft_f,1)-1,2)], cmplx(zero,rfft_f(N-1)) ]
-  f_round_trip(:) = dble(irfft(rfft_f))
-  !call assert(any(abs(f_round_trip - f) < tolerance), "inverse of forward FFT must yield the original function")
+  f_hat(:) = [ &
+    cmplx(rfft_f(0),zero), &
+    [( cmplx(rfft_f(k),rfft_f(k+1)),  k=lbound(rfft_f,1)+1,ubound(rfft_f,1)-1,2)], &
+    cmplx(zero,rfft_f(N-1)) &
+  ]
+  f_round_trip(:) = irfft(rfft_f)
 
-  print *, "f = ", f
-  print *, "f_hat = ", f_hat
-  print *, "f_round_trip = ", f_round_trip
+  print real_format, "f = ", f
+  print complex_format, "f_hat = ", f_hat
+  print real_format, "f_round_trip = ",f_round_trip
 
-  !print '(3(10x,a,10x))',"f", "f_round_trip", "rfft_f"
-  !do m = 1, size(f)
-  !  print *, f(m), f_round_trip(m), rfft_f(m)
-  !end do
-  !print *
+  call assert(all(abs(f_round_trip - f) < tolerance), "inverse of forward FFT must yield the original function")
 
 contains
+
   pure subroutine assert(assertion, description)
     logical, intent(in) :: assertion
     character(len=*), intent(in) :: description
     if (.not. assertion) error stop description
   end subroutine
+
 end program

fpm.toml

@@ -1,4 +1,3 @@
-
 name        = "fftpack"
 description = "A package of fortran subprograms for the fast fourier transform of periodic and other symmetric sequences"
 homepage    = "http://www.netlib.org/fftpack/"
@@ -15,6 +14,11 @@ implicit-typing=true
 implicit-external=true
 source-form="default"
 
+[build]
+auto-executables = false
+auto-tests = true
+auto-examples = true
+
 [dev-dependencies]
 test-drive = { git = "https://github.com/fortran-lang/test-drive", tag = "v0.4.0" }