# Try out NAG Library functions

Explore NAG maths and stats routines with interactive demos
Function ID
C06PCF
Name
nagf_sum_fft_complex_1d
Description
Single one-dimensional complex discrete Fourier transform, complex data type
Keywords
Fast Fourier Transform | FFT | Fourier transforms, complex
This example reads in a sequence of complex data values and prints their discrete Fourier transform (as computed by c06pcf with ${\mathbf{direct}}=\text{'F'}$). It then performs an inverse transform using c06pcf with ${\mathbf{direct}}=\text{'B'}$, and prints the sequence so obtained alongside the original data values.
    Program c06pcfe

!     C06PCF Example Program Text

!     Mark 26.1 Release. NAG Copyright 2016.

!     .. Use Statements ..
Use nag_library, Only: c06pcf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: ieof, ifail, j, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: work(:), x(:), xx(:)
!     .. Executable Statements ..
Write (nout,*) 'C06PCF Example Program Results'
!     Skip heading in data file
loop: Do
If (ieof<0) Then
Exit loop
End If

Allocate (work(2*n+15),x(0:n-1),xx(0:n-1))
xx(0:n-1) = x(0:n-1)

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call c06pcf('F',x,n,work,ifail)

Write (nout,*)
Write (nout,*) 'Components of discrete Fourier transform'
Write (nout,*)
Write (nout,*) '              Real      Imag'
Write (nout,*)
Do j = 0, n - 1
Write (nout,99999) j, x(j)
End Do

Call c06pcf('B',x,n,work,ifail)

Write (nout,*)
Write (nout,*) 'Original sequence as restored by inverse transform'
Write (nout,*)
Write (nout,*) '                 Original                 Restored'
Write (nout,*) '              Real      Imag           Real      Imag'
Write (nout,*)
Do j = 0, n - 1
Write (nout,99999) j, xx(j), x(j)
End Do
Deallocate (work,x,xx)
End Do loop

99999 Format (1X,I5,2(:,5X,'(',F8.5,',',F8.5,')'))
End Program c06pcfe

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