(forward) fourier transform and (backward) inverse fourier transform gives the same result

[hlclemson]

import arraymancer
import fftw3
import std/complex

let shape = @[6]

# Use dummy tensor to create plan
var
    dummy_input = newTensor[Complex64](shape)
    dummy_output = newTensor[Complex64](shape)
var FFT: fftw_plan = fftw_plan_dft(dummy_input, dummy_output, FFTW_FORWARD, FFTW_ESTIMATE)
var inverseFFT: fftw_plan = fftw_plan_dft(dummy_input, dummy_output, FFTW_BACKWARD, FFTW_ESTIMATE)

# Allocate output Tensor
var inputRe = [1.0,2.0,3.0,4.0,5.0,6.0].toTensor.reshape(1, 6)
var inputIm = [0.0,0.0,0.0,0.0,0.0,0.0].toTensor.reshape(1, 6)
var input = map2_inline(inputRe, inputIm):
    complex64(x, y)

# initialize output tensors
var output = newTensor[Complex64](shape)
var output_fft = newTensor[Complex64](shape)
var output_ifft = newTensor[Complex64](shape)

fftw_execute_dft(FFT, input, output) # Execute FFT
var outConj = conjugate(output)
# calculate the power of the signal by elementwise multiplication
var sigMag = output*.outConj

# execute inverse fourier transform
fftw_execute_dft(inverseFFT, sigMag, output_ifft) # Execute a plan on new Tensor
fftw_execute_dft(FFT, sigMag, output_fft) # Execute a plan on new Tensor
echo(output_ifft)
echo(output_fft)

Tensor[Complex[system.float64]] of shape "[6]" on backend "Cpu"
    (546.0, 0.0)    (456.0, 0.0)    (402.0, 0.0)    (384.0, 0.0)    (402.0, 0.0)    (456.0, 0.0)
Tensor[Complex[system.float64]] of shape "[6]" on backend "Cpu"
    (546.0, 0.0)    (456.0, 0.0)    (402.0, 0.0)    (384.0, 0.0)    (402.0, 0.0)    (456.0, 0.0)

[Clonkk]

This is the operation performed by FFTW : https://fftw.org/fftw3_doc/The-1d-Discrete-Fourier-Transform-_0028DFT_0029.html#The-1d-Discrete-Fourier-Transform-_0028DFT_0029

I didn't reproduce locally on UT so that's a bit weird, I'll check your code later.