Merge branch 'flip_fft' into 'NIFTy_6'

Flip fft and ifft

See merge request !451

ChangeLog

 Changes since NIFTy 5:
 
+FFT convention adjusted
+=======================
+
+When going to harmonic space, NIFTy's FFT operator now uses a minus sign in the
+exponent (and, consequently, a plus sign on the adjoint transform). This
+convention is consistent with almost all other numerical FFT libraries.
+
 Interface change in EndomorphicOperator.draw_sample()
 =====================================================
 

nifty6/operators/harmonic_operators.py

@@ -74,11 +74,11 @@ class FFTOperator(LinearOperator):
         self._check_input(x, mode)
         ncells = x.domain[self._space].size
         if x.domain[self._space].harmonic:  # harmonic -> position
-            func = fft.fftn
-            fct = 1.
-        else:
             func = fft.ifftn
             fct = ncells
+        else:
+            func = fft.fftn
+            fct = 1.
         axes = x.domain.axes[self._space]
         tdom = self._tgt(mode)
         tmp = func(x.val, axes=axes)

test/test_operators/test_nft.py

@@ -82,8 +82,7 @@ def test_cartesian():
     vol = ift.full(dom, 1.).s_integrate()
     res1 = fft(fld).val
 
-    # FIXME: we don't understand the conjugate() yet
-    np.testing.assert_allclose(res, res1.conjugate()*vol)
+    np.testing.assert_allclose(res, res1*vol)
 
 
 @pmp('eps', [1e-2, 1e-6, 2e-13])