Integrated real harmonic RGSpace representation deeply into NIFTy.

demos/wiener_filter_via_curvature.py

@@ -2,13 +2,14 @@ import numpy as np
 
 from nifty import RGSpace, PowerSpace, Field, FFTOperator, ComposedOperator,\
                   DiagonalOperator, ResponseOperator, plotting,\
-                  create_power_operator
+                  create_power_operator, nifty_configuration
 from nifty.library import WienerFilterCurvature
 
 
 if __name__ == "__main__":
 
-    distribution_strategy = 'not'
+    nifty_configuration['default_distribution_strategy'] = 'fftw'
+    nifty_configuration['harmonic_rg_base'] = 'real'
 
     # Setting up variable parameters
 
@@ -36,19 +37,17 @@ if __name__ == "__main__":
 
     signal_space = RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
     harmonic_space = FFTOperator.get_default_codomain(signal_space)
-    fft = FFTOperator(harmonic_space, target=signal_space,
-                      domain_dtype=np.complex, target_dtype=np.float)
-    power_space = PowerSpace(harmonic_space,
-                             distribution_strategy=distribution_strategy)
+    fft = FFTOperator(harmonic_space, target=signal_space)
+    power_space = PowerSpace(harmonic_space)
 
     # Creating the mock data
-    S = create_power_operator(harmonic_space, power_spectrum=power_spectrum,
-                              distribution_strategy=distribution_strategy)
+    S = create_power_operator(harmonic_space, power_spectrum=power_spectrum)
 
-    mock_power = Field(power_space, val=power_spectrum,
-                       distribution_strategy=distribution_strategy)
+    mock_power = Field(power_space, val=power_spectrum)
     np.random.seed(43)
     mock_harmonic = mock_power.power_synthesize(real_signal=True)
+    if nifty_configuration['harmonic_rg_base'] == 'real':
+        mock_harmonic = mock_harmonic.real
     mock_signal = fft(mock_harmonic)
 
     R = ResponseOperator(signal_space, sigma=(response_sigma,))
@@ -74,9 +73,10 @@ if __name__ == "__main__":
 
     plotter = plotting.RG2DPlotter()
     plotter.path = 'mock_signal.html'
-    plotter(mock_signal)
+    plotter(mock_signal.real)
     plotter.path = 'data.html'
-    plotter(Field(signal_space,
-                  val=data.val.get_full_data().reshape(signal_space.shape)))
+    plotter(Field(
+                signal_space,
+                val=data.val.get_full_data().real.reshape(signal_space.shape)))
     plotter.path = 'map.html'
-    plotter(m_s)
+    plotter(m_s.real)

demos/wiener_filter_via_curvature_real.py

-import numpy as np
-
-from nifty import RGSpace, PowerSpace, Field, RealFFTOperator,\
-                  ComposedOperator, DiagonalOperator, ResponseOperator,\
-                  plotting, create_power_operator
-from nifty.library import WienerFilterCurvature
-
-
-if __name__ == "__main__":
-
-    distribution_strategy = 'not'
-
-    # Setting up variable parameters
-
-    # Typical distance over which the field is correlated
-    correlation_length = 0.05
-    # Variance of field in position space sqrt(<|s_x|^2>)
-    field_variance = 2.
-    # smoothing length of response (in same unit as L)
-    response_sigma = 0.01
-    # The signal to noise ratio
-    signal_to_noise = 0.7
-
-    # note that field_variance**2 = a*k_0/4. for this analytic form of power
-    # spectrum
-    def power_spectrum(k):
-        a = 4 * correlation_length * field_variance**2
-        return a / (1 + k * correlation_length) ** 4
-
-    # Setting up the geometry
-
-    # Total side-length of the domain
-    L = 2.
-    # Grid resolution (pixels per axis)
-    N_pixels = 512
-
-    signal_space = RGSpace([N_pixels, N_pixels], distances=L/N_pixels)
-    harmonic_space = RealFFTOperator.get_default_codomain(signal_space)
-    fft = RealFFTOperator(harmonic_space, target=signal_space)
-    power_space = PowerSpace(harmonic_space,
-                             distribution_strategy=distribution_strategy)
-
-    # Creating the mock data
-    S = create_power_operator(harmonic_space, power_spectrum=power_spectrum,
-                              distribution_strategy=distribution_strategy)
-
-    mock_power = Field(power_space, val=power_spectrum,
-                       distribution_strategy=distribution_strategy)
-    np.random.seed(43)
-    mock_harmonic = mock_power.power_synthesize(real_signal=True)
-    mock_harmonic = mock_harmonic.real + mock_harmonic.imag
-    mock_signal = fft(mock_harmonic)
-
-    R = ResponseOperator(signal_space, sigma=(response_sigma,))
-    data_domain = R.target[0]
-    R_harmonic = ComposedOperator([fft, R], default_spaces=[0, 0])
-
-    N = DiagonalOperator(data_domain,
-                         diagonal=mock_signal.var()/signal_to_noise,
-                         bare=True)
-    noise = Field.from_random(domain=data_domain,
-                              random_type='normal',
-                              std=mock_signal.std()/np.sqrt(signal_to_noise),
-                              mean=0)
-    data = R(mock_signal) + noise
-
-    # Wiener filter
-
-    j = R_harmonic.adjoint_times(N.inverse_times(data))
-    wiener_curvature = WienerFilterCurvature(S=S, N=N, R=R_harmonic)
-
-    m = wiener_curvature.inverse_times(j)
-    m_s = fft(m)
-
-    plotter = plotting.RG2DPlotter()
-    plotter.path = 'mock_signal.html'
-    plotter(mock_signal)
-    plotter.path = 'data.html'
-    plotter(Field(signal_space,
-                  val=data.val.get_full_data().reshape(signal_space.shape)))
-    plotter.path = 'map.html'
-    plotter(m_s)

nifty/config/nifty_config.py

@@ -70,11 +70,18 @@ variable_default_distribution_strategy = keepers.Variable(
                                          if z == 'fftw' else True),
                               genus='str')
 
+variable_harmonic_rg_base = keepers.Variable(
+                                'harmonic_rg_base',
+                                ['real', 'complex'],
+                                lambda z: z in ['real', 'complex'],
+                                genus='str')
+
 nifty_configuration = keepers.get_Configuration(
                  name='NIFTy',
                  variables=[variable_fft_module,
                             variable_default_field_dtype,
-                            variable_default_distribution_strategy],
+                            variable_default_distribution_strategy,
+                            variable_harmonic_rg_base],
                  file_name='NIFTy.conf',
                  search_paths=[os.path.expanduser('~') + "/.config/nifty/",
                                os.path.expanduser('~') + "/.config/",

nifty/field.py

@@ -19,7 +19,6 @@
 from __future__ import division
 
 import ast
-import itertools
 import numpy as np
 
 from keepers import Versionable,\

nifty/operators/fft_operator/__init__.py

@@ -18,4 +18,3 @@
 
 from transformations import *
 from .fft_operator import FFTOperator
-from .real_fft_operator import RealFFTOperator

nifty/operators/fft_operator/fft_operator.py

@@ -142,17 +142,11 @@ class FFTOperator(LinearOperator):
             backward_class, self.target[0], self.domain[0], module=module)
 
         # Store the dtype information
-        if domain_dtype is None:
-            self.logger.info("Setting domain_dtype to np.complex.")
-            self.domain_dtype = np.complex
-        else:
-            self.domain_dtype = np.dtype(domain_dtype)
+        self.domain_dtype = \
+            None if domain_dtype is None else np.dtype(domain_dtype)
 
-        if target_dtype is None:
-            self.logger.info("Setting target_dtype to np.complex.")
-            self.target_dtype = np.complex
-        else:
-            self.target_dtype = np.dtype(target_dtype)
+        self.target_dtype = \
+            None if target_dtype is None else np.dtype(target_dtype)
 
     def _times(self, x, spaces):
         spaces = utilities.cast_axis_to_tuple(spaces, len(x.domain))
@@ -172,8 +166,10 @@ class FFTOperator(LinearOperator):
             result_domain = list(x.domain)
             result_domain[spaces[0]] = self.target[0]
 
+        result_dtype = \
+            new_val.dtype if self.target_dtype is None else self.target_dtype
         result_field = x.copy_empty(domain=result_domain,
-                                    dtype=self.target_dtype)
+                                    dtype=result_dtype)
         result_field.set_val(new_val=new_val, copy=True)
 
         return result_field
@@ -196,8 +192,11 @@ class FFTOperator(LinearOperator):
             result_domain = list(x.domain)
             result_domain[spaces[0]] = self.domain[0]
 
+        result_dtype = \
+            new_val.dtype if self.domain_dtype is None else self.domain_dtype
+
         result_field = x.copy_empty(domain=result_domain,
-                                    dtype=self.domain_dtype)
+                                    dtype=result_dtype)
         result_field.set_val(new_val=new_val, copy=True)
 
         return result_field

nifty/operators/fft_operator/transformations/rg_transforms.py

@@ -260,7 +260,7 @@ class MPIFFT(Transform):
         p()
 
         if p.has_output:
-            result = p.output_array
+            result = p.output_array.copy()
             if result.shape != val.shape:
                 raise ValueError("Output shape is different than input shape. "
                                  "Maybe fftw tries to optimize the "

nifty/operators/fft_operator/transformations/rgrgtransformation.py

@@ -43,6 +43,8 @@ class RGRGTransformation(Transformation):
         else:
             raise ValueError('Unsupported FFT module:' + module)
 
+        self.harmonic_base = nifty_configuration['harmonic_rg_base']
+
     # ---Mandatory properties and methods---
 
     @property
@@ -144,7 +146,31 @@ class RGRGTransformation(Transformation):
             val = self._transform.domain.weight(val, power=1, axes=axes)
 
         # Perform the transformation
-        Tval = self._transform.transform(val, axes, **kwargs)
+        if self.harmonic_base == 'complex':
+            Tval = self._transform.transform(val, axes, **kwargs)
+        else:
+            if issubclass(val.dtype.type, np.complexfloating):
+                Tval_real = self._transform.transform(val.real, axes,
+                                                      **kwargs)
+                Tval_imag = self._transform.transform(val.imag, axes,
+                                                      **kwargs)
+                if self.codomain.harmonic:
+                    Tval_real.data.real += Tval_real.data.imag
+                    Tval_real.data.imag = \
+                        Tval_imag.data.real + Tval_imag.data.imag
+                else:
+                    Tval_real.data.real -= Tval_real.data.imag
+                    Tval_real.data.imag = \
+                        Tval_imag.data.real - Tval_imag.data.imag
+
+                Tval = Tval_real
+            else:
+                Tval = self._transform.transform(val, axes, **kwargs)
+                if self.codomain.harmonic:
+                    Tval.data.real += Tval.data.imag
+                else:
+                    Tval.data.real -= Tval.data.imag
+                Tval = Tval.real
 
         if not self._transform.codomain.harmonic:
             # correct for inverse fft.

nifty/spaces/rg_space/rg_space.py

@@ -36,7 +36,7 @@ from d2o import distributed_data_object,\
                 STRATEGIES as DISTRIBUTION_STRATEGIES
 
 from nifty.spaces.space import Space
-
+from nifty.config import nifty_configuration
 
 class RGSpace(Space):
     """
@@ -122,33 +122,36 @@ class RGSpace(Space):
 #        return fixed_points
 
     def hermitianize_inverter(self, x, axes):
-        # calculate the number of dimensions the input array has
-        dimensions = len(x.shape)
-        # prepare the slicing object which will be used for mirroring
-        slice_primitive = [slice(None), ] * dimensions
-        # copy the input data
-        y = x.copy()
-
-        # flip in the desired directions
-        for k in range(len(axes)):
-            i = axes[k]
-            slice_picker = slice_primitive[:]
-            slice_inverter = slice_primitive[:]
-            if (not self.zerocenter[k]) or self.shape[k] % 2 == 0:
-                slice_picker[i] = slice(1, None, None)
-                slice_inverter[i] = slice(None, 0, -1)
-            else:
-                slice_picker[i] = slice(None)
-                slice_inverter[i] = slice(None, None, -1)
-            slice_picker = tuple(slice_picker)
-            slice_inverter = tuple(slice_inverter)
-
-            try:
-                y.set_data(to_key=slice_picker, data=y,
-                           from_key=slice_inverter)
-            except(AttributeError):
-                y[slice_picker] = y[slice_inverter]
-        return y
+        if nifty_configuration['harmonic_rg_base'] == 'real':
+            return x
+        else:
+            # calculate the number of dimensions the input array has
+            dimensions = len(x.shape)
+            # prepare the slicing object which will be used for mirroring
+            slice_primitive = [slice(None), ] * dimensions
+            # copy the input data
+            y = x.copy()
+
+            # flip in the desired directions
+            for k in range(len(axes)):
+                i = axes[k]
+                slice_picker = slice_primitive[:]
+                slice_inverter = slice_primitive[:]
+                if (not self.zerocenter[k]) or self.shape[k] % 2 == 0:
+                    slice_picker[i] = slice(1, None, None)
+                    slice_inverter[i] = slice(None, 0, -1)
+                else:
+                    slice_picker[i] = slice(None)
+                    slice_inverter[i] = slice(None, None, -1)
+                slice_picker = tuple(slice_picker)
+                slice_inverter = tuple(slice_inverter)
+
+                try:
+                    y.set_data(to_key=slice_picker, data=y,
+                               from_key=slice_inverter)
+                except(AttributeError):
+                    y[slice_picker] = y[slice_inverter]
+            return y
 
     # ---Mandatory properties and methods---
 

nifty/sugar.py

@@ -16,6 +16,8 @@
 # NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
 # and financially supported by the Studienstiftung des deutschen Volkes.
 
+import numpy as np
+
 from nifty import Space,\
                   PowerSpace,\
                   Field,\
@@ -71,9 +73,10 @@ def create_power_operator(domain, power_spectrum, dtype=None,
                distribution_strategy='not')
     f = fp.power_synthesize(mean=1, std=0, real_signal=False,
                             distribution_strategy=distribution_strategy)
-    # MR FIXME: we need the real part here. Could this also be achieved
-    # by setting real_signal=True in the call above?
-    f = f.real
+
+    if not issubclass(fp.dtype.type, np.complexfloating):
+        f = f.real
+
     f **= 2
     return DiagonalOperator(domain, diagonal=f, bare=True)
 

test/test_operators/test_fft_operator.py

@@ -31,14 +31,7 @@ from itertools import product
 from test.common import expand
 from nose.plugins.skip import SkipTest
 
-
-def _harmonic_type(itp):
-    otp = itp
-    if otp == np.float64:
-        otp = np.complex128
-    elif otp == np.float32:
-        otp = np.complex64
-    return otp
+from d2o import STRATEGIES
 
 
 def _get_rtol(tp):
@@ -49,100 +42,119 @@ def _get_rtol(tp):
 
 
 class FFTOperatorTests(unittest.TestCase):
-    @expand(product([10, 11], [False, True], [0.1, 1, 3.7]))
-    def test_RG_distance_1D(self, dim1, zc1, d):
-        foo = RGSpace([dim1], zerocenter=zc1, distances=d)
-        res = foo.get_distance_array('not')
-        assert_equal(res[zc1 * (dim1 // 2)], 0.)
-
-    @expand(product([10, 11], [9, 28], [False, True], [False, True],
-                    [0.1, 1, 3.7]))
-    def test_RG_distance_2D(self, dim1, dim2, zc1, zc2, d):
-        foo = RGSpace([dim1, dim2], zerocenter=[zc1, zc2], distances=d)
-        res = foo.get_distance_array('not')
-        assert_equal(res[zc1 * (dim1 // 2), zc2 * (dim2 // 2)], 0.)
-
     @expand(product(["numpy", "fftw", "fftw_mpi"],
-                    [16, ], [False, True], [False, True],
-                    [0.1, 1, 3.7],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
-    def test_fft1D(self, module, dim1, zc1, zc2, d, itp):
+                    [16, ], [0.1, 1, 3.7], STRATEGIES['global'],
+                    [np.float64, np.float32, np.complex64, np.complex128],
+                    ['real', 'complex']))
+    def test_fft1D(self, module, dim1, d, distribution_strategy, itp, base):
         if module == "fftw_mpi":
             if not hasattr(gdi.get('fftw'), 'FFTW_MPI'):
                 raise SkipTest
         if module == "fftw" and "fftw" not in gdi:
             raise SkipTest
         tol = _get_rtol(itp)
-        a = RGSpace(dim1, zerocenter=zc1, distances=d)
-        b = RGSpace(dim1, zerocenter=zc2, distances=1./(dim1*d), harmonic=True)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=itp,
-                          target_dtype=_harmonic_type(itp), module=module)
+        a = RGSpace(dim1, distances=d)
+        b = RGSpace(dim1, distances=1./(dim1*d), harmonic=True)
+        fft = FFTOperator(domain=a, target=b, module=module)
+        fft._forward_transformation.harmonic_base = base
+        fft._backward_transformation.harmonic_base = base
+
         np.random.seed(16)
         inp = Field.from_random(domain=a, random_type='normal', std=7, mean=3,
-                                dtype=itp)
+                                dtype=itp,
+                                distribution_strategy=distribution_strategy)
         out = fft.adjoint_times(fft.times(inp))
         assert_allclose(inp.val.get_full_data(),
                         out.val.get_full_data(),
                         rtol=tol, atol=tol)
 
     @expand(product(["numpy", "fftw", "fftw_mpi"],
-                    [12, 15], [9, 12], [False, True],
-                    [False, True], [False, True], [False, True], [0.1, 1, 3.7],
-                    [0.4, 1, 2.7],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
-    def test_fft2D(self, module, dim1, dim2, zc1, zc2, zc3, zc4, d1, d2, itp):
+                    [12, 15], [9, 12], [0.1, 1, 3.7],
+                    [0.4, 1, 2.7], STRATEGIES['global'],
+                    [np.float64, np.float32, np.complex64, np.complex128],
+                    ['real', 'complex']))
+    def test_fft2D(self, module, dim1, dim2, d1, d2, distribution_strategy,
+                   itp, base):
         if module == "fftw_mpi":
             if not hasattr(gdi.get('fftw'), 'FFTW_MPI'):
                 raise SkipTest
         if module == "fftw" and "fftw" not in gdi:
             raise SkipTest
         tol = _get_rtol(itp)
-        a = RGSpace([dim1, dim2], zerocenter=[zc1, zc2], distances=[d1, d2])
-        b = RGSpace([dim1, dim2], zerocenter=[zc3, zc4],
+        a = RGSpace([dim1, dim2], distances=[d1, d2])
+        b = RGSpace([dim1, dim2],
                     distances=[1./(dim1*d1), 1./(dim2*d2)], harmonic=True)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=itp,
-                          target_dtype=_harmonic_type(itp), module=module)
+        fft = FFTOperator(domain=a, target=b, module=module)
+        fft._forward_transformation.harmonic_base = base
+        fft._backward_transformation.harmonic_base = base
+
         inp = Field.from_random(domain=a, random_type='normal', std=7, mean=3,
-                                dtype=itp)
+                                dtype=itp,
+                                distribution_strategy=distribution_strategy)
+        out = fft.adjoint_times(fft.times(inp))
+        assert_allclose(inp.val, out.val, rtol=tol, atol=tol)
+
+    @expand(product(["numpy", "fftw", "fftw_mpi"],
+                    [0, 1, 2],
+                    STRATEGIES['global'],
+                    [np.float64, np.float32, np.complex64, np.complex128],
+                    ['real', 'complex']))
+    def test_composed_fft(self, module, index, distribution_strategy, dtype,
+                          base):
+        if module == "fftw_mpi":
+            if not hasattr(gdi.get('fftw'), 'FFTW_MPI'):
+                raise SkipTest
+        if module == "fftw" and "fftw" not in gdi:
+            raise SkipTest
+        tol = _get_rtol(dtype)
+        a = [a1, a2, a3] = [RGSpace((8,)), RGSpace((4, 4)), RGSpace((5, 6))]
+        fft = FFTOperator(domain=a[index], module=module,
+                          default_spaces=(index,))
+        fft._forward_transformation.harmonic_base = base
+        fft._backward_transformation.harmonic_base = base
+
+        inp = Field.from_random(domain=(a1, a2, a3), random_type='normal',
+                                std=7, mean=3, dtype=dtype,
+                                distribution_strategy=distribution_strategy)
         out = fft.adjoint_times(fft.times(inp))
         assert_allclose(inp.val, out.val, rtol=tol, atol=tol)
 
     @expand(product([0, 3, 6, 11, 30],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
+                    [np.float64, np.float32, np.complex64, np.complex128]))
     def test_sht(self, lm, tp):
         if 'pyHealpix' not in gdi:
             raise SkipTest
         tol = _get_rtol(tp)
         a = LMSpace(lmax=lm)
         b = GLSpace(nlat=lm+1)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=tp, target_dtype=tp)
+        fft = FFTOperator(domain=a, target=b)
         inp = Field.from_random(domain=a, random_type='normal', std=7, mean=3,
                                 dtype=tp)
         out = fft.adjoint_times(fft.times(inp))
         assert_allclose(inp.val, out.val, rtol=tol, atol=tol)
 
     @expand(product([128, 256],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
+                    [np.float64, np.float32, np.complex64, np.complex128]))
     def test_sht2(self, lm, tp):
         if 'pyHealpix' not in gdi:
             raise SkipTest
         a = LMSpace(lmax=lm)
         b = HPSpace(nside=lm//2)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=tp, target_dtype=tp)
+        fft = FFTOperator(domain=a, target=b)
         inp = Field.from_random(domain=a, random_type='normal', std=1, mean=0,
                                 dtype=tp)
         out = fft.adjoint_times(fft.times(inp))
         assert_allclose(inp.val, out.val, rtol=1e-3, atol=1e-1)
 
     @expand(product([128, 256],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
+                    [np.float64, np.float32, np.complex64, np.complex128]))
     def test_dotsht(self, lm, tp):
         if 'pyHealpix' not in gdi:
             raise SkipTest
         tol = _get_rtol(tp)
         a = LMSpace(lmax=lm)
         b = GLSpace(nlat=lm+1)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=tp, target_dtype=tp)
+        fft = FFTOperator(domain=a, target=b)
         inp = Field.from_random(domain=a, random_type='normal', std=1, mean=0,
                                 dtype=tp)
         out = fft.times(inp)
@@ -151,14 +163,14 @@ class FFTOperatorTests(unittest.TestCase):
         assert_allclose(v1, v2, rtol=tol, atol=tol)
 
     @expand(product([128, 256],
-                    [np.float64, np.complex128, np.float32, np.complex64]))
+                    [np.float64, np.float32, np.complex64, np.complex128]))
     def test_dotsht2(self, lm, tp):
         if 'pyHealpix' not in gdi:
             raise SkipTest
         tol = _get_rtol(tp)
         a = LMSpace(lmax=lm)
         b = HPSpace(nside=lm//2)
-        fft = FFTOperator(domain=a, target=b, domain_dtype=tp, target_dtype=tp)
+        fft = FFTOperator(domain=a, target=b)
         inp = Field.from_random(domain=a, random_type='normal', std=1, mean=0,
                                 dtype=tp)
         out = fft.times(inp)

test/test_operators/test_real_fft_operator.py

-# This program is free software: you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation, either version 3 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program.  If not, see <http://www.gnu.org/licenses/>.
-#
-# Copyright(C) 2013-2017 Max-Planck-Society
-#
-# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
-# and financially supported by the Studienstiftung des deutschen Volkes.
-
-import unittest
-import numpy as np
-from numpy.testing import assert_equal,\
-    assert_allclose
-from nifty.config import dependency_injector as gdi
-from nifty import Field,\
-    RGSpace,\
-    LMSpace,\
-    HPSpace,\
-    GLSpace,\
-    RealFFTOperator
-from itertools import product
-from test.common import expand
-from nose.plugins.skip import SkipTest
-
-
-def _get_rtol(tp):
-    if (tp == np.float64) or (tp == np.complex128):
-        return 1e-10
-    else:
-        return 1e-5
-
-
-class RealFFTOperatorTests(unittest.TestCase):
-    @expand(product(["numpy", "fftw", "fftw_mpi"],
-                    [16, ], [0.1, 1, 3.7],