Simplify fft + fix PeriodicSampling window

include/ddc/kernels/fft.hpp

@@ -332,29 +332,7 @@ int N(ddc::DiscreteDomain<DDimX...> x_mesh)
     static_assert(
             (is_uniform_point_sampling_v<DDimX> && ...),
             "DDimX dimensions should derive from UniformPointSampling");
-    return ddc::get<DDim>(x_mesh.extents());
-}
-
-template <typename DDim, typename... DDimX>
-double a(ddc::DiscreteDomain<DDimX...> x_mesh)
-{
-    static_assert(
-            (is_uniform_point_sampling_v<DDimX> && ...),
-            "DDimX dimensions should derive from UniformPointSampling");
-    return ((2 * N<DDim>(x_mesh) - 1) * coordinate(ddc::select<DDim>(x_mesh).front())
-            - coordinate(ddc::select<DDim>(x_mesh).back()))
-           / 2 / (N<DDim>(x_mesh) - 1);
-}
-
-template <typename DDim, typename... DDimX>
-double b(ddc::DiscreteDomain<DDimX...> x_mesh)
-{
-    static_assert(
-            (is_uniform_point_sampling_v<DDimX> && ...),
-            "DDimX dimensions should derive from UniformPointSampling");
-    return ((2 * N<DDim>(x_mesh) - 1) * coordinate(ddc::select<DDim>(x_mesh).back())
-            - coordinate(ddc::select<DDim>(x_mesh).front()))
-           / 2 / (N<DDim>(x_mesh) - 1);
+    return static_cast<int>(x_mesh.template extent<DDim>());
 }
 
 // core
@@ -595,7 +573,10 @@ typename DDimFx::template Impl<DDimFx, Kokkos::HostSpace> init_fourier_space(
             ddc::Coordinate<typename DDimFx::continuous_dimension_type>(0),
             ddc::Coordinate<typename DDimFx::continuous_dimension_type>(
                     2 * (ddc::detail::fft::N<DDimX>(x_mesh) - 1)
-                    / (ddc::detail::fft::b<DDimX>(x_mesh) - ddc::detail::fft::a<DDimX>(x_mesh))
+                    * (ddc::detail::fft::N<DDimX>(x_mesh) - 1)
+                    / static_cast<double>(
+                            ddc::detail::fft::N<DDimX>(x_mesh)
+                            * (ddc::coordinate(x_mesh.back()) - ddc::coordinate(x_mesh.front())))
                     * Kokkos::numbers::pi),
             ddc::DiscreteVector<DDimFx>(ddc::detail::fft::N<DDimX>(x_mesh)),
             ddc::DiscreteVector<DDimFx>(ddc::detail::fft::N<DDimX>(x_mesh)));

include/ddc/periodic_sampling.hpp

@@ -57,6 +57,8 @@ class PeriodicSampling : detail::PeriodicSamplingBase
 
         std::size_t m_n_period {2};
 
+        bool m_odd_period {false};
+
     public:
         using discrete_dimension_type = PeriodicSampling;
 
@@ -75,6 +77,7 @@ class PeriodicSampling : detail::PeriodicSamplingBase
             : m_origin(impl.m_origin)
             , m_step(impl.m_step)
             , m_n_period(impl.m_n_period)
+            , m_odd_period(impl.m_odd_period)
         {
         }
 
@@ -90,6 +93,7 @@ class PeriodicSampling : detail::PeriodicSamplingBase
             : m_origin(origin)
             , m_step(step)
             , m_n_period(n_period)
+            , m_odd_period(static_cast<bool>(n_period % 2))
         {
             assert(step > 0);
             assert(n_period > 0);
@@ -127,8 +131,11 @@ class PeriodicSampling : detail::PeriodicSamplingBase
         {
             return m_origin
                    + continuous_element_type(
-                             static_cast<int>((icoord.uid() + m_n_period / 2 - 1) % m_n_period)
-                             - static_cast<int>(m_n_period / 2 - 1))
+                             static_cast<int>(
+                                     (icoord.uid()
+                                      + (m_n_period - static_cast<int>(m_odd_period)) / 2)
+                                     % m_n_period)
+                             - static_cast<int>((m_n_period - static_cast<int>(m_odd_period)) / 2))
                              * m_step;
         }
     };

tests/fft.cpp

@@ -199,6 +199,54 @@ struct RDimX;
 struct RDimY;
 struct RDimZ;
 
+TEST(FourierMesh, Even)
+{
+    double const a = -10;
+    double const b = 10;
+    std::size_t const Nx = 64;
+
+    DDom<DDim<RDimX>> const x_mesh(
+            ddc::init_discrete_space<DDim<RDimX>>(DDim<RDimX>::template init<DDim<RDimX>>(
+                    ddc::Coordinate<RDimX>(a + (b - a) / Nx / 2),
+                    ddc::Coordinate<RDimX>(b - (b - a) / Nx / 2),
+                    DVect<DDim<RDimX>>(Nx))));
+    ddc::init_discrete_space<DFDim<ddc::Fourier<RDimX>>>(
+            ddc::init_fourier_space<DFDim<ddc::Fourier<RDimX>>>(
+                    ddc::DiscreteDomain<DDim<RDimX>>(x_mesh)));
+
+    double const epsilon = 1e-14;
+    for (int i=-static_cast<int>(Nx)/2; i<=static_cast<int>(Nx-2)/2; i++) {
+        EXPECT_NEAR(
+                ddc::coordinate(ddc::DiscreteElement<DFDim<ddc::Fourier<RDimX>>>(i)),
+                2 * i * Kokkos::numbers::pi / (b - a),
+                epsilon);
+    }
+}
+
+TEST(FourierMesh, Odd)
+{
+    double const a = -10;
+    double const b = 10;
+    std::size_t const Nx = 65;
+
+    DDom<DDim<RDimX>> const x_mesh(
+            ddc::init_discrete_space<DDim<RDimX>>(DDim<RDimX>::template init<DDim<RDimX>>(
+                    ddc::Coordinate<RDimX>(a + (b - a) / Nx / 2),
+                    ddc::Coordinate<RDimX>(b - (b - a) / Nx / 2),
+                    DVect<DDim<RDimX>>(Nx))));
+    ddc::init_discrete_space<DFDim<ddc::Fourier<RDimX>>>(
+            ddc::init_fourier_space<DFDim<ddc::Fourier<RDimX>>>(
+                    ddc::DiscreteDomain<DDim<RDimX>>(x_mesh)));
+
+    double const epsilon = 1e-14;
+    for (int i=-static_cast<int>(Nx-1)/2; i<=static_cast<int>(Nx-1)/2; i++) {
+        EXPECT_NEAR(
+                ddc::coordinate(ddc::DiscreteElement<DFDim<ddc::Fourier<RDimX>>>(i)),
+                2 * i * Kokkos::numbers::pi / (b - a),
+                epsilon);
+    }
+}
+
 #if fftw_serial_AVAIL
 TEST(FFTNorm, OFF)
 {