Merge pull request numpy#26354 from WarrenWeckesser/fix-rfft

BUG: Fix rfft for even input length.

Author: charris

numpy/fft/_pocketfft_umath.cpp

@@ -183,12 +183,15 @@ rfft_impl(char **args, npy_intp const *dimensions, npy_intp const *steps,
          * Pocketfft uses FFTpack order, R0,R1,I1,...Rn-1,In-1,Rn[,In] (last
          * for npts odd only). To make unpacking easy, we place the real data
          * offset by one in the buffer, so that we just have to move R0 and
-         * create I0=0. Note that copy_data will zero the In component for
+         * create I0=0. Note that copy_input will zero the In component for
          * even number of points.
          */
         copy_input(ip, step_in, nin, &((T *)op_or_buff)[1], nout*2 - 1);
         plan->exec(&((T *)op_or_buff)[1], *(T *)fp, pocketfft::FORWARD);
         op_or_buff[0] = op_or_buff[0].imag();  // I0->R0, I0=0
+        if (!(npts & 1)) {
+            op_or_buff[nout - 1].imag(0.0);
+        }
         if (buffered) {
             copy_output(op_or_buff, op, step_out, nout);
         }

numpy/fft/tests/test_pocketfft.py

@@ -183,7 +183,6 @@ def test_fft_bad_out(self):
         with pytest.raises(TypeError, match="Cannot cast"):
             np.fft.fft(x, out=np.zeros_like(x, dtype=float))
 
-
     @pytest.mark.parametrize('norm', (None, 'backward', 'ortho', 'forward'))
     def test_ifft(self, norm):
         x = random(30) + 1j*random(30)
@@ -258,6 +257,17 @@ def test_rfft(self):
                 np.fft.rfft(x, n=n) / n,
                 np.fft.rfft(x, n=n, norm="forward"), atol=1e-6)
 
+    def test_rfft_even(self):
+        x = np.arange(8)
+        n = 4
+        y = np.fft.rfft(x, n)
+        assert_allclose(y, np.fft.fft(x[:n])[:n//2 + 1], rtol=1e-14)
+
+    def test_rfft_odd(self):
+        x = np.array([1, 0, 2, 3, -3])
+        y = np.fft.rfft(x)
+        assert_allclose(y, np.fft.fft(x)[:3], rtol=1e-14)
+
     def test_irfft(self):
         x = random(30)
         assert_allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)