Add Numpy crossreferences to hooke.util.fft

diff --git a/FFT_tools.py b/FFT_tools.py
index 107c2166e826d88f579b183c05311b1795ba6517..cd8d587a8d40b57389e30c5b4e16a389c7fe6bcb 100644 (file)
--- a/FFT_tools.py
+++ b/FFT_tools.py
@@ -37,7 +37,7 @@
 """
 Define some FFT wrappers to reduce clutter.
 Provides a unitary discrete FFT and a windowed version.
-Based on numpy.fft.rfft.
+Based on :func:`numpy.fft.rfft`.
 
 Main entry functions:
 
@@ -352,18 +352,18 @@ class TestRFFT (unittest.TestCase):
     Notes
     -----
 
-    The expected return values are [#numpybook]_:
+    The expected return values are [#dft]_:
 
-    .. math:: X_k = \sum_{m=0}^{n-1} x_m \exp^{-j 2\pi k_m/n}
+    .. math:: X_k = \sum_{m=0}^{n-1} x_m \exp^{-2\pi imk/n}
 
-    .. [#numpybook] http://www.tramy.us/numpybook.pdf
+    .. [#dft] See the *Background information* section of :mod:`numpy.fft`.
     """
     def run_rfft(self, xs, Xs):
-        j = complex(0,1)
+        i = complex(0,1)
         n = len(xs)
         Xa = []
         for k in range(n):
-            Xa.append(sum([x*exp(-j*2*pi*k*m/n) for x,m in zip(xs,range(n))]))
+            Xa.append(sum([x*exp(-2*pi*i*m*k/n) for x,m in zip(xs,range(n))]))
             if k < len(Xs):
                 assert (Xs[k]-Xa[k])/abs(Xa[k]) < 1e-6, \
                     "rfft mismatch on element %d: %g != %g, relative error %g" \