MAINT: improve readablility of cross and improve test coverage

1 files changed, 46 insertions, 29 deletions

diff --git a/numpy/core/numeric.py b/numpy/core/numeric.py
index 38c28da6d..a85e8514c 100644
--- a/numpy/core/numeric.py
+++ b/numpy/core/numeric.py
@@ -1522,7 +1522,7 @@ def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None):
     b = rollaxis(b, axisb, b.ndim)
     msg = ("incompatible dimensions for cross product\n"
            "(dimension must be 2 or 3)")
-    if a.shape[-1] not in [2, 3] or b.shape[-1] not in [2, 3]:
+    if a.shape[-1] not in (2, 3) or b.shape[-1] not in (2, 3):
         raise ValueError(msg)
 
         # Create the output array
@@ -1532,45 +1532,62 @@ def cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None):
     dtype = promote_types(a.dtype, b.dtype)
     cp = empty(shape, dtype)
 
+    # create local aliases for readability
+    a0 = a[..., 0]
+    a1 = a[..., 1]
+    if a.shape[-1] == 3:
+        a2 = a[..., 2]
+    b0 = b[..., 0]
+    b1 = b[..., 1]
+    if b.shape[-1] == 3:
+        b2 = b[..., 2]
+    if cp.ndim != 0 and cp.shape[-1] == 3:
+        cp0 = cp[..., 0]
+        cp1 = cp[..., 1]
+        cp2 = cp[..., 2]
+
     if a.shape[-1] == 2:
         if b.shape[-1] == 2:
-            # cp = a[..., 0]*b[..., 1] - a[..., 1]*b[..., 0]
-            multiply(a[..., 0], b[..., 1], out=cp)
-            cp -= a[..., 1]*b[..., 0]
+            # a0 * b1 - a1 * b0
+            multiply(a0, b1, out=cp)
+            cp -= a1 * b0
             if cp.ndim == 0:
                 return cp
             else:
                 # This works because we are moving the last axis
                 return rollaxis(cp, -1, axisc)
         else:
-            # cp[..., 0] = a[..., 1]*b[..., 2]
-            multiply(a[..., 1], b[..., 2], out=cp[..., 0])
-            # cp[..., 1] = -a[..., 0]*b[..., 2]
-            multiply(a[..., 0], b[..., 2], out=cp[..., 1])
-            cp[..., 1] *= - 1
-            # cp[..., 2] = a[..., 0]*b[..., 1] - a[..., 1]*b[..., 0]
-            multiply(a[..., 0], b[..., 1], out=cp[..., 2])
-            cp[..., 2] -= a[..., 1]*b[..., 0]
+            # cp0 = a1 * b2 - 0  (a2 = 0)
+            # cp1 = 0 - a0 * b2  (a2 = 0)
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a1, b2, out=cp0)
+            multiply(a0, b2, out=cp1)
+            negative(cp1, out=cp1)
+            multiply(a0, b1, out=cp2)
+            cp2 -= a1 * b0
     elif a.shape[-1] == 3:
         if b.shape[-1] == 3:
-            # cp[..., 0] = a[..., 1]*b[..., 2] - a[..., 2]*b[..., 1]
-            multiply(a[..., 1], b[..., 2], out=cp[..., 0])
-            cp[..., 0] -= a[..., 2]*b[..., 1]
-            # cp[..., 1] = a[..., 2]*b[..., 0] - a[..., 0]*b[..., 2]
-            multiply(a[..., 2], b[..., 0], out=cp[..., 1])
-            cp[..., 1] -= a[..., 0]*b[..., 2]
-            # cp[..., 2] = a[..., 0]*b[..., 1] - a[..., 1]*b[..., 0]
-            multiply(a[..., 0], b[..., 1], out=cp[..., 2])
-            cp[..., 2] -= a[..., 1]*b[..., 0]
+            # cp0 = a1 * b2 - a2 * b1
+            # cp1 = a2 * b0 - a0 * b2
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a1, b2, out=cp0)
+            tmp = array(a2 * b1)
+            cp0 -= tmp
+            multiply(a2, b0, out=cp1)
+            multiply(a0, b2, out=tmp)
+            cp1 -= tmp
+            multiply(a0, b1, out=cp2)
+            multiply(a1, b0, out=tmp)
+            cp2 -= tmp
         else:
-            # cp[..., 0] = -a[..., 2]*b[..., 1]
-            multiply(a[..., 2], b[..., 1], out=cp[..., 0])
-            cp[..., 0] *= - 1
-            # cp[..., 1] = a[..., 2]*b[..., 0]
-            multiply(a[..., 2], b[..., 0], out=cp[..., 1])
-            # cp[..., 2] = a[..., 0]*b[..., 1] - a[..., 1]*b[..., 0]
-            multiply(a[..., 0], b[..., 1], out=cp[..., 2])
-            cp[..., 2] -= a[..., 1]*b[..., 0]
+            # cp0 = 0 - a2 * b1  (b2 = 0)
+            # cp1 = a2 * b0 - 0  (b2 = 0)
+            # cp2 = a0 * b1 - a1 * b0
+            multiply(a2, b1, out=cp0)
+            negative(cp0, out=cp0)
+            multiply(a2, b0, out=cp1)
+            multiply(a0, b1, out=cp2)
+            cp2 -= a1 * b0
 
     if cp.ndim == 1:
         return cp