linalg: support '0-norm' (scipy ticket #1037)

2 files changed, 7 insertions, 2 deletions

diff --git a/numpy/linalg/linalg.py b/numpy/linalg/linalg.py
index 287b38d9b..0b7aa132e 100644
--- a/numpy/linalg/linalg.py
+++ b/numpy/linalg/linalg.py
@@ -1674,7 +1674,7 @@ def norm(x, ord=None):
 
     Notes
     -----
-    For values of ``ord < 0``, the result is, strictly speaking, not a
+    For values of ``ord <= 0``, the result is, strictly speaking, not a
     mathematical 'norm', but it may still be useful for various numerical
     purposes.
 
@@ -1687,6 +1687,7 @@ def norm(x, ord=None):
     'fro'  Frobenius norm                --
     inf    max(sum(abs(x), axis=1))      max(abs(x))
     -inf   min(sum(abs(x), axis=1))      min(abs(x))
+    0      --                            sum(x != 0)
     1      max(sum(abs(x), axis=0))      as below
     -1     min(sum(abs(x), axis=0))      as below
     2      2-norm (largest sing. value)  as below
@@ -1754,15 +1755,17 @@ def norm(x, ord=None):
 
     """
     x = asarray(x)
-    nd = len(x.shape)
     if ord is None: # check the default case first and handle it immediately
         return sqrt(add.reduce((x.conj() * x).ravel().real))
 
+    nd = x.ndim
     if nd == 1:
         if ord == Inf:
             return abs(x).max()
         elif ord == -Inf:
             return abs(x).min()
+        elif ord == 0:
+            return (x != 0).sum() # Zero norm
         elif ord == 1:
             return abs(x).sum() # special case for speedup
         elif ord == 2:
diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
index 849f30a50..01e96d6a2 100644
--- a/numpy/linalg/tests/test_linalg.py
+++ b/numpy/linalg/tests/test_linalg.py
@@ -282,6 +282,7 @@ class _TestNorm(TestCase):
                     decimal=self.dec)
             np.testing.assert_almost_equal(norm(v,-2), ((205./144)**-0.5),
                     decimal=self.dec)
+            np.testing.assert_almost_equal(norm(v,0), 4, decimal=self.dec)
 
         for v in (a, b, c,):
             _test(v)
@@ -304,6 +305,7 @@ class _TestNorm(TestCase):
 
         self.assertRaises(ValueError, norm, A, 'nofro')
         self.assertRaises(ValueError, norm, A, -3)
+        self.assertRaises(ValueError, norm, A, 0)
 
 class TestNormDouble(_TestNorm):
     dt = np.double