BUG: change default threshold for matrix_rank

The default tolerance threshold for matrix_rank was passing as full rank
some matrices that were numerically rank deficient.  This commit changes
the default tolerance to match the algorithm in MATLAB and Numerical
recipes.

1 files changed, 16 insertions, 1 deletions

diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
index 2a2ec3da5..623939863 100644
--- a/numpy/linalg/tests/test_linalg.py
+++ b/numpy/linalg/tests/test_linalg.py
@@ -3,7 +3,9 @@
 import sys
 
 import numpy as np
-from numpy.testing import *
+from numpy.testing import (TestCase, assert_, assert_equal, assert_raises,
+                           assert_array_equal, assert_almost_equal,
+                           run_module_suite)
 from numpy import array, single, double, csingle, cdouble, dot, identity
 from numpy import multiply, atleast_2d, inf, asarray, matrix
 from numpy import linalg
@@ -451,6 +453,19 @@ class TestMatrixRank(object):
         yield assert_equal, matrix_rank(1), 1
 
 
+def test_reduced_rank():
+    # Test matrices with reduced rank
+    rng = np.random.RandomState(20120714)
+    for i in range(100):
+        # Make a rank deficient matrix
+        X = rng.normal(size=(40, 10))
+        X[:, 0] = X[:, 1] + X[:, 2]
+        # Assert that matrix_rank detected deficiency
+        assert_equal(matrix_rank(X), 9)
+        X[:, 3] = X[:, 4] + X[:, 5]
+        assert_equal(matrix_rank(X), 8)
+
+
 class TestQR(TestCase):
     def test_qr_empty(self):
         a = np.zeros((0,2))