BUG: IRR was returning nan instead of valid negative answer.

This change corrects the following two bugs in numpy.irr:

* When the solution was negative, numpy.irr returned nan instead of the
  correct solution because of the mask applied to the roots. Corrected
  by removing the mask that 0 < res < 1.
* When multiple roots were found, numpy.irr was returning an array of
  all roots rather than a single float. This bug was corrected by
  selecting the single root closest to zero (min(abs(root)).

With these corrections, numpy.irr returns the same result as the
corresponding spreadsheet function in LibreOffice Calc for all test
cases (additional test cases were added to cover cases with multiple
positive and negative roots)

2 files changed, 29 insertions, 6 deletions

diff --git a/numpy/lib/financial.py b/numpy/lib/financial.py
index ec642afd3..c085a5d53 100644
--- a/numpy/lib/financial.py
+++ b/numpy/lib/financial.py
@@ -628,21 +628,29 @@ def irr(values):
 
     Examples
     --------
-    >>> print round(np.irr([-100, 39, 59, 55, 20]), 5)
+    >>> round(irr([-100, 39, 59, 55, 20]), 5)
     0.28095
+    >>> round(irr([-100, 0, 0, 74]), 5)
+    -0.0955
+    >>> round(irr([-100, 100, 0, -7]), 5)
+    -0.0833
+    >>> round(irr([-100, 100, 0, 7]), 5)
+    0.06206
+    >>> round(irr([-5, 10.5, 1, -8, 1]), 5)
+    0.0886
 
     (Compare with the Example given for numpy.lib.financial.npv)
 
     """
     res = np.roots(values[::-1])
-    # Find the root(s) between 0 and 1
-    mask = (res.imag == 0) & (res.real > 0) & (res.real <= 1)
-    res = res[mask].real
+    mask = (res.imag == 0) & (res.real > 0)
     if res.size == 0:
         return np.nan
+    res = res[mask].real
+    # NPV(rate) = 0 can have more than one solution so we return
+    # only the solution closest to zero.
     rate = 1.0/res - 1
-    if rate.size == 1:
-        rate = rate.item()
+    rate = rate.item(np.argmin(np.abs(rate)))
     return rate
 
 def npv(rate, values):
diff --git a/numpy/lib/tests/test_financial.py b/numpy/lib/tests/test_financial.py
index 6b7c6ef53..41a060a3f 100644
--- a/numpy/lib/tests/test_financial.py
+++ b/numpy/lib/tests/test_financial.py
@@ -13,6 +13,21 @@ class TestFinancial(TestCase):
         v = [-150000, 15000, 25000, 35000, 45000, 60000]
         assert_almost_equal(np.irr(v),
                             0.0524, 2)
+        v = [-100, 0, 0, 74]
+        assert_almost_equal(np.irr(v),
+                            -0.0955, 2)
+        v = [-100, 39, 59, 55, 20]
+        assert_almost_equal(np.irr(v),
+                            0.28095, 2)
+        v = [-100, 100, 0, -7]
+        assert_almost_equal(np.irr(v),
+                            -0.0833, 2)
+        v = [-100, 100, 0, 7]
+        assert_almost_equal(np.irr(v),
+                            0.06206, 2)
+        v = [-5, 10.5, 1, -8, 1]
+        assert_almost_equal(np.irr(v),
+                            0.0886, 2)
 
     def test_pv(self):
         assert_almost_equal(np.pv(0.07, 20, 12000, 0),