BUG: Campanion Matrix was scalar, not matrix for degree 1.

The companion matrices returned by the various polynomial types was
a scalar in the degree one case instead of a 2-D array. Fix that and
add a test to check for that result.

Closes #3459.

12 files changed, 102 insertions, 6 deletions

diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index dc1b27d76..db1b637fd 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -1795,7 +1795,7 @@ def chebcompanion(c):
     if len(c) < 2:
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(-c[0]/c[1])
+        return np.array([[-c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py
index 9051bf533..13b9e6845 100644
--- a/numpy/polynomial/hermite.py
+++ b/numpy/polynomial/hermite.py
@@ -1573,7 +1573,7 @@ def hermcompanion(c):
     if len(c) < 2:
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(-.5*c[0]/c[1])
+        return np.array([[-.5*c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py
index 13810c97f..9f10403dd 100644
--- a/numpy/polynomial/hermite_e.py
+++ b/numpy/polynomial/hermite_e.py
@@ -1570,7 +1570,7 @@ def hermecompanion(c):
     if len(c) < 2:
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(-c[0]/c[1])
+        return np.array([[-c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py
index 1cc316bca..ea805e146 100644
--- a/numpy/polynomial/laguerre.py
+++ b/numpy/polynomial/laguerre.py
@@ -1571,7 +1571,7 @@ def lagcompanion(c):
     if len(c) < 2:
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(1 + c[0]/c[1])
+        return np.array([[1 + c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py
index 1440cdf87..c7a1f2dd2 100644
--- a/numpy/polynomial/legendre.py
+++ b/numpy/polynomial/legendre.py
@@ -1596,7 +1596,7 @@ def legcompanion(c):
     if len(c) < 2:
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(-c[0]/c[1])
+        return np.array([[-c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index 7a0b36cde..0b044e8e8 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -39,6 +39,7 @@ Misc Functions
 - `polyvander` -- Vandermonde-like matrix for powers.
 - `polyvander2d` -- Vandermonde-like matrix for 2D power series.
 - `polyvander3d` -- Vandermonde-like matrix for 3D power series.
+- `polycompanion` -- companion matrix in power series form.
 - `polyfit` -- least-squares fit returning a polynomial.
 - `polytrim` -- trim leading coefficients from a polynomial.
 - `polyline` -- polynomial representing given straight line.
@@ -1417,7 +1418,7 @@ def polycompanion(c):
     if len(c) < 2 :
         raise ValueError('Series must have maximum degree of at least 1.')
     if len(c) == 2:
-        return np.array(-c[0]/c[1])
+        return np.array([[-c[0]/c[1]]])
 
     n = len(c) - 1
     mat = np.zeros((n, n), dtype=c.dtype)
diff --git a/numpy/polynomial/tests/test_chebyshev.py b/numpy/polynomial/tests/test_chebyshev.py
index 23a17b464..367d81f58 100644
--- a/numpy/polynomial/tests/test_chebyshev.py
+++ b/numpy/polynomial/tests/test_chebyshev.py
@@ -440,6 +440,22 @@ class TestFitting(TestCase):
         x = [1, 1j, -1, -1j]
         assert_almost_equal(cheb.chebfit(x, x, 1), [0, 1])
 
+
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, cheb.chebcompanion, [])
+        assert_raises(ValueError, cheb.chebcompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(cheb.chebcompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(cheb.chebcompanion([1, 2])[0, 0] == -.5)
+
+
 class TestGauss(TestCase):
 
     def test_100(self):
diff --git a/numpy/polynomial/tests/test_hermite.py b/numpy/polynomial/tests/test_hermite.py
index 785f9b255..327283d0e 100644
--- a/numpy/polynomial/tests/test_hermite.py
+++ b/numpy/polynomial/tests/test_hermite.py
@@ -430,6 +430,22 @@ class TestFitting(TestCase):
         x = [1, 1j, -1, -1j]
         assert_almost_equal(herm.hermfit(x, x, 1), [0, .5])
 
+
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, herm.hermcompanion, [])
+        assert_raises(ValueError, herm.hermcompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(herm.hermcompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(herm.hermcompanion([1, 2])[0, 0] == -.25)
+
+
 class TestGauss(TestCase):
 
     def test_100(self):
diff --git a/numpy/polynomial/tests/test_hermite_e.py b/numpy/polynomial/tests/test_hermite_e.py
index 84c952578..404a46fc7 100644
--- a/numpy/polynomial/tests/test_hermite_e.py
+++ b/numpy/polynomial/tests/test_hermite_e.py
@@ -427,6 +427,22 @@ class TestFitting(TestCase):
         x = [1, 1j, -1, -1j]
         assert_almost_equal(herme.hermefit(x, x, 1), [0, 1])
 
+
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, herme.hermecompanion, [])
+        assert_raises(ValueError, herme.hermecompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(herme.hermecompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(herme.hermecompanion([1, 2])[0, 0] == -.5)
+
+
 class TestGauss(TestCase):
 
     def test_100(self):
diff --git a/numpy/polynomial/tests/test_laguerre.py b/numpy/polynomial/tests/test_laguerre.py
index b7268fe59..38fcce299 100644
--- a/numpy/polynomial/tests/test_laguerre.py
+++ b/numpy/polynomial/tests/test_laguerre.py
@@ -425,6 +425,22 @@ class TestFitting(TestCase):
         x = [1, 1j, -1, -1j]
         assert_almost_equal(lag.lagfit(x, x, 1), [1, -1])
 
+
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, lag.lagcompanion, [])
+        assert_raises(ValueError, lag.lagcompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(lag.lagcompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(lag.lagcompanion([1, 2])[0, 0] == 1.5)
+
+
 class TestGauss(TestCase):
 
     def test_100(self):
diff --git a/numpy/polynomial/tests/test_legendre.py b/numpy/polynomial/tests/test_legendre.py
index ae86f65b6..379bdee31 100644
--- a/numpy/polynomial/tests/test_legendre.py
+++ b/numpy/polynomial/tests/test_legendre.py
@@ -428,6 +428,22 @@ class TestFitting(TestCase):
         x = [1, 1j, -1, -1j]
         assert_almost_equal(leg.legfit(x, x, 1), [0, 1])
 
+
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, leg.legcompanion, [])
+        assert_raises(ValueError, leg.legcompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(leg.legcompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(leg.legcompanion([1, 2])[0, 0] == -.5)
+
+
 class TestGauss(TestCase):
 
     def test_100(self):
diff --git a/numpy/polynomial/tests/test_polynomial.py b/numpy/polynomial/tests/test_polynomial.py
index 3d9519679..583872978 100644
--- a/numpy/polynomial/tests/test_polynomial.py
+++ b/numpy/polynomial/tests/test_polynomial.py
@@ -383,6 +383,21 @@ class TestVander(TestCase):
         assert_(van.shape == (1, 5, 24))
 
 
+class TestCompanion(TestCase):
+
+    def test_raises(self):
+        assert_raises(ValueError, poly.polycompanion, [])
+        assert_raises(ValueError, poly.polycompanion, [1])
+
+    def test_dimensions(self):
+        for i in range(1, 5):
+            coef = [0]*i + [1]
+            assert_(poly.polycompanion(coef).shape == (i, i))
+
+    def test_linear_root(self):
+        assert_(poly.polycompanion([1, 2])[0, 0] == -.5)
+
+
 class TestMisc(TestCase) :
 
     def test_polyfromroots(self) :