BUG: optimize: return a matrix if indeterminate variance

The documentation says pcov is a matrix, so it may be confusing to have
it be a scalar in some pathological cases.

scipy/optimize/minpack.py

@@ -551,12 +551,16 @@ def curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, **kw):
         msg = "Optimal parameters not found: " + errmsg
         raise RuntimeError(msg)
 
-    if not absolute_sigma:
-        if len(ydata) > len(p0) and pcov is not None:
+    if pcov is None:
+        # indeterminate covariance
+        pcov = zeros((len(popt), len(popt)), dtype=float)
+        pcov.fill(inf)
+    elif not absolute_sigma:
+        if len(ydata) > len(p0):
             s_sq = (asarray(func(popt, *args))**2).sum() / (len(ydata) - len(p0))
             pcov = pcov * s_sq
         else:
-            pcov = inf
+            pcov.fill(inf)
 
     if return_full:
         return popt, pcov, infodict, errmsg, ier

scipy/optimize/tests/test_minpack.py

@@ -362,6 +362,19 @@ def f(x, a, b):
         perr = np.sqrt(np.diag(pcov))
         assert_allclose(perr, [3*0.30714756, 3*0.85045308], rtol=1e-3)
 
+        # infinite variances
+
+        def f_flat(x, a, b):
+            return a*x
+
+        popt, pcov = curve_fit(f_flat, xdata, ydata, p0=[2, 0], sigma=sigma)
+        assert_(pcov.shape == (2, 2))
+        assert_array_equal(pcov, np.inf)
+
+        popt, pcov = curve_fit(f, xdata[:2], ydata[:2], p0=[2, 0])
+        assert_(pcov.shape == (2, 2))
+        assert_array_equal(pcov, np.inf)
+
 
 class TestFixedPoint(TestCase):