[Fix] Fix behaviour for rank deficient fits. Add test

pyerrors/fits.py

@@ -567,7 +567,7 @@ def total_least_squares(x, y, func, silent=False, **kwargs):
 
     Notes
     -----
-    Based on the orthogonal distance regression module of scipy.
+    Based on the odrpack orthogonal distance regression library.
 
     Returns
     -------
@@ -670,6 +670,16 @@ def total_least_squares(x, y, func, silent=False, **kwargs):
         print('Residual variance:', output.residual_variance)
 
     if not out.success:
+        # info % 5 gives the convergence status: 1=sum-of-sq, 2=param, 3=both
+        # If odrpack reports rank deficiency (e.g. vanishing chi-squared when
+        # n_obs == n_parms), convergence was still achieved – allow with a warning.
+        if out.info % 5 in [1, 2, 3]:
+            warnings.warn(
+                "ODR fit is rank deficient. This may indicate a vanishing "
+                "chi-squared (n_obs == n_parms). Results may be unreliable.",
+                RuntimeWarning
+            )
+        else:
             raise Exception('The minimization procedure did not converge.')
 
     m = x_f.size

tests/fits_test.py

@@ -468,6 +468,19 @@ def test_total_least_squares():
     assert((outc.fit_parameters[1] - betac[1]).is_zero())
 
 
+def test_total_least_squares_vanishing_chisquare():
+    """Test that a saturated fit (n_obs == n_parms) works without exception."""
+    def func(a, x):
+        return a[0] + a[1] * x
+
+    x = [pe.pseudo_Obs(1.0, 0.1, 'x0'), pe.pseudo_Obs(2.0, 0.1, 'x1')]
+    y = [pe.pseudo_Obs(1.0, 0.1, 'y0'), pe.pseudo_Obs(2.0, 0.1, 'y1')]
+
+    with pytest.warns(RuntimeWarning, match="rank deficient"):
+        out = pe.total_least_squares(x, y, func, silent=True)
+    assert len(out.fit_parameters) == 2
+
+
 def test_odr_derivatives():
     x = []
     y = []