rearange arguments of _match_functions, update tests

kwant_spectrum.py

@@ -419,7 +419,7 @@ def _save_ordering(func):
 
 
 def _match_functions(func, xmin=-1, xmax=1, tol=1E-8, min_iter=10,
-                     interval_converged=None, evaluated=None, max_iter=100000):
+                     max_iter=100000, interval_converged=None, evaluated=None):
     """Match the elements of a vector valued function, such that
     each vector element describes a continous function.
 
@@ -434,13 +434,16 @@ def _match_functions(func, xmin=-1, xmax=1, tol=1E-8, min_iter=10,
         Upper interval boundary to order the function. Defaut = 1.
     tol : float, optional
         Numerical tolerance.
+    min_iter : int, optional
+        Minimal number of iterations of the matching alorithm.
+        Defaut = 10
+    max_iter : int, optional
+        Maximum number of iterations of the matching alorithm. Defaut = 100000
     interval_converged : callable, optional
         Error estimate for the interval.
         Defaut: 3-point estimate for local cubic interpolants
     evaluated : dict, optional
         Dict of precalculated function values
-    max_iter : int, optional
-        Maximum number of iterations of the matching alorithm. Defaut = 100000
 
     Returns
     -------
@@ -501,9 +504,9 @@ def _match_functions(func, xmin=-1, xmax=1, tol=1E-8, min_iter=10,
     assert _is_type(xmin, 'real_number')
     assert _is_type(xmax, 'real_number')
     assert _is_type(tol, 'real_number')
-    assert _is_type(max_iter, 'integer')
     assert _is_type(min_iter, 'integer')
-    assert min_iter > 0
+    assert _is_type(max_iter, 'integer')
+    assert 0 < min_iter < max_iter
     assert tol > 0
     assert callable(func)
 

test_kwant_spectrum.py

@@ -126,7 +126,7 @@ def test_gap_detection_tolerance():
 
     def gap_detected(x0, gap, tol):
         func = partial(gap_function, gap=gap, x0=x0)
-        x, y, dy, *_ = ks._match_functions(func, -1, 1, tol=tol)
+        x, y, dy, *_ = ks._match_functions(func, -1, 1, tol=tol, min_iter=1)
         yy = func(x)[0].T
         return np.allclose(y, yy)
 
@@ -292,6 +292,19 @@ def test_function_mapping():
     xr = 2
     assert not ks._leftmost_crossing(func(xl), func(xr), xl, xr)
 
+    # test from benoit rossignol where
+    # f(-pi) = f(0) = f(pi) = 1 and f'(-pi) = f'(0) = f'(pi) = 0
+    # such that the symmetric center point convergence estimate
+    # (on the points -pi, 0, pi) fails. if no minimal number of splits
+    # is required (which can be simulated by setting min_split = 1) the
+    # algorithm will erroneously assume to be converged with only three points.
+    def f(x):
+        return np.array([[np.cos(2*x)], [-2*np.sin(2*x)]])
+
+    x, y, dy, *_ = ks._match_functions(f, xmin=-np.pi, xmax=np.pi)
+
+    assert len(x) > 3
+
 
 def test_cost_matrix():
     # take linear functions since cost matrix is calculated in linear approx.