fix problem when roots are exactly on knots

kwantspectrum/kwant_spectrum.py

@@ -938,6 +938,9 @@ class BandSketching:
         if derivative_order == 0:  # use tabulated values, faster
             y = self.y[:, band]
             dy = self.dy[:, band]
+        elif derivative_order == 1:
+            y = self.dy[:, band]
+            dy = self._func(self.x, derivative_order + 1)[:, band]
         else:
             y = self._func(self.x, derivative_order)[:, band]
             dy = self._func(self.x, derivative_order + 1)[:, band]
@@ -950,7 +953,22 @@ class BandSketching:
         y[np.abs(y - y_mean) < ytol] = y_mean
         dy[np.abs(dy) < 100 * ytol] = 0  # derivative dy less acurate than y
 
+        g = y - f  # roots of g give the intersection points we are seeking
         roots = self.interpolation(self.x, y - f, dy).roots()
+
+        # the interpolation/rootfinding can fail if roots are exactly on the
+        # knots (the gridpoints self.x). In that case we check if g(i) == 0
+        # and also if the sign on g(i - 1) and g(i + 1) is different
+        # (necessary condition for g(i) == 0). This condition is important
+        # to not find spurious zeros of g when it is actually flat.
+        g_signchange = [np.sign(g[i - 1] * g[i + 1]) == -1
+                        for i in range(1, len(g) - 1)]
+        # at the endpoints, check only that g is not flat
+        g_signchange.append(np.sign(g[-2]) != 0)
+        g_signchange.insert(0, np.sign(g[1]) != 0)
+        roots_on_knots = self.x[np.logical_and(np.abs(g) < ytol, g_signchange)]
+
+        roots = np.append(roots, roots_on_knots)
         roots = remove_nan(roots)
 
         if self.period: