change numeric tol causing problems on 32 bit

kwantspectrum/kwant_spectrum.py

@@ -433,7 +433,7 @@ def _save_ordering(func):
     return wrapper
 
 
-def _match_functions(func, xmin=-1, xmax=1, tol=1E-8, min_iter=10,
+def _match_functions(func, xmin=-1, xmax=1, tol=1E-10, min_iter=10,
                      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.
@@ -555,7 +555,7 @@ def _match_functions(func, xmin=-1, xmax=1, tol=1E-8, min_iter=10,
 
 
 def spectrum(syst, args=(), *, params=None, kmin=-np.pi, kmax=np.pi,
-             orderpoint=0, tol=1E-8, match=_match_functions):
+             orderpoint=0, tol=1E-10, match=_match_functions):
     r"""Interpolate the dispersion function and provide methods to
     simplify curve sketching and analyzation the periodic spectrum.
 
@@ -689,7 +689,7 @@ class BandSketching:
     Finite accuracy of the data and possible unphysical results are taking into
     account by rounding value :math:`tol`.
     """
-    def __init__(self, x, y, dy, mode_function, tol=1E-8,
+    def __init__(self, x, y, dy, mode_function, tol=1E-10,
                  interpolation=_cubic_interpolation):
 
         # type and input checks
@@ -865,19 +865,19 @@ class BandSketching:
 
     def intersect(self, f, band, derivative_order=0,
                   kmin=None, kmax=None, tol=None, ytol=None):
-        r"""Returns all momentum (k) points, that solves the equation:
-        :math:`\partial_k^{n} E(k) = f(k),\, k_{min} \leq k \leq k_{max}`.
+        r"""Returns all momentum (:math:`k`) points which solve the equation:
+        :math:`\partial_k^{m} E_n(k) = f(k),\, k_{min} \leq k \leq k_{max}`.
 
         Parameters
         ----------
         f : scalar numerical value or callable
-            Equation to solve :math:`\partial_k^{n} E(k) = f`.
+            Equation to solve :math:`\partial_k^{m} E_n(k) = f`.
             If `f` is callable, solve equation:
-            :math:`\partial_k^{n} E(k) = f(k)`.
+            :math:`\partial_k^{m} E_n(k) = f(k)`.
         band : int
-            band index, requirement: `0 <= band < nbands`.
+            band index `n`, requirement: `0 <= band < nbands`.
         derivative_order : int, optional
-            Derivative order (n) of the band dispersion. Default is zero.
+            Derivative order `m` of the band dispersion. Default is zero.
         kmin : scalar numeric value, optional
             Lowest `k` point value. Default is `kmin` from initialization.
         kmax : scalar numeric value, optional
@@ -887,10 +887,10 @@ class BandSketching:
             point. Default is the `tol` from initialization.
         ytol : float, optional
             Numerical tolerance to remove noise if the
-            spectrum :math:`\partial_k^{n} E(k)` is almost flat.
-            Values for the spectrum are set to thier mean value
+            spectrum :math:`\partial_k^{m} E_n(k)` is almost flat.
+            Values for the spectrum are set to their mean value
             (averaged over all momentum points where the band is sampled), if
-            they flucutate more than `ytol`.
+            they flucutate less than `ytol`.
             Default is the `tol` from initialization.
 
         Returns
@@ -911,7 +911,7 @@ class BandSketching:
         if tol is None:
             tol = self.tol
         if ytol is None:
-            ytol = self.tol
+            ytol = self.tol * 100  # lower interpolant accuracy
 
         # type and input checks
         assert _is_type(band, 'integer')
@@ -946,8 +946,9 @@ class BandSketching:
         y_mean = np.mean(y)
         if _is_zero(y_mean, ytol):
             y_mean = 0
+
         y[np.abs(y - y_mean) < ytol] = y_mean
-        dy[np.abs(dy) < ytol] = 0
+        dy[np.abs(dy) < 100 * ytol] = 0  # derivative dy less acurate than y
 
         roots = self.interpolation(self.x, y - f, dy).roots()
         roots = remove_nan(roots)

kwantspectrum/tests/test_kwant_spectrum.py

@@ -286,7 +286,7 @@ def test_spectrum_with_flat_band():
     assert spectrum.intersect(f=0, band=1, derivative_order=1).size == 0
     assert_array_almost_equal([0], spectrum.intersect(f=0, band=2, derivative_order=1))
 
-    # the spectrum has also no wendepunkt
+    # the spectrum has also no inflection point
     assert spectrum.intersect(f=0, band=0, derivative_order=2).size == 0
     assert spectrum.intersect(f=0, band=1, derivative_order=2).size == 0
     assert spectrum.intersect(f=0, band=2, derivative_order=2).size == 0