add absolute error condition

1 files changed, 11 insertions, 6 deletions

diff --git a/vquad/core.py b/vquad/core.py
index 2f3cac0..4e08253 100644
--- a/vquad/core.py
+++ b/vquad/core.py
@@ -270,14 +270,19 @@ class Vquad:
             err += ival.err
         return igral, err
 
-    def improve_until(self, tol):
+    def improve_until(self, rtol=0, atol=0):
+        if rtol < 0 or atol < 0:
+            raise ValueError("Tolerances must be positive.")
+        if rtol == 0 and atol == 0:
+            raise ValueError("Either rtol or atol must be nonzero.")
+
         while True:
             self.improve()
             igral, err = self.totals()
 
-            if (err == 0
-                or err < abs(igral) * tol
-                or err - self.err_excess < abs(igral) * tol < self.err_excess
+            tol = max(atol, abs(igral) * rtol)
+            if (err == 0 or err < tol
+                or self.err_excess > tol > err - self.err_excess
                 or not self.ivals):
                 return igral, err
 
@@ -311,6 +316,6 @@ class Vquad:
         return np.concatenate(results)[inv_perm].reshape(shape)
 
 
-def vquad(f, a, b, tol):
+def vquad(f, a, b, rtol=0, atol=0):
     igrator = Vquad(f, a, b)
-    return igrator.improve_until(tol)
+    return igrator.improve_until(rtol, atol)