Merge pull request #537 from tminka/quad

QuadratureRule.summation adds the error across intervals

.gitignore

@@ -55,3 +55,6 @@ mpmath.egg-info/
 # Coverage-related files
 .coverage
 htmlcov/
+
+# Visual Studio files
+.vs/

README.rst

@@ -138,7 +138,7 @@ See the main documentation for more detailed instructions.
 
 The unit tests in mpmath/tests/ can be run via the script
 runtests.py, but it is recommended to run them with py.test
-(http://codespeak.net/py/dist/index.html), especially
+(https://pytest.org/), especially
 to generate more useful reports in case there are failures.
 
 You may also want to check out the demo scripts in the demo

doc/source/setup.txt

@@ -36,6 +36,7 @@ or
 
 If you have an old version of mpmath installed already, you may have to pass ``easy_install`` the ``-U`` flag to force an upgrade.
 
+If installation fails, try deleting the following folders: .eggs, mpmath.egg-info, dist, build
 
 Debian/Ubuntu
 .............

mpmath/calculus/quadrature.py

@@ -211,7 +211,7 @@ class QuadratureRule(object):
         the standard interval and then calls :func:`~mpmath.sum_next`.
         """
         ctx = self.ctx
-        I = err = ctx.zero
+        I = total_err = ctx.zero
         for i in xrange(len(points)-1):
             a, b = points[i], points[i+1]
             if a == b:
@@ -224,23 +224,26 @@ class QuadratureRule(object):
                 f = lambda x: _f(-x) + _f(x)
                 a, b = (ctx.zero, ctx.inf)
             results = []
+            err = ctx.zero
             for degree in xrange(1, max_degree+1):
                 nodes = self.get_nodes(a, b, degree, prec, verbose)
                 if verbose:
                     print("Integrating from %s to %s (degree %s of %s)" % \
                         (ctx.nstr(a), ctx.nstr(b), degree, max_degree))
-                results.append(self.sum_next(f, nodes, degree, prec, results, verbose))
+                result = self.sum_next(f, nodes, degree, prec, results, verbose)
+                results.append(result)
                 if degree > 1:
                     err = self.estimate_error(results, prec, epsilon)
+                    if verbose:
+                        print("Estimated error:", ctx.nstr(err), " epsilon:", ctx.nstr(epsilon), " result: ", ctx.nstr(result))
                     if err <= epsilon:
                         break
-                    if verbose:
-                        print("Estimated error:", ctx.nstr(err))
             I += results[-1]
-        if err > epsilon:
+            total_err += err
+        if total_err > epsilon:
             if verbose:
-                print("Failed to reach full accuracy. Estimated error:", ctx.nstr(err))
-        return I, err
+                print("Failed to reach full accuracy. Estimated error:", ctx.nstr(total_err))
+        return I, total_err
 
     def sum_next(self, f, nodes, degree, prec, previous, verbose=False):
         r"""

mpmath/tests/test_quad.py

@@ -19,6 +19,10 @@ def test_basic_integrals():
         assert ae(quadts(lambda x: 2*sqrt(1-x*x), [-1, 1]), pi)
     mp.dps = 15
 
+def test_multiple_intervals():
+    y,err = quad(lambda x: sign(x), [-0.5, 0.9, 1], maxdegree=2, error=True)
+    assert abs(y-0.5) < 2*err
+
 def test_quad_symmetry():
     assert quadts(sin, [-1, 1]) == 0
     assert quadgl(sin, [-1, 1]) == 0

pytest.ini

@@ -0,0 +1,3 @@
+[pytest]
+markers =
+    slow: marks tests as slow (deselect with '-m "not slow"')