added test to make sure that node-to-node integration using Smat entries integrates polynomials of degree M-1 exactly

Author: Daniel Ruprecht

.travis.yml

@@ -1,7 +1,13 @@
 language: python
+sudo: false
+
 python:
-  - "2.7"
+  - "2.7.10"
 # command to install dependencies
-install: "pip install -r requirements.txt"
-#
-script: py.test -v tests/
+
+install: 
+ - conda update -yes conda
+ - conda install -r requirements.txt
+
+# command to run tests
+script: py.test tests/

requirements.txt

@@ -1,3 +1,2 @@
-py.test
-numpy
+pytest
 scipy

tests/test_collocation.py

@@ -69,8 +69,18 @@ def test_3(self):
         for i in range(0,M):
             int_ex = np.polyval(poly_int_coeff, coll.nodes[i]) - np.polyval(poly_int_coeff, t_start)
             int_coll = np.dot(poly_vals, Q[i,:])
-            assert abs(int_ex - int_coll)<1e-10, "For node type " + type[0] + ", partial quadrature rule failed to integrate polynomial of degree M-1 exactly for M = " + str(M)
+            assert abs(int_ex - int_coll)<1e-12, "For node type " + type[0] + ", partial quadrature from Qmat rule failed to integrate polynomial of degree M-1 exactly for M = " + str(M)
 
-    # TEST 4:
-    # Check that the quadrature rules for [tau_m, tau_m+1] defined by Smat have order equal to number of nodes M
-    # ----------------------------------------------------------------------------------------------------------
+  def test_4(self):
+    for type in classes:
+      for M in range(type[1],type[2]+1):
+        coll = getattr(pySDC.CollocationClasses, type[0])(M, t_start, t_end)
+        S = coll.Smat[1:,1:]
+        # as in TEST 1, create and integrate a polynomial with random coefficients, but now of degree M-1
+        poly_coeff = np.random.rand(M-1)
+        poly_vals  = np.polyval(poly_coeff, coll.nodes)
+        poly_int_coeff = np.polyint(poly_coeff)
+        for i in range(1,M):
+            int_ex = np.polyval(poly_int_coeff, coll.nodes[i]) - np.polyval(poly_int_coeff, coll.nodes[i-1])
+            int_coll = np.dot(poly_vals, S[i,:])
+            assert abs(int_ex - int_coll)<1e-12, "For node type " + type[0] + ", partial quadrature rule from Smat failed to integrate polynomial of degree M-1 exactly for M = " + str(M)