Add examples and update docs

Author: mjhough

dfols/params.py

@@ -113,7 +113,7 @@ def __init__(self, n, npt, maxfun, objfun_has_noise=False):
         self.params["dykstra.d_tol"] = 1e-10
         self.params["dykstra.max_iters"] = 100
         # Matrix rank algorithm
-        self.params["matrix_rank.r_tol"] = 1e-15
+        self.params["matrix_rank.r_tol"] = 1e-18
 
         self.params_changed = {}
         for p in self.params:

dfols/tests/test_util.py

@@ -170,7 +170,7 @@ def runTest(self):
 # Trivial case of full rank
 class TestMatrixRankQR1(unittest.TestCase):
     def runTest(self):
-        mr_tol = 1e-15
+        mr_tol = 1e-18
         A = np.array([
             [1,0,0,0],
             [0,1,0,0],
@@ -183,7 +183,7 @@ def runTest(self):
 # Full rank but QR has negative entries for diag(R)
 class TestMatrixRankQR2(unittest.TestCase):
     def runTest(self):
-        mr_tol = 1e-15
+        mr_tol = 1e-18
         A = np.array([
             [1,2,3,4],
             [0,6,7,8],
@@ -194,15 +194,15 @@ def runTest(self):
         self.assertTrue(rank == 4, "Incorrect rank output")
 
 
-# Full rank but QR has negative entries for diag(R)
+# Not full rank
 class TestMatrixRankQR3(unittest.TestCase):
     def runTest(self):
-        mr_tol = 1e-15
+        mr_tol = 1e-18
         A = np.array([
             [1,2,3,4],
             [2,6,4,8],
-            [-1,-2,-3,-4],
-            [1,3,2,4]])
+            [0,0,0,0],
+            [0,0,0,0]])
         rank, D = qr_rank(A,mr_tol)
         self.assertTrue(np.all(D[0:2] > mr_tol), "Incorrect diagonal matrix output (rows 1,2)")
         self.assertTrue(np.all(D[2:4] <= mr_tol), "Incorrect diagonal matrix output (rows 3,4)")

docs/advanced.rst

@@ -103,6 +103,15 @@ Dynamically Growing Initial Set
 * :code:`growing.gamma_dec` - Trust region decrease parameter during the growing phase. Default is :code:`tr_radius.gamma_dec`.
 * :code:`growing.num_new_dirns_each_iter` - Number of new search directions to add with each iteration where we do not have a full set of search directions. Default is 0, as this approach is not recommended. 
 
+Dykstra's Algorithm
+-------------------------------
+* :code:`dykstra.d_tol` - Tolerance on the stopping conditions of Dykstra's algorithm. Default is :math:`10^{-10}`. 
+* :code:`dykstra.max_iters` - The maximum number of iterations Dykstra's algorithm is allowed to take before stopping. Default is :math:`100`. 
+
+Checking Matrix Rank
+-------------------------------
+* :code:`matrix_rank.r_tol` - Tolerance on what is the smallest posisble diagonal entry value in the QR factorization before being considered zero. Default is :math:`10^{-18}`. 
+
 
 References
 ----------