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MueLu_SchurComplementFactory_def.hpp
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46 #ifndef MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_
47 #define MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_
48 
49 #ifdef HAVE_MUELU_EXPERIMENTAL
50 
51 #include <Xpetra_BlockedCrsMatrix.hpp>
52 #include <Xpetra_MultiVectorFactory.hpp>
53 #include <Xpetra_VectorFactory.hpp>
54 #include <Xpetra_MatrixFactory.hpp>
55 #include <Xpetra_Matrix.hpp>
56 #include <Xpetra_MatrixMatrix.hpp>
57 #include <Xpetra_CrsMatrixWrap.hpp>
58 #include <Xpetra_BlockedCrsMatrix.hpp>
59 #include <Xpetra_CrsMatrix.hpp>
60 #include "MueLu_Level.hpp"
61 #include "MueLu_Monitor.hpp"
62 #include "MueLu_Utilities.hpp"
63 //#include "MueLu_HierarchyHelpers.hpp"
64 
65 #include "MueLu_SchurComplementFactory.hpp"
66 
67 namespace MueLu {
68 
69  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
71  RCP<ParameterList> validParamList = rcp(new ParameterList());
72 
73  SC one = Teuchos::ScalarTraits<SC>::one();
74 
75  validParamList->set<RCP<const FactoryBase> >("A", NoFactory::getRCP()/*null*/, "Generating factory of the matrix A used for building Schur complement\n"
76  "(must be a 2x2 blocked operator)");
77  validParamList->set<SC> ("omega", one, "Scaling parameter in S = A(1,1) - 1/omega A(1,0) diag{A(0,0)}^{-1} A(0,1)");
78  validParamList->set<bool> ("lumping", false, "Use lumping to construct diag(A(0,0)), i.e. use row sum of the abs values on the diagonal "
79  "as approximation of A00 (and A00^{-1})");
80  validParamList->set<bool> ("fixing", false, "Fix diagonal by replacing small entries with 1.0");
81 
82  return validParamList;
83  }
84 
85  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
87  Input(currentLevel, "A");
88  }
89 
90  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
92  FactoryMonitor m(*this, "Build", currentLevel);
93 
94  typedef Teuchos::ScalarTraits<SC> STS;
95  SC zero = STS::zero(), one = STS::one();
96 
97  RCP<Matrix> A = Get<RCP<Matrix> >(currentLevel, "A");
98  RCP<BlockedCrsMatrix> bA = rcp_dynamic_cast<BlockedCrsMatrix>(A);
99  TEUCHOS_TEST_FOR_EXCEPTION(bA.is_null(), Exceptions::BadCast,
100  "MueLu::SchurComplementFactory::Build: input matrix A is not of type BlockedCrsMatrix!");
101 
102  TEUCHOS_TEST_FOR_EXCEPTION(bA->Rows() != 2 || bA->Cols() != 2, Exceptions::RuntimeError,
103  "MueLu::SchurComplementFactory::Build: input matrix A is a " << bA->Rows() << "x" << bA->Cols() << " block matrix. We expect a 2x2 blocked operator.");
104 
105  RCP<Matrix> A00 = bA->getMatrix(0,0);
106  RCP<Matrix> A01 = bA->getMatrix(0,1);
107  RCP<Matrix> A10 = bA->getMatrix(1,0);
108  RCP<Matrix> A11 = bA->getMatrix(1,1);
109 
110  RCP<BlockedCrsMatrix> bA01 = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(A01);
111  bool bIsBlocked = (bA01 == Teuchos::null ? false : true);
112 
113  const ParameterList& pL = GetParameterList();
114  SC omega = pL.get<Scalar>("omega");
115 
116  TEUCHOS_TEST_FOR_EXCEPTION(omega == Teuchos::ScalarTraits<Scalar>::zero(), Exceptions::RuntimeError,
117  "MueLu::SchurComplementFactory::Build: Scaling parameter omega must not be zero to avoid division by zero.");
118 
119  RCP<Matrix> S = Teuchos::null;
120  // only if the off-diagonal blocks A10 and A01 are non-zero we have to do the MM multiplication
121  if(A01.is_null() == false && A10.is_null() == false) {
122  bool lumping = pL.get<bool>("lumping");
123  bool fixing = pL.get<bool>("fixing");
124 
125  RCP<Vector> diag = Teuchos::null;
126  if (!lumping) {
127  diag = VectorFactory::Build(A00->getRangeMap(), true);
128  A00->getLocalDiagCopy(*diag);
129 
130  } else {
132  }
133 
134  // invert diagonal vector. Replace all entries smaller than 1e-4 by one!
135  RCP<Vector> D = (!fixing ? Utilities::GetInverse(diag) : Utilities::GetInverse(diag, 1e-4, STS::one()));
136 
137  // scale with -1/omega
138  D->scale(Teuchos::as<Scalar>(-STS::one()/omega));
139 
140  // left scale matrix T with (scaled) diagonal D
141  // Copy the value of A01 so we can do the left scale.
142  RCP<Matrix> T = MatrixFactory::BuildCopy(A01);
143  T->leftScale(*D);
144 
145  // build Schur complement operator
146  if (!bIsBlocked) {
147  TEUCHOS_TEST_FOR_EXCEPTION(T->getRangeMap()->isSameAs(*(A10->getDomainMap())) == false, Exceptions::RuntimeError,
148  "MueLu::SchurComplementFactory::Build: RangeMap of A01 and domain map of A10 are not the same.");
149 
150  S = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Multiply(*A10, false, *T, false, GetOStream(Statistics2));
151  } else {
152  // nested blocking
153  RCP<BlockedCrsMatrix> bA10 = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(A10);
154  RCP<BlockedCrsMatrix> bT = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(T);
155 
156  TEUCHOS_TEST_FOR_EXCEPTION(bA01->Rows() != bA10->Cols(), Exceptions::RuntimeError,
157  "MueLu::SchurComplementFactory::Build: Block rows and cols of A01 and A10 are not compatible.");
158  TEUCHOS_TEST_FOR_EXCEPTION(bA01->Rows() != bT->Rows() || bA01->Cols() != bT->Cols(), Exceptions::RuntimeError,
159  "MueLu::SchurComplementFactory::Build: The scaled A01 operator has " << bT->Rows() << "x" << bT->Cols() << " blocks, "
160  "but should have " << bA01->Rows() << "x" << bA01->Cols() << " blocks.");
161  TEUCHOS_TEST_FOR_EXCEPTION(bA01->Cols() != bA10->Rows(), Exceptions::RuntimeError,
162  "MueLu::SchurComplementFactory::Build: Block rows and cols of A01 and A10 are not compatible.");
163 
164  S = Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::TwoMatrixMultiplyBlock(*bA10, false, *bT, false, GetOStream(Statistics2));
165  }
166 
167  if (!A11.is_null()) {
168  T = Teuchos::null;
169  Xpetra::MatrixMatrix<Scalar, LocalOrdinal, GlobalOrdinal, Node>::TwoMatrixAdd(*A11, false, one, *S, false, one, T, GetOStream(Statistics2));
170  T->fillComplete();
171  S.swap(T);
172 
173  TEUCHOS_TEST_FOR_EXCEPTION(A11->getRangeMap()->isSameAs(*(S->getRangeMap())) == false, Exceptions::RuntimeError,
174  "MueLu::SchurComplementFactory::Build: RangeMap of A11 and S are not the same.");
175  TEUCHOS_TEST_FOR_EXCEPTION(A11->getDomainMap()->isSameAs(*(S->getDomainMap())) == false, Exceptions::RuntimeError,
176  "MueLu::SchurComplementFactory::Build: DomainMap of A11 and S are not the same.");
177  }
178 
179  }
180  else {
181  if (!A11.is_null()) {
182  S = MatrixFactory::BuildCopy(A11);
183  } else {
184  S = MatrixFactory::Build(A11->getRowMap(), 10 /*A11->getNodeMaxNumRowEntries()*/);
185  S->fillComplete(A11->getDomainMap(),A11->getRangeMap());
186  }
187  }
188 
189  // Check whether Schur complement operator is a 1x1 block matrix.
190  // If so, unwrap it and return the CrsMatrix based Matrix object
191  // We need this, as single-block smoothers expect it this way.
192  // In case of Thyra GIDs we obtain a Schur complement operator in Thyra GIDs
193  // This may make some special handling in feeding the SchurComplement solver Apply routine
194  // necessary!
195  if (bIsBlocked) {
196  RCP<BlockedCrsMatrix> bS = Teuchos::rcp_dynamic_cast<BlockedCrsMatrix>(S);
197 
198  if (bS != Teuchos::null && bS->Rows() == 1 && bS->Cols() == 1) {
199  RCP<Matrix> temp = bS->getCrsMatrix();
200  S.swap(temp);
201  }
202  }
203  // NOTE: "A" generated by this factory is actually the Schur complement
204  // matrix, but it is required as all smoothers expect "A"
205  Set(currentLevel, "A", S);
206  }
207 
208 } // namespace MueLu
209 
210 #endif /* HAVE_MUELU_EXPERIMENTAL */
211 #endif /* MUELU_SCHURCOMPLEMENTFACTORY_DEF_HPP_ */
Exception indicating invalid cast attempted.
Timer to be used in factories. Similar to Monitor but with additional timers.
static Teuchos::ArrayRCP< Scalar > GetLumpedMatrixDiagonal(const Xpetra::Matrix< Scalar, LocalOrdinal, GlobalOrdinal, Node > &A)
void DeclareInput(Level &currentLevel) const
Input.
Namespace for MueLu classes and methods.
Print even more statistics.
Class that holds all level-specific information.
Definition: MueLu_Level.hpp:99
RCP< const ParameterList > GetValidParameterList() const
Return a const parameter list of valid parameters that setParameterList() will accept.
static Teuchos::RCP< Xpetra::Vector< Scalar, LocalOrdinal, GlobalOrdinal, Node > > GetInverse(Teuchos::RCP< const Xpetra::Vector< Scalar, LocalOrdinal, GlobalOrdinal, Node > > v, Magnitude tol=Teuchos::ScalarTraits< Scalar >::eps() *100, Scalar tolReplacement=Teuchos::ScalarTraits< Scalar >::zero())
void Build(Level &currentLevel) const
Build an object with this factory.
Exception throws to report errors in the internal logical of the program.
static const RCP< const NoFactory > getRCP()
Static Get() functions.