LinearOperator<double> epetraRightScale(
const LinearOperator<double>& A,
const Vector<double>& d)
{
/* Extract the underlying Epetra matrix. Type checking is done
* ny rcp_dynamic_cast, so we need no error check here. */
RCP<const Epetra_CrsMatrix> A_crs = EpetraMatrix::getConcretePtr(A);
/* Make a deep copy of A */
RCP<Epetra_CrsMatrix> mtxCopy = rcp(new Epetra_CrsMatrix(*A_crs));
/* Extract the underlying Epetra vector. Type checking is done
* internally, so we need no error check here. */
const Epetra_Vector& epv = EpetraVector::getConcrete(d);
/* Scale the copy */
mtxCopy->RightScale(epv);
/* Prepare an operator object for the scaled matrix */
RCP<LinearOperatorBase<double> > rtn
= rcp(new EpetraMatrix(mtxCopy, A.domain(), A.range()));
return rtn;
}
template <class Scalar> inline
SolverState<Scalar> BlockTriangularSolver<Scalar>
::solve(const LinearOperator<Scalar>& op,
const Vector<Scalar>& rhs,
Vector<Scalar>& soln) const
{
int nRows = op.numBlockRows();
int nCols = op.numBlockCols();
soln = op.domain().createMember();
// bool converged = false;
TEST_FOR_EXCEPTION(nRows != rhs.space().numBlocks(), std::runtime_error,
"number of rows in operator " << op
<< " not equal to number of blocks on RHS "
<< rhs);
TEST_FOR_EXCEPTION(nRows != nCols, std::runtime_error,
"nonsquare block structure in block triangular "
"solver: nRows=" << nRows << " nCols=" << nCols);
bool isUpper = false;
bool isLower = false;
for (int r=0; r<nRows; r++)
{
for (int c=0; c<nCols; c++)
{
if (op.getBlock(r,c).ptr().get() == 0 ||
dynamic_cast<const SimpleZeroOp<Scalar>* >(op.getBlock(r,c).ptr().get()))
{
TEST_FOR_EXCEPTION(r==c, std::runtime_error,
"zero diagonal block (" << r << ", " << c
<< " detected in block "
"triangular solver. Operator is " << op);
continue;
}
else
{
if (r < c) isUpper = true;
if (c < r) isLower = true;
}
}
}
TEST_FOR_EXCEPTION(isUpper && isLower, std::runtime_error,
"block triangular solver detected non-triangular operator "
<< op);
bool oneSolverFitsAll = false;
if ((int) solvers_.size() == 1 && nRows != 1)
{
oneSolverFitsAll = true;
}
for (int i=0; i<nRows; i++)
{
int r = i;
if (isUpper) r = nRows - 1 - i;
Vector<Scalar> rhs_r = rhs.getBlock(r);
for (int j=0; j<i; j++)
{
int c = j;
if (isUpper) c = nCols - 1 - j;
if (op.getBlock(r,c).ptr().get() != 0)
{
rhs_r = rhs_r - op.getBlock(r,c) * soln.getBlock(c);
}
}
SolverState<Scalar> state;
Vector<Scalar> soln_r;
if (oneSolverFitsAll)
{
state = solvers_[0].solve(op.getBlock(r,r), rhs_r, soln_r);
}
else
{
state = solvers_[r].solve(op.getBlock(r,r), rhs_r, soln_r);
}
if (nRows > 1) soln.setBlock(r, soln_r);
else soln = soln_r;
if (state.finalState() != SolveConverged)
{
return state;
}
}
return SolverState<Scalar>(SolveConverged, "block solves converged",
0, ScalarTraits<Scalar>::zero());
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
#ifdef HAVE_CONFIG_H
ParameterXMLFileReader reader(Sundance::searchForFile("SolverParameters/userPrecParams.xml"));
#else
ParameterXMLFileReader reader("userPrecParams.xml");
#endif
ParameterList solverParams = reader.getParameters();
ParameterList innerSolverParams = solverParams.sublist("Inner Solve");
ParameterList outerSolverParams = solverParams.sublist("Outer Solve");
/* create the range space */
int nLocalRows = solverParams.get<int>("nLocal");
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> A = builder.getOp();
Vector<double> x = A.domain().createMember();
int myRank = MPIComm::world().getRank();
int nProcs = MPIComm::world().getNProc();
Thyra::randomize(-ST::one(),+ST::one(),x.ptr().ptr());
#ifdef TRILINOS_6
if (myRank==0) x[0] = 0.0;
if (myRank==nProcs-1) x[nProcs * nLocalRows - 1] = 0.0;
// need to fix operator[] routine
#else
if (myRank==0) x.setElement(0, 0);
if (myRank==nProcs-1) x.setElement(nProcs * nLocalRows - 1, 0.0);
#endif
cout << "x=" << std::endl;
x.print(cout);
Vector<double> y = A*x;
cout << "y=" << std::endl;
y.print(cout);
Vector<double> ans = A.range().createMember();
LinearSolver<double> innerSolver
= LinearSolverBuilder::createSolver(innerSolverParams);
LinearSolver<double> outerSolver
= LinearSolverBuilder::createSolver(outerSolverParams);
/* call the setUserPrec() function to set the operator and solver
* to be used for preconditioning */
outerSolver.setUserPrec(A, innerSolver);
LinearOperator<double> AInv = inverse(A, outerSolver);
ans = AInv * y;
// SolverState<double> state = solver.solve(A, y, ans);
// cout << state << std::endl;
cout << "answer is " << std::endl;
ans.print(cout);
double err = (x-ans).norm2();
cout << "error norm = " << err << std::endl;
double tol = 1.0e-8;
if (err > tol)
{
cout << "User-defined preconditioner test FAILED" << std::endl;
return 1;
}
else
{
cout << "User-defined preconditioner test PASSED" << std::endl;
return 0;
}
}
catch(std::exception& e)
{
cout << "Caught exception: " << e.what() << std::endl;
return -1;
}
}
bool DuffingFloquet()
{
int np = MPIComm::world().getNProc();
TEUCHOS_TEST_FOR_EXCEPT(np != 1);
const double pi = 4.0*atan(1.0);
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Create a periodic mesh */
int nx = 128;
MeshType meshType = new PeriodicMeshType1D();
MeshSource mesher = new PeriodicLineMesher(0.0, 2.0*pi, nx, meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter pts = new DimensionalCellFilter(0);
CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,2.0*pi));
/* Create unknown and test functions, discretized using first-order
* Lagrange interpolants */
Expr u1 = new UnknownFunction(new Lagrange(1), "u1");
Expr u2 = new UnknownFunction(new Lagrange(1), "u2");
Expr v1 = new TestFunction(new Lagrange(1), "v1");
Expr v2 = new TestFunction(new Lagrange(1), "v2");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr x = new CoordExpr(0);
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(4);
double F0 = 0.5;
double gamma = 2.0/3.0;
double a0 = 1.0;
double w0 = 1.0;
double eps = 0.5;
Expr u1Guess = -0.75*cos(x) + 0.237*sin(x);
Expr u2Guess = 0.237*cos(x) + 0.75*sin(x);
DiscreteSpace discSpace(mesh,
List(new Lagrange(1), new Lagrange(1)),
vecType);
L2Projector proj(discSpace, List(u1Guess, u2Guess));
Expr u0 = proj.project();
Expr rhs1 = u2;
Expr rhs2 = -w0*w0*u1 - gamma*u2 - eps*w0*w0*pow(u1,3.0)/a0/a0
+ F0*w0*w0*sin(x);
/* Define the weak form */
Expr eqn = Integral(interior,
v1*(dx*u1 - rhs1) + v2*(dx*u2 - rhs2),
quad);
Expr dummyBC ;
NonlinearProblem prob(mesh, eqn, dummyBC, List(v1,v2), List(u1,u2),
u0, vecType);
ParameterXMLFileReader reader("nox.xml");
ParameterList solverParams = reader.getParameters();
Out::root() << "finding periodic solution" << endl;
NOXSolver solver(solverParams);
prob.solve(solver);
/* unfold the solution onto a non-periodic mesh */
Expr uP = unfoldPeriodicDiscreteFunction(u0, "u_p");
Out::root() << "uP=" << uP << endl;
Mesh unfoldedMesh = DiscreteFunction::discFunc(uP)->mesh();
DiscreteSpace unfDiscSpace = DiscreteFunction::discFunc(uP)->discreteSpace();
FieldWriter writer = new MatlabWriter("Floquet.dat");
writer.addMesh(unfoldedMesh);
writer.addField("u_p[0]", new ExprFieldWrapper(uP[0]));
writer.addField("u_p[1]", new ExprFieldWrapper(uP[1]));
Array<Expr> a(2);
a[0] = new Sundance::Parameter(0.0, "a1");
a[1] = new Sundance::Parameter(0.0, "a2");
Expr bc = EssentialBC(left, v1*(u1-uP[0]-a[0]) + v2*(u2-uP[1]-a[1]), quad);
NonlinearProblem unfProb(unfoldedMesh, eqn, bc,
List(v1,v2), List(u1,u2), uP, vecType);
unfProb.setEvalPoint(uP);
LinearOperator<double> J = unfProb.allocateJacobian();
Vector<double> b = J.domain().createMember();
LinearSolver<double> linSolver
= LinearSolverBuilder::createSolver("amesos.xml");
SerialDenseMatrix<int, double> F(a.size(), a.size());
for (int i=0; i<a.size(); i++)
{
Out::root() << "doing perturbed orbit #" << i << endl;
for (int j=0; j<a.size(); j++)
{
if (i==j) a[j].setParameterValue(1.0);
else a[j].setParameterValue(0.0);
}
unfProb.computeJacobianAndFunction(J, b);
Vector<double> w = b.copy();
linSolver.solve(J, b, w);
Expr w_i = new DiscreteFunction(unfDiscSpace, w);
for (int j=0; j<a.size(); j++)
{
Out::root() << "postprocessing" << i << endl;
writer.addField("w[" + Teuchos::toString(i)
+ ", " + Teuchos::toString(j) + "]", new ExprFieldWrapper(w_i[j]));
Expr g = Integral(right, w_i[j], quad);
F(j,i) = evaluateIntegral(unfoldedMesh, g);
}
}
writer.write();
Out::root() << "Floquet matrix = " << endl
<< F << endl;
Out::root() << "doing eigenvalue analysis" << endl;
Array<double> ew_r(a.size());
Array<double> ew_i(a.size());
int lWork = 6*a.size();
Array<double> work(lWork);
int info = 0;
LAPACK<int, double> lapack;
lapack.GEEV('N','N', a.size(), F.values(),
a.size(), &(ew_r[0]), &(ew_i[0]), 0, 1, 0, 1, &(work[0]), lWork,
&info);
TEUCHOS_TEST_FOR_EXCEPTION(info != 0,
std::runtime_error,
"LAPACK GEEV returned error code =" << info);
Array<double> ew(a.size());
for (int i=0; i<a.size(); i++)
{
ew[i] = sqrt(ew_r[i]*ew_r[i]+ew_i[i]*ew_i[i]);
Out::root() << setw(5) << i
<< setw(16) << ew_r[i]
<< setw(16) << ew_i[i]
<< setw(16) << ew[i]
<< endl;
}
double err = ::fabs(ew[0] - 0.123);
return SundanceGlobal::checkTest(err, 0.001);
}
inline bool LinearCombinationTester<Scalar>
::selfModifyingOpTests() const
{
bool pass = true;
RandomSparseMatrixBuilder<double> ABuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> BBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> CBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
LinearOperator<double> A = ABuilder.getOp();
LinearOperator<double> B = BBuilder.getOp();
LinearOperator<double> C = CBuilder.getOp();
VectorSpace<Scalar> vs = A.domain();
A = identityOperator(vs);
B = identityOperator(vs);
C = identityOperator(vs);
Vector<Scalar> x = A.domain().createMember();
Vector<Scalar> y = A.domain().createMember();
Vector<Scalar> z = A.domain().createMember();
this->randomizeVec(x);
this->randomizeVec(y);
this->randomizeVec(z);
Vector<Scalar> a = x.copy();
Vector<Scalar> b = y.copy();
Vector<Scalar> c = z.copy();
Out::os() << "starting linear combination tests" << std::endl;
x = 2.0*A*x;
Scalar err = (x - 2.0*A*a).norm2();
if (!this->checkTest(spec_, err, "x=2.0*A*x")) pass = false;
a = x.copy();
x = x + y;
err = (x - (a + y)).norm2();
if (!this->checkTest(spec_, err, "x=x+y")) pass = false;
a = x.copy();
x = y + x;
err = (x - (y + a)).norm2();
if (!this->checkTest(spec_, err, "x=y+x")) pass = false;
a = x.copy();
x = A*x + B*y;
err = (x - (A*a + B*y)).norm2();
if (!this->checkTest(spec_, err, "x=A*x+B*y")) pass = false;
a = x.copy();
x = B*y + A*x;
err = (x - (B*y + A*a)).norm2();
if (!this->checkTest(spec_, err, "x=B*y+A*x")) pass = false;
a = x.copy();
x = A*x + (B*y + C*x);
err = (x - (A*a + (B*y + C*a))).norm2();
if (!this->checkTest(spec_, err, "x=A*x + (B*y + C*x)")) pass = false;
a = x.copy();
x = (A*x + B*y) + C*x;
err = (x - ((A*a + B*y) + C*a)).norm2();
if (!this->checkTest(spec_, err, "x=(A*x + B*y) + C*x")) pass = false;
/* test assignment of OpTimesLC into empty and non-empty vectors */
Vector<Scalar> u;
u = 2.0*A*B*x;
err = (u - 2.0*A*B*x).norm2();
if (!this->checkTest(spec_, err, "(empty) u=2*A*B*x")) pass = false;
u = 2.0*A*B*x;
err = (u - 2.0*A*B*x).norm2();
if (!this->checkTest(spec_, err, "(non-empty) u=2*A*B*x")) pass = false;
/* test assignment of LC2 into empty and non-empty vectors */
Vector<Scalar> v;
v = 2.0*x + 3.0*y;
err = (v - (2.0*x + 3.0*y)).norm2();
if (!this->checkTest(spec_, err, "(empty) v=2*x + 3*y")) pass = false;
v = 2.0*x + 3.0*y;
err = (v - (2.0*x + 3.0*y)).norm2();
if (!this->checkTest(spec_, err, "(non-empty) v=2*x + 3*y")) pass = false;
/* test assignment of LC3 into empty and non-empty vectors */
Vector<Scalar> w;
w = 2.0*x + 3.0*y + 5.0*z;
err = (w - (2.0*x + 3.0*y + 5.0*z)).norm2();
if (!this->checkTest(spec_, err, "(empty) w=2*x + 3*y + 5*z")) pass = false;
w = 2.0*x + 3.0*y + 5.0*z;
err = (w - (2.0*x + 3.0*y + 5.0*z)).norm2();
if (!this->checkTest(spec_, err, "(non-empty) w=2*x + 3*y + 5*z")) pass = false;
/* test assignment of LC4 into empty and non-empty vectors */
Vector<Scalar> w2;
w2 = 2.0*x + 3.0*y + 5.0*z + 7.0*u;
err = (w2 - (2.0*x + 3.0*y + 5.0*z + 7.0*u)).norm2();
if (!this->checkTest(spec_, err,
"(empty) w2=2*x + 3*y + 5*z + 7*u")) pass = false;
w2 = 2.0*x + 3.0*y + 5.0*z + 7.0*u;
err = (w2 - (2.0*x + 3.0*y + 5.0*z + 7.0*u)).norm2();
if (!this->checkTest(spec_, err,
"(non-empty) w2=2*x + 3*y + 5*z + 7*u")) pass = false;
/* test assignment of LC3 into one of the operands */
x = 2.0*x + 3.0*y + 5.0*z;
err = (w - x).norm2(); // Note: w contains 2x + 3y + 5z
if (!this->checkTest(spec_, err, "x=2*x + 3*y + 5*z")) pass = false;
return pass;
}
inline bool LinearCombinationTester<Scalar>
::nonModifyingOpTests() const
{
bool pass = true;
RandomSparseMatrixBuilder<double> ABuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> BBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
RandomSparseMatrixBuilder<double> CBuilder(nLocalRows_, nLocalRows_,
onProcDensity_, offProcDensity_,
vecType_);
LinearOperator<double> A = ABuilder.getOp();
LinearOperator<Scalar> B = BBuilder.getOp();
LinearOperator<Scalar> C = CBuilder.getOp();
Vector<Scalar> x = A.domain().createMember();
Vector<Scalar> y = A.domain().createMember();
Vector<Scalar> z = A.domain().createMember();
this->randomizeVec(x);
this->randomizeVec(y);
this->randomizeVec(z);
TESTER(x*2.0, 2.0*x);
TESTER(2.0*(x + y), 2.0*x + 2.0*y);
TESTER(2.0*(x - y), 2.0*x - 2.0*y);
TESTER((2.0*x + y) - y, 2.0*x);
TESTER(-1.0*y + (2.0*x + y), 2.0*x);
TESTER((x + y)*2.0, 2.0*x + 2.0*y);
TESTER((x - y)*2.0, 2.0*x - 2.0*y);
TESTER(2.0*(x - y), -2.0*(y - x));
TESTER(0.25*(2.0*(x + y) - 2.0*(x - y)), y);
TESTER((2.0*A)*x, 2.0*(A*x));
TESTER(2.0*(A*x), (A*x)*2.0);
TESTER(A*(B*x), (A*B)*x);
TESTER(2.0*A*(B*x), A*(B*(2.0*x)));
TESTER(3.0*(2.0*A)*x, 6.0*(A*x));
TESTER(y + A*x, A*x + y);
TESTER(z + (A*x + B*y), (B*y + A*x) + z);
TESTER(z - (A*x + B*y), -1.0*((B*y + A*x) - z));
TESTER(C*z + (A*x + B*y), (B*y + A*x) + C*z);
TESTER(C*z - (A*x + B*y), -1.0*((B*y + A*x) - C*z));
TESTER(2.0*z + (A*x + B*y), (B*y + A*x) + 2.0*z);
TESTER(2.0*z - (A*x + B*y), -1.0*((B*y + A*x) - 2.0*z));
TESTER(A*x - y, -1.0*(y - A*x));
TESTER(A*x + B*y, B*y + A*x);
TESTER(A*x - B*y - A*x + B*y +z, z);
TESTER(2.0*(A*x + y), 2.0*A*x + 2.0*y);
TESTER(2.0*(A*x + B*y), A*x + B*y + A*x + B*y);
TESTER(2.0*(y + A*x), 2.0*y + 2.0*(A*x));
TESTER(x + 2.0*A*y, x + 2.0*(A*y));
TESTER(2.0*A*y + x, 2.0*(A*y) + x);
TESTER(2.0*A*(3.0*B)*y, 6.0*(A*B*y));
TESTER(2.0*A*(3.0*B)*y, 6.0*(A*(B*y)));
TESTER(2.0*A*(3.0*B + 2.0*A)*x, 6.0*A*B*x + 4.0*A*A*x );
TESTER(2.0*(A*x + B*y), 2.0*A*x + 2.0*B*y);
TESTER(2.0*(A*x - B*y), 2.0*A*x - 2.0*B*y);
TESTER(2.0*(A*x + B*y + z), 2.0*A*x + 2.0*B*y + 2.0*z);
TESTER(2.0*(A*x + 3.0*B*y), 2.0*A*x + 6.0*B*y);
TESTER(2.0*(A*x + 3.0*(z + B*y)), 2.0*A*x + 6.0*B*y + 6.0*z);
TESTER(2.0*(z + A*x + B*y + z), 2.0*A*x + 2.0*B*y + 4.0*z);
TESTER(2.0*(3.0*(z + A*x) + B*y), 6.0*z + 6.0*A*x + 2.0*B*y);
TESTER(2.0*(3.0*(z + A*x) + 4.0*(B*y + z)), 6.0*z + 6.0*A*x + 8.0*B*y + 8.0*z);
TESTER((A*x + B*y) + (A*y + B*x), (A + B)*x + (A+B)*y);
TESTER((A*x + B*y) - (A*y + B*x), A*x - A*y + B*y - B*x);
TESTER((A*x + B*y) + 2.0*(A*y + B*x), A*(x + 2.0*y) + B*(2.0*x + y));
TESTER((A*x + B*y) - 2.0*(A*y + B*x), A*(x - 2.0*y) + B*(y - 2.0*x));
return pass;
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
ParameterXMLFileReader reader("anasazi-ml.xml");
ParameterList solverParams = reader.getParameters().sublist("Eigensolver");
/* create the range space */
int nLocalRows = 40;
MatrixLaplacian1D builder(nLocalRows, type);
typedef Anasazi::MultiVec<double> MV;
typedef Anasazi::Operator<double> OP;
LinearOperator<double> A = builder.getOp();
LinearOperator<double> M;
Teuchos::RCP<Anasazi::OutputManager<double> > MyOM = Teuchos::rcp( new Anasazi::BasicOutputManager<double>() );
MyOM->setVerbosity(Anasazi::Warnings);
int nv = 1;
RCP<const Array<Vector<double> > > initMV = rcp(new Array<Vector<double> >(nv));
RCP<Array<Vector<double> > > nc
= rcp_const_cast<Array<Vector<double> > >(initMV);
for (int i=0; i<nv; i++)
{
(*nc)[i] = A.domain().createMember();
(*nc)[i].randomize();
}
#ifdef BLARF
bool mvPass = Anasazi::TestMultiVecTraits<double,Array<Vector<double> > >(MyOM,initMV);
if (mvPass) Out::os() << "******* MV unit test PASSED ******* " << endl;
else Out::os() << "******* MV unit test FAILED ******* " << endl;
RCP<const LinearOperator<double> > APtr = rcp(&A, false);
bool opPass = Anasazi::TestOperatorTraits<double, Array<Vector<double> >, LinearOperator<double> >(MyOM, initMV, APtr);
if (opPass) Out::os() << "******* OP unit test PASSED ******* " << endl;
else Out::os() << "******* OP unit test FAILED ******* " << endl;
#endif
Eigensolver<double> solver = new AnasaziEigensolver<double>(solverParams);
Array<Vector<double> > ev;
Array<std::complex<double> > ew;
solver.solve(A, M, ev, ew);
Out::os() << "Eigenvalues are " << ew << endl;
const double pi = 4.0*atan(1.0);
double err = 0.0;
for (int i=0; i<ev.size(); i++)
{
double x = (i+1)*pi;
err += ::fabs(ew[i].real()-x*x)/x/x;
}
err = err / ew.size();
Out::os() << "error = " << err << endl;
if (err < 0.01)
{
cout << "Belos poisson solve test PASSED" << std::endl;
return 0;
}
else
{
cout << "Belos poisson solve test FAILED" << std::endl;
return 1;
}
}
catch(std::exception& e)
{
cout << "Caught exception: " << e.what() << std::endl;
return -1;
}
}
int main(int argc, char *argv[])
{
typedef Teuchos::ScalarTraits<double> ST;
try
{
GlobalMPISession session(&argc, &argv);
MPIComm::world().synchronize();
VectorType<double> type = new EpetraVectorType();
/* create the range space */
int nLocalRows = 10;
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> A = builder.getOp();
int nBlocks = 3;
Array<Vector<double> > x(nBlocks);
Array<VectorSpace<double> > space(nBlocks);
for (int i=0; i<nBlocks; i++)
{
space[i] = A.domain();
x[i] = A.domain().createMember();
Thyra::randomize(-ST::one(),+ST::one(),x[i].ptr().ptr());
}
VectorSpace<double> blockSpace = productSpace(space);
LinearOperator<double> bigA = makeBlockOperator(blockSpace, blockSpace);
Vector<double> bigRHS = blockSpace.createMember();
Vector<double> bigX = blockSpace.createMember();
for (int i=0; i<nBlocks; i++)
{
bigX.setBlock(i, x[i]);
for (int j=i; j<nBlocks; j++)
{
MatrixLaplacian1D builder(nLocalRows, type);
LinearOperator<double> Aij = builder.getOp();
bigA.setBlock(i,j,Aij);
}
}
bigA.endBlockFill();
bigRHS = bigA * bigX;
Vector<double> bigSoln = blockSpace.createMember();
#ifdef HAVE_CONFIG_H
ParameterXMLFileReader reader(Sundance::searchForFile("SolverParameters/poissonParams.xml"));
#else
ParameterXMLFileReader reader("poissonParams.xml");
#endif
ParameterList solverParams = reader.getParameters();
LinearSolver<double> solver
= LinearSolverBuilder::createSolver(solverParams);
LinearSolver<double> blockSolver
= new BlockTriangularSolver<double>(solver);
SolverState<double> state = blockSolver.solve(bigA, bigRHS, bigSoln);
std::cerr << state << std::endl;
double err = (bigSoln - bigX).norm2();
std::cerr << "error norm = " << err << std::endl;
double tol = 1.0e-8;
if (err > tol)
{
std::cerr << "Poisson solve test FAILED" << std::endl;
return 1;
}
else
{
std::cerr << "Poisson solve test PASSED" << std::endl;
return 0;
}
}
catch(std::exception& e)
{
std::cerr << "Caught exception: " << e.what() << std::endl;
return -1;
}
return 0;
}
Preconditioner<double>
PCDPreconditionerFactory::
createPreconditioner(const LinearOperator<double>& K) const
{
Tabs tab;
LinearOperator<double> F = K.getBlock(0,0);
// F.setName("F");
LinearOperator<double> FInv = inverse(F, FSolver_);
// FInv.setName("FInv");
LinearOperator<double> Bt = K.getBlock(0,1);
// Bt.setName("Bt");
LinearOperator<double> Fp = FpProb_.getOperator();
LinearOperator<double> Mp = MpProb_.getOperator();
// Mp.setName("Mp");
LinearOperator<double> MpInv = inverse(Mp, MpSolver_);
// MpInv.setName("MpInv");
LinearOperator<double> Ap = ApProb_.getOperator();
// Ap.setName("Ap");
LinearOperator<double> ApInv = inverse(Ap, ApSolver_);
// ApInv.setName("ApInv");
VectorSpace<double> pDomain = Bt.domain();
VectorSpace<double> uDomain = F.domain();
LinearOperator<double> Iu = identityOperator(uDomain);
// Iu.setName("Iu");
LinearOperator<double> Ip = identityOperator(pDomain);
// Ip.setName("Ip");
LinearOperator<double> XInv = MpInv * Fp * ApInv;
VectorSpace<double> rowSpace = K.range();
VectorSpace<double> colSpace = K.domain();
LinearOperator<double> Q1 = makeBlockOperator(colSpace, rowSpace);
// Q1.setName("Q1");
LinearOperator<double> Q2 = makeBlockOperator(colSpace, rowSpace);
// Q2.setName("Q2");
LinearOperator<double> Q3 = makeBlockOperator(colSpace, rowSpace);
//Q3.setName("Q3");
Q1.setBlock(0, 0, FInv);
Q1.setBlock(1, 1, Ip);
Q1.endBlockFill();
Q2.setBlock(0, 0, Iu);
Q2.setBlock(0, 1, -1.0*Bt);
Q2.setBlock(1, 1, Ip);
Q2.endBlockFill();
Q3.setBlock(0, 0, Iu);
Q3.setBlock(1, 1, -1.0*XInv);
Q3.endBlockFill();
LinearOperator<double> P1 = Q2 * Q3;
LinearOperator<double> PInv = Q1 * P1;
return new GenericRightPreconditioner<double>(PInv);
}