//! initialize a newly created preconditioner object
void PreconditionerFactory::initializePrec(const RCP<const LinearOpSourceBase<double> > & ASrc,
const RCP<const Thyra::MultiVectorBase<double> > & solnVec,
PreconditionerBase<double> * prec,
const ESupportSolveUse supportSolveUse) const
{
Preconditioner * blkPrec = dynamic_cast<Preconditioner *>(prec);
blkPrec->setSourceVector(Teuchos::rcp_const_cast<Thyra::MultiVectorBase<double> >(solnVec));
initializePrec(ASrc,prec,supportSolveUse);
}
double CMT::MLR::evaluate(
const pair<ArrayXXd, ArrayXXd>& data,
const Preconditioner& preconditioner) const
{
return -logLikelihood(preconditioner(data.first, data.second)).mean() / log(2.)
- preconditioner.logJacobian(data).mean() / log(2.);
}
void DefaultIterativeSolver<BasisFunctionType, ResultType>::initializeSolver(
const Teuchos::RCP<Teuchos::ParameterList>& paramList,
const Preconditioner<ResultType>& preconditioner)
{
m_impl->solverWrapper->setPreconditioner(preconditioner.get());
m_impl->solverWrapper->initializeSolver(paramList);
}
double CMT::MLR::evaluate(
const MatrixXd& input,
const MatrixXd& output,
const Preconditioner& preconditioner) const
{
return -logLikelihood(preconditioner(input, output)).mean() / log(2.)
- preconditioner.logJacobian(input, output).mean() / log(2.);
}
bool IterativeSolvers::pcg(const IRCMatrix &A,
Vector &x,
const Vector &b,
const Preconditioner &M) {
/*!
Solves Ax=b using the preconditioned conjugate gradient method.
*/
const idx N = x.getLength();
real resid(100.0);
Vector p(N), z(N), q(N);
real alpha;
real normr(0);
real normb = norm(b);
real rho(0), rho_1(0), beta(0);
Vector r = b - A * x;
if (normb == 0.0)
normb = 1;
resid = norm(r) / normb;
if (resid <= IterativeSolvers::toler) {
IterativeSolvers::toler = resid;
IterativeSolvers::maxIter = 0;
return true;
}
// MAIN LOOP
idx i = 1;
for (; i <= IterativeSolvers::maxIter; i++) {
M.solveMxb(z, r);
rho = dot(r, z);
if (i == 1)
p = z;
else {
beta = rho / rho_1;
aypx(beta, p, z); // p = beta*p + z;
}
// CALCULATES q = A*p AND dp = dot(q,p)
real dp = multiply_dot(A, p, q);
alpha = rho / dp;
normr = 0;
#ifdef USES_OPENMP
#pragma omp parallel for reduction(+:normr)
#endif
for (idx j = 0 ; j < N ; ++j) {
x[j] += alpha * p[j]; // x + alpha(0) * p;
r[j] -= alpha * q[j]; // r - alpha(0) * q;
normr += r[j] * r[j];
}
normr = sqrt(normr);
resid = normr / normb;
if (resid <= IterativeSolvers::toler) {
IterativeSolvers::toler = resid;
IterativeSolvers::maxIter = i;
return true;
}
rho_1 = rho;
}
IterativeSolvers::toler = resid;
return false;
}
SolverState<double> PCGSolver::solve(const LinearOperator<double>& A,
const Vector<double>& b,
Vector<double>& x) const
{
if (precFactory_.ptr().get() == 0)
{
return solveUnprec(A, b, x);
}
else
{
SolverState<double> rtn;
Preconditioner<double> prec = precFactory_.createPreconditioner(A);
if (prec.isIdentity())
{
rtn = solveUnprec(A, b, x);
}
else if (prec.isTwoSided())
{
LinearOperator<double> P = prec.left();
LinearOperator<double> Q = prec.right();
LinearOperator<double> PAQ = P*A*Q;
Vector<double> Pb = P*b;
Vector<double> y;
rtn = solveUnprec(PAQ, Pb, y);
x = Q*y;
}
else if (prec.hasRight())
{
LinearOperator<double> Q = prec.right();
LinearOperator<double> AQ = A*Q;
Vector<double> y;
rtn = solveUnprec(AQ, b, y);
x = Q*y;
}
else if (prec.hasLeft())
{
LinearOperator<double> P = prec.left();
LinearOperator<double> PA = P*A;
Vector<double> Pb = P*b;
rtn = solveUnprec(PA, Pb, x);
}
else
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::runtime_error,
"Inconsistent preconditioner state "
"in PGCSolver::solve()");
}
return rtn;
}
}
int CG(const MMatrix &A, MVector &x, const MVector &b, const Preconditioner &M, int &max_iter, Real &tol)
{
Real resid;
MVector p, z, q;
MVector alpha(1), beta(1), rho(1), rho_1(1);
MVector r = b - A*x;
Real normb = norm(b);
if (normb == 0.0) normb = 1;
if ((resid = norm(r) / normb) <= tol){
tol = resid;
max_iter = 0;
return 0;
}
for (int i = 1; i <= max_iter; i++)
{
// Assign Z
z = M.solve(r);
rho.p_[0] = dot(r, z);
// Assign P
if (i == 1)
p = z;
else {
beta.p_[0] = rho.p_[0] / rho_1.p_[0];
p = z + beta.p_[0] * p;
}
// Assign Q
q = A*p;
alpha.p_[0] = rho.p_[0] / dot(p, q);
// Change X and R
x += alpha.p_[0] * p;
r -= alpha.p_[0] * q;
// Check tol
if ((resid = norm(r) / normb) <= tol)
{
tol = resid;
max_iter = i;
return 0;
}
rho_1.p_[0] = rho.p_[0];
}
tol = resid;
return 1;
}
//! initialize a newly created preconditioner object
void PreconditionerFactory::initializePrec(const RCP<const LinearOpSourceBase<double> > & ASrc,
PreconditionerBase<double> * prec,
const ESupportSolveUse supportSolveUse) const
{
// get the blocked linear operator
LinearOp A = Teuchos::rcp_const_cast<Thyra::LinearOpBase<double> >(ASrc->getOp());
Preconditioner * blkPrec = dynamic_cast<Preconditioner *>(prec);
TEUCHOS_ASSERT(blkPrec!=0);
// grab the state object
RCP<PreconditionerState> state = blkPrec->getStateObject();
state->setInitialized(false);
// build the preconditioner
const RCP<const LinearOpBase<double> > M = buildPreconditionerOperator(A,*state);
// set the request handler for the
setOpRequestHandler(*this,M);
// must first cast that to be initialized
DefaultPreconditioner<double> & dPrec = Teuchos::dyn_cast<DefaultPreconditioner<double> >(*prec);
dPrec.initializeUnspecified(Teuchos::rcp_const_cast<LinearOpBase<double> >(M));
}
SolverState<double> BelosSolver::solve(const LinearOperator<double>& A,
const Vector<double>& rhs,
Vector<double>& soln) const
{
typedef Anasazi::SimpleMV MV;
typedef LinearOperator<double> OP;
typedef Belos::LinearProblem<double, MV, OP> LP;
TEUCHOS_TEST_FOR_EXCEPT(!A.ptr().get());
TEUCHOS_TEST_FOR_EXCEPT(!rhs.ptr().get());
if (!soln.ptr().get())
{
soln = rhs.copy();
/* KRL 8 Jun 2012: set x0 to zero to workaround bug in Belos */
soln.zero();
}
if (rhs.norm2()==0.0)
{
soln.zero();
SolverStatusCode code = SolveConverged;
SolverState<double> state(code, "Detected trivial solution", 0, 0.0);
return state;
}
RCP<OP> APtr = rcp(new LinearOperator<double>(A));
RCP<MV> bPtr = rcp(new MV(1));
(*bPtr)[0] = rhs;
RCP<MV> ansPtr = rcp(new MV(1));
(*ansPtr)[0] = soln;
RCP<LP> prob = rcp(new LP(APtr, ansPtr, bPtr));
TEUCHOS_TEST_FOR_EXCEPT(!prob->setProblem());
if (pf_.ptr().get())
{
Preconditioner<double> P = pf_.createPreconditioner(A);
if (P.hasLeft())
{
prob->setLeftPrec(rcp(new OP(P.left())));
}
if (P.hasRight())
{
prob->setRightPrec(rcp(new OP(P.right())));
}
}
if (!hasSolver_)
{
ParameterList plist = parameters();
RCP<ParameterList> belosList = rcp(&plist, false);
std::string solverType = parameters().get<string>("Method");
if (solverType=="GMRES")
{
solver_=rcp(new Belos::BlockGmresSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="CG")
{
solver_=rcp(new Belos::BlockCGSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="TFQMR")
{
solver_=rcp(new Belos::TFQMRSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="GCRODR")
{
solver_=rcp(new Belos::GCRODRSolMgr<double, MV, OP>(prob, belosList));
hasSolver_ = true; // only cache recycling solvers
}
else if (solverType=="RCG")
{
solver_=rcp(new Belos::RCGSolMgr<double, MV, OP>(prob, belosList));
hasSolver_ = true; // only cache recycling solvers
}
else
{
TEUCHOS_TEST_FOR_EXCEPT(!(solverType=="GMRES" || solverType=="CG"));
}
}
else // reset problem
{
solver_->setProblem( prob );
}
Belos::ReturnType rtn = solver_->solve();
int numIters = solver_->getNumIters();
double resid = solver_->achievedTol();
SolverStatusCode code = SolveFailedToConverge;
if (rtn==Belos::Converged) code = SolveConverged;
SolverState<double> state(code, "Belos solver completed", numIters, resid);
return state;
}
SolverState<double> BelosSolver::solve(const LinearOperator<double>& A,
const Vector<double>& rhs,
Vector<double>& soln) const
{
typedef Thyra::MultiVectorBase<double> MV;
typedef Thyra::LinearOpBase<double> OP;
typedef Belos::LinearProblem<double, MV, OP> LP;
TEST_FOR_EXCEPT(!A.ptr().get());
TEST_FOR_EXCEPT(!rhs.ptr().get());
/* get Thyra objects */
RCP<OP> APtr = A.ptr();
RCP<MV> bPtr = rhs.ptr();
if (!soln.ptr().get()) soln = rhs.copy();
RCP<MV> ansPtr = soln.ptr();
RCP<LP> prob = rcp(new LP(APtr, ansPtr, bPtr));
TEST_FOR_EXCEPT(!prob->setProblem());
if (pf_.ptr().get())
{
Preconditioner<double> P = pf_.createPreconditioner(A);
if (P.hasLeft())
{
prob->setLeftPrec(P.left().ptr());
}
if (P.hasRight())
{
prob->setRightPrec(P.right().ptr());
}
}
ParameterList plist = parameters();
RCP<ParameterList> belosList = rcp(&plist, false);
RCP<Belos::SolverManager<double, MV, OP> > solver ;
std::string solverType = parameters().get<string>("Method");
if (solverType=="GMRES")
{
solver=rcp(new Belos::BlockGmresSolMgr<double, MV, OP>(prob, belosList));
}
else if (solverType=="CG")
{
solver=rcp(new Belos::BlockCGSolMgr<double, MV, OP>(prob, belosList));
}
else
{
TEST_FOR_EXCEPT(!(solverType=="GMRES" || solverType=="CG"));
}
Belos::ReturnType rtn = solver->solve();
int numIters = solver->getNumIters();
double resid = -1.0;
SolverStatusCode code = SolveFailedToConverge;
if (rtn==Belos::Converged) code = SolveConverged;
SolverState<double> state(code, "Belos solver completed", numIters, resid);
return state;
}
bool IterativeSolvers::gmres(const IRCMatrix &A,
Vector &x,
const Vector &b,
const Preconditioner &M) {
const idx N = x.getLength();
idx i, j = 1, k;
Vector s(maxInnerIter + 1);
Vector cs(maxInnerIter + 1);
Vector sn(maxInnerIter + 1);
Vector w(N);
real normb = norm(M.solve(b));
Vector r = M.solve(b - A * x);
real beta = norm(r);
if (normb == 0.0)
normb = 1;
real res(norm(r) / normb);
if (res <= toler) {
toler = res;
maxIter = 0;
return true;
}
Vector *v = new Vector[maxInnerIter + 1];
for (idx id = 0; id < maxInnerIter + 1; ++id)
v[id] = Vector(N);
// CREATE HESSENBERG MATRIX NEEDED TO STORE INTERMEDIATES
DenseMatrix H(maxInnerIter + 1, maxInnerIter);
Vector temp(N);
Vector temp2(maxInnerIter + 1);
// MAIN LOOP
while (j <= maxIter) {
v[0] = r * (1.0 / beta);
s = 0.0;
s(0) = beta;
// INNER ITERATIONS
for (i = 0; i < maxInnerIter && j <= maxIter; i++, j++) {
// CALCULATE w = M^{-1}(A*v[i])
multiply(A, v[i], temp);
M.solveMxb(w, temp);
// PRE-CALCULATE DOT PRODUCTS IN PARALLEL
// H(k,i) = dot( v[k], w)
#ifdef USES_OPENMP
#pragma omp parallel for
#endif
for (k = 0; k <= i ; ++k) {
register real dp(0);
for (idx id = 0 ; id < N ; ++id)
dp += w[id] * v[k][id];
H(k, i) = dp; //dot(w,v[k]);
}
for (k = 0; k <= i; ++k) {
// w -= v[k]*H(k,i) without temporaries
register real tempr = H(k, i);
#ifdef USES_OPENMP
#pragma omp parallel for // why is this loop so critical??
#endif
for (idx id = 0 ; id < N ; ++id)
w[id] -= v[k][id] * tempr;
}
// BELOW PARALLEL REGION CALCULATES:
// H(i+1,i) = norm(w);
// v[i+1] = w * (1.0 / H(i+1, i));
H(i + 1, i) = 0;
real tempr(0);
#ifdef USES_OPENMP
#pragma omp parallel shared(tempr)
#endif
{
#ifdef USES_OPENMP
#pragma omp for reduction(+:tempr)
#endif
for (idx id = 0 ; id < N ; ++id)
tempr += w[id] * w[id]; //norm(w);
#ifdef USES_OPENMP
#pragma omp single
#endif
{
H(i + 1, i) = sqrt(tempr);
tempr = (1.0 / H(i + 1, i));
}
#ifdef USES_OPENMP
#pragma omp for
#endif
for (idx id = 0 ; id < N ; ++id)
v[i + 1][id] = w[id] * tempr;
}// end for omp parallel
for (k = 0; k < i; k++)
ApplyPlaneRotation(H(k, i), H(k + 1, i), cs(k), sn(k));
GeneratePlaneRotation(H(i, i), H(i + 1, i), cs(i), sn(i));
ApplyPlaneRotation(H(i, i), H(i + 1, i), cs(i), sn(i));
ApplyPlaneRotation(s(i), s(i + 1), cs(i), sn(i));
res = fabs(s(i + 1)) / normb;
if (res < toler) {
// COPY S INTO temp WITHOUT RESIZING
for (idx id = 0 ; id < maxInnerIter + 1 ; ++id)
temp2[id] = s[id];
Update(x, i, H, temp2, v);
toler = res;
maxIter = j;
delete [] v;
return true;
}
}// end for i IINNER ITERATIONS
// COPY S INTO temp WITHOUT RESIZING
for (idx id = 0 ; id < maxInnerIter + 1 ; ++id)
temp2[id] = s[id];
Update(x, maxInnerIter - 1, H, temp2, v);
//multiply(A, x, temp); //r = M.solve(b - A * x);
M.solveMxb(r, b - A * x);
beta = norm(r);
res = beta / normb;
if (res < toler) {
toler = res;
maxIter = j;
delete [] v;
return true;
}
}
toler = res;
delete [] v;
return false;
}
// Conjugate gradient with preconditioner.
/*static*/ bool ConjugateGradientSolver(const Preconditioner & preconditioner, const SparseMatrix & A, const FullVector & b, FullVector & x, float epsilon)
{
nvDebugCheck( A.isSquare() );
nvDebugCheck( A.width() == b.dimension() );
nvDebugCheck( A.width() == x.dimension() );
int i = 0;
const int D = A.width();
const int i_max = 4 * D; // Convergence should be linear, but in some cases, it's not.
FullVector r(D); // residual
FullVector p(D); // search direction
FullVector q(D); //
FullVector s(D); // preconditioned
float delta_0;
float delta_old;
float delta_new;
float alpha;
float beta;
// r = b - A·x
copy(b, r);
sgemv(-1, A, x, 1, r);
// p = M^-1 · r
preconditioner.apply(r, p);
//copy(r, p);
delta_new = dot(r, p);
delta_0 = delta_new;
while (i < i_max && delta_new > epsilon*epsilon*delta_0)
{
i++;
// q = A·p
mult(A, p, q);
// alpha = delta_new / p·q
alpha = delta_new / dot(p, q);
// x = alfa·p + x
saxpy(alpha, p, x);
if ((i & 31) == 0) // recompute r after 32 steps
{
// r = b - A·x
copy(b, r);
sgemv(-1, A, x, 1, r);
}
else
{
// r = r - alfa·q
saxpy(-alpha, q, r);
}
// s = M^-1 · r
preconditioner.apply(r, s);
//copy(r, s);
delta_old = delta_new;
delta_new = dot( r, s );
beta = delta_new / delta_old;
// p = s + beta·p
scal(beta, p);
saxpy(1, s, p);
}
return delta_new <= epsilon*epsilon*delta_0;
}
void DefaultIterativeSolver<BasisFunctionType, ResultType>::setPreconditioner(
const Preconditioner<ResultType>& preconditioner)
{
m_impl->solverWrapper->setPreconditioner(preconditioner.get());
}