static void PruneInductionCandidate(int tnum, LOOP *l)
{
if (tempInfo[tnum]->size >= ISZ_FLOAT)
{
briggsReset(candidates, tnum);
}
else
{
QUAD *I = tempInfo[tnum]->instructionDefines;
switch(I->dc.opcode)
{
case i_phi:
{
PHIDATA *pd = I->dc.v.phi;
struct _phiblock *pb = pd->temps;
while (pb)
{
if (!briggsTest(candidates, pb->Tn) && !isInvariant(pb->Tn, l))
{
briggsReset(candidates, tnum);
break;
}
pb = pb->next;
}
}
break;
case i_add:
case i_sub:
if (I->temps & TEMP_RIGHT)
{
int tn2 = I->dc.right->offset->v.sp->value.i;
if (!briggsTest(candidates, tn2))
briggsReset(candidates, tnum);
}
/* FALLTHROUGH */
case i_neg:
case i_assn:
if (I->temps & TEMP_LEFT)
{
int tn2 = I->dc.left->offset->v.sp->value.i;
if (!briggsTest(candidates, tn2))
briggsReset(candidates, tnum);
}
break;
default:
diag("PruneInductionCandidate: invalid form");
break;
}
}
}
//
// Find loop invariant instructions in a given block.
// We can do this block by block because we are traversing the dominator
// tree in pre-order, which accumulating invariants in our set.
//
void LicmPass::inspectBlock(const Loop* loop, BasicBlock* block,
Invariants& invariants) {
// No need to iterate over subloops because they will already have their
// instructions hoisted. Skip if we are in the subloop.
bool top_level = isTopLevel(loop, block);
if (!top_level) {
return;
}
// Iterate through all the intructions.
for (BasicBlock::iterator J = block->begin(), JE = block->end();
J != JE; ++J) {
Instruction& instr = *J;
bool invariant = isInvariant(loop, invariants, &instr);
if (invariant) {
invariants.insert(&instr);
}
}
}
//
// Check if instruction is invariant.
//
bool LicmPass::isInvariant(const Loop* loop,
Invariants& invariants, Instruction* instr) {
// Must also satisfy these conditions to ensure safety of movement.
if (!isSafeToSpeculativelyExecute(instr) ||
instr->mayReadFromMemory() ||
isa<LandingPadInst>(instr)) {
return false;
}
// See if all operands are invariant.
for (User::op_iterator OI = instr->op_begin(), OE = instr->op_end();
OI != OE; ++OI) {
Value *operand = *OI;
if (!isInvariant(loop, invariants, operand)) {
return false;
}
}
// Satisfies all conditions.
return true;
}
Stokhos::ProductLanczosPCEBasis<ordinal_type, value_type>::
ProductLanczosPCEBasis(
ordinal_type p,
const Teuchos::Array< Stokhos::OrthogPolyApprox<ordinal_type, value_type> >& pce,
const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad,
const Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk,
const Teuchos::ParameterList& params_) :
name("Product Lanczos PCE Basis"),
params(params_)
{
Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type,value_type> > pce_basis = pce[0].basis();
ordinal_type pce_sz = pce_basis->size();
// Check if basis is a product basis
Teuchos::RCP<const Stokhos::ProductBasis<ordinal_type,value_type> > prod_basis = Teuchos::rcp_dynamic_cast<const Stokhos::ProductBasis<ordinal_type,value_type> >(pce_basis);
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,value_type> > > coord_bases;
if (prod_basis != Teuchos::null)
coord_bases = prod_basis->getCoordinateBases();
// Build Lanczos basis for each pce
bool project = params.get("Project", true);
bool normalize = params.get("Normalize", true);
bool limit_integration_order = params.get("Limit Integration Order", false);
bool use_stieltjes = params.get("Use Old Stieltjes Method", false);
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double > > > coordinate_bases;
Teuchos::Array<int> is_invariant(pce.size(),-2);
for (ordinal_type i=0; i<pce.size(); i++) {
// Check for pce's lying in invariant subspaces, which are pce's that
// depend on only a single dimension. In this case use the corresponding
// original coordinate basis. Convention is: -2 -- not invariant, -1 --
// constant, i >= 0 pce depends only on dimension i
if (prod_basis != Teuchos::null)
is_invariant[i] = isInvariant(pce[i]);
if (is_invariant[i] >= 0) {
coordinate_bases.push_back(coord_bases[is_invariant[i]]);
}
// Exclude constant pce's from the basis since they don't represent
// stochastic dimensions
else if (is_invariant[i] != -1) {
if (use_stieltjes) {
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::StieltjesPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), quad, false,
normalize, project, Cijk)));
}
else {
if (project)
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::LanczosProjPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), Cijk,
normalize, limit_integration_order)));
else
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::LanczosPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), quad,
normalize, limit_integration_order)));
}
}
}
ordinal_type d = coordinate_bases.size();
// Build tensor product basis
tensor_lanczos_basis =
Teuchos::rcp(
new Stokhos::CompletePolynomialBasis<ordinal_type,value_type>(
coordinate_bases,
params.get("Cijk Drop Tolerance", 1.0e-15),
params.get("Use Old Cijk Algorithm", false)));
// Build reduced quadrature
Teuchos::ParameterList sg_params;
sg_params.sublist("Basis").set< Teuchos::RCP< const Stokhos::OrthogPolyBasis<ordinal_type,value_type> > >("Stochastic Galerkin Basis", tensor_lanczos_basis);
sg_params.sublist("Quadrature") = params.sublist("Reduced Quadrature");
reduced_quad =
Stokhos::QuadratureFactory<ordinal_type,value_type>::create(sg_params);
// Build Psi matrix -- Psi_ij = Psi_i(x^j)*w_j/<Psi_i^2>
const Teuchos::Array<value_type>& weights = quad->getQuadWeights();
const Teuchos::Array< Teuchos::Array<value_type> >& points =
quad->getQuadPoints();
const Teuchos::Array< Teuchos::Array<value_type> >& basis_vals =
quad->getBasisAtQuadPoints();
ordinal_type nqp = weights.size();
SDM Psi(pce_sz, nqp);
for (ordinal_type i=0; i<pce_sz; i++)
for (ordinal_type k=0; k<nqp; k++)
Psi(i,k) = basis_vals[k][i]*weights[k]/pce_basis->norm_squared(i);
// Build Phi matrix -- Phi_ij = Phi_i(y(x^j))
ordinal_type sz = tensor_lanczos_basis->size();
Teuchos::Array<value_type> red_basis_vals(sz);
Teuchos::Array<value_type> pce_vals(d);
Phi.shape(sz, nqp);
for (int k=0; k<nqp; k++) {
ordinal_type jdx = 0;
for (int j=0; j<pce.size(); j++) {
// Exclude constant pce's
if (is_invariant[j] != -1) {
// Use the identity mapping for invariant subspaces
if (is_invariant[j] >= 0)
pce_vals[jdx] = points[k][is_invariant[j]];
else
pce_vals[jdx] = pce[j].evaluate(points[k], basis_vals[k]);
jdx++;
}
}
tensor_lanczos_basis->evaluateBases(pce_vals, red_basis_vals);
for (int i=0; i<sz; i++)
Phi(i,k) = red_basis_vals[i];
}
bool verbose = params.get("Verbose", false);
// Compute matrix A mapping reduced space to original
A.shape(pce_sz, sz);
ordinal_type ret =
A.multiply(Teuchos::NO_TRANS, Teuchos::TRANS, 1.0, Psi, Phi, 0.0);
TEUCHOS_ASSERT(ret == 0);
//print_matlab(std::cout << "A = " << std::endl, A);
// Compute pseudo-inverse of A mapping original space to reduced
// A = U*S*V^T -> A^+ = V*S^+*U^T = (S^+*V^T)^T*U^T where
// S^+ is a diagonal matrix comprised of the inverse of the diagonal of S
// for each nonzero, and zero otherwise
Teuchos::Array<value_type> sigma;
SDM U, Vt;
value_type rank_threshold = params.get("Rank Threshold", 1.0e-12);
ordinal_type rank = svd_threshold(rank_threshold, A, sigma, U, Vt);
Ainv.shape(sz, pce_sz);
TEUCHOS_ASSERT(rank == Vt.numRows());
for (ordinal_type i=0; i<Vt.numRows(); i++)
for (ordinal_type j=0; j<Vt.numCols(); j++)
Vt(i,j) = Vt(i,j) / sigma[i];
ret = Ainv.multiply(Teuchos::TRANS, Teuchos::TRANS, 1.0, Vt, U, 0.0);
TEUCHOS_ASSERT(ret == 0);
//print_matlab(std::cout << "Ainv = " << std::endl, Ainv);
if (verbose) {
std::cout << "rank = " << rank << std::endl;
std::cout << "diag(S) = [";
for (ordinal_type i=0; i<rank; i++)
std::cout << sigma[i] << " ";
std::cout << "]" << std::endl;
// Check A = U*S*V^T
SDM SVt(rank, Vt.numCols());
for (ordinal_type i=0; i<Vt.numRows(); i++)
for (ordinal_type j=0; j<Vt.numCols(); j++)
SVt(i,j) = Vt(i,j) * sigma[i] * sigma[i]; // since we divide by sigma
// above
SDM err_A(pce_sz,sz);
err_A.assign(A);
ret = err_A.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, -1.0, U, SVt,
1.0);
TEUCHOS_ASSERT(ret == 0);
std::cout << "||A - U*S*V^T||_infty = " << err_A.normInf() << std::endl;
//print_matlab(std::cout << "A - U*S*V^T = " << std::endl, err_A);
// Check Ainv*A == I
SDM err(sz,sz);
err.putScalar(0.0);
for (ordinal_type i=0; i<sz; i++)
err(i,i) = 1.0;
ret = err.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, Ainv, A,
-1.0);
TEUCHOS_ASSERT(ret == 0);
std::cout << "||Ainv*A - I||_infty = " << err.normInf() << std::endl;
//print_matlab(std::cout << "Ainv*A-I = " << std::endl, err);
// Check A*Ainv == I
SDM err2(pce_sz,pce_sz);
err2.putScalar(0.0);
for (ordinal_type i=0; i<pce_sz; i++)
err2(i,i) = 1.0;
ret = err2.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, A, Ainv, -1.0);
TEUCHOS_ASSERT(ret == 0);
std::cout << "||A*Ainv - I||_infty = " << err2.normInf() << std::endl;
//print_matlab(std::cout << "A*Ainv-I = " << std::endl, err2);
}
}
Stokhos::ProductLanczosGramSchmidtPCEBasis<ordinal_type, value_type>::
ProductLanczosGramSchmidtPCEBasis(
ordinal_type max_p,
const Teuchos::Array< Stokhos::OrthogPolyApprox<ordinal_type, value_type> >& pce,
const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad,
const Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk,
const Teuchos::ParameterList& params_) :
name("Product Lanczos Gram-Schmidt PCE Basis"),
params(params_),
p(max_p)
{
Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type,value_type> > pce_basis = pce[0].basis();
pce_sz = pce_basis->size();
// Check if basis is a product basis
Teuchos::RCP<const Stokhos::ProductBasis<ordinal_type,value_type> > prod_basis = Teuchos::rcp_dynamic_cast<const Stokhos::ProductBasis<ordinal_type,value_type> >(pce_basis);
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,value_type> > > coord_bases;
if (prod_basis != Teuchos::null)
coord_bases = prod_basis->getCoordinateBases();
// Build Lanczos basis for each pce
bool project = params.get("Project", true);
bool normalize = params.get("Normalize", true);
bool limit_integration_order = params.get("Limit Integration Order", false);
bool use_stieltjes = params.get("Use Old Stieltjes Method", false);
Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double > > > coordinate_bases;
Teuchos::Array<int> is_invariant(pce.size(),-2);
for (ordinal_type i=0; i<pce.size(); i++) {
// Check for pce's lying in invariant subspaces, which are pce's that
// depend on only a single dimension. In this case use the corresponding
// original coordinate basis. Convention is: -2 -- not invariant, -1 --
// constant, i >= 0 pce depends only on dimension i
if (prod_basis != Teuchos::null)
is_invariant[i] = isInvariant(pce[i]);
if (is_invariant[i] >= 0) {
coordinate_bases.push_back(coord_bases[is_invariant[i]]);
}
// Exclude constant pce's from the basis since they don't represent
// stochastic dimensions
else if (is_invariant[i] != -1) {
if (use_stieltjes) {
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::StieltjesPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), quad, false,
normalize, project, Cijk)));
}
else {
if (project)
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::LanczosProjPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), Cijk,
normalize, limit_integration_order)));
else
coordinate_bases.push_back(
Teuchos::rcp(
new Stokhos::LanczosPCEBasis<ordinal_type,value_type>(
p, Teuchos::rcp(&(pce[i]),false), quad,
normalize, limit_integration_order)));
}
}
}
d = coordinate_bases.size();
// Build tensor product basis
tensor_lanczos_basis =
Teuchos::rcp(
new Stokhos::CompletePolynomialBasis<ordinal_type,value_type>(
coordinate_bases,
params.get("Cijk Drop Tolerance", 1.0e-15),
params.get("Use Old Cijk Algorithm", false)));
// Build Psi matrix -- Psi_ij = Psi_i(x^j)*w_j/<Psi_i^2>
const Teuchos::Array<value_type>& weights = quad->getQuadWeights();
const Teuchos::Array< Teuchos::Array<value_type> >& points =
quad->getQuadPoints();
const Teuchos::Array< Teuchos::Array<value_type> >& basis_vals =
quad->getBasisAtQuadPoints();
ordinal_type nqp = weights.size();
SDM Psi(pce_sz, nqp);
for (ordinal_type i=0; i<pce_sz; i++)
for (ordinal_type k=0; k<nqp; k++)
Psi(i,k) = basis_vals[k][i]*weights[k]/pce_basis->norm_squared(i);
// Build Phi matrix -- Phi_ij = Phi_i(y(x^j))
sz = tensor_lanczos_basis->size();
Teuchos::Array<value_type> red_basis_vals(sz);
Teuchos::Array<value_type> pce_vals(d);
SDM Phi(sz, nqp);
SDM F(nqp, d);
for (int k=0; k<nqp; k++) {
ordinal_type jdx = 0;
for (int j=0; j<pce.size(); j++) {
// Exclude constant pce's
if (is_invariant[j] != -1) {
// Use the identity mapping for invariant subspaces
if (is_invariant[j] >= 0)
pce_vals[jdx] = points[k][is_invariant[j]];
else
pce_vals[jdx] = pce[j].evaluate(points[k], basis_vals[k]);
F(k,jdx) = pce_vals[jdx];
jdx++;
}
}
tensor_lanczos_basis->evaluateBases(pce_vals, red_basis_vals);
for (int i=0; i<sz; i++)
Phi(i,k) = red_basis_vals[i];
}
bool verbose = params.get("Verbose", false);
// Compute matrix A mapping reduced space to original
SDM A(pce_sz, sz);
ordinal_type ret =
A.multiply(Teuchos::NO_TRANS, Teuchos::TRANS, 1.0, Psi, Phi, 0.0);
TEUCHOS_ASSERT(ret == 0);
// Rescale columns of A to have unit norm
const Teuchos::Array<value_type>& basis_norms = pce_basis->norm_squared();
for (ordinal_type j=0; j<sz; j++) {
value_type nrm = 0.0;
for (ordinal_type i=0; i<pce_sz; i++)
nrm += A(i,j)*A(i,j)*basis_norms[i];
nrm = std::sqrt(nrm);
for (ordinal_type i=0; i<pce_sz; i++)
A(i,j) /= nrm;
}
// Compute our new basis -- each column of Qp is the coefficients of the
// new basis in the original basis. Constraint pivoting so first d+1
// columns and included in Qp.
value_type rank_threshold = params.get("Rank Threshold", 1.0e-12);
std::string orthogonalization_method =
params.get("Orthogonalization Method", "Householder");
Teuchos::Array<value_type> w(pce_sz, 1.0);
SDM R;
Teuchos::Array<ordinal_type> piv(sz);
for (int i=0; i<d+1; i++)
piv[i] = 1;
typedef Stokhos::OrthogonalizationFactory<ordinal_type,value_type> SOF;
sz = SOF::createOrthogonalBasis(
orthogonalization_method, rank_threshold, verbose, A, w, Qp, R, piv);
// Original basis at quadrature points -- needed to transform expansions
// in this basis back to original
SDM B(nqp, pce_sz);
for (ordinal_type i=0; i<nqp; i++)
for (ordinal_type j=0; j<pce_sz; j++)
B(i,j) = basis_vals[i][j];
// Evaluate new basis at original quadrature points
Q.reshape(nqp, sz);
ret = Q.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, B, Qp, 0.0);
TEUCHOS_ASSERT(ret == 0);
// Compute reduced quadrature rule
Stokhos::ReducedQuadratureFactory<ordinal_type,value_type> quad_factory(
params.sublist("Reduced Quadrature"));
Teuchos::SerialDenseMatrix<ordinal_type, value_type> Q2;
reduced_quad = quad_factory.createReducedQuadrature(Q, Q2, F, weights);
// Basis is orthonormal by construction
norms.resize(sz, 1.0);
}
