/usr/include/trilinos/Stokhos_TensorProductPseudoSpectralOperator.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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// ***********************************************************************
//
// Stokhos Package
// Copyright (2009) Sandia Corporation
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#ifndef STOKHOS_TENSOR_PRODUCT_PSEUDO_SPECTRAL_OPERATOR_HPP
#define STOKHOS_TENSOR_PRODUCT_PSEUDO_SPECTRAL_OPERATOR_HPP
#include "Stokhos_PseudoSpectralOperator.hpp"
#include "Stokhos_ProductBasis.hpp"
#include "Stokhos_TensorProductBasis.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_BLAS.hpp"
namespace Stokhos {
/*!
* \brief An operator for building pseudo-spectral coefficients using
* tensor-product quadrature.
*/
template <typename ordinal_t,
typename value_t,
typename point_compare_type =
typename DefaultPointCompare<ordinal_t,value_t>::type>
class TensorProductPseudoSpectralOperator :
public PseudoSpectralOperator<ordinal_t,value_t,point_compare_type> {
public:
typedef ordinal_t ordinal_type;
typedef value_t value_type;
typedef PseudoSpectralOperator<ordinal_type,value_type,point_compare_type> base_type;
typedef typename base_type::point_type point_type;
typedef typename base_type::point_set_type point_set_type;
typedef typename base_type::point_map_type point_map_type;
typedef typename base_type::iterator iterator;
typedef typename base_type::const_iterator const_iterator;
typedef typename base_type::set_iterator set_iterator;
typedef typename base_type::const_set_iterator const_set_iterator;
typedef MultiIndex<ordinal_type> multiindex_type;
//! Constructor
TensorProductPseudoSpectralOperator(
const ProductBasis<ordinal_type,value_type>& product_basis,
bool use_pst_ = false,
multiindex_type multiindex = multiindex_type(),
const point_compare_type& point_compare = point_compare_type()) :
use_pst(use_pst_),
coeff_sz(product_basis.size()),
dim(product_basis.dimension()),
points(point_compare),
reorder(false) {
// Check if we need to reorder for PST
// This isn't a perfect test since it doesn't catch not tensor-product
// bases
typedef LexographicLess< MultiIndex<ordinal_type> > lexo_type;
if (use_pst) {
typedef TensorProductBasis<ordinal_type,value_type,lexo_type> tb_type;
const tb_type *tb = dynamic_cast<const tb_type*>(&product_basis);
if (tb == NULL)
reorder = true;
}
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,value_type> > > bases_ = product_basis.getCoordinateBases();
// Make sure order of each 1-D basis is large enough for
// supplied set of coefficients
Teuchos::Array< Teuchos::RCP<const OneDOrthogPolyBasis<ordinal_type,value_type> > > bases(bases_);
multiindex_type max_orders = product_basis.getMaxOrders();
for (ordinal_type i=0; i<dim; ++i) {
if (bases[i]->order() < max_orders[i])
bases[i] = bases[i]->cloneWithOrder(max_orders[i]);
}
// Check for default quadrature order
if (multiindex.dimension() == 0)
multiindex = max_orders;
// Compute quad points, weights, values
Teuchos::Array< Teuchos::Array<value_type> > gp(dim);
Teuchos::Array< Teuchos::Array<value_type> > gw(dim);
Teuchos::Array< Teuchos::Array< Teuchos::Array<value_type> > > gv(dim);
multiindex_type n(dim);
if (use_pst) {
qp2pce_k.resize(dim);
pce2qp_k.resize(dim);
}
for (ordinal_type k=0; k<dim; k++) {
bases[k]->getQuadPoints(2*multiindex[k], gp[k], gw[k], gv[k]);
n[k] = gp[k].size()-1;
// Generate quadrature operators for PST
if (use_pst) {
ordinal_type npc = bases[k]->size();
ordinal_type nqp = gp[k].size();
qp2pce_k[k].reshape(npc,nqp);
pce2qp_k[k].reshape(nqp,npc);
qp2pce_k[k].putScalar(1.0);
pce2qp_k[k].putScalar(1.0);
for (ordinal_type j=0; j<nqp; j++) {
for (ordinal_type i=0; i<npc; i++) {
qp2pce_k[k](i,j) *= gw[k][j]*gv[k][j][i] /
bases[k]->norm_squared(i);
pce2qp_k[k](j,i) *= gv[k][j][i];
}
}
}
}
// Generate points and weights
Stokhos::TensorProductIndexSet<ordinal_type> pointIndexSet(n);
typedef typename TensorProductIndexSet<ordinal_type>::iterator index_iterator;
index_iterator point_iterator = pointIndexSet.begin();
index_iterator point_end = pointIndexSet.end();
point_type point(dim);
while (point_iterator != point_end) {
value_type w = 1.0;
for (ordinal_type k=0; k<dim; k++) {
point[k] = gp[k][(*point_iterator)[k]];
w *= gw[k][(*point_iterator)[k]];
}
points[point] = std::make_pair(w,ordinal_type(0));
++point_iterator;
}
// Generate linear ordering of points
ordinal_type nqp = points.size();
point_map.resize(nqp);
ordinal_type idx=0;
typename point_set_type::iterator di = points.begin();
typename point_set_type::iterator di_end = points.end();
while (di != di_end) {
di->second.second = idx;
point_map[idx] = di->first;
++idx;
++di;
}
// Build permutation array for reordering if coefficients aren't
// lexographically ordered
if (use_pst && reorder) {
typedef std::map<multiindex_type,ordinal_type,lexo_type> reorder_type;
reorder_type reorder_map;
for (ordinal_type i=0; i<coeff_sz; ++i)
reorder_map[product_basis.term(i)] = i;
perm.resize(coeff_sz);
ordinal_type idx = 0;
for (typename reorder_type::iterator it = reorder_map.begin();
it != reorder_map.end(); ++it)
perm[idx++] = it->second;
TEUCHOS_ASSERT(idx == coeff_sz);
}
// Generate quadrature operator for direct apply
// Always do this because we may not use PST in some situations
ordinal_type npc = product_basis.size();
qp2pce.reshape(npc,nqp);
pce2qp.reshape(nqp,npc);
qp2pce.putScalar(1.0);
pce2qp.putScalar(1.0);
for (point_iterator = pointIndexSet.begin();
point_iterator != point_end;
++point_iterator) {
for (ordinal_type k=0; k<dim; k++)
point[k] = gp[k][(*point_iterator)[k]];
ordinal_type j = points[point].second;
for (ordinal_type i=0; i<npc; i++) {
for (ordinal_type k=0; k<dim; k++) {
ordinal_type l = (*point_iterator)[k];
ordinal_type m = product_basis.term(i)[k];
qp2pce(i,j) *= gw[k][l]*gv[k][l][m] / bases[k]->norm_squared(m);
pce2qp(j,i) *= gv[k][l][m];
}
}
}
}
//! Destructor
virtual ~TensorProductPseudoSpectralOperator() {}
//! Number of points
ordinal_type point_size() const { return points.size(); }
//! Number of coefficients
ordinal_type coeff_size() const { return coeff_sz; }
//! Iterator to begining of point set
iterator begin() { return point_map.begin(); }
//! Iterator to end of point set
iterator end() { return point_map.end(); }
//! Iterator to begining of point set
const_iterator begin() const { return point_map.begin(); }
//! Iterator to end of point set
const_iterator end() const { return point_map.end(); }
//! Iterator to begining of point set
set_iterator set_begin() { return points.begin(); }
//! Iterator to end of point set
set_iterator set_end() { return points.end(); }
//! Iterator to begining of point set
const_set_iterator set_begin() const { return points.begin(); }
//! Iterator to end of point set
const_set_iterator set_end() const { return points.end(); }
//! Get point index for given point
ordinal_type index(const point_type& point) const {
const_set_iterator it = points.find(point);
TEUCHOS_TEST_FOR_EXCEPTION(
it == points.end(), std::logic_error, "Invalid term " << point);
return it->second.second;
}
//! Get point for given index
const point_type& point(ordinal_type n) const { return point_map[n]; }
//! Transform values at quadrature points to PCE coefficients
/*!
* \c input is a vector storing values of a function at the quadrature
* points, and \c result will contain the resulting polynomial chaos
* coefficients. \c input and \c result can have multiple columns for
* vector-valued functions and set \c trans to true if these (multi-)
* vectors are layed out in a transposed fashion.
*/
virtual void transformQP2PCE(
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans = false) const {
if (use_pst)
apply_pst(qp2pce_k, alpha, input, result, beta, trans, false, reorder);
else
apply_direct(qp2pce, alpha, input, result, beta, trans);
}
//! Transform PCE coefficients to quadrature values
/*!
* \c input is a vector storing polynomial chaos coefficients
* and \c result will contain the resulting values at the quadrature points.
* \c input and \c result can have multiple columns for
* vector-valued functions and set \c trans to true if these (multi-)
* vectors are layed out in a transposed fashion.
*/
virtual void transformPCE2QP(
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans = false) const {
// Only use PST if it was requested and number of rows/columns match
// (since we may allow fewer rows in input than columns of pce2qp)
bool can_use_pst = use_pst;
if (trans)
can_use_pst = can_use_pst && (input.numCols() == pce2qp.numRows());
else
can_use_pst = can_use_pst && (input.numRows() == pce2qp.numRows());
if (can_use_pst)
apply_pst(pce2qp_k, alpha, input, result, beta, trans, reorder, false);
else
apply_direct(pce2qp, alpha, input, result, beta, trans);
}
protected:
//! Apply transformation operator using direct method
void apply_direct(
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& A,
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans) const {
if (trans) {
TEUCHOS_ASSERT(input.numCols() <= A.numCols());
TEUCHOS_ASSERT(result.numCols() == A.numRows());
TEUCHOS_ASSERT(result.numRows() == input.numRows());
blas.GEMM(Teuchos::NO_TRANS, Teuchos::TRANS, input.numRows(),
A.numRows(), input.numCols(), alpha, input.values(),
input.stride(), A.values(), A.stride(), beta,
result.values(), result.stride());
}
else {
TEUCHOS_ASSERT(input.numRows() <= A.numCols());
TEUCHOS_ASSERT(result.numRows() == A.numRows());
TEUCHOS_ASSERT(result.numCols() == input.numCols());
blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS, A.numRows(),
input.numCols(), input.numRows(), alpha, A.values(),
A.stride(), input.values(), input.stride(), beta,
result.values(), result.stride());
}
}
//! Apply tranformation operator using PST method
/*!
* For k=1,...,d, let A_k be the m_k-by-n_k quadrature operator for
* dimension k and A = A_1 \otimes ... \otimes A_d be m-\by-n where
* m = m_1...m_d and n = n_1...n_d. For any two matrices
* B and C and vector x, (B \otimes C)x = vec( C*X*B^T ) =
* vec( C*(B*X^T)^T ) where x = vec(X), and the vec() operator makes a
* vector out of a matrix by stacking columns. Applying this formula
* recursively to A yields the simple algorithm for computing y = A*x
* (x is n-by-1 and y is m-by-1):
* X = x;
* for k=1:d
* n = n / n_k;
* X = reshape(X, n, n_k);
* X = A_k*X';
* n = n * m_k;
* end
* y = reshape(X, m, 1);
*
* When x has p columns, it is somehwat more complicated because the
* standard transpose above isn't correct. Instead the transpose
* needs to be applied to each p block in X.
*
* The strategy here for dealing with transposed input and result
* is to transpose them when copying to/from the temporary buffers
* used in the algorithm.
*/
void apply_pst(
const Teuchos::Array< Teuchos::SerialDenseMatrix<ordinal_type,value_type> >& Ak,
const value_type& alpha,
const Teuchos::SerialDenseMatrix<ordinal_type,value_type>& input,
Teuchos::SerialDenseMatrix<ordinal_type,value_type>& result,
const value_type& beta,
bool trans,
bool reorder_input,
bool reorder_result) const {
ordinal_type n, m, p;
if (trans) {
TEUCHOS_ASSERT(input.numRows() == result.numRows());
n = input.numCols();
p = input.numRows();
m = result.numCols();
}
else {
TEUCHOS_ASSERT(input.numCols() == result.numCols());
n = input.numRows();
p = input.numCols();
m = result.numRows();
}
ordinal_type M = 1;
ordinal_type N = 1;
for (ordinal_type k=0; k<dim; ++k) {
M *= Ak[k].numRows();
N *= Ak[k].numCols();
}
TEUCHOS_ASSERT(n == N);
TEUCHOS_ASSERT(m == M);
ordinal_type sz = std::max(n,m);
// Temporary buffers used in algorithm
Teuchos::Array<value_type> tmp1(sz*p), tmp2(sz*p);
// Copy input to tmp1 (transpose if necessary)
if (trans) {
if (reorder_input) {
ordinal_type idx;
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<n; i++) {
idx = perm[i];
tmp1[i+j*n] = input(j,idx);
}
}
else {
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<n; i++)
tmp1[i+j*n] = input(j,i);
}
}
else {
if (reorder_input) {
ordinal_type idx;
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<n; i++) {
idx = perm[i];
tmp1[i+j*n] = input(idx,j);
}
}
else {
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<n; i++)
tmp1[i+j*n] = input(i,j);
}
}
// Loop over each term in Kronecker product
for (ordinal_type k=0; k<dim; k++) {
ordinal_type mk = Ak[k].numRows();
ordinal_type nk = Ak[k].numCols();
n = n / nk;
// x = reshape(x, n, n_k)
Teuchos::SerialDenseMatrix<ordinal_type,value_type> x(
Teuchos::View, &tmp1[0], n, n, nk*p);
// y = x'
Teuchos::SerialDenseMatrix<ordinal_type,value_type> y(
Teuchos::View, &tmp2[0], nk, nk, n*p);
for (ordinal_type l=0; l<p; l++)
for (ordinal_type j=0; j<n; j++)
for (ordinal_type i=0; i<nk; i++)
y(i,j+l*n) = x(j,i+l*nk);
// x = A_k*x
Teuchos::SerialDenseMatrix<ordinal_type,value_type> z(
Teuchos::View, &tmp1[0], mk, mk, n*p);
ordinal_type ret =
z.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, Ak[k], y, 0.0);
TEUCHOS_ASSERT(ret == 0);
n = n * mk;
}
// Sum answer into result (transposing and/or reordering if necessary)
if (trans) {
if (reorder_result) {
ordinal_type idx;
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<m; i++) {
idx = perm[i];
result(j,idx) = beta*result(j,idx) + alpha*tmp1[i+j*m];
}
}
else {
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<m; i++)
result(j,i) = beta*result(j,i) + alpha*tmp1[i+j*m];
}
}
else {
if (reorder_result) {
ordinal_type idx;
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<m; i++) {
idx = perm[i];
result(idx,j) = beta*result(idx,j) + alpha*tmp1[i+j*m];
}
}
else {
for (ordinal_type j=0; j<p; j++)
for (ordinal_type i=0; i<m; i++)
result(i,j) = beta*result(i,j) + alpha*tmp1[i+j*m];
}
}
}
protected:
//! Use partial-summation-transformation
bool use_pst;
//! Number of coefficients
ordinal_type coeff_sz;
//! Dimension
ordinal_type dim;
//! Quadrature points
point_set_type points;
//! Map index to point term
point_map_type point_map;
//! Do we need to reorder coefficients for PST
bool reorder;
//! Permutation array when reordering for PST
Teuchos::Array<ordinal_type> perm;
//! Matrix mapping points to coefficients
Teuchos::SerialDenseMatrix<ordinal_type,value_type> qp2pce;
//! Matrix mapping coefficients to points
Teuchos::SerialDenseMatrix<ordinal_type,value_type> pce2qp;
//! Matrix mapping points to coefficients for each dimension for PST
Teuchos::Array< Teuchos::SerialDenseMatrix<ordinal_type,value_type> > qp2pce_k;
//! Matrix mapping coefficients to points for each dimension for PST
Teuchos::Array< Teuchos::SerialDenseMatrix<ordinal_type,value_type> > pce2qp_k;
//! BLAS wrappers
Teuchos::BLAS<ordinal_type,value_type> blas;
};
}
#endif
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