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opm-simulators/opm/autodiff/AutoDiffHelpers.hpp
babrodtk 38865cac31 Cleaned up comments
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/*
Copyright 2013 SINTEF ICT, Applied Mathematics.
Copyright 2015 IRIS
This file is part of the Open Porous Media project (OPM).
OPM is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OPM is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with OPM. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef OPM_AUTODIFFHELPERS_HEADER_INCLUDED
#define OPM_AUTODIFFHELPERS_HEADER_INCLUDED
#include <opm/autodiff/AutoDiffBlock.hpp>
#include <opm/autodiff/GridHelpers.hpp>
#include <opm/core/grid.h>
#include <opm/core/utility/ErrorMacros.hpp>
#include <opm/parser/eclipse/EclipseState/Grid/NNC.hpp>
#include <opm/parser/eclipse/EclipseState/EclipseState.hpp>
#include <iostream>
#include <vector>
namespace Opm
{
// -------------------- class HelperOps --------------------
/// Contains vectors and sparse matrices that represent subsets or
/// operations on (AD or regular) vectors of data.
struct HelperOps
{
typedef Eigen::SparseMatrix<double> M;
typedef AutoDiffBlock<double>::V V;
/// A list of internal faces.
typedef Eigen::Array<int, Eigen::Dynamic, 1> IFaces;
IFaces internal_faces;
/// Extract for each internal face the difference of its adjacent cells' values (first - second).
M ngrad;
/// Extract for each face the difference of its adjacent cells' values (second - first).
M grad;
/// Extract for each face the average of its adjacent cells' values.
M caver;
/// Extract for each cell the sum of its adjacent interior faces' (signed) values.
M div;
/// Extract for each face the difference of its adjacent cells' values (first - second).
/// For boundary faces, one of the entries per row (corresponding to the outside) is zero.
M fullngrad;
/// Extract for each cell the sum of all its adjacent faces' (signed) values.
M fulldiv;
/// Non-neighboring connections
typedef Eigen::Array<int, Eigen::Dynamic, 2, Eigen::RowMajor> TwoColInt;
TwoColInt nnc_cells;
/// The NNC transmissibilities
V nnc_trans;
/// Constructs all helper vectors and matrices.
template<class Grid>
HelperOps(const Grid& grid, Opm::EclipseStateConstPtr eclState = EclipseStateConstPtr () )
{
using namespace AutoDiffGrid;
const int nc = numCells(grid);
const int nf = numFaces(grid);
// Define some neighbourhood-derived helper arrays.
TwoColInt nbi;
extractInternalFaces(grid, internal_faces, nbi);
int num_internal = internal_faces.size();
// num_connections may also include non-neighboring connections
int num_connections = num_internal;
int numNNC = 0;
// handle non-neighboring connections
std::shared_ptr<const NNC> nnc = eclState ? eclState->getNNC()
: std::shared_ptr<const Opm::NNC>();
const bool has_nnc = nnc && nnc->hasNNC();
if (has_nnc) {
numNNC = nnc->numNNC();
num_connections += numNNC;
//std::cout << "Added " << numNNC << " NNC" <<std::endl;
nbi.resize(num_internal, 2);
// the nnc's acts on global indicies and must be mapped to cell indicies
size_t cartesianSize = eclState->getEclipseGrid()->getCartesianSize();
std::vector<int> global2localIdx(cartesianSize,0);
for (int i = 0; i< nc; ++i) {
global2localIdx[ globalCell( grid )[i] ] = i;
}
const std::vector<size_t>& NNC1 = nnc->nnc1();
const std::vector<size_t>& NNC2 = nnc->nnc2();
nnc_cells.resize(numNNC,2);
for (int i = 0; i < numNNC; ++i) {
nnc_cells(i,0) = global2localIdx[NNC1[i]];
nnc_cells(i,1) = global2localIdx[NNC2[i]];
}
// store the nnc transmissibilities for later usage.
nnc_trans = Eigen::Map<const V>(nnc->trans().data(), numNNC);
} else {
nnc_trans.resize(0);
nnc_cells.resize(0, 2); // Required to have two columns.
}
// std::cout << "nbi = \n" << nbi << std::endl;
// Create matrices.
ngrad.resize(num_connections, nc);
caver.resize(num_connections, nc);
typedef Eigen::Triplet<double> Tri;
std::vector<Tri> ngrad_tri;
std::vector<Tri> caver_tri;
ngrad_tri.reserve(2*num_connections);
caver_tri.reserve(2*num_connections);
for (int i = 0; i < num_internal; ++i) {
ngrad_tri.emplace_back(i, nbi(i,0), 1.0);
ngrad_tri.emplace_back(i, nbi(i,1), -1.0);
caver_tri.emplace_back(i, nbi(i,0), 0.5);
caver_tri.emplace_back(i, nbi(i,1), 0.5);
}
// add contribution from NNC
if (has_nnc) {
for (int i = 0; i < numNNC; ++i) {
ngrad_tri.emplace_back(i+num_internal, nnc_cells(i,0), 1.0);
ngrad_tri.emplace_back(i+num_internal, nnc_cells(i,1), -1.0);
caver_tri.emplace_back(i+num_internal, nnc_cells(i,0), 0.5);
caver_tri.emplace_back(i+num_internal, nnc_cells(i,1), 0.5);
}
}
ngrad.setFromTriplets(ngrad_tri.begin(), ngrad_tri.end());
caver.setFromTriplets(caver_tri.begin(), caver_tri.end());
grad = -ngrad;
div = ngrad.transpose();
std::vector<Tri> fullngrad_tri;
fullngrad_tri.reserve(2*(nf+numNNC));
typename ADFaceCellTraits<Grid>::Type nb = faceCellsToEigen(grid);
for (int i = 0; i < nf; ++i) {
if (nb(i,0) >= 0) {
fullngrad_tri.emplace_back(i, nb(i,0), 1.0);
}
if (nb(i,1) >= 0) {
fullngrad_tri.emplace_back(i, nb(i,1), -1.0);
}
}
// add contribution from NNC
if (has_nnc) {
for (int i = 0; i < numNNC; ++i) {
fullngrad_tri.emplace_back(i+nf, nnc_cells(i,0), 1.0);
fullngrad_tri.emplace_back(i+nf, nnc_cells(i,1), -1.0);
}
}
fullngrad.resize(nf+numNNC, nc);
fullngrad.setFromTriplets(fullngrad_tri.begin(), fullngrad_tri.end());
fulldiv = fullngrad.transpose();
}
};
// -------------------- upwinding helper class --------------------
/// Upwind selection in absence of counter-current flow (i.e.,
/// without effects of gravity and/or capillary pressure).
template <typename Scalar>
class UpwindSelector {
public:
typedef AutoDiffBlock<Scalar> ADB;
template<class Grid>
UpwindSelector(const Grid& g,
const HelperOps& h,
const typename ADB::V& ifaceflux)
{
using namespace AutoDiffGrid;
typedef HelperOps::IFaces::Index IFIndex;
const IFIndex nif = h.internal_faces.size();
typename ADFaceCellTraits<Grid>::Type
face_cells = faceCellsToEigen(g);
// num connections may possibly include NNCs
int num_nnc = h.nnc_trans.size();
int num_connections = nif + num_nnc;
assert(num_connections == ifaceflux.size());
// Define selector structure.
typedef typename Eigen::Triplet<Scalar> Triplet;
std::vector<Triplet> s; s.reserve(num_connections);
for (IFIndex iface = 0; iface < nif; ++iface) {
const int f = h.internal_faces[iface];
const int c1 = face_cells(f,0);
const int c2 = face_cells(f,1);
assert ((c1 >= 0) && (c2 >= 0));
// Select upwind cell.
const int c = (ifaceflux[iface] >= 0) ? c1 : c2;
s.push_back(Triplet(iface, c, Scalar(1)));
}
if (num_nnc > 0) {
for (int i = 0; i < num_nnc; ++i) {
const int c = (ifaceflux[i+nif] >= 0) ? h.nnc_cells(i,0) : h.nnc_cells(i,1);
s.push_back(Triplet(i+nif,c,Scalar(1)));
}
}
// Assemble explicit selector operator.
select_.resize(num_connections, numCells(g));
select_.setFromTriplets(s.begin(), s.end());
}
/// Apply selector to multiple per-cell quantities.
std::vector<ADB>
select(const std::vector<ADB>& xc) const
{
// Absence of counter-current flow means that the same
// selector applies to all quantities, 'x', defined per
// cell.
std::vector<ADB> xf; xf.reserve(xc.size());
for (typename std::vector<ADB>::const_iterator
b = xc.begin(), e = xc.end(); b != e; ++b)
{
xf.push_back(select_ * (*b));
}
return xf;
}
/// Apply selector to single per-cell ADB quantity.
ADB select(const ADB& xc) const
{
return select_*xc;
}
/// Apply selector to single per-cell constant quantity.
typename ADB::V select(const typename ADB::V& xc) const
{
return (select_*xc.matrix()).array();
}
private:
Eigen::SparseMatrix<double> select_;
};
namespace {
template <typename Scalar, class IntVec>
typename Eigen::SparseMatrix<Scalar>
constructSupersetSparseMatrix(const int full_size, const IntVec& indices)
{
const int subset_size = indices.size();
if (subset_size == 0) {
Eigen::SparseMatrix<Scalar> mat(full_size, 0);
return mat;
}
Eigen::SparseMatrix<Scalar> mat(full_size, subset_size);
mat.reserve(Eigen::VectorXi::Constant(subset_size, 1));
for (int i = 0; i < subset_size; ++i) {
mat.insert(indices[i], i) = 1;
}
return mat;
}
} // anon namespace
/// Returns x(indices).
template <typename Scalar, class IntVec>
Eigen::Array<Scalar, Eigen::Dynamic, 1>
subset(const Eigen::Array<Scalar, Eigen::Dynamic, 1>& x,
const IntVec& indices)
{
typedef typename Eigen::Array<Scalar, Eigen::Dynamic, 1>::Index Index;
const Index size = indices.size();
Eigen::Array<Scalar, Eigen::Dynamic, 1> ret( size );
for( Index i=0; i<size; ++i )
ret[ i ] = x[ indices[ i ] ];
return std::move(ret);
}
/// Returns x(indices).
template <typename Scalar, class IntVec>
AutoDiffBlock<Scalar>
subset(const AutoDiffBlock<Scalar>& x,
const IntVec& indices)
{
const Eigen::SparseMatrix<Scalar> sub
= constructSupersetSparseMatrix<Scalar>(x.value().size(), indices).transpose().eval();
return sub * x;
}
/// Returns v where v(indices) == x, v(!indices) == 0 and v.size() == n.
template <typename Scalar, class IntVec>
AutoDiffBlock<Scalar>
superset(const AutoDiffBlock<Scalar>& x,
const IntVec& indices,
const int n)
{
return constructSupersetSparseMatrix<Scalar>(n, indices) * x;
}
/// Returns v where v(indices) == x, v(!indices) == 0 and v.size() == n.
template <typename Scalar, class IntVec>
Eigen::Array<Scalar, Eigen::Dynamic, 1>
superset(const Eigen::Array<Scalar, Eigen::Dynamic, 1>& x,
const IntVec& indices,
const int n)
{
return constructSupersetSparseMatrix<Scalar>(n, indices) * x.matrix();
}
/// Construct square sparse matrix with the
/// elements of d on the diagonal.
/// Need to mark this as inline since it is defined in a header and not a template.
inline
Eigen::SparseMatrix<double>
spdiag(const AutoDiffBlock<double>::V& d)
{
typedef Eigen::SparseMatrix<double> M;
const int n = d.size();
M mat(n, n);
mat.reserve(Eigen::ArrayXi::Ones(n, 1));
for (M::Index i = 0; i < n; ++i) {
mat.insert(i, i) = d[i];
}
return mat;
}
/// Selection. Choose first of two elements if selection basis element is nonnegative.
template <typename Scalar>
class Selector {
public:
typedef AutoDiffBlock<Scalar> ADB;
enum CriterionForLeftElement { GreaterEqualZero, GreaterZero, Zero, NotEqualZero, LessZero, LessEqualZero, NotNaN };
Selector(const typename ADB::V& selection_basis,
CriterionForLeftElement crit = GreaterEqualZero)
{
// Define selector structure.
const int n = selection_basis.size();
// Over-reserving so we do not have to count.
left_elems_.reserve(n);
right_elems_.reserve(n);
for (int i = 0; i < n; ++i) {
bool chooseleft = false;
switch (crit) {
case GreaterEqualZero:
chooseleft = selection_basis[i] >= 0.0;
break;
case GreaterZero:
chooseleft = selection_basis[i] > 0.0;
break;
case Zero:
chooseleft = selection_basis[i] == 0.0;
break;
case NotEqualZero:
chooseleft = selection_basis[i] != 0.0;
break;
case LessZero:
chooseleft = selection_basis[i] < 0.0;
break;
case LessEqualZero:
chooseleft = selection_basis[i] <= 0.0;
break;
case NotNaN:
chooseleft = !isnan(selection_basis[i]);
break;
default:
OPM_THROW(std::logic_error, "No such criterion: " << crit);
}
if (chooseleft) {
left_elems_.push_back(i);
} else {
right_elems_.push_back(i);
}
}
}
/// Apply selector to ADB quantities.
ADB select(const ADB& x1, const ADB& x2) const
{
if (right_elems_.empty()) {
return x1;
} else if (left_elems_.empty()) {
return x2;
} else {
return superset(subset(x1, left_elems_), left_elems_, x1.size())
+ superset(subset(x2, right_elems_), right_elems_, x2.size());
}
}
/// Apply selector to ADB quantities.
typename ADB::V select(const typename ADB::V& x1, const typename ADB::V& x2) const
{
if (right_elems_.empty()) {
return x1;
} else if (left_elems_.empty()) {
return x2;
} else {
return superset(subset(x1, left_elems_), left_elems_, x1.size())
+ superset(subset(x2, right_elems_), right_elems_, x2.size());
}
}
private:
std::vector<int> left_elems_;
std::vector<int> right_elems_;
};
/// Returns the input expression, but with all Jacobians collapsed to one.
template <class Matrix>
inline
void
collapseJacs(const AutoDiffBlock<double>& x, Matrix& jacobian)
{
typedef AutoDiffBlock<double> ADB;
const int nb = x.numBlocks();
typedef Eigen::Triplet<double> Tri;
int nnz = 0;
for (int block = 0; block < nb; ++block) {
nnz += x.derivative()[block].nonZeros();
}
std::vector<Tri> t;
t.reserve(nnz);
int block_col_start = 0;
for (int block = 0; block < nb; ++block) {
const ADB::M& jac1 = x.derivative()[block];
Eigen::SparseMatrix<double> jac;
jac1.toSparse(jac);
for (Eigen::SparseMatrix<double>::Index k = 0; k < jac.outerSize(); ++k) {
for (Eigen::SparseMatrix<double>::InnerIterator i(jac, k); i ; ++i) {
if (i.value() != 0.0) {
t.push_back(Tri(i.row(),
i.col() + block_col_start,
i.value()));
}
}
}
block_col_start += jac.cols();
}
// Build final jacobian.
jacobian = Matrix(x.size(), block_col_start);
jacobian.setFromTriplets(t.begin(), t.end());
}
/// Returns the input expression, but with all Jacobians collapsed to one.
inline
AutoDiffBlock<double>
collapseJacs(const AutoDiffBlock<double>& x)
{
Eigen::SparseMatrix<double> comb_jac;
collapseJacs( x, comb_jac );
// Build final jacobian.
typedef AutoDiffBlock<double> ADB;
std::vector<ADB::M> jacs(1);
jacs[0] = AutoDiffMatrix(std::move(comb_jac));
ADB::V val = x.value();
return ADB::function(std::move(val), std::move(jacs));
}
/// Returns the vertical concatenation [ x; y ] of the inputs.
inline
AutoDiffBlock<double>
vertcat(const AutoDiffBlock<double>& x,
const AutoDiffBlock<double>& y)
{
const int nx = x.size();
const int ny = y.size();
const int n = nx + ny;
std::vector<int> xind(nx);
for (int i = 0; i < nx; ++i) {
xind[i] = i;
}
std::vector<int> yind(ny);
for (int i = 0; i < ny; ++i) {
yind[i] = nx + i;
}
return superset(x, xind, n) + superset(y, yind, n);
}
/// Returns the vertical concatenation [ x[0]; x[1]; ...; x[n-1] ] of the inputs.
/// This function also collapses the Jacobian matrices into one like collapsJacs().
inline
AutoDiffBlock<double>
vertcatCollapseJacs(const std::vector<AutoDiffBlock<double> >& x)
{
typedef AutoDiffBlock<double> ADB;
if (x.empty()) {
return ADB::null();
}
// Count sizes, nonzeros.
const int nx = x.size();
int size = 0;
int nnz = 0;
int elem_with_deriv = -1;
int num_blocks = 0;
for (int elem = 0; elem < nx; ++elem) {
size += x[elem].size();
if (x[elem].derivative().empty()) {
// No nnz contributions from this element.
continue;
} else {
if (elem_with_deriv == -1) {
elem_with_deriv = elem;
num_blocks = x[elem].numBlocks();
}
}
if (x[elem].blockPattern() != x[elem_with_deriv].blockPattern()) {
OPM_THROW(std::runtime_error, "vertcatCollapseJacs(): all arguments must have the same block pattern");
}
for (int block = 0; block < num_blocks; ++block) {
nnz += x[elem].derivative()[block].nonZeros();
}
}
int num_cols = 0;
for (int block = 0; block < num_blocks; ++block) {
num_cols += x[elem_with_deriv].derivative()[block].cols();
}
// Build value for result.
ADB::V val(size);
int pos = 0;
for (int elem = 0; elem < nx; ++elem) {
const int loc_size = x[elem].size();
val.segment(pos, loc_size) = x[elem].value();
pos += loc_size;
}
assert(pos == size);
// Return a constant if we have no derivatives at all.
if (num_blocks == 0) {
return ADB::constant(std::move(val));
}
// Set up for batch insertion of all Jacobian elements.
typedef Eigen::SparseMatrix<double> M;
typedef Eigen::Triplet<double> Tri;
std::vector<Tri> t;
t.reserve(nnz);
{
int block_row_start = 0;
M jac;
for (int elem = 0; elem < nx; ++elem) {
int block_col_start = 0;
if (!x[elem].derivative().empty()) {
for (int block = 0; block < num_blocks; ++block) {
x[elem].derivative()[block].toSparse(jac);
for (M::Index k = 0; k < jac.outerSize(); ++k) {
for (M::InnerIterator i(jac, k); i ; ++i) {
t.push_back(Tri(i.row() + block_row_start,
i.col() + block_col_start,
i.value()));
}
}
block_col_start += jac.cols();
}
}
block_row_start += x[elem].size();
}
}
// Build final jacobian.
M comb_jac = M(size, num_cols);
comb_jac.reserve(nnz);
comb_jac.setFromTriplets(t.begin(), t.end());
std::vector<ADB::M> jac(1);
jac[0] = ADB::M(std::move(comb_jac));
// Use move semantics to return result efficiently.
return ADB::function(std::move(val), std::move(jac));
}
class Span
{
public:
explicit Span(const int num)
: num_(num),
stride_(1),
start_(0)
{
}
Span(const int num, const int stride, const int start)
: num_(num),
stride_(stride),
start_(start)
{
}
int operator[](const int i) const
{
assert(i >= 0 && i < num_);
return start_ + i*stride_;
}
int size() const
{
return num_;
}
class SpanIterator
{
public:
SpanIterator(const Span* span, const int index)
: span_(span),
index_(index)
{
}
SpanIterator operator++()
{
++index_;
return *this;
}
SpanIterator operator++(int)
{
SpanIterator before_increment(*this);
++index_;
return before_increment;
}
bool operator<(const SpanIterator& rhs) const
{
assert(span_ == rhs.span_);
return index_ < rhs.index_;
}
bool operator==(const SpanIterator& rhs) const
{
assert(span_ == rhs.span_);
return index_ == rhs.index_;
}
bool operator!=(const SpanIterator& rhs) const
{
assert(span_ == rhs.span_);
return index_ != rhs.index_;
}
int operator*()
{
return (*span_)[index_];
}
private:
const Span* span_;
int index_;
};
typedef SpanIterator iterator;
typedef SpanIterator const_iterator;
SpanIterator begin() const
{
return SpanIterator(this, 0);
}
SpanIterator end() const
{
return SpanIterator(this, num_);
}
bool operator==(const Span& rhs)
{
return num_ == rhs.num_ && start_ == rhs.start_ && stride_ == rhs.stride_;
}
private:
const int num_;
const int stride_;
const int start_;
};
/// Return a vector of (-1.0, 0.0 or 1.0), depending on sign per element.
inline Eigen::ArrayXd sign (const Eigen::ArrayXd& x)
{
const int n = x.size();
Eigen::ArrayXd retval(n);
for (int i = 0; i < n; ++i) {
retval[i] = x[i] < 0.0 ? -1.0 : (x[i] > 0.0 ? 1.0 : 0.0);
}
return retval;
}
} // namespace Opm
#endif // OPM_AUTODIFFHELPERS_HEADER_INCLUDED
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