mirror of
https://github.com/OPM/opm-simulators.git
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538 lines
19 KiB
C++
538 lines
19 KiB
C++
/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef OPM_AUTODIFFBLOCK_HEADER_INCLUDED
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#define OPM_AUTODIFFBLOCK_HEADER_INCLUDED
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#include "disable_warning_pragmas.h"
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#include <Eigen/Eigen>
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#include <Eigen/Sparse>
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#include "reenable_warning_pragmas.h"
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#include <vector>
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#include <cassert>
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namespace Opm
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{
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/// A class for forward-mode automatic differentiation with vector
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/// values and sparse jacobian matrices.
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///
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/// The class contains a (column) vector of values and multiple
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/// sparse matrices representing its partial derivatives. Each
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/// such matrix has a number of rows equal to the number of rows
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/// in the value vector, and a number of columns equal to the
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/// number of discrete variables we want to compute the
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/// derivatives with respect to. The reason to have multiple such
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/// jacobians instead of just one is to allow simpler grouping of
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/// variables, making it easier to implement various
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/// preconditioning schemes. Only basic arithmetic operators are
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/// implemented for this class, reflecting our needs so far.
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///
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/// The class is built on the Eigen library, using an Eigen array
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/// type to contain the values and Eigen sparse matrices for the
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/// jacobians. The overloaded operators are intended to behave in
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/// a similar way to Eigen arrays, meaning for example that the *
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/// operator is elementwise multiplication. The only exception is
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/// multiplication with a sparse matrix from the left, which is
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/// treated as an Eigen matrix operation.
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///
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/// There are no public constructors, instead we use the Named
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/// Constructor pattern. In general, one needs to know which
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/// variables one wants to compute the derivatives with respect to
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/// before constructing an AutoDiffBlock. Some of the constructors
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/// require you to pass a block pattern. This should be a vector
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/// containing the number of columns you want for each jacobian
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/// matrix.
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///
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/// For example: you want the derivatives with respect to three
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/// different variables p, r and s. Assuming that there are 10
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/// elements in p, and 20 in each of r and s, the block pattern is
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/// { 10, 20, 20 }. When creating the variables p, r and s in your
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/// program you have two options:
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/// - Use the variable() constructor three times, passing the
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/// index (0 for p, 1 for r and 2 for s), initial value of
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/// each variable and the block pattern.
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/// - Use the variables() constructor passing only the initial
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/// values of each variable. The block pattern will be
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/// inferred from the size of the initial value vectors.
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/// This is usually the simplest option if you have multiple
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/// variables. Note that this constructor returns a vector
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/// of all three variables, so you need to use index access
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/// (operator[]) to get the individual variables (that is p,
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/// r and s).
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///
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/// After this, the r variable for example will have a size() of
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/// 20 and three jacobian matrices. The first is a 20 by 10 zero
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/// matrix, the second is a 20 by 20 identity matrix, and the
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/// third is a 20 by 20 zero matrix.
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template <typename Scalar>
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class AutoDiffBlock
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{
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public:
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/// Underlying type for values.
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typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> V;
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/// Underlying type for jacobians.
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typedef Eigen::SparseMatrix<Scalar> M;
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/// Construct an empty AutoDiffBlock.
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static AutoDiffBlock null()
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{
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V val;
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std::vector<M> jac;
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return AutoDiffBlock(val, jac);
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}
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/// Create an AutoDiffBlock representing a constant.
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/// \param[in] val values
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static AutoDiffBlock constant(const V& val)
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{
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return AutoDiffBlock(val);
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}
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/// Create an AutoDiffBlock representing a constant.
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/// This variant requires specifying the block sizes used
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/// for the Jacobians even though the Jacobian matrices
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/// themselves will be zero.
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/// \param[in] val values
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/// \param[in] blocksizes block pattern
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static AutoDiffBlock constant(const V& val, const std::vector<int>& blocksizes)
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{
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std::vector<M> jac;
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const int num_elem = val.size();
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const int num_blocks = blocksizes.size();
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// For constants, all jacobian blocks are zero.
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jac.resize(num_blocks);
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for (int i = 0; i < num_blocks; ++i) {
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jac[i] = M(num_elem, blocksizes[i]);
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}
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return AutoDiffBlock(val, jac);
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}
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/// Create an AutoDiffBlock representing a single variable block.
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/// \param[in] index index of the variable you are constructing
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/// \param[in] val values
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/// \param[in] blocksizes block pattern
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/// The resulting object will have size() equal to block_pattern[index].
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/// Its jacobians will all be zero, except for derivative()[index], which
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/// will be an identity matrix.
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static AutoDiffBlock variable(const int index, const V& val, const std::vector<int>& blocksizes)
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{
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std::vector<M> jac;
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const int num_elem = val.size();
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const int num_blocks = blocksizes.size();
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// First, set all jacobian blocks to zero...
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jac.resize(num_blocks);
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for (int i = 0; i < num_blocks; ++i) {
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jac[i] = M(num_elem, blocksizes[i]);
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}
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// ... then set the one corrresponding to this variable to identity.
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assert(blocksizes[index] == num_elem);
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jac[index].reserve(Eigen::VectorXi::Constant(val.size(), 1));
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for (typename M::Index row = 0; row < val.size(); ++row) {
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jac[index].insert(row, row) = Scalar(1.0);
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}
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return AutoDiffBlock(val, jac);
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}
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/// Create an AutoDiffBlock by directly specifying values and jacobians.
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/// \param[in] val values
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/// \param[in] jac vector of jacobians
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static AutoDiffBlock function(const V& val, const std::vector<M>& jac)
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{
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return AutoDiffBlock(val, jac);
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}
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/// Construct a set of primary variables, each initialized to
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/// a given vector.
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static std::vector<AutoDiffBlock> variables(const std::vector<V>& initial_values)
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{
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const int num_vars = initial_values.size();
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std::vector<int> bpat;
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for (int v = 0; v < num_vars; ++v) {
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bpat.push_back(initial_values[v].size());
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}
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std::vector<AutoDiffBlock> vars;
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for (int v = 0; v < num_vars; ++v) {
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vars.emplace_back(variable(v, initial_values[v], bpat));
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}
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return vars;
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}
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/// Elementwise operator +=
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AutoDiffBlock& operator+=(const AutoDiffBlock& rhs)
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{
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if (jac_.empty()) {
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jac_ = rhs.jac_;
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} else if (!rhs.jac_.empty()) {
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assert (numBlocks() == rhs.numBlocks());
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assert (value().size() == rhs.value().size());
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const int num_blocks = numBlocks();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac_[block].rows() == rhs.jac_[block].rows());
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assert(jac_[block].cols() == rhs.jac_[block].cols());
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jac_[block] += rhs.jac_[block];
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}
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}
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val_ += rhs.val_;
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return *this;
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}
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/// Elementwise operator -=
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AutoDiffBlock& operator-=(const AutoDiffBlock& rhs)
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{
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if (jac_.empty()) {
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const int num_blocks = rhs.numBlocks();
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jac_.resize(num_blocks);
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for (int block = 0; block < num_blocks; ++block) {
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jac_[block] = -rhs.jac_[block];
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}
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} else if (!rhs.jac_.empty()) {
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assert (numBlocks() == rhs.numBlocks());
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assert (value().size() == rhs.value().size());
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const int num_blocks = numBlocks();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac_[block].rows() == rhs.jac_[block].rows());
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assert(jac_[block].cols() == rhs.jac_[block].cols());
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jac_[block] -= rhs.jac_[block];
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}
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}
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val_ -= rhs.val_;
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return *this;
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}
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/// Elementwise operator +
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AutoDiffBlock operator+(const AutoDiffBlock& rhs) const
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{
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if (jac_.empty() && rhs.jac_.empty()) {
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return constant(val_ + rhs.val_);
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}
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if (jac_.empty()) {
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return val_ + rhs;
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}
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if (rhs.jac_.empty()) {
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return *this + rhs.val_;
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}
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std::vector<M> jac = jac_;
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assert(numBlocks() == rhs.numBlocks());
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int num_blocks = numBlocks();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac[block].rows() == rhs.jac_[block].rows());
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assert(jac[block].cols() == rhs.jac_[block].cols());
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jac[block] += rhs.jac_[block];
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}
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return function(val_ + rhs.val_, jac);
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}
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/// Elementwise operator -
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AutoDiffBlock operator-(const AutoDiffBlock& rhs) const
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{
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if (jac_.empty() && rhs.jac_.empty()) {
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return constant(val_ - rhs.val_);
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}
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if (jac_.empty()) {
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return val_ - rhs;
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}
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if (rhs.jac_.empty()) {
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return *this - rhs.val_;
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}
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std::vector<M> jac = jac_;
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assert(numBlocks() == rhs.numBlocks());
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int num_blocks = numBlocks();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac[block].rows() == rhs.jac_[block].rows());
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assert(jac[block].cols() == rhs.jac_[block].cols());
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jac[block] -= rhs.jac_[block];
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}
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return function(val_ - rhs.val_, jac);
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}
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/// Elementwise operator *
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AutoDiffBlock operator*(const AutoDiffBlock& rhs) const
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{
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if (jac_.empty() && rhs.jac_.empty()) {
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return constant(val_ * rhs.val_);
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}
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if (jac_.empty()) {
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return val_ * rhs;
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}
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if (rhs.jac_.empty()) {
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return *this * rhs.val_;
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}
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int num_blocks = numBlocks();
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std::vector<M> jac(num_blocks);
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assert(numBlocks() == rhs.numBlocks());
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typedef Eigen::DiagonalMatrix<Scalar, Eigen::Dynamic> D;
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D D1 = val_.matrix().asDiagonal();
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D D2 = rhs.val_.matrix().asDiagonal();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac_[block].rows() == rhs.jac_[block].rows());
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assert(jac_[block].cols() == rhs.jac_[block].cols());
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jac[block] = D2*jac_[block] + D1*rhs.jac_[block];
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}
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return function(val_ * rhs.val_, jac);
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}
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/// Elementwise operator /
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AutoDiffBlock operator/(const AutoDiffBlock& rhs) const
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{
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if (jac_.empty() && rhs.jac_.empty()) {
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return constant(val_ / rhs.val_);
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}
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if (jac_.empty()) {
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return val_ / rhs;
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}
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if (rhs.jac_.empty()) {
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return *this / rhs.val_;
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}
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int num_blocks = numBlocks();
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std::vector<M> jac(num_blocks);
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assert(numBlocks() == rhs.numBlocks());
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typedef Eigen::DiagonalMatrix<Scalar, Eigen::Dynamic> D;
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D D1 = val_.matrix().asDiagonal();
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D D2 = rhs.val_.matrix().asDiagonal();
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D D3 = (1.0/(rhs.val_*rhs.val_)).matrix().asDiagonal();
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for (int block = 0; block < num_blocks; ++block) {
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assert(jac_[block].rows() == rhs.jac_[block].rows());
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assert(jac_[block].cols() == rhs.jac_[block].cols());
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jac[block] = D3 * (D2*jac_[block] - D1*rhs.jac_[block]);
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}
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return function(val_ / rhs.val_, jac);
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}
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/// I/O.
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template <class Ostream>
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Ostream&
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print(Ostream& os) const
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{
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int num_blocks = jac_.size();
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os << "Value =\n" << val_ << "\n\nJacobian =\n";
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for (int i = 0; i < num_blocks; ++i) {
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os << "Sub Jacobian #" << i << '\n' << jac_[i] << "\n";
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}
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return os;
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}
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/// Number of elements
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int size() const
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{
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return val_.size();
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}
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/// Number of Jacobian blocks.
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int numBlocks() const
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{
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return jac_.size();
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}
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/// Sizes (number of columns) of Jacobian blocks.
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std::vector<int> blockPattern() const
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{
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const int nb = numBlocks();
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std::vector<int> bp(nb);
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for (int block = 0; block < nb; ++block) {
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bp[block] = jac_[block].cols();
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}
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return bp;
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}
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/// Function value.
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const V& value() const
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{
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return val_;
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}
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/// Function derivatives.
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const std::vector<M>& derivative() const
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{
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return jac_;
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}
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private:
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AutoDiffBlock(const V& val)
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: val_(val)
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{
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}
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AutoDiffBlock(const V& val,
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const std::vector<M>& jac)
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: val_(val), jac_(jac)
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{
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#ifndef NDEBUG
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const int num_elem = val_.size();
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const int num_blocks = jac_.size();
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for (int block = 0; block < num_blocks; ++block) {
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assert(num_elem == jac_[block].rows());
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}
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#endif
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}
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V val_;
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std::vector<M> jac_;
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};
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// --------- Free functions and operators for AutoDiffBlock ---------
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/// Stream output.
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template <class Ostream, typename Scalar>
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Ostream&
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operator<<(Ostream& os, const AutoDiffBlock<Scalar>& fw)
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{
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return fw.print(os);
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}
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/// Multiply with sparse matrix from the left.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator*(const typename AutoDiffBlock<Scalar>::M& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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int num_blocks = rhs.numBlocks();
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std::vector<typename AutoDiffBlock<Scalar>::M> jac(num_blocks);
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assert(lhs.cols() == rhs.value().rows());
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for (int block = 0; block < num_blocks; ++block) {
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jac[block] = lhs*rhs.derivative()[block];
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}
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typename AutoDiffBlock<Scalar>::V val = lhs*rhs.value().matrix();
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return AutoDiffBlock<Scalar>::function(val, jac);
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}
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/// Elementwise multiplication with constant on the left.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator*(const typename AutoDiffBlock<Scalar>::V& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) * rhs;
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}
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/// Elementwise multiplication with constant on the right.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator*(const AutoDiffBlock<Scalar>& lhs,
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const typename AutoDiffBlock<Scalar>::V& rhs)
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{
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return rhs * lhs; // Commutative operation.
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}
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/// Elementwise addition with constant on the left.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator+(const typename AutoDiffBlock<Scalar>::V& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) + rhs;
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}
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/// Elementwise addition with constant on the right.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator+(const AutoDiffBlock<Scalar>& lhs,
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const typename AutoDiffBlock<Scalar>::V& rhs)
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{
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return rhs + lhs; // Commutative operation.
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}
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/// Elementwise subtraction with constant on the left.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator-(const typename AutoDiffBlock<Scalar>::V& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) - rhs;
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}
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/// Elementwise subtraction with constant on the right.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator-(const AutoDiffBlock<Scalar>& lhs,
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const typename AutoDiffBlock<Scalar>::V& rhs)
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{
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return lhs - AutoDiffBlock<Scalar>::constant(rhs, lhs.blockPattern());
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}
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/// Elementwise division with constant on the left.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator/(const typename AutoDiffBlock<Scalar>::V& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) / rhs;
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}
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/// Elementwise division with constant on the right.
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator/(const AutoDiffBlock<Scalar>& lhs,
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const typename AutoDiffBlock<Scalar>::V& rhs)
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{
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return lhs / AutoDiffBlock<Scalar>::constant(rhs, lhs.blockPattern());
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}
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/**
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* @brief Operator for multiplication with a scalar on the right-hand side
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*
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* @param lhs The left-hand side AD forward block
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* @param rhs The scalar to multiply with
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* @return The product
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*/
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator*(const AutoDiffBlock<Scalar>& lhs,
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const Scalar& rhs)
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{
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std::vector< typename AutoDiffBlock<Scalar>::M > jac;
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jac.reserve( lhs.numBlocks() );
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for (int block=0; block<lhs.numBlocks(); block++) {
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jac.emplace_back( lhs.derivative()[block] * rhs );
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}
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return AutoDiffBlock<Scalar>::function( lhs.value() * rhs, jac );
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}
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/**
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* @brief Operator for multiplication with a scalar on the left-hand side
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*
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* @param lhs The scalar to multiply with
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* @param rhs The right-hand side AD forward block
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* @return The product
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*/
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template <typename Scalar>
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AutoDiffBlock<Scalar> operator*(const Scalar& lhs,
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const AutoDiffBlock<Scalar>& rhs)
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{
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return rhs * lhs; // Commutative operation.
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}
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} // namespace Opm
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#endif // OPM_AUTODIFFBLOCK_HEADER_INCLUDED
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