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opm-simulators/opm/autodiff/AutoDiffBlock.hpp

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/*
Copyright 2013 SINTEF ICT, Applied Mathematics.
Copyright 2016 IRIS AS
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_AUTODIFFBLOCK_HEADER_INCLUDED
#define OPM_AUTODIFFBLOCK_HEADER_INCLUDED
#include <opm/common/utility/platform_dependent/disable_warnings.h>
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <opm/autodiff/fastSparseOperations.hpp>
#include <opm/common/utility/platform_dependent/reenable_warnings.h>
#include <opm/autodiff/AutoDiffMatrix.hpp>
#include <utility>
#include <vector>
#include <cassert>
#include <iostream>
namespace Opm
{
/// A class for forward-mode automatic differentiation with vector
/// values and sparse jacobian matrices.
///
/// The class contains a (column) vector of values and multiple
/// sparse matrices representing its partial derivatives. Each
/// such matrix has a number of rows equal to the number of rows
/// in the value vector, and a number of columns equal to the
/// number of discrete variables we want to compute the
/// derivatives with respect to. The reason to have multiple such
/// jacobians instead of just one is to allow simpler grouping of
/// variables, making it easier to implement various
/// preconditioning schemes. Only basic arithmetic operators are
/// implemented for this class, reflecting our needs so far.
///
/// The class is built on the Eigen library, using an Eigen array
/// type to contain the values and Eigen sparse matrices for the
/// jacobians. The overloaded operators are intended to behave in
/// a similar way to Eigen arrays, meaning for example that the *
/// operator is elementwise multiplication. The only exception is
/// multiplication with a sparse matrix from the left, which is
/// treated as an Eigen matrix operation.
///
/// There are no public constructors, instead we use the Named
/// Constructor pattern. In general, one needs to know which
/// variables one wants to compute the derivatives with respect to
/// before constructing an AutoDiffBlock. Some of the constructors
/// require you to pass a block pattern. This should be a vector
/// containing the number of columns you want for each jacobian
/// matrix.
///
/// For example: you want the derivatives with respect to three
/// different variables p, r and s. Assuming that there are 10
/// elements in p, and 20 in each of r and s, the block pattern is
/// { 10, 20, 20 }. When creating the variables p, r and s in your
/// program you have two options:
/// - Use the variable() constructor three times, passing the
/// index (0 for p, 1 for r and 2 for s), initial value of
/// each variable and the block pattern.
/// - Use the variables() constructor passing only the initial
/// values of each variable. The block pattern will be
/// inferred from the size of the initial value vectors.
/// This is usually the simplest option if you have multiple
/// variables. Note that this constructor returns a vector
/// of all three variables, so you need to use index access
/// (operator[]) to get the individual variables (that is p,
/// r and s).
///
/// After this, the r variable for example will have a size() of
/// 20 and three jacobian matrices. The first is a 20 by 10 zero
/// matrix, the second is a 20 by 20 identity matrix, and the
/// third is a 20 by 20 zero matrix.
template <typename Scalar>
class AutoDiffBlock
{
public:
/// Underlying type for values.
typedef Eigen::Array<Scalar, Eigen::Dynamic, 1> V;
/// Underlying type for jacobians.
typedef AutoDiffMatrix M;
/// Construct an empty AutoDiffBlock.
static AutoDiffBlock null()
{
return AutoDiffBlock(V(), {});
}
/// Create an AutoDiffBlock representing a constant.
/// \param[in] val values
static AutoDiffBlock constant(V&& val)
{
return AutoDiffBlock(std::move(val));
}
/// Create an AutoDiffBlock representing a constant.
/// \param[in] val values
static AutoDiffBlock constant(const V& val)
{
return AutoDiffBlock(val);
}
/// Create an AutoDiffBlock representing a constant.
/// This variant requires specifying the block sizes used
/// for the Jacobians even though the Jacobian matrices
/// themselves will be zero.
/// \param[in] val values
/// \param[in] blocksizes block pattern
static AutoDiffBlock constant(const V& val, const std::vector<int>& blocksizes)
{
std::vector<M> jac;
const int num_elem = val.size();
const int num_blocks = blocksizes.size();
// For constants, all jacobian blocks are zero.
jac.resize(num_blocks);
for (int i = 0; i < num_blocks; ++i) {
jac[i] = M(num_elem, blocksizes[i]);
}
V val_copy(val);
return AutoDiffBlock(std::move(val_copy), std::move(jac));
}
/// Create an AutoDiffBlock representing a single variable block.
/// \param[in] index index of the variable you are constructing
/// \param[in] val values
/// \param[in] blocksizes block pattern
/// The resulting object will have size() equal to block_pattern[index].
/// Its jacobians will all be zero, except for derivative()[index], which
/// will be an identity matrix.
static AutoDiffBlock variable(const int index, V&& val, const std::vector<int>& blocksizes)
{
std::vector<M> jac;
const int num_elem = val.size();
const int num_blocks = blocksizes.size();
// First, set all jacobian blocks to zero...
jac.resize(num_blocks);
for (int i = 0; i < num_blocks; ++i) {
jac[i] = M(num_elem, blocksizes[i]);
}
// ... then set the one corrresponding to this variable to identity.
assert(blocksizes[index] == num_elem);
jac[index] = M::createIdentity(val.size());
return AutoDiffBlock(std::move(val), std::move(jac));
}
/// Create an AutoDiffBlock representing a single variable block.
/// \param[in] index index of the variable you are constructing
/// \param[in] val values
/// \param[in] blocksizes block pattern
/// The resulting object will have size() equal to block_pattern[index].
/// Its jacobians will all be zero, except for derivative()[index], which
/// will be an identity matrix.
static AutoDiffBlock variable(const int index, const V& val, const std::vector<int>& blocksizes)
{
V value = val;
return variable(index, std::move(value), blocksizes);
}
/// Create an AutoDiffBlock by directly specifying values and jacobians.
/// This version of function() moves its arguments and is therefore
/// quite efficient, but leaves the argument variables empty (but valid).
/// \param[in] val values
/// \param[in] jac vector of jacobians
static AutoDiffBlock function(V&& val, std::vector<M>&& jac)
{
return AutoDiffBlock(std::move(val), std::move(jac));
}
/// Create an AutoDiffBlock by directly specifying values and jacobians.
/// This version of function() copies its arguments and is therefore
/// less efficient than the other (moving) overload.
/// \param[in] val values
/// \param[in] jac vector of jacobians
static AutoDiffBlock function(const V& val, const std::vector<M>& jac)
{
V val_copy(val);
std::vector<M> jac_copy(jac);
return AutoDiffBlock(std::move(val_copy), std::move(jac_copy));
}
/// Construct a set of primary variables, each initialized to
/// a given vector.
static std::vector<AutoDiffBlock> variables(const std::vector<V>& initial_values)
{
const int num_vars = initial_values.size();
std::vector<int> bpat;
for (int v = 0; v < num_vars; ++v) {
bpat.push_back(initial_values[v].size());
}
std::vector<AutoDiffBlock> vars;
for (int v = 0; v < num_vars; ++v) {
vars.emplace_back(variable(v, initial_values[v], bpat));
}
return vars;
}
/// Elementwise operator +=
AutoDiffBlock& operator+=(const AutoDiffBlock& rhs)
{
if (jac_.empty()) {
jac_ = rhs.jac_;
} else if (!rhs.jac_.empty()) {
assert (numBlocks() == rhs.numBlocks());
assert (value().size() == rhs.value().size());
const int num_blocks = numBlocks();
#if HAVE_OPENMP
#pragma omp parallel for schedule(static)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac_[block].rows() == rhs.jac_[block].rows());
assert(jac_[block].cols() == rhs.jac_[block].cols());
jac_[block] += rhs.jac_[block];
}
}
val_ += rhs.val_;
return *this;
}
/// Elementwise operator -=
AutoDiffBlock& operator-=(const AutoDiffBlock& rhs)
{
if (jac_.empty()) {
const int num_blocks = rhs.numBlocks();
jac_.resize(num_blocks);
#if HAVE_OPENMP
#pragma omp parallel for schedule(static)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
jac_[block] = rhs.jac_[block] * (-1.0);
}
} else if (!rhs.jac_.empty()) {
assert (numBlocks() == rhs.numBlocks());
assert (value().size() == rhs.value().size());
const int num_blocks = numBlocks();
#if HAVE_OPENMP
#pragma omp parallel for schedule(static)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac_[block].rows() == rhs.jac_[block].rows());
assert(jac_[block].cols() == rhs.jac_[block].cols());
jac_[block] -= rhs.jac_[block];
}
}
val_ -= rhs.val_;
return *this;
}
/// Elementwise operator +
AutoDiffBlock operator+(const AutoDiffBlock& rhs) const
{
if (jac_.empty() && rhs.jac_.empty()) {
return constant(val_ + rhs.val_);
}
if (jac_.empty()) {
return val_ + rhs;
}
if (rhs.jac_.empty()) {
return *this + rhs.val_;
}
std::vector<M> jac = jac_;
assert(numBlocks() == rhs.numBlocks());
int num_blocks = numBlocks();
#if HAVE_OPENMP
#pragma omp parallel for schedule(static)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac[block].rows() == rhs.jac_[block].rows());
assert(jac[block].cols() == rhs.jac_[block].cols());
jac[block] += rhs.jac_[block];
}
return function(val_ + rhs.val_, std::move(jac));
}
/// Elementwise operator -
AutoDiffBlock operator-(const AutoDiffBlock& rhs) const
{
if (jac_.empty() && rhs.jac_.empty()) {
return constant(val_ - rhs.val_);
}
if (jac_.empty()) {
return val_ - rhs;
}
if (rhs.jac_.empty()) {
return *this - rhs.val_;
}
std::vector<M> jac = jac_;
assert(numBlocks() == rhs.numBlocks());
int num_blocks = numBlocks();
#if HAVE_OPENMP
#pragma omp parallel for schedule(static)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac[block].rows() == rhs.jac_[block].rows());
assert(jac[block].cols() == rhs.jac_[block].cols());
jac[block] -= rhs.jac_[block];
}
return function(val_ - rhs.val_, std::move(jac));
}
/// Elementwise operator *
AutoDiffBlock operator*(const AutoDiffBlock& rhs) const
{
if (jac_.empty() && rhs.jac_.empty()) {
return constant(val_ * rhs.val_);
}
if (jac_.empty()) {
return val_ * rhs;
}
if (rhs.jac_.empty()) {
return *this * rhs.val_;
}
int num_blocks = numBlocks();
std::vector<M> jac(num_blocks);
assert(numBlocks() == rhs.numBlocks());
M D1(val_.matrix().asDiagonal());
M D2(rhs.val_.matrix().asDiagonal());
#if HAVE_OPENMP
#pragma omp parallel for schedule(dynamic)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac_[block].rows() == rhs.jac_[block].rows());
assert(jac_[block].cols() == rhs.jac_[block].cols());
if( jac_[block].nonZeros() == 0 && rhs.jac_[block].nonZeros() == 0 ) {
jac[block] = M( D2.rows(), jac_[block].cols() );
}
else if( jac_[block].nonZeros() == 0 )
jac[block] = D1*rhs.jac_[block];
else if ( rhs.jac_[block].nonZeros() == 0 ) {
jac[block] = D2*jac_[block];
}
else {
jac[block] = D2*jac_[block];
jac[block] += D1*rhs.jac_[block];
}
}
return function(val_ * rhs.val_, std::move(jac));
}
/// Elementwise operator /
AutoDiffBlock operator/(const AutoDiffBlock& rhs) const
{
if (jac_.empty() && rhs.jac_.empty()) {
return constant(val_ / rhs.val_);
}
if (jac_.empty()) {
return val_ / rhs;
}
if (rhs.jac_.empty()) {
return *this / rhs.val_;
}
int num_blocks = numBlocks();
std::vector<M> jac(num_blocks);
assert(numBlocks() == rhs.numBlocks());
M D1(val_.matrix().asDiagonal());
M D2(rhs.val_.matrix().asDiagonal());
M D3((1.0/(rhs.val_*rhs.val_)).matrix().asDiagonal());
#if HAVE_OPENMP
#pragma omp parallel for schedule(dynamic)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
assert(jac_[block].rows() == rhs.jac_[block].rows());
assert(jac_[block].cols() == rhs.jac_[block].cols());
if( jac_[block].nonZeros() == 0 && rhs.jac_[block].nonZeros() == 0 ) {
jac[block] = M( D3.rows(), jac_[block].cols() );
}
else if( jac_[block].nonZeros() == 0 ) {
jac[block] = D3 * ( D1*rhs.jac_[block]) * (-1.0);
}
else if ( rhs.jac_[block].nonZeros() == 0 )
{
jac[block] = D3 * (D2*jac_[block]);
}
else {
jac[block] = D3 * (D2*jac_[block] + (D1*rhs.jac_[block]*(-1.0)));
}
}
return function(val_ / rhs.val_, std::move(jac));
}
/// I/O.
template <class Ostream>
Ostream&
print(Ostream& os) const
{
int num_blocks = jac_.size();
os << "Value =\n" << val_ << "\n\nJacobian =\n";
for (int i = 0; i < num_blocks; ++i) {
Eigen::SparseMatrix<double> m;
jac_[i].toSparse(m);
os << "Sub Jacobian #" << i << '\n' << m << "\n";
}
return os;
}
/// Efficient swap function.
void swap(AutoDiffBlock& other)
{
val_.swap(other.val_);
jac_.swap(other.jac_);
}
/// Number of elements
int size() const
{
return val_.size();
}
/// Number of Jacobian blocks.
int numBlocks() const
{
return jac_.size();
}
/// Sizes (number of columns) of Jacobian blocks.
std::vector<int> blockPattern() const
{
const int nb = numBlocks();
std::vector<int> bp(nb);
for (int block = 0; block < nb; ++block) {
bp[block] = jac_[block].cols();
}
return bp;
}
/// Function value.
const V& value() const
{
return val_;
}
/// Function derivatives.
const std::vector<M>& derivative() const
{
return jac_;
}
private:
AutoDiffBlock(const V& val)
: val_(val)
{
}
AutoDiffBlock(V&& val)
: val_(std::move(val))
{
}
AutoDiffBlock(V&& val, std::vector<M>&& jac)
: val_(std::move(val)), jac_(std::move(jac))
{
#ifndef NDEBUG
const int num_elem = val_.size();
const int num_blocks = jac_.size();
for (int block = 0; block < num_blocks; ++block) {
assert(num_elem == jac_[block].rows());
}
#endif
}
V val_;
std::vector<M> jac_;
};
// --------- Free functions and operators for AutoDiffBlock ---------
/// Stream output.
template <class Ostream, typename Scalar>
Ostream&
operator<<(Ostream& os, const AutoDiffBlock<Scalar>& fw)
{
return fw.print(os);
}
/// Multiply with AutoDiffMatrix from the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const typename AutoDiffBlock<Scalar>::M& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
int num_blocks = rhs.numBlocks();
std::vector<typename AutoDiffBlock<Scalar>::M> jac(num_blocks);
assert(lhs.cols() == rhs.value().rows());
#if HAVE_OPENMP
#pragma omp parallel for schedule(dynamic)
#endif // HAVE_OPENMP
for (int block = 0; block < num_blocks; ++block) {
fastSparseProduct(lhs, rhs.derivative()[block], jac[block]);
}
typename AutoDiffBlock<Scalar>::V val = lhs*rhs.value().matrix();
return AutoDiffBlock<Scalar>::function(std::move(val), std::move(jac));
}
/// Multiply with Eigen sparse matrix from the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const Eigen::SparseMatrix<Scalar>& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
int num_blocks = rhs.numBlocks();
std::vector<typename AutoDiffBlock<Scalar>::M> jac(num_blocks);
assert(lhs.cols() == rhs.value().rows());
for (int block = 0; block < num_blocks; ++block) {
fastSparseProduct(lhs, rhs.derivative()[block], jac[block]);
}
typename AutoDiffBlock<Scalar>::V val = lhs*rhs.value().matrix();
return AutoDiffBlock<Scalar>::function(std::move(val), std::move(jac));
}
/// Elementwise multiplication with constant on the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const typename AutoDiffBlock<Scalar>::V& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) * rhs;
}
/// Elementwise multiplication with constant on the right.
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const AutoDiffBlock<Scalar>& lhs,
const typename AutoDiffBlock<Scalar>::V& rhs)
{
return rhs * lhs; // Commutative operation.
}
/// Elementwise addition with constant on the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator+(const typename AutoDiffBlock<Scalar>::V& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) + rhs;
}
/// Elementwise addition with constant on the right.
template <typename Scalar>
AutoDiffBlock<Scalar> operator+(const AutoDiffBlock<Scalar>& lhs,
const typename AutoDiffBlock<Scalar>::V& rhs)
{
return rhs + lhs; // Commutative operation.
}
/// Elementwise subtraction with constant on the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator-(const typename AutoDiffBlock<Scalar>::V& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) - rhs;
}
/// Elementwise subtraction with constant on the right.
template <typename Scalar>
AutoDiffBlock<Scalar> operator-(const AutoDiffBlock<Scalar>& lhs,
const typename AutoDiffBlock<Scalar>::V& rhs)
{
return lhs - AutoDiffBlock<Scalar>::constant(rhs, lhs.blockPattern());
}
/// Elementwise division with constant on the left.
template <typename Scalar>
AutoDiffBlock<Scalar> operator/(const typename AutoDiffBlock<Scalar>::V& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
return AutoDiffBlock<Scalar>::constant(lhs, rhs.blockPattern()) / rhs;
}
/// Elementwise division with constant on the right.
template <typename Scalar>
AutoDiffBlock<Scalar> operator/(const AutoDiffBlock<Scalar>& lhs,
const typename AutoDiffBlock<Scalar>::V& rhs)
{
return lhs / AutoDiffBlock<Scalar>::constant(rhs, lhs.blockPattern());
}
/**
* @brief Operator for multiplication with a scalar on the right-hand side
*
* @param lhs The left-hand side AD forward block
* @param rhs The scalar to multiply with
* @return The product
*/
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const AutoDiffBlock<Scalar>& lhs,
const Scalar& rhs)
{
std::vector< typename AutoDiffBlock<Scalar>::M > jac;
jac.reserve( lhs.numBlocks() );
for (int block=0; block<lhs.numBlocks(); block++) {
jac.emplace_back( lhs.derivative()[block] * rhs );
}
return AutoDiffBlock<Scalar>::function( lhs.value() * rhs, std::move(jac) );
}
/**
* @brief Operator for multiplication with a scalar on the left-hand side
*
* @param lhs The scalar to multiply with
* @param rhs The right-hand side AD forward block
* @return The product
*/
template <typename Scalar>
AutoDiffBlock<Scalar> operator*(const Scalar& lhs,
const AutoDiffBlock<Scalar>& rhs)
{
return rhs * lhs; // Commutative operation.
}
/**
* @brief Computes the value of base raised to the power of exponent
*
* @param base The AD forward block
* @param exponent double
* @return The value of base raised to the power of exponent
*/
template <typename Scalar>
AutoDiffBlock<Scalar> pow(const AutoDiffBlock<Scalar>& base,
const double exponent)
{
const typename AutoDiffBlock<Scalar>::V val = base.value().pow(exponent);
const typename AutoDiffBlock<Scalar>::V derivative = exponent * base.value().pow(exponent - 1.0);
const typename AutoDiffBlock<Scalar>::M derivative_diag(derivative.matrix().asDiagonal());
std::vector< typename AutoDiffBlock<Scalar>::M > jac (base.numBlocks());
for (int block = 0; block < base.numBlocks(); block++) {
fastSparseProduct(derivative_diag, base.derivative()[block], jac[block]);
}
return AutoDiffBlock<Scalar>::function( std::move(val), std::move(jac) );
}
/**
* @brief Computes the value of base raised to the power of exponent
*
* @param base The AD forward block
* @param exponent Array of exponents
* @return The value of base raised to the power of exponent elementwise
*/
template <typename Scalar>
AutoDiffBlock<Scalar> pow(const AutoDiffBlock<Scalar>& base,
const typename AutoDiffBlock<Scalar>::V& exponent)
{
// Add trivial derivatives and use the AD pow function
return pow(base,AutoDiffBlock<Scalar>::constant(exponent));
}
/**
* @brief Computes the value of base raised to the power of exponent
*
* @param base Array of base values
* @param exponent The AD forward block
* @return The value of base raised to the power of exponent elementwise
*/
template <typename Scalar>
AutoDiffBlock<Scalar> pow(const typename AutoDiffBlock<Scalar>::V& base,
const AutoDiffBlock<Scalar>& exponent)
{
// Add trivial derivatives and use the AD pow function
return pow(AutoDiffBlock<Scalar>::constant(base),exponent);
}
/**
* @brief Computes the value of base raised to the power of exponent
*
* @param base The base AD forward block
* @param exponent The exponent AD forward block
* @return The value of base raised to the power of exp
*/
template <typename Scalar>
AutoDiffBlock<Scalar> pow(const AutoDiffBlock<Scalar>& base,
const AutoDiffBlock<Scalar>& exponent)
{
const int num_elem = base.value().size();
assert(exponent.size() == num_elem);
typename AutoDiffBlock<Scalar>::V val (num_elem);
for (int i = 0; i < num_elem; ++i) {
val[i] = std::pow(base.value()[i], exponent.value()[i]);
}
// (f^g)' = f^g * ln(f) * g' + g * f^(g-1) * f' = der1 + der2
// if f' is empty only der1 is calculated
// if g' is empty only der2 is calculated
// if f' and g' are non empty they should have the same size
int num_blocks = std::max (base.numBlocks(), exponent.numBlocks());
if (!base.derivative().empty() && !exponent.derivative().empty()) {
assert(exponent.numBlocks() == base.numBlocks());
}
std::vector< typename AutoDiffBlock<Scalar>::M > jac (num_blocks);
if ( !exponent.derivative().empty() ) {
typename AutoDiffBlock<Scalar>::V der1 = val;
for (int i = 0; i < num_elem; ++i) {
der1[i] *= std::log(base.value()[i]);
}
std::vector< typename AutoDiffBlock<Scalar>::M > jac1 (exponent.numBlocks());
const typename AutoDiffBlock<Scalar>::M der1_diag(der1.matrix().asDiagonal());
for (int block = 0; block < exponent.numBlocks(); block++) {
fastSparseProduct(der1_diag, exponent.derivative()[block], jac1[block]);
jac[block] = jac1[block];
}
}
if ( !base.derivative().empty() ) {
typename AutoDiffBlock<Scalar>::V der2 = exponent.value();
for (int i = 0; i < num_elem; ++i) {
der2[i] *= std::pow(base.value()[i], exponent.value()[i] - 1.0);
}
std::vector< typename AutoDiffBlock<Scalar>::M > jac2 (base.numBlocks());
const typename AutoDiffBlock<Scalar>::M der2_diag(der2.matrix().asDiagonal());
for (int block = 0; block < base.numBlocks(); block++) {
fastSparseProduct(der2_diag, base.derivative()[block], jac2[block]);
if (!exponent.derivative().empty()) {
jac[block] += jac2[block];
} else {
jac[block] = jac2[block];
}
}
}
return AutoDiffBlock<Scalar>::function(std::move(val), std::move(jac));
}
} // namespace Opm
#endif // OPM_AUTODIFFBLOCK_HEADER_INCLUDED
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