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https://github.com/OPM/opm-simulators.git
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Add simple library for automatic differentiation
No build system or automatic test cases at this point.
This commit is contained in:
Bård Skaflestad
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310
AutoDiff.hpp
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310
AutoDiff.hpp
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/*===========================================================================
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//
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// File: AutoDiff.hpp
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//
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// Created: 2013-04-29 10:51:23+0200
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//
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// Authors: Knut-Andreas Lie <Knut-Andreas.Lie@sintef.no>
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// Halvor M. Nilsen <HalvorMoll.Nilsen@sintef.no>
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// Atgeirr F. Rasmussen <atgeirr@sintef.no>
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// Xavier Raynaud <Xavier.Raynaud@sintef.no>
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// Bård Skaflestad <Bard.Skaflestad@sintef.no>
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//
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//==========================================================================*/
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/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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Copyright 2013 Statoil ASA.
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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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#include <cmath>
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#ifndef OPM_AUTODIFF_HPP_HEADER
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#define OPM_AUTODIFF_HPP_HEADER
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namespace AutoDiff {
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template <typename Scalar>
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class Forward {
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public:
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explicit Forward(const Scalar& x)
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: x_(x), dx_(Scalar(1))
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{}
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Forward(const Scalar x, const Scalar dx)
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: x_(x), dx_(dx)
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{}
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Forward&
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operator +=(const Scalar& rhs)
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{
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x_ += rhs;
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return *this;
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}
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Forward&
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operator +=(const Forward& rhs)
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{
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x_ += rhs.x_;
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dx_ += rhs.dx_;
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return *this;
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}
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Forward&
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operator -=(const Scalar& rhs)
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{
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x_ -= rhs;
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return *this;
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}
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Forward&
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operator -=(const Forward& rhs)
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{
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x_ -= rhs.x_;
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dx_ -= rhs.dx_;
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return *this;
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}
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Forward&
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operator *=(const Scalar& rhs)
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{
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x_ *= rhs;
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dx_ *= rhs;
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return *this;
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}
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Forward&
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operator *=(const Forward& rhs)
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{
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x_ *= rhs.x_;
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dx_ *= dx_*rhs.x_ + x_*rhs.dx_;
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return *this;
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}
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Forward&
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operator /=(const Scalar& rhs)
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{
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x_ /= rhs;
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dx_ /= rhs;
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return *this;
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}
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Forward&
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operator /=(const Forward& rhs)
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{
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x_ /= rhs.x_;
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dx_ = (dx_*rhs.x_ - x_*rhs.dx_) / (rhs.x_ * rhs.x_);
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return *this;
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}
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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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os << "(x,dx) = (" << x_ << ',' << dx_ << ")";
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return os;
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}
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const Scalar val() const { return x_ ; }
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const Scalar der() const { return dx_; }
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private:
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Scalar x_ ;
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Scalar dx_;
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};
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template <class Ostream, typename Scalar>
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Ostream&
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operator<<(Ostream& os, const Forward<Scalar>& fw)
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{
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return fw.print(os);
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}
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template <typename Scalar>
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Forward<Scalar>
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operator +(const Forward<Scalar>& lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = lhs;
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ret += rhs;
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator +(const T lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = rhs;
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ret += Scalar(lhs);
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator +(const Forward<Scalar>& lhs,
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const T rhs)
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{
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Forward<Scalar> ret = lhs;
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ret += Scalar(rhs);
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return ret;
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}
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template <typename Scalar>
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Forward<Scalar>
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operator -(const Forward<Scalar>& lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = lhs;
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ret -= rhs;
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator -(const T lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret(Scalar(lhs) - rhs.val(), -rhs.der());
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator -(const Forward<Scalar>& lhs,
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const T rhs)
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{
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Forward<Scalar> ret = lhs;
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ret -= Scalar(rhs);
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return ret;
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}
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template <typename Scalar>
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Forward<Scalar>
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operator *(const Forward<Scalar>& lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = lhs;
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ret *= rhs;
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator *(const T lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = rhs;
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ret *= Scalar(lhs);
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator *(const Forward<Scalar>& lhs,
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const T rhs)
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{
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Forward<Scalar> ret = lhs;
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ret *= Scalar(rhs);
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return ret;
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}
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template <typename Scalar>
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Forward<Scalar>
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operator /(const Forward<Scalar>& lhs,
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const Forward<Scalar>& rhs)
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{
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Forward<Scalar> ret = lhs;
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ret /= rhs;
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator /(const T lhs,
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const Forward<Scalar>& rhs)
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{
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Scalar a = Scalar(lhs) / rhs.val();
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Scalar b = -Scalar(lhs) / (rhs.val() * rhs.val());
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Forward<Scalar> ret(a, b);
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return ret;
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}
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template <typename Scalar, typename T>
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Forward<Scalar>
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operator /(const Forward<Scalar>& lhs,
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const T rhs)
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{
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Scalar a = rhs.val() / Scalar(lhs);
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Scalar b = rhs.der() / Scalar(lhs);
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Forward<Scalar> ret(a, b);
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return ret;
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}
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template <typename Scalar>
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Forward<Scalar>
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cos(const Forward<Scalar>& x)
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{
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Forward<Scalar> ret( std::cos(x.val()),
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-std::sin(x.val()) * x.der());
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return ret;
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}
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template <typename Scalar>
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Forward<Scalar>
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sqrt(const Forward<Scalar>& x)
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{
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Scalar a = std::sqrt(x.val());
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Scalar b = Scalar(1.0) / (Scalar(2.0) * a);
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Forward<Scalar> ret(a, b * x.der());
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return ret;
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}
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} // namespace AutoDiff
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namespace std {
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using AutoDiff::cos;
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using AutoDiff::sqrt;
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}
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#endif /* OPM_AUTODIFF_HPP_HEADER */
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101
find_zero.cpp
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101
find_zero.cpp
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@ -0,0 +1,101 @@
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/*===========================================================================
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//
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// File: find_zero.cpp
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//
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// Created: 2013-04-29 11:58:29+0200
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//
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// Authors: Knut-Andreas Lie <Knut-Andreas.Lie@sintef.no>
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// Halvor M. Nilsen <HalvorMoll.Nilsen@sintef.no>
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// Atgeirr F. Rasmussen <atgeirr@sintef.no>
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// Xavier Raynaud <Xavier.Raynaud@sintef.no>
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// Bård Skaflestad <Bard.Skaflestad@sintef.no>
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//
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//==========================================================================*/
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/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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Copyright 2013 Statoil ASA.
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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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#include "AutoDiff.hpp"
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#include <iostream>
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#include <cmath>
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struct Func
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{
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template <typename T>
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T operator()(T x) const
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{
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#if 1
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T r = std::sqrt(std::cos(x * x) + x) - 1.2;
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return r;
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#else
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return x;
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// const int n = 6;
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// double xv[6] = { 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 };
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// double yv[6] = { -0.5, -0.3, -0.1, 0.1, 0.3, 0.5 };
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// int interv = -1;
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// for (int i = 0; i < n; ++i) {
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// if (x < xv[i]) {
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// interv = i - 1;
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// break;
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// }
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// }
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// T t = (x - xv[interv])/(xv[interv+1] - xv[interv]);
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// return (1.0 - t)*yv[interv] + t*yv[interv+1];
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#endif
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}
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};
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// template <class ErrorPolicy = ThrowOnError>
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class Newton
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{
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public:
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/// Implements a scalar Newton solve.
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template <class Functor>
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inline static double solve(const Functor& f,
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const double initial_guess,
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const int max_iter,
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const double tolerance,
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int& iterations_used)
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{
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double x = initial_guess;
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iterations_used = 0;
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while (std::abs(f(x)) > tolerance && ++iterations_used < max_iter) {
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AutoDiff::Forward<double> xfad(x);
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AutoDiff::Forward<double> rfad = f(xfad);
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x = x - rfad.val()/rfad.der();
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}
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return x;
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}
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};
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int main()
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{
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int iter = 0;
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const double atol = 1.0e-13;
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const double soln = Newton::solve(Func(), 0.1, 30, atol, iter);
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std::cout.precision(16);
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std::cout << "Solution is: " << soln
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<< " using " << iter << " iterations." << '\n';
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std::cout << " f(x) = " << Func()(soln) << '\n';
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}
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67
test_ad.cpp
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67
test_ad.cpp
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@ -0,0 +1,67 @@
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/*===========================================================================
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//
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// File: test_ad.cpp
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//
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// Created: 2013-04-29 11:12:34+0200
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//
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// Authors: Knut-Andreas Lie <Knut-Andreas.Lie@sintef.no>
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// Halvor M. Nilsen <HalvorMoll.Nilsen@sintef.no>
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// Atgeirr F. Rasmussen <atgeirr@sintef.no>
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// Xavier Raynaud <Xavier.Raynaud@sintef.no>
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// Bård Skaflestad <Bard.Skaflestad@sintef.no>
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//
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//==========================================================================*/
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/*
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Copyright 2013 SINTEF ICT, Applied Mathematics.
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Copyright 2013 Statoil ASA.
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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
|
||||
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.
|
||||
|
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You should have received a copy of the GNU General Public License
|
||||
along with OPM. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "AutoDiff.hpp"
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#include <iostream>
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int
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main()
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{
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AutoDiff::Forward<double> a(0.0);
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AutoDiff::Forward<double> b(1.0);
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std::cout << "a: " << a << '\n';
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std::cout << "b: " << b << '\n';
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std::cout << "a + b: " << a + b << '\n';
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a = b;
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std::cout << "a: " << a << '\n';
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std::cout << "b: " << b << '\n';
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std::cout << "a + b: " << a + b << '\n';
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a = AutoDiff::Forward<double>(0.0);
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std::cout << "a: " << a << '\n';
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a += 1;
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std::cout << "a: " << a << '\n';
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std::cout << "a + 1: " << (a + 1) << '\n';
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std::cout << "1 + a: " << (1.0f + a) << '\n';
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a = AutoDiff::Forward<double>(1);
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std::cout << "a: " << a << '\n';
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std::cout << "a - 1: " << (a - 1) << '\n';
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std::cout << "a - b: " << (a - b) << '\n';
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}
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