steepestDescent.h

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// Xerus - A General Purpose Tensor Library
// Copyright (C) 2014-2017 Benjamin Huber and Sebastian Wolf. 
// 
// Xerus is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published
// by the Free Software Foundation, either version 3 of the License,
// or (at your option) any later version.
// 
// Xerus 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 Affero General Public License for more details.
// 
// You should have received a copy of the GNU Affero General Public License
// along with Xerus. If not, see <http://www.gnu.org/licenses/>.
//
// For further information on Xerus visit https://libXerus.org 
// or contact us at contact@libXerus.org.

#pragma once

#include "../ttNetwork.h"
#include "../performanceData.h"
#include "retractions.h"

namespace xerus {

    
    void line_search(TTTensor &_x, value_t &_alpha, const TTTangentVector &_direction, value_t _derivative, value_t &_residual,
                     std::function<void(TTTensor &, const TTTangentVector &)> _retraction,
                     std::function<value_t()> _calculate_residual,
                     value_t _changeInAlpha = 0.5
    );
    
    class SteepestDescentVariant {
    protected:
        double solve(const TTOperator *_Ap, TTTensor &_x, const TTTensor &_b, size_t _numSteps, value_t _convergenceEpsilon, PerformanceData &_perfData = NoPerfData) const;
    
    public:
        size_t numSteps; 
        value_t convergenceEpsilon; 
        bool assumeSymmetricPositiveDefiniteOperator; 
        TTOperator *preconditioner;
        
        TTRetractionII retraction; 
        
        // TODO preconditioner
        
        SteepestDescentVariant(size_t _numSteps, value_t _convergenceEpsilon, bool _symPosOp, TTRetractionII _retraction)
                : numSteps(_numSteps), convergenceEpsilon(_convergenceEpsilon),
                  assumeSymmetricPositiveDefiniteOperator(_symPosOp), preconditioner(nullptr), retraction(_retraction)
        { }
        
        SteepestDescentVariant(TTRetractionII _retraction)
                : numSteps(0), convergenceEpsilon(0.0), assumeSymmetricPositiveDefiniteOperator(false), preconditioner(nullptr), retraction(_retraction)
        { }
        
        double operator()(const TTOperator &_A, TTTensor &_x, const TTTensor &_b, value_t _convergenceEpsilon, PerformanceData &_perfData = NoPerfData) const {
            return solve(&_A, _x, _b, numSteps, _convergenceEpsilon, _perfData);
        }
        
        double operator()(const TTOperator &_A, TTTensor &_x, const TTTensor &_b, size_t _numSteps, PerformanceData &_perfData = NoPerfData) const {
            return solve(&_A, _x, _b, _numSteps, convergenceEpsilon, _perfData);
        }
        
        double operator()(const TTOperator &_A, TTTensor &_x, const TTTensor &_b, PerformanceData &_perfData = NoPerfData) const {
            return solve(&_A, _x, _b, numSteps, convergenceEpsilon, _perfData);
        }
        
        double operator()(TTTensor &_x, const TTTensor &_b, value_t _convergenceEpsilon, PerformanceData &_perfData = NoPerfData) const {
            return solve(nullptr, _x, _b, numSteps, _convergenceEpsilon, _perfData);
        }
        
        double operator()(TTTensor &_x, const TTTensor &_b, size_t _numSteps, PerformanceData &_perfData = NoPerfData) const {
            return solve(nullptr, _x, _b, _numSteps, convergenceEpsilon, _perfData);
        }
        
        double operator()(TTTensor &_x, const TTTensor &_b, PerformanceData &_perfData = NoPerfData) const {
            return solve(nullptr, _x, _b, numSteps, convergenceEpsilon, _perfData);
        }
    };
    
    extern const SteepestDescentVariant SteepestDescent;
}