tridiagonaloperator.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
 Copyright (C) 2003, 2004, 2005, 2006 StatPro Italia srl
 Copyright (C) 2011 Ferdinando Ametrano
 
 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/
 
 QuantLib is free software: you can redistribute it and/or modify it
 under the terms of the QuantLib license.  You should have received a
 copy of the license along with this program; if not, please email
 <quantlib-dev@lists.sf.net>. The license is also available online at
 <http://quantlib.org/license.shtml>.
 
 This program 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 license for more details.
*/
 
/*! \file tridiagonaloperator.hpp
    \brief tridiagonal operator
*/
 
#ifndef quantlib_tridiagonal_operator_hpp
#define quantlib_tridiagonal_operator_hpp
 
#include <ql/math/array.hpp>
#include <ql/math/comparison.hpp>
#include <ql/shared_ptr.hpp>
 
namespace QuantLib {
 
    //! Base implementation for tridiagonal operator
    /*! \warning to use real time-dependant algebra, you must overload
                 the corresponding operators in the inheriting
                 time-dependent class.
 
        \ingroup findiff
    */
    class TridiagonalOperator {
        // unary operators
        friend TridiagonalOperator operator+(const TridiagonalOperator&);
        friend TridiagonalOperator operator-(const TridiagonalOperator&);
        // binary operators
        friend TridiagonalOperator operator+(const TridiagonalOperator&,
                                             const TridiagonalOperator&);
        friend TridiagonalOperator operator-(const TridiagonalOperator&,
                                             const TridiagonalOperator&);
        friend TridiagonalOperator operator*(Real,
                                             const TridiagonalOperator&);
        friend TridiagonalOperator operator*(const TridiagonalOperator&,
                                             Real);
        friend TridiagonalOperator operator/(const TridiagonalOperator&,
                                             Real);
      public:
        typedef Array array_type;
        // constructors
        explicit TridiagonalOperator(Size size = 0);
        TridiagonalOperator(const Array& low,
                            const Array& mid,
                            const Array& high);
        TridiagonalOperator(const TridiagonalOperator&) = default;
        TridiagonalOperator(TridiagonalOperator&&) noexcept;
        TridiagonalOperator& operator=(const TridiagonalOperator&);
        TridiagonalOperator& operator=(TridiagonalOperator&&) noexcept;
        ~TridiagonalOperator() = default;
        //! \name Operator interface
        //@{
        //! apply operator to a given array
        Array applyTo(const Array& v) const;
        //! solve linear system for a given right-hand side
        Array solveFor(const Array& rhs) const;
        /*! solve linear system for a given right-hand side
            without result Array allocation. The rhs and result parameters
            can be the same Array, in which case rhs will be changed
        */
        void solveFor(const Array& rhs,
                      Array& result) const;
        //! solve linear system with SOR approach
        Array SOR(const Array& rhs,
                  Real tol) const;
        //! identity instance
        static TridiagonalOperator identity(Size size);
        //@}
        //! \name Inspectors
        //@{
        Size size() const { return n_; }
        bool isTimeDependent() const { return !!timeSetter_; }
        const Array& lowerDiagonal() const { return lowerDiagonal_; }
        const Array& diagonal() const { return diagonal_; }
        const Array& upperDiagonal() const { return upperDiagonal_; }
        //@}
        //! \name Modifiers
        //@{
        void setFirstRow(Real, Real);
        void setMidRow(Size, Real, Real, Real);
        void setMidRows(Real, Real, Real);
        void setLastRow(Real, Real);
        void setTime(Time t);
        //@}
        //! \name Utilities
        //@{
        void swap(TridiagonalOperator&) noexcept;
        //@}
        //! encapsulation of time-setting logic
        class TimeSetter {
          public:
            virtual ~TimeSetter() = default;
            virtual void setTime(Time t,
                                 TridiagonalOperator& L) const = 0;
        };
      protected:
        Size n_;
        Array diagonal_, lowerDiagonal_, upperDiagonal_;
        mutable Array temp_;
        ext::shared_ptr<TimeSetter> timeSetter_;
    };
 
    /* \relates TridiagonalOperator */
    void swap(TridiagonalOperator&, TridiagonalOperator&) noexcept;
 
 
    // inline definitions
 
    inline TridiagonalOperator::TridiagonalOperator(TridiagonalOperator&& from) noexcept : n_(0) {
        swap(from);
    }
 
    inline TridiagonalOperator& TridiagonalOperator::operator=(
                                const TridiagonalOperator& from) {
        TridiagonalOperator temp(from);
        swap(temp);
        return *this;
    }
 
    inline TridiagonalOperator&
    TridiagonalOperator::operator=(TridiagonalOperator&& from) noexcept {
        swap(from);
        return *this;
    }
 
    inline void TridiagonalOperator::setFirstRow(Real valB,
                                                 Real valC) {
        diagonal_[0]      = valB;
        upperDiagonal_[0] = valC;
    }
 
    inline void TridiagonalOperator::setMidRow(Size i,
                                               Real valA,
                                               Real valB,
                                               Real valC) {
        QL_REQUIRE(i>=1 && i<=n_-2,
                   "out of range in TridiagonalSystem::setMidRow");
        lowerDiagonal_[i-1] = valA;
        diagonal_[i]        = valB;
        upperDiagonal_[i]   = valC;
    }
 
    inline void TridiagonalOperator::setMidRows(Real valA,
                                                Real valB,
                                                Real valC) {
        for (Size i=1; i<=n_-2; i++) {
            lowerDiagonal_[i-1] = valA;
            diagonal_[i]        = valB;
            upperDiagonal_[i]   = valC;
        }
    }
 
    inline void TridiagonalOperator::setLastRow(Real valA,
                                                Real valB) {
        lowerDiagonal_[n_-2] = valA;
        diagonal_[n_-1]      = valB;
    }
 
    inline void TridiagonalOperator::setTime(Time t) {
        if (timeSetter_ != nullptr)
            timeSetter_->setTime(t, *this);
    }
 
    inline void TridiagonalOperator::swap(TridiagonalOperator& from) noexcept {
        std::swap(n_, from.n_);
        diagonal_.swap(from.diagonal_);
        lowerDiagonal_.swap(from.lowerDiagonal_);
        upperDiagonal_.swap(from.upperDiagonal_);
        temp_.swap(from.temp_);
        timeSetter_.swap(from.timeSetter_);
    }
 
 
    // Time constant algebra
 
    inline TridiagonalOperator operator+(const TridiagonalOperator& D) {
        TridiagonalOperator D1 = D;
        return D1;
    }
 
    inline TridiagonalOperator operator-(const TridiagonalOperator& D) {
        Array low = -D.lowerDiagonal_,
            mid = -D.diagonal_,
            high = -D.upperDiagonal_;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline TridiagonalOperator operator+(const TridiagonalOperator& D1,
                                         const TridiagonalOperator& D2) {
        Array low = D1.lowerDiagonal_ + D2.lowerDiagonal_,
            mid = D1.diagonal_ + D2.diagonal_,
            high = D1.upperDiagonal_ + D2.upperDiagonal_;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline TridiagonalOperator operator-(const TridiagonalOperator& D1,
                                         const TridiagonalOperator& D2) {
        Array low = D1.lowerDiagonal_ - D2.lowerDiagonal_,
            mid = D1.diagonal_ - D2.diagonal_,
            high = D1.upperDiagonal_ - D2.upperDiagonal_;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline TridiagonalOperator operator*(Real a,
                                         const TridiagonalOperator& D) {
        Array low = D.lowerDiagonal_ * a,
            mid = D.diagonal_ * a,
            high = D.upperDiagonal_ * a;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline TridiagonalOperator operator*(const TridiagonalOperator& D,
                                         Real a) {
        Array low = D.lowerDiagonal_ * a,
            mid = D.diagonal_ * a,
            high = D.upperDiagonal_ * a;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline TridiagonalOperator operator/(const TridiagonalOperator& D,
                                         Real a) {
        Array low = D.lowerDiagonal_ / a,
            mid = D.diagonal_ / a,
            high = D.upperDiagonal_ / a;
        TridiagonalOperator result(low, mid, high);
        return result;
    }
 
    inline void swap(TridiagonalOperator& L1,
                     TridiagonalOperator& L2) noexcept {
        L1.swap(L2);
    }
 
}
 
#endif