/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2006, 2015 Ferdinando Ametrano

 Copyright (C) 2006 Cristina Duminuco

 Copyright (C) 2005, 2006 Klaus Spanderen

 Copyright (C) 2007 Giorgio Facchinetti

 Copyright (C) 2015 Paolo Mazzocchi

 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

 <https://www.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.

*/

#include <ql/math/distributions/normaldistribution.hpp>

#include <ql/math/interpolations/abcdinterpolation.hpp>

#include <ql/math/optimization/constraint.hpp>

#include <ql/math/optimization/levenbergmarquardt.hpp>

#include <ql/math/optimization/method.hpp>

#include <ql/pricingengines/blackformula.hpp>

#include <ql/termstructures/volatility/abcd.hpp>

#include <ql/termstructures/volatility/abcdcalibration.hpp>

#include <utility>

namespace QuantLib {

    // to constrained <- from unconstrained

    Array AbcdCalibration::AbcdParametersTransformation::direct(const Array& x) const {

        y_[1] = x[1];

        y_[2] = std::exp(x[2]);

        y_[3] = std::exp(x[3]);

        y_[0] = std::exp(x[0]) - y_[3];

        return y_;

    }

    // to unconstrained <- from constrained

    Array AbcdCalibration::AbcdParametersTransformation::inverse(const Array& x) const {

        y_[1] = x[1];

        y_[2] = std::log(x[2]);

        y_[3] = std::log(x[3]);

        y_[0] = std::log(x[0] + x[3]);

        return y_;

    }

    // to constrained <- from unconstrained

    AbcdCalibration::AbcdCalibration(const std::vector<Real>& t,

                                     const std::vector<Real>& blackVols,

                                     Real a,

                                     Real b,

                                     Real c,

                                     Real d,

                                     bool aIsFixed,

                                     bool bIsFixed,

                                     bool cIsFixed,

                                     bool dIsFixed,

                                     bool vegaWeighted,

                                     ext::shared_ptr<EndCriteria> endCriteria,

                                     ext::shared_ptr<OptimizationMethod> optMethod)

    : aIsFixed_(aIsFixed), bIsFixed_(bIsFixed), cIsFixed_(cIsFixed), dIsFixed_(dIsFixed), a_(a),

      b_(b), c_(c), d_(d), abcdEndCriteria_(EndCriteria::None),

      endCriteria_(std::move(endCriteria)), optMethod_(std::move(optMethod)),

      weights_(blackVols.size(), 1.0 / blackVols.size()), vegaWeighted_(vegaWeighted), times_(t),

      blackVols_(blackVols) {

        AbcdMathFunction::validate(a, b, c, d);

        QL_REQUIRE(blackVols.size()==t.size(),

                       "mismatch between number of times (" << t.size() <<

                       ") and blackVols (" << blackVols.size() << ")");

        // if no optimization method or endCriteria is provided, we provide one

        if (!optMethod_) {

            Real epsfcn = 1.0e-8;

            Real xtol = 1.0e-8;

            Real gtol = 1.0e-8;

            bool useCostFunctionsJacobian = false;

            optMethod_ = ext::shared_ptr<OptimizationMethod>(new

                LevenbergMarquardt(epsfcn, xtol, gtol, useCostFunctionsJacobian));

        }

        if (!endCriteria_) {

            Size maxIterations = 10000;

            Size maxStationaryStateIterations = 1000;

            Real rootEpsilon = 1.0e-8;

            Real functionEpsilon = 0.3e-4;     // Why 0.3e-4 ?

            Real gradientNormEpsilon = 0.3e-4; // Why 0.3e-4 ?

            endCriteria_ = ext::make_shared<EndCriteria>(maxIterations, maxStationaryStateIterations,

                            rootEpsilon, functionEpsilon, gradientNormEpsilon);

        }

    }

    void AbcdCalibration::compute() {

        if (vegaWeighted_) {

            Real weightsSum = 0.0;

            for (Size i=0; i<times_.size() ; i++) {

                Real stdDev = std::sqrt(blackVols_[i]* blackVols_[i]* times_[i]);

                // when strike==forward, the blackFormulaStdDevDerivative becomes

                weights_[i] = CumulativeNormalDistribution().derivative(.5*stdDev);

                weightsSum += weights_[i];

            }

            // weight normalization

            for (Size i=0; i<times_.size() ; i++) {

                weights_[i] /= weightsSum;

            }

        }

        // there is nothing to optimize

        if (aIsFixed_ && bIsFixed_ && cIsFixed_ && dIsFixed_) {

            abcdEndCriteria_ = EndCriteria::None;

            //error_ = interpolationError();

            //maxError_ = interpolationMaxError();

            return;

        } else {

            AbcdError costFunction(this);

            transformation_ = ext::shared_ptr<ParametersTransformation>(new

                AbcdParametersTransformation);

            Array guess(4);

            guess[0] = a_;

            guess[1] = b_;

            guess[2] = c_;

            guess[3] = d_;

            std::vector<bool> parameterAreFixed(4);

            parameterAreFixed[0] = aIsFixed_;

            parameterAreFixed[1] = bIsFixed_;

            parameterAreFixed[2] = cIsFixed_;

            parameterAreFixed[3] = dIsFixed_;

            Array inversedTransformatedGuess(transformation_->inverse(guess));

            ProjectedCostFunction projectedAbcdCostFunction(costFunction,

                            inversedTransformatedGuess, parameterAreFixed);

            Array projectedGuess

                (projectedAbcdCostFunction.project(inversedTransformatedGuess));

            NoConstraint constraint;

            Problem problem(projectedAbcdCostFunction, constraint, projectedGuess);

            abcdEndCriteria_ = optMethod_->minimize(problem, *endCriteria_);

            Array projectedResult(problem.currentValue());

            Array transfResult(projectedAbcdCostFunction.include(projectedResult));

            Array result = transformation_->direct(transfResult);

            AbcdMathFunction::validate(a_, b_, c_, d_);

            a_ = result[0];

            b_ = result[1];

            c_ = result[2];

            d_ = result[3];

        }

    }

    Real AbcdCalibration::value(Real x) const {

        return abcdBlackVolatility(x,a_,b_,c_,d_);

    }

    std::vector<Real> AbcdCalibration::k(const std::vector<Real>& t,

                                         const std::vector<Real>& blackVols) const {

        QL_REQUIRE(blackVols.size()==t.size(),

               "mismatch between number of times (" << t.size() <<

               ") and blackVols (" << blackVols.size() << ")");

        std::vector<Real> k(t.size());

        for (Size i=0; i<t.size() ; i++) {

            k[i]=blackVols[i]/value(t[i]);

        }

        return k;

    }

    Real AbcdCalibration::error() const {

        Size n = times_.size();

        Real error, squaredError = 0.0;

        for (Size i=0; i<times_.size() ; i++) {

            error = (value(times_[i]) - blackVols_[i]);

            squaredError += error * error * weights_[i];

        }

        return std::sqrt(n*squaredError/(n-1));

    }

    Real AbcdCalibration::maxError() const {

        Real error, maxError = QL_MIN_REAL;

        for (Size i=0; i<times_.size() ; i++) {

            error = std::fabs(value(times_[i]) - blackVols_[i]);

            maxError = std::max(maxError, error);

        }

        return maxError;

    }

    // calculate weighted differences

    Array AbcdCalibration::errors() const {

        Array results(times_.size());

        for (Size i=0; i<times_.size() ; i++) {

            results[i] = (value(times_[i]) - blackVols_[i])* std::sqrt(weights_[i]);

        }

        return results;

    }

    EndCriteria::Type AbcdCalibration::endCriteria() const{

        return abcdEndCriteria_;

    }

}