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

/*

 Copyright (C) 2014 Jose Aparicio

 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/experimental/math/tcopulapolicy.hpp>

#include <numeric>

#include <algorithm>

namespace QuantLib {

    TCopulaPolicy::TCopulaPolicy(

        const std::vector<std::vector<Real> >& factorWeights, 

        const initTraits& vals)

    {

        for (int tOrder : vals.tOrders) {

            // require no T is of order 2 (finite variance)

            QL_REQUIRE(tOrder > 2, "Non finite variance T in latent model.");

            distributions_.emplace_back(tOrder);

            // inverses T variaces used in normalization of the random factors

            // For low values of the T order this number is very close to zero 

            // and it enters the expressions dividing them, which introduces 

            // numerical errors.

            varianceFactors_.push_back(std::sqrt((tOrder - 2.) / tOrder));

        }

        for (const auto& factorWeight : factorWeights) {

            // This ensures the latent model is 'canonical'

            QL_REQUIRE(vals.tOrders.size() == factorWeight.size() + 1,

                       // num factors plus one

                       "Incompatible number of T functions and number of factors.");

            Real factorsNorm = std::inner_product(factorWeight.begin(), factorWeight.end(),

                                                  factorWeight.begin(), Real(0.));

            QL_REQUIRE(factorsNorm < 1., 

                "Non normal random factor combination.");

            Real idiosyncFctr = std::sqrt(1.-factorsNorm);

            // linear comb factors ajusted for the variance renormalization:

            std::vector<Real> normFactorWeights;

            normFactorWeights.reserve(factorWeight.size());

            for (Size iFactor = 0; iFactor < factorWeight.size(); iFactor++)

                normFactorWeights.push_back(factorWeight[iFactor] * varianceFactors_[iFactor]);

            // idiosincratic term, all Z factors are assumed identical.

            normFactorWeights.push_back(idiosyncFctr * varianceFactors_.back());

            latentVarsCumul_.emplace_back(vals.tOrders, normFactorWeights);

            latentVarsInverters_.emplace_back(vals.tOrders, normFactorWeights);

        }

    }

    std::vector<Real> TCopulaPolicy::allFactorCumulInverter(

        const std::vector<Real>& probs) const 

    {

    #if defined(QL_EXTRA_SAFETY_CHECKS)

        QL_REQUIRE(probs.size()-latentVarsCumul_.size() 

            == distributions_.size()-1, 

            "Incompatible sample and latent model sizes");

    #endif

        std::vector<Real> result(probs.size());

        Size indexSystemic = 0;

        std::transform(probs.begin(), probs.begin() + varianceFactors_.size()-1,

                       result.begin(),

                       [&](Probability p) { return inverseCumulativeDensity(p, indexSystemic++); });

        std::transform(probs.begin() + varianceFactors_.size()-1, probs.end(),

                       result.begin()+ varianceFactors_.size()-1,

                       [&](Probability p) { return inverseCumulativeZ(p); });

        return result;

    }

}