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

/*

 Copyright (C) 2003, 2004, 2009 Ferdinando Ametrano

 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl

 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.

*/

/*! \file getcovariance.hpp

    \brief Covariance matrix calculation

*/

#ifndef quantlib_montecarlo_get_covariance_h

#define quantlib_montecarlo_get_covariance_h

#include <ql/math/matrix.hpp>

#include <ql/utilities/dataformatters.hpp>

#include <ql/math/matrixutilities/pseudosqrt.hpp>

namespace QuantLib {

    //! Calculation of covariance from correlation and standard deviations

    /*! Combines the correlation matrix and the vector of standard deviations

        to return the covariance matrix.

        Note that only the symmetric part of the correlation matrix is

        used. Also it is assumed that the diagonal member of the

        correlation matrix equals one.

        \pre The correlation matrix must be symmetric with the diagonal

             members equal to one.

        \test tested on know values and cross checked with

              CovarianceDecomposition

    */

    template<class DataIterator>

    Matrix getCovariance(DataIterator stdDevBegin,

                         DataIterator stdDevEnd,

                         const Matrix& corr,

                         Real tolerance = 1.0e-12){

        Size size = std::distance(stdDevBegin, stdDevEnd);

        QL_REQUIRE(corr.rows() == size,

                   "dimension mismatch between volatilities (" << size <<

                   ") and correlation rows (" << corr.rows() << ")");

        QL_REQUIRE(corr.columns() == size,

                   "correlation matrix is not square: " << size <<

                   " rows and " << corr.columns() << " columns");

        Matrix covariance(size,size);

        Size i, j;

        DataIterator iIt, jIt;

        for (i=0, iIt=stdDevBegin; i<size; ++i, ++iIt){

            for (j=0, jIt=stdDevBegin; j<i; ++j, ++jIt){

                QL_REQUIRE(std::fabs(corr[i][j]-corr[j][i]) <= tolerance,

                           "correlation matrix not symmetric:"

                           << "\nc[" << i << "," << j << "] = " << corr[i][j]

                           << "\nc[" << j << "," << i << "] = " << corr[j][i]);

                covariance[i][i] = (*iIt) * (*iIt);

                covariance[i][j] = (*iIt) * (*jIt) *

                    0.5 * (corr[i][j] + corr[j][i]);

                covariance[j][i] = covariance[i][j];

            }

            QL_REQUIRE(std::fabs(corr[i][i]-1.0) <= tolerance,

                       "invalid correlation matrix, "

                       << "diagonal element of the " << io::ordinal(i+1)

                       << " row is " << corr[i][i] << " instead of 1.0");

            covariance[i][i] = (*iIt) * (*iIt);

        }

        return covariance;

    }

Unexecuted instantiation: QuantLib::Matrix QuantLib::getCovariance<double*>(double*, double*, QuantLib::Matrix const&, double)

Unexecuted instantiation: QuantLib::Matrix QuantLib::getCovariance<double const*>(double const*, double const*, QuantLib::Matrix const&, double)

    //! Covariance decomposition into correlation and variances

    /*! Extracts the correlation matrix and the vector of variances

        out of the input covariance matrix.

        Note that only the lower symmetric part of the covariance matrix is

        used.

        \pre The covariance matrix must be symmetric.

        \test cross checked with getCovariance

    */

    class CovarianceDecomposition {

      public:

        /*! \pre covarianceMatrix must be symmetric */

        CovarianceDecomposition(

            const Matrix& covarianceMatrix,

            Real tolerance = 1.0e-12);

        /*! returns the variances Array */

        const Array& variances() const { return variances_; }

        /*! returns the standard deviations Array */

        const Array& standardDeviations() const {return stdDevs_; }

        /*! returns the correlation matrix */

        const Matrix& correlationMatrix() const { return correlationMatrix_; }

      private:

        Array variances_, stdDevs_;

        Matrix correlationMatrix_;

    };

}

#endif