MvNormal.h

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#ifndef EIGENRAND_MVDISTS_MVNORMAL_H
#define EIGENRAND_MVDISTS_MVNORMAL_H
 
namespace Eigen
{
    namespace Rand
    {
        namespace detail
        {
            template<typename _Scalar, Index Dim, typename _Mat>
            Matrix<_Scalar, Dim, Dim> get_lt(const MatrixBase<_Mat>& mat)
            {
                LLT<Matrix<_Scalar, Dim, Dim>> llt(mat);
                if (llt.info() == Eigen::Success)
                {
                    return llt.matrixL();
                }
                else
                {
                    SelfAdjointEigenSolver<Matrix<_Scalar, Dim, Dim>> solver(mat);
                    if (solver.info() != Eigen::Success)
                    {
                        throw std::runtime_error{ "The matrix cannot be solved!" };
                    }
                    return solver.eigenvectors() * solver.eigenvalues().cwiseMax(0).cwiseSqrt().asDiagonal();
                }
            }
 
            class FullMatrix {};
            class LowerTriangular {};
            class InvLowerTriangular {};
        }
 
        constexpr detail::FullMatrix full_matrix;
        constexpr detail::LowerTriangular lower_triangular;
        constexpr detail::InvLowerTriangular inv_lower_triangular;
        
 
        template<typename _Scalar, Index Dim = -1>
        class MvNormalGen : public MvVecGenBase<MvNormalGen<_Scalar, Dim>, _Scalar, Dim>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "`MvNormalGen` needs floating point types.");
 
            Matrix<_Scalar, Dim, 1> mean;
            Matrix<_Scalar, Dim, Dim> lt;
            StdNormalGen<_Scalar> stdnorm;
 
        public:
            template<typename MeanTy, typename LTTy>
            MvNormalGen(const MatrixBase<MeanTy>& _mean, const MatrixBase<LTTy>& _lt, detail::LowerTriangular)
                : mean{ _mean }, lt{ _lt }
            {
                eigen_assert(_mean.cols() == 1 && _mean.rows() == _lt.rows() && _lt.rows() == _lt.cols());
            }
 
            template<typename MeanTy, typename CovTy>
            MvNormalGen(const MatrixBase<MeanTy>& _mean, const MatrixBase<CovTy>& _cov, detail::FullMatrix = {})
                : MvNormalGen{ _mean, detail::template get_lt<_Scalar, Dim>(_cov), lower_triangular }
            {
            }
 
            MvNormalGen(const MvNormalGen&) = default;
            MvNormalGen(MvNormalGen&&) = default;
 
            MvNormalGen& operator=(const MvNormalGen&) = default;
            MvNormalGen& operator=(MvNormalGen&&) = default;
 
            Index dims() const { return mean.rows(); }
 
            template<typename Urng>
            inline auto generate(Urng&& urng, Index samples)
                -> decltype((lt * stdnorm.template generate<Matrix<_Scalar, Dim, -1>>(mean.rows(), samples, std::forward<Urng>(urng))).colwise() + mean)
            {
                return (lt * stdnorm.template generate<Matrix<_Scalar, Dim, -1>>(mean.rows(), samples, std::forward<Urng>(urng))).colwise() + mean;
            }
 
            template<typename Urng>
            inline auto generate(Urng&& urng)
                -> decltype((lt * stdnorm.template generate<Matrix<_Scalar, Dim, 1>>(mean.rows(), 1, std::forward<Urng>(urng))).colwise() + mean)
            {
                return (lt * stdnorm.template generate<Matrix<_Scalar, Dim, 1>>(mean.rows(), 1, std::forward<Urng>(urng))).colwise() + mean;
            }
        };
 
        template<typename MeanTy, typename CovTy>
        inline auto makeMvNormalGen(const MatrixBase<MeanTy>& mean, const MatrixBase<CovTy>& cov)
            -> MvNormalGen<typename MatrixBase<MeanTy>::Scalar, MatrixBase<MeanTy>::RowsAtCompileTime>
        {
            static_assert(
                std::is_same<typename MatrixBase<MeanTy>::Scalar, typename MatrixBase<CovTy>::Scalar>::value,
                "Derived::Scalar must be the same with `mean` and `cov`'s Scalar."
            );
            static_assert(
                MatrixBase<MeanTy>::RowsAtCompileTime == MatrixBase<CovTy>::RowsAtCompileTime &&
                MatrixBase<CovTy>::RowsAtCompileTime == MatrixBase<CovTy>::ColsAtCompileTime,
                "assert: mean.RowsAtCompileTime == cov.RowsAtCompileTime && cov.RowsAtCompileTime == cov.ColsAtCompileTime"
            );
            return { mean, cov };
        }
 
        template<typename MeanTy, typename LTTy>
        inline auto makeMvNormalGenFromLt(const MatrixBase<MeanTy>& mean, const MatrixBase<LTTy>& lt)
            -> MvNormalGen<typename MatrixBase<MeanTy>::Scalar, MatrixBase<MeanTy>::RowsAtCompileTime>
        {
            static_assert(
                std::is_same<typename MatrixBase<MeanTy>::Scalar, typename MatrixBase<LTTy>::Scalar>::value,
                "Derived::Scalar must be the same with `mean` and `lt`'s Scalar."
            );
            static_assert(
                MatrixBase<MeanTy>::RowsAtCompileTime == MatrixBase<LTTy>::RowsAtCompileTime &&
                MatrixBase<LTTy>::RowsAtCompileTime == MatrixBase<LTTy>::ColsAtCompileTime,
                "assert: mean.RowsAtCompileTime == lt.RowsAtCompileTime && lt.RowsAtCompileTime == lt.ColsAtCompileTime"
            );
            return { mean, lt, lower_triangular };
        }
 
        template<typename _Scalar, Index Dim>
        class WishartGen : public MvMatGenBase<WishartGen<_Scalar, Dim>, _Scalar, Dim>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "`WishartGen` needs floating point types.");
 
            Index df;
            Matrix<_Scalar, Dim, Dim> chol;
            StdNormalGen<_Scalar> stdnorm;
            std::vector<ChiSquaredGen<_Scalar>> chisqs;
        public:
            template<typename ScaleTy>
            WishartGen(Index _df, const MatrixBase<ScaleTy>& _lt, detail::LowerTriangular)
                : df{ _df }, chol{ _lt }
            {
                eigen_assert(df > chol.rows() - 1);
                eigen_assert(chol.rows() == chol.cols());
 
                for (Index i = 0; i < chol.rows(); ++i)
                {
                    chisqs.emplace_back(df - i);
                }
            }
 
            template<typename ScaleTy>
            WishartGen(Index _df, const MatrixBase<ScaleTy>& _scale, detail::FullMatrix = {})
                : WishartGen{ _df, detail::template get_lt<_Scalar, Dim>(_scale), lower_triangular }
            {
                eigen_assert(_scale.rows() == _scale.cols());
            }
 
            WishartGen(const WishartGen&) = default;
            WishartGen(WishartGen&&) = default;
 
            WishartGen& operator=(const WishartGen&) = default;
            WishartGen& operator=(WishartGen&&) = default;
 
            Index dims() const { return chol.rows(); }
 
            template<typename Urng>
            inline Matrix<_Scalar, Dim, -1> generate(Urng&& urng, Index samples)
            {
                const Index dim = chol.rows();
                const Index normSamples = samples * dim * (dim - 1) / 2;
                using ArrayXs = Array<_Scalar, -1, 1>;
                Matrix<_Scalar, Dim, -1> rand_mat(dim, dim * samples), tmp(dim, dim * samples);
                
                _Scalar* ptr = tmp.data();
                Map<ArrayXs>{ ptr, normSamples } = stdnorm.template generate<ArrayXs>(normSamples, 1, urng);
                for (Index j = 0; j < samples; ++j)
                {
                    for (Index i = 0; i < dim - 1; ++i)
                    {
                        rand_mat.col(i + j * dim).tail(dim - 1 - i) = Map<ArrayXs>{ ptr, dim - 1 - i };
                        ptr += dim - 1 - i;
                    }
                }
                
                for (Index i = 0; i < dim; ++i)
                {
                    _Scalar* ptr = tmp.data();
                    Map<ArrayXs>{ ptr, samples } = chisqs[i].template generate<ArrayXs>(samples, 1, urng).sqrt();
                    for (Index j = 0; j < samples; ++j)
                    {
                        rand_mat(i, i + j * dim) = *ptr++;
                    }
                }
 
                for (Index j = 0; j < samples; ++j)
                {
                    rand_mat.middleCols(j * dim, dim).template triangularView<StrictlyUpper>().setZero();
                }
                tmp.noalias() = chol * rand_mat;
                
                for (Index j = 0; j < samples; ++j)
                {
                    auto t = tmp.middleCols(j * dim, dim);
                    rand_mat.middleCols(j * dim, dim).noalias() = t * t.transpose();
                }
                return rand_mat;
            }
 
            template<typename Urng>
            inline Matrix<_Scalar, Dim, -1> generate(Urng&& urng)
            {
                const Index dim = chol.rows();
                const Index normSamples = dim * (dim - 1) / 2;
                using ArrayXs = Array<_Scalar, -1, 1>;
                Matrix<_Scalar, Dim, Dim> rand_mat(dim, dim);
                Map<ArrayXs>{ rand_mat.data(), normSamples } = stdnorm.template generate<ArrayXs>(normSamples, 1, urng);
 
                for (Index i = 0; i < dim / 2; ++i)
                {
                    rand_mat.col(dim - 2 - i).tail(i + 1) = rand_mat.col(i).head(i + 1);
                }
                
                for (Index i = 0; i < dim; ++i)
                {
                    rand_mat(i, i) = chisqs[i].template generate<Array<_Scalar, 1, 1>>(1, 1, urng).sqrt()(0);
                }
                rand_mat.template triangularView<StrictlyUpper>().setZero();
 
                auto t = (chol * rand_mat).eval();
                return (t * t.transpose()).eval();
            }
        };
 
        template<typename ScaleTy>
        inline auto makeWishartGen(Index df, const MatrixBase<ScaleTy>& scale)
            -> WishartGen<typename MatrixBase<ScaleTy>::Scalar, MatrixBase<ScaleTy>::RowsAtCompileTime>
        {
            static_assert(
                MatrixBase<ScaleTy>::RowsAtCompileTime == MatrixBase<ScaleTy>::ColsAtCompileTime,
                "assert: scale.RowsAtCompileTime == scale.ColsAtCompileTime"
            );
            return { df, scale };
        }
 
        template<typename LTTy>
        inline auto makeWishartGenFromLt(Index df, const MatrixBase<LTTy>& lt)
            -> WishartGen<typename MatrixBase<LTTy>::Scalar, MatrixBase<LTTy>::RowsAtCompileTime>
        {
            static_assert(
                MatrixBase<LTTy>::RowsAtCompileTime == MatrixBase<LTTy>::ColsAtCompileTime,
                "assert: lt.RowsAtCompileTime == lt.ColsAtCompileTime"
                );
            return { df, lt, lower_triangular };
        }
 
        template<typename _Scalar, Index Dim>
        class InvWishartGen : public MvMatGenBase<InvWishartGen<_Scalar, Dim>, _Scalar, Dim>
        {
            static_assert(std::is_floating_point<_Scalar>::value, "`InvWishartGen` needs floating point types.");
 
            Index df;
            Matrix<_Scalar, Dim, Dim> chol;
            StdNormalGen<_Scalar> stdnorm;
            std::vector<ChiSquaredGen<_Scalar>> chisqs;
        public:
            template<typename ScaleTy>
            InvWishartGen(Index _df, const MatrixBase<ScaleTy>& _ilt, detail::InvLowerTriangular)
                : df{ _df }, chol{ _ilt }
            {
                eigen_assert(df > chol.rows() - 1);
                eigen_assert(chol.rows() == chol.cols());
 
                for (Index i = 0; i < chol.rows(); ++i)
                {
                    chisqs.emplace_back(df - i);
                }
            }
 
            template<typename ScaleTy>
            InvWishartGen(Index _df, const MatrixBase<ScaleTy>& _scale, detail::FullMatrix = {})
                : InvWishartGen{ _df, detail::template get_lt<_Scalar, Dim>(_scale.inverse()), inv_lower_triangular }
            {
                eigen_assert(_scale.rows() == _scale.cols());   
            }
 
            InvWishartGen(const InvWishartGen&) = default;
            InvWishartGen(InvWishartGen&&) = default;
 
            InvWishartGen& operator=(const InvWishartGen&) = default;
            InvWishartGen& operator=(InvWishartGen&&) = default;
 
            Index dims() const { return chol.rows(); }
 
            template<typename Urng>
            inline Matrix<_Scalar, Dim, -1> generate(Urng&& urng, Index samples)
            {
                const Index dim = chol.rows();
                const Index normSamples = samples * dim * (dim - 1) / 2;
                using ArrayXs = Array<_Scalar, -1, 1>;
                Matrix<_Scalar, Dim, -1> rand_mat(dim, dim * samples), tmp(dim, dim * samples);
 
                _Scalar* ptr = tmp.data();
                Map<ArrayXs>{ ptr, normSamples } = stdnorm.template generate<ArrayXs>(normSamples, 1, urng);
                for (Index j = 0; j < samples; ++j)
                {
                    for (Index i = 0; i < dim - 1; ++i)
                    {
                        rand_mat.col(i + j * dim).tail(dim - 1 - i) = Map<ArrayXs>{ ptr, dim - 1 - i };
                        ptr += dim - 1 - i;
                    }
                }
 
                for (Index i = 0; i < dim; ++i)
                {
                    _Scalar* ptr = tmp.data();
                    Map<ArrayXs>{ ptr, samples } = chisqs[i].template generate<ArrayXs>(samples, 1, urng).sqrt();
                    for (Index j = 0; j < samples; ++j)
                    {
                        rand_mat(i, i + j * dim) = *ptr++;
                    }
                }
 
                for (Index j = 0; j < samples; ++j)
                {
                    rand_mat.middleCols(j * dim, dim).template triangularView<StrictlyUpper>().setZero();
                }
                tmp.noalias() = chol * rand_mat;
 
                auto id = Eigen::Matrix<_Scalar, Dim, Dim>::Identity(dim, dim);
                for (Index j = 0; j < samples; ++j)
                {
                    auto t = tmp.middleCols(j * dim, dim);
                    auto u = rand_mat.middleCols(j * dim, dim);
                    u.noalias() = t.template triangularView<Lower>().solve(id);
                    t.noalias() = u.transpose() * u;
                }
                return tmp;
            }
 
            template<typename Urng>
            inline Matrix<_Scalar, Dim, -1> generate(Urng&& urng)
            {
                const Index dim = chol.rows();
                const Index normSamples = dim * (dim - 1) / 2;
                using ArrayXs = Array<_Scalar, -1, 1>;
                Matrix<_Scalar, Dim, Dim> rand_mat(dim, dim);
                Map<ArrayXs>{ rand_mat.data(), normSamples } = stdnorm.template generate<ArrayXs>(normSamples, 1, urng);
 
                for (Index i = 0; i < dim / 2; ++i)
                {
                    rand_mat.col(dim - 2 - i).tail(i + 1) = rand_mat.col(i).head(i + 1);
                }
 
                for (Index i = 0; i < dim; ++i)
                {
                    rand_mat(i, i) = chisqs[i].template generate<Array<_Scalar, 1, 1>>(1, 1, urng).sqrt()(0);
                }
                rand_mat.template triangularView<StrictlyUpper>().setZero();
 
                auto t = (chol * rand_mat).eval();
                auto id = Eigen::Matrix<_Scalar, Dim, Dim>::Identity(dim, dim);
                rand_mat.noalias() = t.template triangularView<Lower>().solve(id);
 
                return (rand_mat.transpose() * rand_mat).eval();
            }
        };
 
        template<typename ScaleTy>
        inline auto makeInvWishartGen(Index df, const MatrixBase<ScaleTy>& scale)
            -> InvWishartGen<typename MatrixBase<ScaleTy>::Scalar, MatrixBase<ScaleTy>::RowsAtCompileTime>
        {
            static_assert(
                MatrixBase<ScaleTy>::RowsAtCompileTime == MatrixBase<ScaleTy>::ColsAtCompileTime,
                "assert: scale.RowsAtCompileTime == scale.ColsAtCompileTime"
            );
            return { df, scale };
        }
 
        template<typename ILTTy>
        inline auto makeInvWishartGenFromIlt(Index df, const MatrixBase<ILTTy>& ilt)
            -> InvWishartGen<typename MatrixBase<ILTTy>::Scalar, MatrixBase<ILTTy>::RowsAtCompileTime>
        {
            static_assert(
                MatrixBase<ILTTy>::RowsAtCompileTime == MatrixBase<ILTTy>::ColsAtCompileTime,
                "assert: ilt.RowsAtCompileTime == ilt.ColsAtCompileTime"
            );
            return { df, ilt, inv_lower_triangular };
        }
    }
}
 
#endif