//
// predModule.cpp: implementation of predictor module using Eigen
//
// Copyright (C) 2011-2013 Douglas Bates, Martin Maechler, Ben Bolker and Steve Walker
//
// This file is part of lme4.

#include "predModule.h"
#include <RcppEigenStubs.cpp>

namespace lme4 {
    using    Rcpp::as;

    using     std::invalid_argument;
    using     std::runtime_error;

    using   Eigen::ArrayXd;

    typedef Eigen::Map<MatrixXd>  MMat;
    typedef Eigen::Map<VectorXd>  MVec;
    typedef Eigen::Map<VectorXi>  MiVec;

    merPredD::merPredD(SEXP X, SEXP Lambdat, SEXP LamtUt, SEXP Lind,
                       SEXP RZX, SEXP Ut, SEXP Utr, SEXP V, SEXP VtV,
                       SEXP Vtr, SEXP Xwts, SEXP Zt, SEXP beta0,
                       SEXP delb, SEXP delu, SEXP theta, SEXP u0)
        : d_X(       as<MMat>(X)),
          d_RZX(     as<MMat>(RZX)),
          d_V(       as<MMat>(V)),
          d_VtV(     as<MMat>(VtV)),
          d_Zt(      as<MSpMatrixd>(Zt)),
          d_Ut(      as<MSpMatrixd>(Ut)),
          d_LamtUt(  as<MSpMatrixd>(LamtUt)),
          d_Lambdat( as<MSpMatrixd>(Lambdat)),
          d_theta(   as<MVec>(theta)),
          d_Vtr(     as<MVec>(Vtr)),
          d_Utr(     as<MVec>(Utr)),
          d_Xwts(    as<MVec>(Xwts)),
          d_beta0(   as<MVec>(beta0)),
          d_delb(    as<MVec>(delb)),
          d_delu(    as<MVec>(delu)),
          d_u0(      as<MVec>(u0)),
          d_Lind(    as<MiVec>(Lind)),
          d_N(       d_X.rows()),
          d_p(       d_X.cols()),
          d_q(       d_Zt.rows()),
          d_RX(      d_p)
    {                           // Check consistency of dimensions
        if (d_N != d_Zt.cols())
            throw invalid_argument("Z dimension mismatch");
        if (d_Lind.size() != d_Lambdat.nonZeros())
            throw invalid_argument("size of Lind does not match nonzeros in Lambda");
        // checking of the range of Lind is now done in R code for reference class
	// initialize beta0, u0, delb, delu and VtV

	if (d_V.cols() > 0) {
	    d_VtV.setZero();
	    d_VtV.selfadjointView<Eigen::Upper>().rankUpdate(d_V.adjoint());
	}
        d_RX.compute(d_VtV);    // ensure d_RX is initialized even in the 0-column X case

        setTheta(d_theta);          // starting values into Lambda
        d_L.cholmod().final_ll = 1; // force an LL' decomposition
        updateLamtUt();
        d_L.analyzePattern(d_LamtUt * d_LamtUt.transpose()); // perform symbolic analysis
        if (d_L.info() != Eigen::Success)
            throw runtime_error("CholeskyDecomposition.analyzePattern failed");
    }

    void merPredD::updateLamtUt() {
        // This complicated code bypasses problems caused by Eigen's
        // sparse/sparse matrix multiplication pruning zeros.  The
        // Cholesky decomposition croaks if the structure of d_LamtUt changes.
        MVec(d_LamtUt.valuePtr(), d_LamtUt.nonZeros()).setZero();
        for (Index j = 0; j < d_Ut.outerSize(); ++j) {
            for(MSpMatrixd::InnerIterator rhsIt(d_Ut, j); rhsIt; ++rhsIt) {
                Scalar                        y(rhsIt.value());
                Index                         k(rhsIt.index());
                MSpMatrixd::InnerIterator prdIt(d_LamtUt, j);
                for (MSpMatrixd::InnerIterator lhsIt(d_Lambdat, k); lhsIt; ++lhsIt) {
                    Index                     i = lhsIt.index();
                    while (prdIt && prdIt.index() != i) ++prdIt;
                    if (!prdIt) throw runtime_error("logic error in updateLamtUt");
                    prdIt.valueRef()           += lhsIt.value() * y;
                }
            }
        }
    }

    VectorXd merPredD::b(const double& f) const {return d_Lambdat.adjoint() * u(f);}

    VectorXd merPredD::beta(const double& f) const {return d_beta0 + f * d_delb;}

    VectorXd merPredD::linPred(const double& f) const {
        return d_X * beta(f) + d_Zt.adjoint() * b(f);
    }

    Rcpp::List merPredD::condVar(const Rcpp::Environment& rho) const {
        const Rcpp::List ll(as<Rcpp::List>(rho["flist"])), trmlst(as<Rcpp::List>(rho["terms"]));
        const int nf(ll.size());
        const MiVec nl(as<MiVec>(rho["nlevs"])),
            nct(as<MiVec>(rho["nctot"])), off(as<MiVec>(rho["offsets"]));
        // ll : flist
        // trmlst : terms : list with one element per factor, indicating corresponding term
        // nf : : number of unique factors
        // nl : nlevs : number of levels for each unique factor
        // nct : nctot : total number of components per factor
        // off : offsets : points to where each term starts
        Rcpp::List ans(nf);
        ans.names() = clone(as<Rcpp::CharacterVector>(ll.names()));
        const SpMatrixd d_Lambda(d_Lambdat.adjoint());
        for (int i = 0; i < nf; i++) {
            int         ncti(nct[i]), nli(nl[i]);
            Rcpp::NumericVector ansi(ncti * ncti * nli);
            ansi.attr("dim") = Rcpp::IntegerVector::create(ncti, ncti, nli);
            ans[i] = ansi;
            const MiVec trms(as<MiVec>(trmlst(i)));
            // ncti : total number of components in factor i
            // nli : number of levels in factor i
            // ansi : array in which to store condVar's for factor i
            // trms : pointers to terms corresponding to factor i
            if (trms.size() == 1) { // simple case
                int offset = off[trms[0] - 1];
                for (int j = 0; j < nli; ++j) {
                    MatrixXd LvT(d_Lambdat.innerVectors(offset + j * ncti, ncti));
                    MatrixXd Lv(LvT.adjoint());
                    d_L.solveInPlace(LvT, CHOLMOD_A);
                    MatrixXd rr(Lv * LvT);
                    std::copy(rr.data(), rr.data() + rr.size(), &ansi[j * ncti * ncti]);
                }
            } else {
                throw std::runtime_error("multiple terms per factor not yet written");
            }
        }
        return ans;
    }

    VectorXd merPredD::u(const double& f) const {return d_u0 + f * d_delu;}

    merPredD::Scalar merPredD::sqrL(const double& f) const {return u(f).squaredNorm();}

    void merPredD::updateL() {
        updateLamtUt();
        // More complicated code to handle the case of zeros in
        // potentially nonzero positions.  The factorize_p method is
        // for a SparseMatrix<double>, not a MappedSparseMatrix<double>.
        SpMatrixd  m(d_LamtUt.rows(), d_LamtUt.cols());
        m.resizeNonZeros(d_LamtUt.nonZeros());
        std::copy(d_LamtUt.valuePtr(),
                  d_LamtUt.valuePtr() + d_LamtUt.nonZeros(),
                  m.valuePtr());
        std::copy(d_LamtUt.innerIndexPtr(),
                  d_LamtUt.innerIndexPtr() + d_LamtUt.nonZeros(),
                  m.innerIndexPtr());
        std::copy(d_LamtUt.outerIndexPtr(),
                  d_LamtUt.outerIndexPtr() + d_LamtUt.cols() + 1,
                  m.outerIndexPtr());
        d_L.factorize_p(m, Eigen::ArrayXi(), 1.);
        d_ldL2 = ::M_chm_factor_ldetL2(d_L.factor());
    }

    void merPredD::setTheta(const VectorXd& theta) {

        if (theta.size() != d_theta.size()) {
            Rcpp::Rcout << "(" << theta.size() << "!=" <<
                d_theta.size() << ")" << std::endl;
            // char errstr[100];
            // sprintf(errstr,"theta size mismatch (%d != %d)",
            //      theta.size(),d_theta.size());
            throw invalid_argument("theta size mismatch");
        }
        // update theta
        std::copy(theta.data(), theta.data() + theta.size(), 
                  d_theta.data());
        // update Lambdat
        int    *lipt = d_Lind.data();
        double *LamX = d_Lambdat.valuePtr(), *thpt = d_theta.data();
        for (int i = 0; i < d_Lind.size(); ++i) {
            LamX[i] = thpt[lipt[i] - 1];
        }
    }

    void merPredD::setZt(const VectorXd& ZtNonZero) {
        double *ZtX = d_Zt.valuePtr(); // where the nonzero values of Zt live
        std::copy(ZtNonZero.data(), ZtNonZero.data() + ZtNonZero.size(), ZtX);
    }


    merPredD::Scalar merPredD::solve() {
        d_delu          = d_Utr - d_u0;
        d_L.solveInPlace(d_delu, CHOLMOD_P);
        d_L.solveInPlace(d_delu, CHOLMOD_L);    // d_delu now contains cu
        d_CcNumer       = d_delu.squaredNorm(); // numerator of convergence criterion

        d_delb          = d_RX.matrixL().solve(d_Vtr - d_RZX.adjoint() * d_delu);
        d_CcNumer      += d_delb.squaredNorm(); // increment CcNumer
        d_RX.matrixU().solveInPlace(d_delb);

        d_delu         -= d_RZX * d_delb;
        d_L.solveInPlace(d_delu, CHOLMOD_Lt);
        d_L.solveInPlace(d_delu, CHOLMOD_Pt);
        return d_CcNumer;
    }

    merPredD::Scalar merPredD::solveU() {
        d_delb.setZero(); // in calculation of linPred delb should be zero after solveU
        d_delu          = d_Utr - d_u0;
        d_L.solveInPlace(d_delu, CHOLMOD_P);
        d_L.solveInPlace(d_delu, CHOLMOD_L);    // d_delu now contains cu
        d_CcNumer       = d_delu.squaredNorm(); // numerator of convergence criterion
        d_L.solveInPlace(d_delu, CHOLMOD_Lt);
        d_L.solveInPlace(d_delu, CHOLMOD_Pt);
  return d_CcNumer;
    }

    void merPredD::updateXwts(const ArrayXd& sqrtXwt) {
        if (d_Xwts.size() != sqrtXwt.size())
            throw invalid_argument("updateXwts: dimension mismatch");
        std::copy(sqrtXwt.data(), sqrtXwt.data() + sqrtXwt.size(), d_Xwts.data());
        if (sqrtXwt.size() == d_V.rows()) { // W is diagonal
            d_V              = d_Xwts.asDiagonal() * d_X;
            for (int j = 0; j < d_N; ++j)
                for (MSpMatrixd::InnerIterator Utj(d_Ut, j), Ztj(d_Zt, j);
                     Utj && Ztj; ++Utj, ++Ztj)
                    Utj.valueRef() = Ztj.value() * d_Xwts.data()[j];
        } else {
            SpMatrixd      W(d_V.rows(), sqrtXwt.size());
            const double *pt = sqrtXwt.data();
            W.reserve(sqrtXwt.size());
            for (Index j = 0; j < W.cols(); ++j, ++pt) {
                W.startVec(j);
                W.insertBack(j % d_V.rows(), j) = *pt;
            }
            W.finalize();
            d_V              = W * d_X;
            SpMatrixd      Ut(d_Zt * W.adjoint());
            if (Ut.cols() != d_Ut.cols())
                throw std::runtime_error("Size mismatch in updateXwts");

            // More complex code to handle the pruning of zeros
            MVec(d_Ut.valuePtr(), d_Ut.nonZeros()).setZero();
            for (int j = 0; j < d_Ut.outerSize(); ++j) {
                MSpMatrixd::InnerIterator lhsIt(d_Ut, j);
                for (SpMatrixd::InnerIterator  rhsIt(Ut, j); rhsIt; ++rhsIt, ++lhsIt) {
                    Index                         k(rhsIt.index());
                    while (lhsIt && lhsIt.index() != k) ++lhsIt;
                    if (lhsIt.index() != k)
                        throw std::runtime_error("Pattern mismatch in updateXwts");
                    lhsIt.valueRef() = rhsIt.value();
                }
            }
        }
	// avoid crossprod of n-by-0 matrix: GH #794
        if (d_V.cols() > 0) d_VtV.setZero().selfadjointView<Eigen::Upper>().rankUpdate(d_V.adjoint());
        updateL();
    }

    void merPredD::updateDecomp() {
        updateDecomp(NULL);
    }
    
    // using a point so as to detect NULL
    void merPredD::updateDecomp(const MatrixXd* xPenalty) {  // update L, RZX and RX
        int debug=0;
        
        if (debug) Rcpp::Rcout << "start updateDecomp" << std::endl;
        updateL();
        if (debug) {
            Rcpp::Rcout << "updateDecomp 2: dimensions (RZX, LamtUt,V)" << 
                d_RZX.cols() << " " << d_RZX.rows() << " " <<
                d_LamtUt.cols() << " " << d_LamtUt.rows() << " " <<
                d_V.cols() << " " << d_V.rows() << " " <<
                std::endl;
        }
        if (d_LamtUt.cols() != d_V.rows()) {
            ::Rf_warning("dimension mismatch in updateDecomp()");
            // Rcpp::Rcout << "WARNING: dimension mismatch in updateDecomp(): " <<
            // " LamtUt=" << d_LamtUt.rows() << "x" << d_LamtUt.cols() << 
            // "; V=" << d_V.rows() << "x" << d_V.cols() << " " <<
            // std::endl;
        }
        d_RZX         = d_LamtUt * d_V;
        if (debug) Rcpp::Rcout << "updateDecomp 3" << std::endl;
        if (d_p > 0) {
            d_L.solveInPlace(d_RZX, CHOLMOD_P);
            d_L.solveInPlace(d_RZX, CHOLMOD_L);
            if (debug) Rcpp::Rcout << "updateDecomp 4" << std::endl;
            MatrixXd      VtVdown(d_VtV);
            
            if (xPenalty == NULL)
                d_RX.compute(VtVdown.selfadjointView<Eigen::Upper>().rankUpdate(d_RZX.adjoint(), -1));
            else {
                d_RX.compute(VtVdown.selfadjointView<Eigen::Upper>().rankUpdate(d_RZX.adjoint(), -1).rankUpdate(*xPenalty, 1));
            }
            if (debug) Rcpp::Rcout << "updateDecomp 5" << std::endl;
            if (d_RX.info() != Eigen::Success)
                Rcpp::stop("Downdated VtV is not positive definite");
            d_ldRX2         = 2. * d_RX.matrixLLT().diagonal().array().abs().log().sum();
            if (debug) Rcpp::Rcout << "updateDecomp 6" << std::endl;
        }
    }

    void merPredD::updateRes(const VectorXd& wtres) {
        if (d_V.rows() != wtres.size())
            throw invalid_argument("updateRes: dimension mismatch");
        d_Vtr           = d_V.adjoint() * wtres;
        d_Utr           = d_LamtUt * wtres;
    }

    void merPredD::installPars(const Scalar& f) {
        d_u0 = u(f);
        d_beta0 = beta(f);
        d_delb.setZero();
        d_delu.setZero();
    }

    void merPredD::setBeta0(const VectorXd& nBeta) {
        if (nBeta.size() != d_p) throw invalid_argument("setBeta0: dimension mismatch");
        std::copy(nBeta.data(), nBeta.data() + d_p, d_beta0.data());
    }

    void merPredD::setDelb(const VectorXd& newDelb) {
        if (newDelb.size() != d_p)
            throw invalid_argument("setDelb: dimension mismatch");
        std::copy(newDelb.data(), newDelb.data() + d_p, d_delb.data());
    }

    void merPredD::setDelu(const VectorXd& newDelu) {
        if (newDelu.size() != d_q)
            throw invalid_argument("setDelu: dimension mismatch");
        std::copy(newDelu.data(), newDelu.data() + d_q, d_delu.data());
    }

    void merPredD::setU0(const VectorXd& newU0) {
        if (newU0.size() != d_q) throw invalid_argument("setU0: dimension mismatch");
        std::copy(newU0.data(), newU0.data() + d_q, d_u0.data());
    }

    template <typename T>
    struct Norm_Rand : std::function<T(T)> {
        const T operator()(const T& x) const {return ::norm_rand();}
    };

    inline static VectorXd Random_Normal(int size, double sigma) {
        return ArrayXd(size).unaryExpr(Norm_Rand<double>()) * sigma;
    }

    void merPredD::MCMC_beta_u(const Scalar& sigma) {
        VectorXd del2(d_RX.matrixU().solve(Random_Normal(d_p, sigma)));
        d_delb += del2;
        VectorXd del1(Random_Normal(d_q, sigma) - d_RZX * del2);
        d_L.solveInPlace(del1, CHOLMOD_Lt);
        d_delu += del1;
    }

    VectorXi merPredD::Pvec() const {
        int*                 ppt((int*)d_L.factor()->Perm);
        VectorXi             ans(d_q);
        std::copy(ppt, ppt + d_q, ans.data());
        return ans;
    }

    MatrixXd merPredD::RX() const {
        return d_RX.matrixU();
    }

    MatrixXd merPredD::RXi() const { // inverse RX
        return d_RX.matrixU().solve(MatrixXd::Identity(d_p,d_p));
    }

    MatrixXd merPredD::unsc() const { // unscaled var-cov mat of FE
        // R translation: tcrossprod(RXi)
        return MatrixXd(MatrixXd(d_p, d_p).setZero().
                        selfadjointView<Eigen::Lower>().
                        rankUpdate(RXi()));
    }

    VectorXd merPredD::RXdiag() const {
        return d_RX.matrixLLT().diagonal();
    }
}
