rowvec dF2du(unsigned row, irowvec causes, const DataPairs &data, const gmat &sigma, vec u){
// Attaining variance covariance matrix etc. (conditional on u)
vmat cond_sig = sigma(causes);
vec cond_mean = cond_sig.proj*u;
rowvec alp = data.alpha_get(row, causes);
rowvec gam = data.gamma_get(row, causes);
colvec alpgam = alp.t() - gam.t();
double cdf = pn(alpgam, cond_mean, cond_sig.vcov);
vec ll = sqrt(diagvec(cond_sig.vcov));
mat Lambda = diagmat(ll);
mat iLambda = diagmat(1/ll);
mat R = iLambda*cond_sig.vcov*iLambda;
mat LR = Lambda*R;
double r = R(0,1);
vec ytilde = iLambda*(alpgam - cond_mean);
vecmat D = Dbvn(ytilde(0),ytilde(1),r);
mat M = -LR*D.V;
vec dcdfdu = trans(cond_sig.proj)*cond_sig.inv*M;
rowvec dF2du_1 = data.dpiduMarg_get(row, causes(0), 0)*data.piMarg_get(row, causes(1), 1)*cdf ;
rowvec dF2du_2 = data.dpiduMarg_get(row, causes(1), 1)*data.piMarg_get(row, causes(0), 0)*cdf;
vec dF2du_3 = data.piMarg_get(row, causes(0), 0)*data.piMarg_get(row, causes(1), 1)*dcdfdu;
rowvec dF2du = dF2du_1 + dF2du_2 + dF2du_3.t();
return(dF2du);
};
arma::mat grassmannQ::retract(double stepSize, std::string method,bool first){
if(retraction==1){ //QR
Yt=Y+stepSize*descD;
arma::qr_econ(retract_U,retract_V,Yt);
if(retract_V(0,0)<0){
retract_U=-retract_U;
}
Yt=retract_U;
}else if(retraction==0){
if(first){
arma::mat U_svd;
arma::svd_econ(U_svd,retract_Sigma,retract_V,-xi);
retract_U=arma::mat(n,2*p,arma::fill::zeros);
retract_U(arma::span::all,arma::span(0,p-1))=Y*retract_V;
retract_U(arma::span::all,arma::span(p,2*p-1))=U_svd;
}
arma::mat retract_middle;
retract_middle=arma::mat(2*p,p,arma::fill::zeros);
retract_middle(arma::span(0,p-1),arma::span::all)
=diagmat(cos(retract_Sigma*stepSize));
retract_middle(arma::span(p,2*p-1),arma::span::all)
=diagmat(sin(retract_Sigma*stepSize));
Yt=retract_U*retract_middle*retract_V.t();
}
return Yt;
}
inline
mat
CovMeans_mat_kth::mehrtash_suggestion(mat cov_i)
{
//Following Mehrtash suggestions as per email dated June26th 2014
mat new_covi;
double THRESH = 0.000001;
new_covi = 0.5*(cov_i + cov_i.t());
vec D;
mat V;
eig_sym(D, V, new_covi);
uvec q1 = find(D < THRESH);
if (q1.n_elem>0)
{
for (uword pos = 0; pos < q1.n_elem; ++pos)
{
D( q1(pos) ) = THRESH;
}
new_covi = V*diagmat(D)*V.t();
}
return new_covi;
//end suggestions
}
//------------------------------------------------------------------------------
void OrbitalEquation::computeOneParticleReducedDensity()
{
// All possible spatial orbitals
for(int i=0; i< nOrbitals; i++){
for(int j=i; j<nOrbitals; j++){
invRho(i,j) = reducedOneParticleOperator(2*i,2*j);
invRho(i,j) += reducedOneParticleOperator(2*i+1,2*j+1);
invRho(j,i) = conj(invRho(i,j));
}
}
#ifdef DEBUG
//#if 1
cout << "OrbitalEquation::computeOneParticleReducedDensity()" << endl;
cout << "Trace(rho) = " << real(trace(invRho)) << " nParticles = " << nParticles << endl;
#endif
#if 0
//---------------------------
// Regularization
//---------------------------
const double e = 1e-10;
cx_mat rho_U;
vec rho_lambda;
eig_sym(rho_lambda, rho_U, invRho);
rho_lambda = rho_lambda + e*exp(-rho_lambda*(1.0/e));
cx_mat X = rho_U*diagmat(1.0/rho_lambda)*rho_U.t();
invRho += e*X;
//---------------------------
#endif
}
void QUIC_SVD::ExtractSVD(arma::mat& u,
arma::mat& v,
arma::mat& sigma)
{
// Calculate A * V_hat, necessary for further calculations.
arma::mat projectedMat;
if (dataset.n_cols > dataset.n_rows)
projectedMat = dataset.t() * basis;
else
projectedMat = dataset * basis;
// Calculate the squared projected matrix.
arma::mat projectedMatSquared = projectedMat.t() * projectedMat;
// Calculate the SVD of the above matrix.
arma::mat uBar, vBar;
arma::vec sigmaBar;
arma::svd(uBar, sigmaBar, vBar, projectedMatSquared);
// Calculate the approximate SVD of the original matrix, using the SVD of the
// squared projected matrix.
v = basis * vBar;
sigma = arma::sqrt(diagmat(sigmaBar));
u = projectedMat * vBar * sigma.i();
// Since columns are sampled, the unitary matrices have to be exchanged, if
// the transposed matrix is not passed.
if (dataset.n_cols > dataset.n_rows)
{
arma::mat tempMat = u;
u = v;
v = tempMat;
}
}
// Reconstruct block in the image sequence after thresholding
arma::cube Reconstruct(double lambda) {
arma::cube v = arma::zeros<arma::cube>(Nx, Ny, T);
arma::cube weights = arma::zeros<arma::cube>(Nx, Ny, T);
arma::mat block, Ublock, Vblock;
arma::vec Sblock;
block.set_size(Bs*Bs, T);
Ublock.set_size(Bs*Bs, T);
Sblock.set_size(T);
Vblock.set_size(T, T);
#pragma omp parallel for shared(v, weights) \
private(block, Ublock, Sblock, Vblock)
for (int it = 0; it < newVecSize; it++) {
Ublock = U[it];
Sblock = S[it];
Vblock = V[it];
// Basic singular value thresholding
// arma::vec Snew = arma::sign(Sblock)
// % arma::max(
// arma::abs(Sblock) - lambda,
// arma::zeros<arma::vec>(T));
// Gaussian-weighted singular value thresholding
arma::vec wvec = arma::abs(Sblock.max()
* arma::exp(-1
* lambda
* arma::square(Sblock)/2));
// Apply threshold
arma::vec Snew = arma::sign(Sblock)
% arma::max(
arma::abs(Sblock) - wvec,
arma::zeros<arma::vec>(T));
// Reconstruct from SVD
block = Ublock * diagmat(Snew) * Vblock.t();
// Deal with block weights (TODO: currently all weights = 1)
for (int k = 0; k < T; k++) {
int newy = patches(0, actualpatches(it), k);
int newx = patches(1, actualpatches(it), k);
v(arma::span(newy, newy+Bs-1),
arma::span(newx, newx+Bs-1),
arma::span(k, k)) += arma::reshape(block.col(k), Bs, Bs);
weights(arma::span(newy, newy+Bs-1),
arma::span(newx, newx+Bs-1),
arma::span(k, k)) += arma::ones<arma::mat>(Bs, Bs);
}
}
// Include the weighting
v /= weights;
v.elem(find_nonfinite(v)).zeros();
return v;
}
void WhitenFeatureMajorMatrix(const mat& matX,
mat& matXWhitened,
mat& matWhitening)
{
mat matU, matV;
vec s;
svd(matU, s, matV, cov(matX));
matWhitening = matU * diagmat(1 / sqrt(s)) * trans(matV);
matXWhitened = matX * matWhitening;
}
//update gradient and hessian
void el_sem_naive::set_gradient_hessian(vec &grad, mat &hessian)
{
int i;
hessian.zeros();
d_ = (constraints_.t() * dual_) + 1.0;
grad = -sum( constraints_ * diagmat( 1.0 / d_), 1);
for(i = 0; i < n_ ; i ++) {
hessian += constraints_.col(i) * constraints_.col(i).t() / pow(d_(i),2);
}
}
// Posterior Density Function to sample Theta
double f_theta( colvec logTheta, colvec mTheta, mat Otheta, double Tau, mat Y, mat Fit, rowvec Sigma, double logEHRTime )
{
double prior, like, post;
colvec cTheta = ( logTheta - mTheta ) ;
prior = - 0.5 * Tau * as_scalar( cTheta.t() * Otheta * cTheta );
mat D = diagmat( 1 / Sigma );
like = - 0.5 * accu( pow ( log( Y ) - log( Fit ), 2 ) * D ); // Need to figure out what to do with Sigma
// Conditional Posterior -----------------------------------------------------------
post = prior + like + Rf_dnorm4( logEHRTime, 0, 1, 1 );
return post;
}
void origNISim::initialize() {
mat W_t(maxVertexId, maxVertexId, fill::zeros);
for (int i = 0; i < maxVertexId; i++) {
int e = origGraphSrc[i + 1], s = origGraphSrc[i];
for (int j = s; j < e; j++) {
W_t(i, origGraphDst[j]) = 1.0;
}
}
double sumRow;
double Degr = 0;
for (int i = 0; i < maxVertexId; i++) {
sumRow = 0;
for (int j = 0; j < maxVertexId; j++)
sumRow += W_t(i, j);
if (sumRow == 0.0) {
printf("node %d has no ingoing edges\n", i);
} else {
for (int j = 0; j < maxVertexId; j++)
W_t(i, j) = W_t(i, j) / sumRow;
}
Degr += sumRow;
}
//start svd
Mat<double> U;
Col<double> s;
Mat<double> V_t;
svd(U, s, V_t, W_t);
mat V = V_t.t();
U = U.submat(0, 0, maxVertexId - 1, Rank - 1);
V = V.submat(0, 0, Rank - 1, maxVertexId - 1);
s = s.submat(0, 0, Rank - 1, 0);
Ku = kron(U, U);//kronecker roduct
mat sigma = kron(s, s);//one column
mat K_sigma = diagmat(sigma);
Kv = kron(V, V);
mat K_vu = Kv * Ku;
mat I(maxVertexId, maxVertexId);
I.eye();
A = inv(inv(K_sigma) - decayFactor * K_vu);
V_r = Kv * vectorise(I);
A.save(Apath);
V_r.save(V_rpath);
Kv.save(Kvpath);
Ku.save(Kupath);
}
// Returns the linear predictor from the full step
Rcpp::NumericVector
densePred::gamma(const Rcpp::NumericVector& xwts,
const Rcpp::NumericVector& wtres)
throw (std::runtime_error) {
int n = d_X.nrow();
if (xwts.size() != n || wtres.size() != n)
throw
std::runtime_error("length(xwts) or length(wtres) != nrow(X)");
arma::vec a_xwts = arma::vec(xwts.begin(), n, false, true),
a_wtres = arma::vec(wtres.begin(), n, false, true);
arma::vec tmp = solve(diagmat(a_xwts) * a_X, a_wtres);
std::copy(tmp.begin(), tmp.end(), a_delta.begin());
d_coef = d_coef0 + d_delta;
return NumericVector(wrap(a_X * a_coef));
}
arma::vec QRPMMCPP (arma::mat xr,arma::vec yr,arma::vec betar,arma::vec betaoldr,
double to,int m,double ta,double lamdar){
double toler = (to);
int maxit=(m);
double tau=(ta),lamda=(lamdar);
arma:: mat x=(xr),product,xt;
arma:: vec W,newX,z,signw,v,r,y=(yr),E,delta;
arma:: vec betaold,beta=(betar),qrbeta=(betaoldr);
arma::uvec order, index;
int n=x.n_rows;
x.insert_cols( 0, arma::ones(n) );
int p=x.n_cols;
double error=10000,epsilon=0.9999,epsilonprime;
//toler=1e-3;
int iteration=1;
//beta= solve(x.t()*x, x.t()*y);
product.ones(p,n);
epsilonprime=toler*p/2;
xt=x.t();
qrbeta.insert_rows(0,1);
while (iteration<=maxit&& error>toler)
{
betaold=beta;
r=y-x*beta;
v=1-2*tau-r/(arma::abs(r)+epsilon);
E=lamda*arma::abs(beta)/beta/(epsilonprime+arma::abs(beta))/qrbeta/qrbeta;
E(0)=0;
W=1/(epsilon+abs(r));
for (int i=0;i<n;i++)
{ product.col(i)=xt.col(i)*W(i);}
delta=arma::solve(product*x-diagmat(E),xt*v-E%beta);
beta=beta-delta;
error=sum(abs(delta));
iteration++;
}
arma::vec betanew=beta;
return betanew;
}
inline
bool
op_sqrtmat_sympd::apply_direct(Mat<typename T1::elem_type>& out, const Base<typename T1::elem_type,T1>& expr)
{
arma_extra_debug_sigprint();
#if defined(ARMA_USE_LAPACK)
{
typedef typename T1::pod_type T;
typedef typename T1::elem_type eT;
const unwrap<T1> U(expr.get_ref());
const Mat<eT>& X = U.M;
arma_debug_check( (X.is_square() == false), "sqrtmat_sympd(): given matrix must be square sized" );
Col< T> eigval;
Mat<eT> eigvec;
const bool status = auxlib::eig_sym_dc(eigval, eigvec, X);
if(status == false) { return false; }
const uword N = eigval.n_elem;
const T* eigval_mem = eigval.memptr();
bool all_pos = true;
for(uword i=0; i<N; ++i) { all_pos = (eigval_mem[i] < T(0)) ? false : all_pos; }
if(all_pos == false) { return false; }
eigval = sqrt(eigval);
out = eigvec * diagmat(eigval) * eigvec.t();
return true;
}
#else
{
arma_ignore(out);
arma_ignore(expr);
arma_stop_logic_error("sqrtmat_sympd(): use of LAPACK must be enabled");
return false;
}
#endif
}
arma::mat Mahalanobis::getDecomposition() {
mat Z;
mat U, V;
vec s;
svd_econ(U, s, V, M);
for(int i = 0; i < s.n_elem; ++i)
s(i) = sqrt(s(i));
mat matS = diagmat(s);
Z = U * matS;
return Z;
}
/**
* Participation coefficient is a measure of diversity of intermodular
* connections of individual nodes.
* Inputs: W, binary/weighted, directed/undirected
* connection matrix
* Ci, community affiliation vector
* Output: P, participation coefficient
* Note: The output for directed graphs is the "out-neighbor"
* participation coefficient.
* Reference: Guimera R, Amaral L. Nature (2005) 433:895-900.
*/
rowvec Connectome::participationCoefficient(const mat &W, const urowvec &Ci)
{
uint n = W.n_rows;
mat binaryW = zeros(n,n);
binaryW(find(W!=0)).fill(1);
rowvec Ko = sum(binaryW,0);
// A^T = (B C)^T = C^T B^T = C B^T since C = C^T
mat Gc = diagmat(conv_to<rowvec>::from(Ci))*strans(abs(sign(W)));
rowvec Kc2 = zeros(1,n);
for (uint i=0;i<=Ci.max();++i) {
mat c = zeros(n,n);
c(find(Gc==i)).fill(1);
Kc2 += arma::pow(sum((W%c),0),2);
}
rowvec P = ones(1,n) - Kc2/arma::pow(Ko,2);
P(find(Ko == 0)).fill(0);
return P;
}
arma::mat TogersonMetricLearner::generateY(arma::mat B) {
mat Y;
mat U, V;
vec s;
U.fill(0.0);
V.fill(0.0);
s.fill(0.0);
svd(U, s, V, B);
for(int i = 0; i < s.n_elem; ++i)
s(i) = sqrt(s(i));
mat matS = diagmat(s);
Y = U * matS;
return Y;
}
inline
bool
op_princomp::direct_princomp
(
Mat< std::complex<typename T1::pod_type> >& coeff_out,
Mat< std::complex<typename T1::pod_type> >& score_out,
Col< typename T1::pod_type >& latent_out,
Col< std::complex<typename T1::pod_type> >& tsquared_out,
const Base< std::complex<typename T1::pod_type>, T1 >& X,
const typename arma_cx_only<typename T1::elem_type>::result* junk
)
{
arma_extra_debug_sigprint();
arma_ignore(junk);
typedef typename T1::pod_type T;
typedef std::complex<T> eT;
const unwrap_check<T1> Y( X.get_ref(), score_out );
const Mat<eT>& in = Y.M;
const uword n_rows = in.n_rows;
const uword n_cols = in.n_cols;
if(n_rows > 1) // more than one sample
{
// subtract the mean - use score_out as temporary matrix
score_out = in; score_out.each_row() -= mean(in);
// singular value decomposition
Mat<eT> U;
Col< T> s;
const bool svd_ok = svd(U, s, coeff_out, score_out);
if(svd_ok == false) { return false; }
// normalize the eigenvalues
s /= std::sqrt( double(n_rows - 1) );
// project the samples to the principals
score_out *= coeff_out;
if(n_rows <= n_cols) // number of samples is less than their dimensionality
{
score_out.cols(n_rows-1,n_cols-1).zeros();
Col<T> s_tmp = zeros< Col<T> >(n_cols);
s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
s = s_tmp;
// compute the Hotelling's T-squared
s_tmp.rows(0,n_rows-2) = 1.0 / s_tmp.rows(0,n_rows-2);
const Mat<eT> S = score_out * diagmat(Col<T>(s_tmp));
tsquared_out = sum(S%S,1);
}
else
{
// compute the Hotelling's T-squared
const Mat<eT> S = score_out * diagmat(Col<T>(T(1) / s));
tsquared_out = sum(S%S,1);
}
// compute the eigenvalues of the principal vectors
latent_out = s%s;
}
else // 0 or 1 samples
{
coeff_out.eye(n_cols, n_cols);
score_out.copy_size(in);
score_out.zeros();
latent_out.set_size(n_cols);
latent_out.zeros();
tsquared_out.set_size(n_rows);
tsquared_out.zeros();
}
return true;
}
inline
void
op_princomp::direct_princomp
(
Mat< std::complex<T> >& coeff_out,
Mat< std::complex<T> >& score_out,
Col<T>& latent_out,
Col< std::complex<T> >& tsquared_out,
const Mat< std::complex<T> >& in
)
{
arma_extra_debug_sigprint();
typedef std::complex<T> eT;
const u32 n_rows = in.n_rows;
const u32 n_cols = in.n_cols;
if(n_rows > 1) // more than one sample
{
// subtract the mean - use score_out as temporary matrix
score_out = in - repmat(mean(in), n_rows, 1);
// singular value decomposition
Mat<eT> U;
Col<T> s;
const bool svd_ok = svd(U,s,coeff_out,score_out);
if(svd_ok == false)
{
arma_print("princomp(): singular value decomposition failed");
coeff_out.reset();
score_out.reset();
latent_out.reset();
tsquared_out.reset();
return;
}
//U.reset();
// normalize the eigenvalues
s /= std::sqrt(n_rows - 1);
// project the samples to the principals
score_out *= coeff_out;
if(n_rows <= n_cols) // number of samples is less than their dimensionality
{
score_out.cols(n_rows-1,n_cols-1).zeros();
Col<T> s_tmp = zeros< Col<T> >(n_cols);
s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
s = s_tmp;
// compute the Hotelling's T-squared
s_tmp.rows(0,n_rows-2) = 1.0 / s_tmp.rows(0,n_rows-2);
const Mat<eT> S = score_out * diagmat(Col<T>(s_tmp));
tsquared_out = sum(S%S,1);
}
else
{
// compute the Hotelling's T-squared
const Mat<eT> S = score_out * diagmat(Col<T>(T(1) / s));
tsquared_out = sum(S%S,1);
}
// compute the eigenvalues of the principal vectors
latent_out = s%s;
}
else // single sample - row
{
if(n_rows == 1)
{
coeff_out = eye< Mat<eT> >(n_cols, n_cols);
score_out.copy_size(in);
score_out.zeros();
latent_out.set_size(n_cols);
latent_out.zeros();
tsquared_out.set_size(1);
tsquared_out.zeros();
}
else
{
coeff_out.reset();
score_out.reset();
latent_out.reset();
tsquared_out.reset();
}
}
}
void uhfsolve::setupUnitMatrices(){
//Bring overlap matrix to unit form, set up V
eig_sym(s_diag,U,Bs.S); //following Thijssen, p38-39
V = U*diagmat(1.0/sqrt(s_diag));
}
//' @title Master Wrapper for the GMWM Estimator
//' @description This function generates WV, GMWM Estimator, and an initial test estimate.
//' @param data A \code{vec} containing the data.
//' @param theta A \code{vec} with dimensions N x 1 that contains user-supplied initial values for parameters
//' @param desc A \code{vector<string>} indicating the models that should be considered.
//' @param objdesc A \code{field<vec>} containing a list of parameters (e.g. AR(1) = c(1,1), ARMA(p,q) = c(p,q,1))
//' @param model_type A \code{string} that represents the model transformation
//' @param starting A \code{bool} that indicates whether the supplied values are guessed (T) or are user-based (F).
//' @param alpha A \code{double} that handles the alpha level of the confidence interval (1-alpha)*100
//' @param compute_v A \code{string} that describes what kind of covariance matrix should be computed.
//' @param K An \code{int} that controls how many times theta is updated.
//' @param H An \code{int} that controls how many bootstrap replications are done.
//' @param G An \code{int} that controls how many guesses at different parameters are made.
//' @param robust A \code{bool} that indicates whether the estimation should be robust or not.
//' @param eff A \code{double} that specifies the amount of efficiency required by the robust estimator.
//' @return A \code{field<mat>} that contains a list of ever-changing estimates...
//' @author JJB
//' @references Wavelet variance based estimation for composite stochastic processes, S. Guerrier and Robust Inference for Time Series Models: a Wavelet-Based Framework, S. Guerrier
//' @keywords internal
//' @export
//' @backref src/gmwm_logic.cpp
//' @backref src/gmwm_logic.h
// [[Rcpp::export]]
arma::field<arma::mat> gmwm_master_cpp(arma::vec& data,
arma::vec theta,
const std::vector<std::string>& desc, const arma::field<arma::vec>& objdesc,
std::string model_type, bool starting,
double alpha,
std::string compute_v, unsigned int K, unsigned int H,
unsigned int G,
bool robust, double eff){
// Obtain counts of the different models we need to work with
std::map<std::string, int> models = count_models(desc);
// HACK METHOD (todo: formalize it)
// Determine if we need to difference
if(models["SARIMA"] > 0){
// Note: s, i, si are 6,7,8 => 5,6,7
for(unsigned int i = 0; i < desc.size(); i ++){
if(objdesc(i).n_elem > 3){
arma::vec sarima_desc = objdesc(i);
// Do we need to difference?
if(sarima_desc(6) > 0 || sarima_desc(7) > 0){
// Perform differencing in specific order...
// First non-seasonal and then seasonal.
if(sarima_desc(6) > 0){
// Lag is always 1, number of differences is (i)
data = diff_cpp(data, 1, sarima_desc(6));
}
if(sarima_desc(7) > 0){
// Lag is always seasonality (s) and differences is (si).
data = diff_cpp(data, sarima_desc(5), sarima_desc(7));
}
// Kill loop. We only handle the tsmodel object with the first difference.
break;
}
}
}
}
// ------ Variable Declarations
// Length of the Time Series
unsigned int N = data.n_elem;
// Number of Scales (J)
unsigned int nlevels = floor(log2(N));
// Number of parameters
unsigned int np = theta.n_elem;
// Take the mean of the first difference
double expect_diff = mean_diff(data);
// Guessed values of Theta (user supplied or generated)
arma::vec guessed_theta = theta;
// MODWT decomp
arma::field<arma::vec> modwt_decomp = modwt_cpp(data, "haar", nlevels, "periodic", true);
// Obtain WV and confidence intervals
arma::mat wvar = wvar_cpp(modwt_decomp, robust, eff, alpha, "eta3");
// Extract
arma::vec wv_empir = wvar.col(0);
arma::vec ci_lo = wvar.col(1);
arma::vec ci_hi = wvar.col(2);
//-------------------------
// Obtain Covariance Matrix
//-------------------------
arma::mat V;
// compute_cov_cpp is the hard core function. It can only be improved by using parallelization.
if(compute_v == "diag" || compute_v == "full"){
arma::field<arma::mat> Vout = compute_cov_cpp(modwt_decomp, nlevels, compute_v, robust, eff);
if(robust){
V = Vout(1);
}else{
V = Vout(0);
}
}else{
V = fast_cov_cpp(wvar.col(2), wvar.col(1));
}
// Obtain the Omega matrix
arma::mat omega = arma::inv(diagmat(V));
// Store the original V matrix (in case of bootstrapping) for use in the update function
arma::mat orgV = V;
// Calculate the values of the Scales
arma::vec scales = scales_cpp(nlevels);
// Min-Max / N
double ranged = dr_slope(data);
// Guess starting values for the theta parameters
if(starting){
// Always run guessing algorithm
theta = guess_initial(desc, objdesc, model_type, np, expect_diff, N, wvar, scales, ranged, G);
// If under ARMA case and only ARMA is in the model,
// then see how well these values are.
if(desc.size() == 1 && (desc[0] == "SARIMA" || desc[0] == "ARMA11") && N <= 1000){
// Use R's ARIMA function to estimate parameter space
arma::vec theta2 = Rcpp_ARIMA(data, objdesc(0)); // Only 1 objdesc in the available.
// Obtain the obj function under omega with these initial guesses
// DO >>NOT<< USE Yannick's to optimize starting values!!!!
double mle_css_obj = getObjFun(theta2, desc, objdesc, model_type, omega, wv_empir, scales);
// Obtain the objective function under Yannick's starting algorithm
double init_guess_obj = getObjFunStarting(theta, desc, objdesc, model_type, wv_empir, scales);
// What performs better?
if(mle_css_obj < init_guess_obj){
// Disable starting value optimization if using MLE.
theta = theta2;
starting = false;
}
}
guessed_theta = theta;
}
// Obtain the GMWM estimator's estimates.
theta = gmwm_engine(theta, desc, objdesc, model_type,
wv_empir, omega, scales, starting);
// Optim may return a very small value. In this case, instead of saying its zero (yielding a transform issue), make it EPSILON.
theta = code_zero(theta);
// Enable bootstrapping
if(compute_v == "bootstrap"){
for(unsigned int k = 0; k < K; k++){
// Create the full V matrix
V = cov_bootstrapper(theta, desc, objdesc, N, robust, eff, H, false);
// Update the omega matrix
omega = arma::inv(diagmat(V));
// The theta update in this case MUST not use Yannick's starting algorithm. Hence, the false value.
theta = gmwm_engine(theta, desc, objdesc, model_type, wv_empir, omega, scales, false);
// Optim may return a very small value. In this case, instead of saying its zero (yielding a transform issue), make it EPSILON.
theta = code_zero(theta);
}
}
if(desc[0] == "SARIMA" && desc.size() == 1){
arma::vec temp = objdesc(0);
unsigned int p = temp(0);
if(p != 0 && invert_check(arma::join_cols(arma::ones<arma::vec>(1), -theta.rows(0, p - 1))) == false){
Rcpp::Rcout << "WARNING: This ARMA model contains AR coefficients that are NON-STATIONARY!" << std::endl;
}
}
// Order AR1s / GM so largest phi is first!
if(models["AR1"] > 1 || models["GM"] > 1){
theta = order_AR1s(theta, desc, objdesc);
}
// Obtain the objective value function
arma::vec obj_value(1);
obj_value(0) = getObjFun(theta, desc, objdesc, model_type, omega, wv_empir, scales);
arma::vec dr_s(1);
dr_s(0) = ranged;
// Decomposition of the WV.
arma::mat decomp_theo = decomp_theoretical_wv(theta, desc, objdesc, scales);
arma::vec theo = decomp_to_theo_wv(decomp_theo);
// Export information back
arma::field<arma::mat> out(13);
out(0) = theta;
out(1) = guessed_theta;
out(2) = wv_empir;
out(3) = ci_lo;
out(4) = ci_hi;
out(5) = V;
out(6) = orgV;
out(7) = expect_diff;
out(8) = theo;
out(9) = decomp_theo;
out(10) = obj_value;
out(11) = omega;
out(12) = dr_s;
return out;
}
inline
bool
op_princomp::direct_princomp
(
Mat<eT>& coeff_out,
Mat<eT>& score_out,
Col<eT>& latent_out,
Col<eT>& tsquared_out,
const Mat<eT>& in
)
{
arma_extra_debug_sigprint();
const u32 n_rows = in.n_rows;
const u32 n_cols = in.n_cols;
if(n_rows > 1) // more than one sample
{
// subtract the mean - use score_out as temporary matrix
score_out = in - repmat(mean(in), n_rows, 1);
// singular value decomposition
Mat<eT> U;
Col<eT> s;
const bool svd_ok = svd(U,s,coeff_out,score_out);
if(svd_ok == false)
{
return false;
}
//U.reset(); // TODO: do we need this ? U will get automatically deleted anyway
// normalize the eigenvalues
s /= std::sqrt( double(n_rows - 1) );
// project the samples to the principals
score_out *= coeff_out;
if(n_rows <= n_cols) // number of samples is less than their dimensionality
{
score_out.cols(n_rows-1,n_cols-1).zeros();
//Col<eT> s_tmp = zeros< Col<eT> >(n_cols);
Col<eT> s_tmp(n_cols);
s_tmp.zeros();
s_tmp.rows(0,n_rows-2) = s.rows(0,n_rows-2);
s = s_tmp;
// compute the Hotelling's T-squared
s_tmp.rows(0,n_rows-2) = eT(1) / s_tmp.rows(0,n_rows-2);
const Mat<eT> S = score_out * diagmat(Col<eT>(s_tmp));
tsquared_out = sum(S%S,1);
}
else
{
// compute the Hotelling's T-squared
const Mat<eT> S = score_out * diagmat(Col<eT>( eT(1) / s));
tsquared_out = sum(S%S,1);
}
// compute the eigenvalues of the principal vectors
latent_out = s%s;
}
else // 0 or 1 samples
{
coeff_out.eye(n_cols, n_cols);
score_out.copy_size(in);
score_out.zeros();
latent_out.set_size(n_cols);
latent_out.zeros();
tsquared_out.set_size(n_rows);
tsquared_out.zeros();
}
return true;
}
inline
void
CovMeans_mat_kth::gmm_one_video( std::string load_feat_video_i, std::string load_labels_video_i, int sc, int pe, int act, const int Ng )
{
//cout << all_people (pe) << "_" << actions(act) << " ";
mat mat_features_video_i;
mat_features_video_i.load( load_feat_video_i, hdf5_binary );
int n_vec = mat_features_video_i.n_cols;
//cout << " " << n_vec;
bool is_finite = mat_features_video_i.is_finite();
if (!is_finite )
{
cout << "is_finite?? " << is_finite << endl;
cout << mat_features_video_i.n_rows << " " << mat_features_video_i.n_cols << endl;
getchar();
}
gmm_diag gmm_model;
gmm_diag bg_model;
bool status_em = false;
int rep_em=0;
int km_iter = 10;
int em_iter = 5;
double var_floor = 1e-10;
bool print_mode = false;
while (!status_em)
{
bool status_kmeans = false;
//int rep_km = 0;
while (!status_kmeans)
{
arma_rng::set_seed_random();
status_kmeans = gmm_model.learn(mat_features_video_i, Ng, eucl_dist, random_subset, km_iter, 0, var_floor, print_mode); //Only Kmeans
bg_model = gmm_model;
//rep_km++;
}
status_em = gmm_model.learn(mat_features_video_i, Ng, eucl_dist, keep_existing, 0, em_iter, var_floor, print_mode);
rep_em++;
if (rep_em==9)
{
status_em = true;
gmm_model = bg_model;
}
}
//cout <<"EM was repeated " << rep_em << endl << endl;
mat dcov = gmm_model.dcovs;
mat means = gmm_model.means;
mat cov_i, logM_cov_i, V;
vec mean_i, D;
std::stringstream save_folder;
save_folder << "./CovMeans/sc" << sc << "/scale" << scale_factor << "-shift"<< shift ;
for (int i=1; i<=Ng; ++i)
{
//cout << i << " out " << Ng << endl;
cov_i = diagmat( dcov.col(i-1) );
cov_i = mehrtash_suggestion(cov_i);
mean_i = means.col(i -1);
eig_sym(D, V, cov_i);
mat logM_cov_i = V*diagmat( log(D) )*V.t();
std::stringstream save_Covs;
save_Covs << save_folder.str() << "/Cov_"<< i << "_out_" << Ng << "_" << all_people (pe) << "_" << actions(act) << ".h5";
std::stringstream save_logMCovs;
save_logMCovs << save_folder.str() << "/logM_Cov_" << i << "_out_" << Ng << "_" << all_people (pe) << "_" << actions(act) << ".h5";
std::stringstream save_Means;
save_Means << save_folder.str() << "/Means_" << i << "_out_" << Ng << "_" << all_people (pe) << "_" << actions(act) << ".h5";
//cout << save_Covs.str() << endl;
cov_i.save( save_Covs.str(), hdf5_binary );
logM_cov_i.save( save_logMCovs.str(), hdf5_binary );
mean_i.save( save_Means.str(), hdf5_binary );
}
}
inline
void
CovMeans_mat_kth::one_video_one_cov( std::string load_feat_video_i, std::string load_labels_video_i, int sc, int pe, int act )
{
// #pragma omp critical
// {
// cout << load_feat_video_i << endl;
// getchar();
// }
mat mat_features_video_i;
mat_features_video_i.load( load_feat_video_i, hdf5_binary );
int n_vec = mat_features_video_i.n_cols;
std::stringstream save_folder;
//Shifting both
save_folder << "./CovMeans/sc" << sc << "/scale" << scale_factor << "-shift"<< shift ;
{
// If you want to use. You have to add the flag_shift in this method.
// if (flag_shift) //Horizontal Shift
// {
//
// save_folder << "./kth-one-CovsMeans-mat/sc" << sc << "/scale" << scale_factor << "-horshift"<< shift ;
//
// }
//
// if (!flag_shift)//Vertical Shift
// {
// save_folder << "./kth-one-CovsMeans-mat/sc" << sc << "/scale" << scale_factor << "-vershift"<< shift ;
// }
//
}
running_stat_vec<rowvec> stat_seg(true);
for (int l=0; l<n_vec; ++l)
{
vec sample = mat_features_video_i.col(l);
stat_seg (sample);
}
std::stringstream save_Covs;
save_Covs << save_folder.str() << "/Cov_" << all_people (pe) << "_" << actions(act) << ".h5";
std::stringstream save_logMCovs;
save_logMCovs << save_folder.str() << "/logM_Cov_" << all_people (pe) << "_" << actions(act) << ".h5";
std::stringstream save_Means;
save_Means << save_folder.str() << "/Means_" << all_people (pe) << "_" << actions(act) << ".h5";
double THRESH = 0.000001;
mat cov_i = stat_seg.cov();
vec mean_i = stat_seg.mean();
//Following Mehrtash suggestions as per email dated June26th 2014
cov_i = 0.5*(cov_i + cov_i.t());
vec D;
mat V;
eig_sym(D, V, cov_i);
uvec q1 = find(D < THRESH);
if (q1.n_elem>0)
{
for (uword pos = 0; pos < q1.n_elem; ++pos)
{
D( q1(pos) ) = THRESH;
}
cov_i = V*diagmat(D)*V.t();
}
//end suggestions
eig_sym(D, V, cov_i);
mat logM_cov_i = V*diagmat( log(D) )*V.t();
#pragma omp critical
{
cout << "saving " << all_people (pe) << endl;
cov_i.save( save_Covs.str(), hdf5_binary );
logM_cov_i.save( save_logMCovs.str(), hdf5_binary );
mean_i.save( save_Means.str(), hdf5_binary );
}
}
arma::mat Vespucci::Math::Smoothing::SVDDenoise(const arma::mat &X, arma::uword k, arma::mat &U, arma::vec &s, arma::mat &V)
{
arma::svds(U, s, V, arma::sp_mat(X), k);
return -1 * U * diagmat(s) * V.t();
}
// Dictionary step for optimization.
double SparseCoding::OptimizeDictionary(const arma::mat& data,
const arma::mat& codes,
const arma::uvec& adjacencies)
{
// Count the number of atomic neighbors for each point x^i.
arma::uvec neighborCounts = arma::zeros<arma::uvec>(data.n_cols, 1);
if (adjacencies.n_elem > 0)
{
// This gets the column index. Intentional integer division.
size_t curPointInd = (size_t) (adjacencies(0) / atoms);
size_t nextColIndex = (curPointInd + 1) * atoms;
for (size_t l = 1; l < adjacencies.n_elem; ++l)
{
// If l no longer refers to an element in this column, advance the column
// number accordingly.
if (adjacencies(l) >= nextColIndex)
{
curPointInd = (size_t) (adjacencies(l) / atoms);
nextColIndex = (curPointInd + 1) * atoms;
}
++neighborCounts(curPointInd);
}
}
// Handle the case of inactive atoms (atoms not used in the given coding).
std::vector<size_t> inactiveAtoms;
for (size_t j = 0; j < atoms; ++j)
{
if (arma::accu(codes.row(j) != 0) == 0)
inactiveAtoms.push_back(j);
}
const size_t nInactiveAtoms = inactiveAtoms.size();
const size_t nActiveAtoms = atoms - nInactiveAtoms;
// Efficient construction of Z restricted to active atoms.
arma::mat matActiveZ;
if (nInactiveAtoms > 0)
{
math::RemoveRows(codes, inactiveAtoms, matActiveZ);
}
if (nInactiveAtoms > 0)
{
Log::Warn << "There are " << nInactiveAtoms
<< " inactive atoms. They will be re-initialized randomly.\n";
}
Log::Debug << "Solving Dual via Newton's Method.\n";
// Solve using Newton's method in the dual - note that the final dot
// multiplication with inv(A) seems to be unavoidable. Although more
// expensive, the code written this way (we use solve()) should be more
// numerically stable than just using inv(A) for everything.
arma::vec dualVars = arma::zeros<arma::vec>(nActiveAtoms);
//vec dualVars = 1e-14 * ones<vec>(nActiveAtoms);
// Method used by feature sign code - fails miserably here. Perhaps the
// MATLAB optimizer fmincon does something clever?
//vec dualVars = 10.0 * randu(nActiveAtoms, 1);
//vec dualVars = diagvec(solve(dictionary, data * trans(codes))
// - codes * trans(codes));
//for (size_t i = 0; i < dualVars.n_elem; i++)
// if (dualVars(i) < 0)
// dualVars(i) = 0;
bool converged = false;
// If we have any inactive atoms, we must construct these differently.
arma::mat codesXT;
arma::mat codesZT;
if (inactiveAtoms.empty())
{
codesXT = codes * trans(data);
codesZT = codes * trans(codes);
}
else
{
codesXT = matActiveZ * trans(data);
codesZT = matActiveZ * trans(matActiveZ);
}
double normGradient = 0;
double improvement = 0;
for (size_t t = 1; (t != maxIterations) && !converged; ++t)
{
arma::mat A = codesZT + diagmat(dualVars);
arma::mat matAInvZXT = solve(A, codesXT);
arma::vec gradient = -arma::sum(arma::square(matAInvZXT), 1);
gradient += 1;
arma::mat hessian = -(-2 * (matAInvZXT * trans(matAInvZXT)) % inv(A));
arma::vec searchDirection = -solve(hessian, gradient);
//printf("%e\n", norm(searchDirection, 2));
// Armijo line search.
const double c = 1e-4;
double alpha = 1.0;
const double rho = 0.9;
double sufficientDecrease = c * dot(gradient, searchDirection);
// A maxIterations parameter for the Armijo line search may be a good idea,
// but it doesn't seem to be causing any problems for now.
while (true)
{
// Calculate objective.
double sumDualVars = arma::sum(dualVars);
double fOld = -(-trace(trans(codesXT) * matAInvZXT) - sumDualVars);
double fNew = -(-trace(trans(codesXT) * solve(codesZT +
diagmat(dualVars + alpha * searchDirection), codesXT)) -
(sumDualVars + alpha * arma::sum(searchDirection)));
if (fNew <= fOld + alpha * sufficientDecrease)
{
searchDirection = alpha * searchDirection;
improvement = fOld - fNew;
break;
}
alpha *= rho;
}
// Take step and print useful information.
dualVars += searchDirection;
normGradient = arma::norm(gradient, 2);
Log::Debug << "Newton Method iteration " << t << ":" << std::endl;
Log::Debug << " Gradient norm: " << std::scientific << normGradient
<< "." << std::endl;
Log::Debug << " Improvement: " << std::scientific << improvement << ".\n";
if (normGradient < newtonTolerance)
converged = true;
}
if (inactiveAtoms.empty())
{
// Directly update dictionary.
dictionary = trans(solve(codesZT + diagmat(dualVars), codesXT));
}
else
{
arma::mat activeDictionary = trans(solve(codesZT +
diagmat(dualVars), codesXT));
// Update all atoms.
size_t currentInactiveIndex = 0;
for (size_t i = 0; i < atoms; ++i)
{
if (inactiveAtoms[currentInactiveIndex] == i)
{
// This atom is inactive. Reinitialize it randomly.
dictionary.col(i) = (data.col(math::RandInt(data.n_cols)) +
data.col(math::RandInt(data.n_cols)) +
data.col(math::RandInt(data.n_cols)));
dictionary.col(i) /= arma::norm(dictionary.col(i), 2);
// Increment inactive index counter.
++currentInactiveIndex;
}
else
{
// Update estimate.
dictionary.col(i) = activeDictionary.col(i - currentInactiveIndex);
}
}
}
return normGradient;
}
inline
void
op_pinv::apply(Mat<typename T1::elem_type>& out, const Op<T1,op_pinv>& in)
{
arma_extra_debug_sigprint();
typedef typename T1::elem_type eT;
typedef typename get_pod_type<eT>::result T;
const bool use_divide_and_conquer = (in.aux_uword_a == 1);
T tol = access::tmp_real(in.aux);
arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
const Proxy<T1> P(in.m);
const uword n_rows = P.get_n_rows();
const uword n_cols = P.get_n_cols();
if( (n_rows*n_cols) == 0 )
{
out.set_size(n_cols,n_rows);
return;
}
// economical SVD decomposition
Mat<eT> U;
Col< T> s;
Mat<eT> V;
bool status = false;
if(use_divide_and_conquer)
{
status = (n_cols > n_rows) ? auxlib::svd_dc_econ(U, s, V, trans(P.Q)) : auxlib::svd_dc_econ(U, s, V, P.Q);
}
else
{
status = (n_cols > n_rows) ? auxlib::svd_econ(U, s, V, trans(P.Q), 'b') : auxlib::svd_econ(U, s, V, P.Q, 'b');
}
if(status == false)
{
out.reset();
arma_bad("pinv(): svd failed");
return;
}
const uword s_n_elem = s.n_elem;
const T* s_mem = s.memptr();
// set tolerance to default if it hasn't been specified
if( (tol == T(0)) && (s_n_elem > 0) )
{
tol = (std::max)(n_rows, n_cols) * s_mem[0] * std::numeric_limits<T>::epsilon();
}
uword count = 0;
for(uword i = 0; i < s_n_elem; ++i)
{
count += (s_mem[i] >= tol) ? uword(1) : uword(0);
}
if(count > 0)
{
Col<T> s2(count);
T* s2_mem = s2.memptr();
uword count2 = 0;
for(uword i=0; i < s_n_elem; ++i)
{
const T val = s_mem[i];
if(val >= tol) { s2_mem[count2] = T(1) / val; ++count2; }
}
if(n_rows >= n_cols)
{
out = ( (V.n_cols > count) ? V.cols(0,count-1) : V ) * diagmat(s2) * trans( (U.n_cols > count) ? U.cols(0,count-1) : U );
}
else
{
out = ( (U.n_cols > count) ? U.cols(0,count-1) : U ) * diagmat(s2) * trans( (V.n_cols > count) ? V.cols(0,count-1) : V );
}
}
else
{
out.zeros(n_cols, n_rows);
}
}
inline
void
op_pinv::direct_pinv(Mat<eT>& out, const Mat<eT>& A, const eT in_tol)
{
arma_extra_debug_sigprint();
typedef typename get_pod_type<eT>::result T;
T tol = access::tmp_real(in_tol);
arma_debug_check((tol < T(0)), "pinv(): tolerance must be >= 0");
const uword n_rows = A.n_rows;
const uword n_cols = A.n_cols;
// economical SVD decomposition
Mat<eT> U;
Col< T> s;
Mat<eT> V;
const bool status = (n_cols > n_rows) ? auxlib::svd_econ(U,s,V,trans(A),'b') : auxlib::svd_econ(U,s,V,A,'b');
if(status == false)
{
out.reset();
arma_bad("pinv(): svd failed");
return;
}
const uword s_n_elem = s.n_elem;
const T* s_mem = s.memptr();
// set tolerance to default if it hasn't been specified as an argument
if( (tol == T(0)) && (s_n_elem > 0) )
{
tol = (std::max)(n_rows, n_cols) * eop_aux::direct_eps( op_max::direct_max(s_mem, s_n_elem) );
}
// count non zero valued elements in s
uword count = 0;
for(uword i = 0; i < s_n_elem; ++i)
{
if(s_mem[i] > tol)
{
++count;
}
}
if(count != 0)
{
Col<T> s2(count);
T* s2_mem = s2.memptr();
uword count2 = 0;
for(uword i=0; i < s_n_elem; ++i)
{
const T val = s_mem[i];
if(val > tol)
{
s2_mem[count2] = T(1) / val;
++count2;
}
}
if(n_rows >= n_cols)
{
out = ( V.n_cols > count ? V.cols(0,count-1) : V ) * diagmat(s2) * trans( U.n_cols > count ? U.cols(0,count-1) : U );
}
else
{
out = ( U.n_cols > count ? U.cols(0,count-1) : U ) * diagmat(s2) * trans( V.n_cols > count ? V.cols(0,count-1) : V );
}
}
else
{
out.zeros(n_cols, n_rows);
}
}
//' @title Update Wrapper for the GMWM Estimator
//' @description This function uses information obtained previously (e.g. WV covariance matrix) to re-estimate a different model parameterization
//' @param theta A \code{vec} with dimensions N x 1 that contains user-supplied initial values for parameters
//' @param desc A \code{vector<string>} indicating the models that should be considered.
//' @param objdesc A \code{field<vec>} containing a list of parameters (e.g. AR(1) = c(1,1), ARMA(p,q) = c(p,q,1))
//' @param model_type A \code{string} that represents the model transformation
//' @param wv_empir A \code{vec} that contains the empirical wavelet variance
//' @param omega A \code{mat} that represents the covariance matrix.
//' @param scales A \code{vec} that contains the scales or taus (2^(1:J))
//' @param starting A \code{bool} that indicates whether we guessed starting (T) or the user supplied estimates (F).
//' @return A \code{field<mat>} that contains the parameter estimates from GMWM estimator.
//' @author JJB
//' @references Wavelet variance based estimation for composite stochastic processes, S. Guerrier and Robust Inference for Time Series Models: a Wavelet-Based Framework, S. Guerrier
//' @keywords internal
//' @backref src/gmwm_logic.cpp
//' @backref src/gmwm_logic.h
// [[Rcpp::export]]
arma::field<arma::mat> gmwm_update_cpp(arma::vec theta,
const std::vector<std::string>& desc, const arma::field<arma::vec>& objdesc,
std::string model_type, unsigned int N, double expect_diff, double ranged,
const arma::mat& orgV, const arma::vec& scales, const arma::mat& wv,
bool starting,
std::string compute_v, unsigned int K, unsigned int H,
unsigned int G,
bool robust, double eff){
// Number of parameters
unsigned int np = theta.n_elem;
// Guessed Values
arma::vec guessed_theta = theta;
// V matrix
arma::mat V = orgV;
// Diagonal Omega Matrix
arma::mat omega = arma::inv(diagmat(V));
arma::vec wv_empir = wv.col(0);
// Do we need to run a guessing algorithm?
if(starting){
theta = guess_initial(desc, objdesc, model_type, np, expect_diff, N, wv, scales, ranged, G);
guessed_theta = theta;
}
// Obtain the GMWM estimator estimates.
theta = gmwm_engine(theta, desc, objdesc, model_type,
wv_empir, omega, scales, starting);
theta = code_zero(theta);
// Bootstrap the V matrix
if(compute_v == "bootstrap"){
for(unsigned int k = 0; k < K; k++){
// False here means we create the "full V" matrix
V = cov_bootstrapper(theta, desc, objdesc, N, robust, eff, H, false);
omega = arma::inv(diagmat(V));
// The theta update in this case MUST not use Yannick's starting algorithm. Hence, the false value.
theta = gmwm_engine(theta, desc, objdesc, model_type, wv_empir, omega, scales, false);
// Optim may return a very small value. In this case, instead of saying its zero (yielding a transform issue), make it EPSILON.
theta = code_zero(theta);
}
}
std::map<std::string, int> models = count_models(desc);
// Order AR1s so largest phi is first!
if(models["AR1"] > 1 || models["GM"] > 1){
theta = order_AR1s(theta, desc, objdesc);
}
// Obtain the theoretical WV.
arma::mat decomp_theo = decomp_theoretical_wv(theta, desc, objdesc, scales);
arma::vec theo = decomp_to_theo_wv(decomp_theo);
// Obtain the objective value function
arma::vec obj_value(1);
obj_value(0) = getObjFun(theta, desc, objdesc, model_type, omega, wv_empir, scales);
// Export calculations to R.
arma::field<arma::mat> out(6);
out(0) = theta;
out(1) = guessed_theta;
out(2) = V;
out(3) = theo;
out(4) = decomp_theo;
out(5) = obj_value;
return out;
}