/**
   * The update rule for the basis matrix W.
   * The function takes in all the matrices and only changes the
   * value of the W matrix.
   *
   * @param V Input matrix to be factorized.
   * @param W Basis matrix to be updated.
   * @param H Encoding matrix.
   */
  inline void WUpdate(const arma::sp_mat& V,
                      arma::mat& W,
                      const arma::mat& H)
  {
    if(!isStart) (*it)++;
    else isStart = false;

    if(*it == V.end())
    {
        delete it;
        it = new arma::sp_mat::const_iterator(V.begin());
    }

    size_t currentUserIndex = it->col();
    size_t currentItemIndex = it->row();

    arma::mat deltaW(1, W.n_cols);
    deltaW.zeros();

    deltaW += (**it - arma::dot(W.row(currentItemIndex), H.col(currentUserIndex)))
                                      * arma::trans(H.col(currentUserIndex));
    if(kw != 0) deltaW -= kw * W.row(currentItemIndex);

    W.row(currentItemIndex) += u*deltaW;
  }
Example #2
0
// [[Rcpp::export]]
arma::sp_mat sparseIterators(arma::sp_mat SM, double val) {
    arma::sp_mat::iterator begin = SM.begin();
    arma::sp_mat::iterator end   = SM.end();
    
    for (arma::sp_mat::iterator it = begin; it != end; ++it)
      (*it) += val;
    
    return SM;
}
Example #3
0
//' Compute ego/alter edge coordinates considering alter's size and aspect ratio
//'
//' Given a graph, vertices' positions and sizes, calculates the absolute positions
//' of the endpoints of the edges considering the plot's aspect ratio.
//'
//' @param graph A square matrix of size \eqn{n}. Adjacency matrix.
//' @param toa Integer vector of size \eqn{n}. Times of adoption.
//' @param x Numeric vector of size \eqn{n}. x-coordinta of vertices.
//' @param y Numeric vector of size \eqn{n}. y-coordinta of vertices.
//' @param vertex_cex Numeric vector of size \eqn{n}. Vertices' sizes in terms
//' of the x-axis (see \code{\link{symbols}}).
//' @param undirected Logical scalar. Whether the graph is undirected or not.
//' @param no_contemporary Logical scalar. Whether to return (compute) edges'
//' coordiantes for vertices with the same time of adoption (see details).
//' @param dev Numeric vector of size 2. Height and width of the device (see details).
//' @param ran Numeric vector of size 2. Range of the x and y axis (see details).
//' @param curved Logical vector.
//' @return A numeric matrix of size \eqn{m\times 5}{m * 5} with the following
//' columns:
//' \item{x0, y0}{Edge origin}
//' \item{x1, y1}{Edge target}
//' \item{alpha}{Relative angle between \code{(x0,y0)} and \code{(x1,y1)} in terms
//' of radians}
//' With \eqn{m} as the number of resulting edges.
//' @details
//'
//' In order to make the plot's visualization more appealing, this function provides
//' a straight forward way of computing the tips of the edges considering the
//' aspect ratio of the axes range. In particular, the following corrections are
//' made at the moment of calculating the egdes coords:
//'
//' \itemize{
//' \item{Instead of using the actual distance between ego and alter, a relative
//' one is calculated as follows
//' \deqn{d'=\left[(x_0-x_1)^2 + (y_0' - y_1')^2\right]^\frac{1}{2}}{d'=sqrt[(x0-x1)^2 + (y0'-y1')^2]}
//' where \eqn{%
//' y_i'=y_i\times\frac{\max x - \min x}{\max y - \min y} }{%
//' yi' = yi * [max(x) - min(x)]/[max(y) - min(y)]}
//' }
//' \item{Then, for the relative elevation angle, \code{alpha}, the relative distance \eqn{d'}
//' is used, \eqn{\alpha'=\arccos\left( (x_0 - x_1)/d' \right)}{\alpha' = acos[ (x0 - x1)/d' ]}}
//' \item{Finally, the edge's endpoint's (alter) coordinates are computed as follows: %
//' \deqn{%
//'   x_1' = x_1 + \cos(\alpha')\times v_1}{%
//'   x1' = x1 + cos(\alpha') * v1
//' }
//' \deqn{%
//'   y_1' = y_1 -+ \sin(\alpha')\times v_1 \times\frac{\max y - \min y}{\max x - \min x} }{%
//'   y1' = y1 -+ sin(\alpha')*[max(y) - min(y)]/[max(x) - min(x)]
//' }
//' Where \eqn{v_1}{v1} is alter's size in terms of the x-axis, and the sign of
//' the second term in \eqn{y_1'}{y1'} is negative iff \eqn{y_0 < y_1}{y0<y1}.
//' }
//' }
//'
//' The same process (with sign inverted) is applied to the edge starting piont.
//' The resulting values, \eqn{x_1',y_1'}{x1',y1'} can be used with the function
//' \code{\link{arrows}}. This is the workhorse function used in \code{\link{plot_threshold}}.
//'
//' The \code{dev} argument provides a reference to rescale the plot accordingly
//' to the device, and former, considering the size of the margins as well (this
//' can be easily fetched via \code{par("pin")}, plot area in inches).
//'
//' On the other hand, \code{ran} provides a reference for the adjustment
//' according to the range of the data, this is \code{range(x)[2] - range(x)[1]}
//' and \code{range(y)[2] - range(y)[1]} respectively.
//'
//' @keywords misc dplot
//' @examples
//' # --------------------------------------------------------------------------
//' data(medInnovationsDiffNet)
//' library(sna)
//'
//' # Computing coordinates
//' set.seed(79)
//' coords <- sna::gplot(as.matrix(medInnovationsDiffNet$graph[[1]]))
//'
//' # Getting edge coordinates
//' vcex <- rep(1.5, nnodes(medInnovationsDiffNet))
//' ecoords <- edges_coords(
//'   medInnovationsDiffNet$graph[[1]],
//'   diffnet.toa(medInnovationsDiffNet),
//'   x = coords[,1], y = coords[,2],
//'   vertex_cex = vcex,
//'   dev = par("pin")
//'   )
//'
//' ecoords <- as.data.frame(ecoords)
//'
//' # Plotting
//' symbols(coords[,1], coords[,2], circles=vcex,
//'   inches=FALSE, xaxs="i", yaxs="i")
//'
//' with(ecoords, arrows(x0,y0,x1,y1, length=.1))
//' @export
// [[Rcpp::export]]
NumericMatrix edges_coords(
    const arma::sp_mat & graph,
    const arma::colvec & toa,
    const arma::colvec & x,
    const arma::colvec & y,
    const arma::colvec & vertex_cex,
    bool undirected=true,
    bool no_contemporary=true,
    NumericVector dev = NumericVector::create(),
    NumericVector ran = NumericVector::create(),
    LogicalVector curved = LogicalVector::create()
) {

  // The output matrix has the following
  // - x0 and y0
  // - x1 and y1
  // - alpha
  std::vector< double > x0;
  std::vector< double > y0;
  std::vector< double > x1;
  std::vector< double > y1;
  std::vector< double > alpha;

  // Rescaling the vertex sizes
  arma::colvec vertex_size(vertex_cex);

  // If yexpand is too small, just throw an error
  if (ran.length() == 0) {
    ran = NumericVector::create(2);
    ran[0] = x.max() - x.min();
    ran[1] = y.max() - y.min();
  }

  // Expansion factor for y
  double yexpand = 1.0;
  if ( ran[1] > 1e-5 ) yexpand = ran[1]/ran[0];

  // Adjusting for device size
  if (dev.length() == 0)
    dev = NumericVector::create(2,1.0);

  // Curved?
  if (curved.length() == 0)
    curved = LogicalVector::create(graph.n_nonzero, true);

  yexpand = yexpand * (dev[0]/dev[1]);

  for(arma::sp_mat::const_iterator it = graph.begin(); it != graph.end(); ++it) {

    int i = it.row();
    int j = it.col();

    // Checking conditions
    if (undirected && (i < j)) continue;
    if (no_contemporary && (toa(i)==toa(j)) ) continue;

    // Computing angle
    double a = atan2((y(j) - y(i))/yexpand, x(j) - x(i));
    alpha.push_back(a);

    // Adding the xs and the ys
    x0.push_back(x.at(i) + cos(a)*vertex_size.at(i));
    x1.push_back(x.at(j) - cos(a)*vertex_size.at(j));

    // The formula needs an extra help to figure out the ys
    y0.push_back(y.at(i) + sin(a)*vertex_size.at(i)*yexpand);
    y1.push_back(y.at(j) - sin(a)*vertex_size.at(j)*yexpand);
  }

  // Building up the output
  int e = x0.size();
  NumericMatrix out(e,5);
  for(int i=0; i<e; ++i) {
    out(i,0) = x0[i];
    out(i,1) = y0[i];
    out(i,2) = x1[i];
    out(i,3) = y1[i];
    out(i,4) = alpha[i];
  }

  colnames(out) = CharacterVector::create("x0", "y0", "x1", "y1", "alpha");

  return out;

}
Example #4
0
// compute the log likelihood and its gradient w.r.t. theta
int dtq::compGrad(void)
{
  // remember, everything here is for equispaced data
  // we'll save the non-equispaced case for our scala + spark code :)
  if ((! haveData) || (! haveMyh)) return 1;
  if (spi<1) return 1;

  loglikmat = arma::zeros(ltvec-1,numts);

  if (spi==1) // special case
  {
  } 
  else
  {
    // strategy: precompute and store common elements in Mats and Cubs

    // compute gradf and gradg at all spatial grid points
    arma::mat gradfy = arma::zeros(ylen,curtheta.n_elem);
    arma::mat gradgy = arma::zeros(ylen,curtheta.n_elem);
    this->gradFGyvec(gradfy, gradgy);

    // ompute gradf and gradg at all the data points
    arma::cube gradfdata = arma::zeros(curtheta.n_elem, (ltvec-1), numts);
    arma::cube gradgdata = arma::zeros(curtheta.n_elem, (ltvec-1), numts);
    this->gradFGdata(gradfdata, gradgdata);
    
    // initialize cubes to store all states and adjoints,
    // at all internal time points (spi-1),
    // for each pair of time series points (ltvec-1),
    // and at all spatial grid points (ylen)
    arma::cube dtqcube = arma::zeros(ylen,(ltvec-1),(spi-1));
    arma::cube adjcube = arma::zeros(ylen,(ltvec-1),(spi-1));

    // temporary matrix to store the initial state, phatinit
    arma::mat phatinit = arma::zeros(ylen,(ltvec-1));
    
    // cube to store the gradient of the initial state w.r.t. theta
    arma::cube phatgrad = arma::zeros(ylen,(ltvec-1),curtheta.n_elem);

    // build the big matrix of initial conditions
    // and the gradients of those initial conditions!
    this->phatinitgrad(phatinit, phatgrad, gradfdata, gradgdata);
    dtqcube.slice(0) = phatinit;

    // propagate states forward in time by (spi-2) steps
    if (spi >= 3)
      for (int i=1; i<=(spi-2); i++)
        dtqcube.slice(i) = myk * prop * dtqcube.slice(i-1);

    // now multiply on the left by the Gamma vectors
    const arma::vec muvec = yvec + fy*myh;
    const arma::vec sigvec = gy*sqrt(myh);
    arma::cube allgamma = arma::zeros(ylen,numts,(ltvec-1));
    for (int j=0; j<(ltvec-1); j++)
    {
      for (int l=0; l<numts; l++)
      {
        allgamma.slice(j).col(l) = myk*gausspdf((*odata)(j+1,l),muvec,sigvec);
        loglikmat(j,l) = log(arma::dot(allgamma.slice(j).col(l),dtqcube.slice(spi-2).col(j)));
      }
    }

    // std::cout << loglikmat << '\n';

    // initialize the adjoint calculation
    for (int j=0; j<(ltvec-1); j++)
      for (int l=0; l<numts; l++)
        adjcube.slice(spi-2).col(j) += allgamma.slice(j).col(l) / exp(loglikmat(j,l));

    // propagate adjoints backward in time by (spi-2) steps
    arma::sp_mat transprop = prop.t();
    if (spi >= 3)
      for (int i=(spi-2); i>=1; i--)
        adjcube.slice(i-1) = myk * transprop * adjcube.slice(i);

    // stuff that we need for a bunch of gradients
    gradloglik = arma::zeros(curtheta.n_elem);
    arma::vec gvecm1 = arma::pow(gy,-1);
    arma::vec gvecm2 = arma::pow(gy,-2);
    arma::vec gvecm3 = arma::pow(gy,-3);

    // actual gradient calculation
    // proceed element-wise through theta_i
    for (int i=0; i<curtheta.n_elem; i++)
    {
      arma::vec temp1 = gvecm2 % gradfy.col(i);
      arma::vec temp2 = gvecm1 % gradgy.col(i);
      arma::vec temp3 = (1.0/myh)*gvecm3 % gradgy.col(i);
      arma::sp_mat::const_iterator start = prop.begin();
      arma::sp_mat::const_iterator end = prop.end();
      arma::umat dkdtloc(2, prop.n_nonzero);
      arma::vec dkdtval(prop.n_nonzero);
      unsigned int dkdtc = 0;
      for (arma::sp_mat::const_iterator it = start; it != end; ++it)
      {
        dkdtloc(0,dkdtc) = it.row();
        dkdtloc(1,dkdtc) = it.col();
        dkdtc++;
      }
#pragma omp parallel for
      for (unsigned int dkdtcount=0; dkdtcount < prop.n_nonzero; dkdtcount++)
      {
        unsigned int orow = dkdtloc(0,dkdtcount);
        unsigned int ocol = dkdtloc(1,dkdtcount);
        double comval = yvec(orow) - muvec(ocol);
        dkdtval(dkdtcount) = myk*(prop.values[dkdtcount])*( comval*temp1(ocol) - temp2(ocol) + temp3(ocol)*comval*comval );
      }
      arma::sp_mat dkdtheta(dkdtloc, dkdtval, ylen, ylen, false, true);

      // implement formula (22) from the DSAA paper
      // need gradient of Gamma{F-1}
      double tally = 0.0;
#pragma omp parallel for reduction(+:tally)
      for (int j=0; j<(ltvec-1); j++)
      {
        tally += arma::dot(phatgrad.slice(i).col(j),adjcube.slice(0).col(j));
      }

#pragma omp parallel for collapse(2) reduction(+:tally)
      for (int j=0; j<(ltvec-1); j++)
        for (int l=0; l<numts; l++)
        {
          double xi = (*odata)((j+1),l);
          arma::vec gammagrad = (xi-muvec) % temp1;
          gammagrad += arma::pow(xi-muvec,2) % temp3;
          gammagrad -= temp2;
          gammagrad = gammagrad % allgamma.slice(j).col(l);
          tally += arma::dot(gammagrad,dtqcube.slice(spi-2).col(j)) / exp(loglikmat(j,l));
        }

      // we have tested and found that the dot product is better than the
      // triple matrix product here, i.e., it is worth taking the transpose
      // arma::mat dkdtheta = dkdthetatrans.t();
#pragma omp parallel for collapse(2) reduction(+:tally)
      for (int j=0; j<(ltvec-1); j++)
        for (int l=0; l<(spi-2); l++)
        {
          tally += arma::dot((dkdtheta*dtqcube.slice(l).col(j)),adjcube.slice(l+1).col(j));
        }
      gradloglik(i) = tally;
    }
  }
  haveLoglik = true;
  haveGradloglik = true;
  return 0;
}