R/matrix_multiplication.R

In stephenslab/VEB.Boost: This package provides the functionality to perform VEB-Boosting.

#' @title Computes standardized.X \%*\% b
#' @param X an n by p matrix with three attributes: scaled:center, scaled:scale, and attr(X, 'd')
#' @param b a p vector
#' @return an n vector
#' @importFrom Matrix t
#' @importFrom Matrix tcrossprod
#' @keywords internal
compute_Xb = function(X, b){
  if(is.list(X)){
    n_var = unlist(lapply(X,get_ncol)) # number of variables for each element of X
    b_split = split_vector(b,n_var) # split b into a list of vectors
    Xb = mapply(compute_Xb,X,b_split,SIMPLIFY=FALSE) # apply compute_Xb to elements of lists X,b_split
    # return(Reduce(`+`, Xb)) # add the results up
    # the below is actually faster than calling Reduce
    res = Xb[[1]]
    if (length(Xb) > 1) {
      for (j in 2:length(Xb)) {
        res = res + Xb[[j]]
      }
    }
    return(res)
  } else {
    cm = get_cm(X)
    csd = get_csd(X)
    #scale Xb
    #when X is a trend filtering matrix or stumps matrix, use special matrix mult
    if(is.tfg_matrix(X)){
      scaled.Xb <- compute_tfg_Xb(X,b/csd)
    } else
    #when X is an ordinary sparse/dense matrix
       scaled.Xb <- tcrossprod(X, t(b/csd))
    #center Xb
    Xb <- scaled.Xb - sum(cm*b/csd)
    return(as.numeric(Xb))
  }
}

#' @title Computes t(standardized.X)\%*\%y using sparse multiplication trick
#' @param X an n by p unstandardized matrix with three attributes: scaled:center, scaled:scale, and attr(X, 'd')
#' @param y an n vector
#' @return a p vector
#' @importFrom Matrix t
#' @importFrom Matrix crossprod
compute_Xty = function(X, y){
  if(is.list(X)){ # perform Xty for each element in list and concatenate the results
    unlist(lapply(X,compute_Xty,y=y))
  } else {
    cm = get_cm(X)
    csd = get_csd(X)

    #when X is a trend filtering matrix
    if(is.tfg_matrix(X))
      scaled.Xty <- compute_tfg_Xty(X,y)/csd
    #when X is an ordinary sparse/dense matrix
    else{
      ytX <- crossprod(y, X)
      scaled.Xty <- t(ytX/csd)
    }
    #center Xty
    centered.scaled.Xty <- scaled.Xty - cm/csd * sum(y)
    return(as.numeric(centered.scaled.Xty))
  }
}

#' @title Computes M\%*\%t(standardized.X) using sparse multiplication trick
#' @param M a L by p matrix
#' @param X an n by p unstandardized matrix with three attributes: scaled:center, scaled:scale, and attr(X, 'd')
#' @return a L by n matrix
#' @importFrom Matrix t
compute_MXt = function(M, X){
  cm = get_cm(X)
  csd = get_csd(X)
  #when X is a trend filtering matrix
  if ( is.tfg_matrix(X) | is.list(X)) {
    return(as.matrix(t(apply(M,1,function(b) compute_Xb(X, b)))))
  }
  #when X is an ordinary sparse/dense matrix
  else return(as.matrix(tcrossprod(M,sweep(X,2,csd,"/")) - drop(tcrossprod(M, t(cm/csd)))))

    # This should be the same as
    #
    #   t(apply(M, 1, function(b) compute_Xb(X, b))))
    #
    # as well as
    #
    #   M %*% (t(X)/csd) - drop(tcrossprod(M,t(cm/csd)))
    #
    # but should be more memory-efficient.
}




# computes (X - X_avg)^2 %*% b
compute_X2b = function(X, b, X_avg = 0) {
  if (is.list(X)) {
    n_var = sapply(X, get_ncol) # number of variables for each element of X
    b_split = split_vector(b, n_var) # split b into a list of vectors
    X_avg_split = split_vector(X_avg, n_var)
    X2b = mapply(compute_X2b, X, b_split, X_avg_split, SIMPLIFY = FALSE) # apply compute_X2b to elements of lists X, b_split
    # return(Reduce(`+`, X2b)) # add the results up
    # the below is actually faster than calling Reduce
    res = X2b[[1]]
    if (length(X2b) > 1) {
      for (j in 2:length(X2b)) {
        res = res + X2b[[j]]
      }
    }
    return(res)
  } else {
    if (is.tfg_matrix(X)) {
      # X is boolean matrix, so X^2 = X
      return(compute_Xb(X, b) - 2*compute_Xb(X, b*X_avg) + sum(X_avg^2 * b))
    } else {
      return(compute_Xb(attr(X, "X2"), b) - 2*compute_Xb(X, b*X_avg) + sum(X_avg^2 * b))
    }
  }
}

# computes t((X - X_avg)^2) %*% y
compute_X2ty = function(X, y, X_avg = 0) {
  if (is.list(X)) {
    X_avg_split = split_vector(X_avg, sapply(X, get_ncol))
    y_list = rep(list(y), length(X_avg_split))
    return(unlist(mapply(compute_X2ty, X, y_list, X_avg_split)))
  } else {
    if (is.tfg_matrix(X)) {
      # X is boolean matrix, so X^2 = X
      return(as.numeric(compute_Xty(X, y)) * (1 - 2*X_avg) + (X_avg^2 * sum(y)))
    } else {
      return(as.numeric(compute_Xty(attr(X, "X2"), y) - 2*compute_Xty(X, y)*X_avg + (X_avg^2 * sum(y))))
    }
  }
}