R/RcppExports.R

In cpr: Control Polygon Reduction

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#' Knot Insertion, Removal, and Reinsertion
#' 
#' Functions for the insertion, removal, and reinsertion of internal knots for
#' B-splines.
#'
#' \code{refine_ordinate} provides the estimated ordinates of the control
#' polygon's vertex sequence after inserting the value \code{x} into the knot
#' vector \code{xi}.
#'
#' \code{coarsen_ordinate} provides the estimated ordinates of the control
#' polygon's vertex sequence after the removal of the the value \code{x} from the
#' knot vector \code{xi}.  The expected input for this function is the value
#' \code{x} to insert into \code{xi}.  That is, to find the estimate of the
#' coarsened ordinates by removing the value 2 from the vector (0, 0, 0, 0, 1,
#' 2, 3, 4, 4, 4, 4) (the knot vector for a cubic B-spline with boundary knots
#' at zero and four and internal knots 1, 2, 3) should be specified by
#' \code{coarsen_ordinate(x = 2, xi = c(0, 0, 0, 0, 1, 3, 4, 4, 4, 4), theta)}.
#'
#' The function \code{hat_ordinate} is the coarsen-then-refine estimate of the
#' ordinate vector.  The name comes from the the use of a hat matrix based on the
#' in knot insertion matrix.
#'
#' Examples for the \code{refine_ordinate}, \code{coarsen_ordinate}, and
#' \code{hat_ordinate} are best shown in the vignette, 
#' \code(vignette("cpr-pkg", package = "cpr")}.
#'
#' \code{iknot_weights} returns a vector with the 'importance weight' of each
#' of the internal knots in \code{xi}.
#'
#' @author Peter DeWitt \email{dewittpe@gmail.com}
#'
#' @param x the value of the knot to be inserted into the knot vector
#' @param xi the (whole) knot vector, including the repeated boundary knots.
#'   Regardless of refinement or coarsening, this vector should be the
#'   'reduced' vector such that x will be added to it.  See details and
#'   examples.
#' @param theta the ordinates of the control polygon vertices
#' @param order the order of the B-spline, defaults to 4 for cubic splines
#'
#' @return numeric vectors
#'
#' @examples
#' \dontrun{
#' # See the vignette
#' vignette("cpr-pkg", package = "cpr")
#' }
#'
#' @export
#' @rdname boehm
refine_ordinate <- function(x, xi, theta, order = 4L) {
    .Call('cpr_refine_ordinate', PACKAGE = 'cpr', x, xi, theta, order)
}

#' @export
#' @rdname boehm
coarsen_ordinate <- function(x, xi, theta, order = 4L) {
    .Call('cpr_coarsen_ordinate', PACKAGE = 'cpr', x, xi, theta, order)
}

#' @export
#' @rdname boehm
hat_ordinate <- function(x, xi, theta, order = 4L) {
    .Call('cpr_hat_ordinate', PACKAGE = 'cpr', x, xi, theta, order)
}

#' @export
#' @rdname boehm
insertion_matrix <- function(x, xi, order = 4L) {
    .Call('cpr_insertion_matrix', PACKAGE = 'cpr', x, xi, order)
}

weigh_iknots <- function(xi, theta, order = 4L, p = 2L) {
    .Call('cpr_weigh_iknots', PACKAGE = 'cpr', xi, theta, order, p)
}

bbasis__impl <- function(x, iknots, bknots, order) {
    .Call('cpr_bbasis__impl', PACKAGE = 'cpr', x, iknots, bknots, order)
}

bsplineD1__impl <- function(x, j, order, knots) {
    .Call('cpr_bsplineD1__impl', PACKAGE = 'cpr', x, j, order, knots)
}

bsplineD2__impl <- function(x, j, order, knots) {
    .Call('cpr_bsplineD2__impl', PACKAGE = 'cpr', x, j, order, knots)
}

diag_only <- function(A, B) {
    .Call('cpr_diag_only', PACKAGE = 'cpr', A, B)
}

#' Rank of a Matrix
#'
#' Determine the rank (number of linearly independent columns) of a matrix.
#'
#' Implimentation via the Armadillo C++ linear algrebra library.  The function
#' returns the rank of the matix \code{x}.  The computation is based on the
#' singular value decomposition of the matrix; a std::runtime_error excetion
#' will be thrown if the decomposition fails.  Any singular values less than
#' the tolerance are treated as zeros.  The tolerance is max(m, n) * max_sv *
#' datum::eps, where m is the number of rows of x, n is the number of columns
#' of x, max_sv is the maximal singular value of x, and datum::eps is the
#' difference between 1 and the least value greater than 1 that is
#' representable.
#'
#' @author Peter DeWitt \email{dewittpe@gmail.com}
#'
#' @param x a numeric matrix
#'
#' @return
#' the rank of the matrix as a numeric value.
#'
#' @example examples/matrix_rank.R
#'
#' @references
#'
#' Conrad Sanderson and Ryan Curtin.  Armadillo: a template-based C++ library
#' for linear algebra.  Journal of Open Source Software, Vol. 1, pp. 26, 2016.
#'
#' @export
matrix_rank <- function(x) {
    .Call('cpr_matrix_rank', PACKAGE = 'cpr', x)
}

tp__impl <- function(A, B) {
    .Call('cpr_tp__impl', PACKAGE = 'cpr', A, B)
}