## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:
##
## Redistributions of source code must retain the above copyright
## notice, this list of conditions and the following disclaimer.
##
## Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in
## the documentation and/or other materials provided with the
## distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
## "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
## LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
## A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
## HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
## DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
## THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
## (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#' @name refmatrix
#' @rdname refmatrix
#'
#' @title Matrix to Row Echelon Form
#'
#' @description
#' Transform a matrix to row echelon form.
#'
#' @param m a matrix
#' @param A a square matrix representing the coefficients of a linear
#' system in \code{solvematrix}
#' @param b a vector representing the right-hand side of the linear
#' system in \code{solvematrix}
#'
#' @details
#' \code{refmatrix} reduces a matrix to row echelon form. This is not a
#' reduced row echelon form, though that can be easily calculated from
#' the diagonal. This function works on non-square matrices.
#'
#' \code{rrefmatrix} returns the reduced row echelon matrix.
#'
#' \code{solvematrix} solves a linear system using \code{rrefmatrix}.
#'
#' @return the modified matrix
#'
#' @family linear
#'
#' @examples
#' A <- matrix(c(1, 2, -7, -1, -1, 1, 2, 1, 5), 3)
#' refmatrix(A)
#'
#' @export
refmatrix <- function(m) {
count.rows <- nrow(m)
count.cols <- ncol(m)
piv <- 1
for(row.curr in 1:count.rows) {
if(piv <= count.cols) {
i <- row.curr
while(m[i, piv] == 0 && i < count.rows) {
i <- i + 1
if(i > count.rows) {
i <- row.curr
piv <- piv + 1
if(piv > count.cols)
return(m)
}
}
if(i != row.curr)
m <- swaprows(m, i, row.curr)
for(j in row.curr:count.rows)
if(j != row.curr) {
k <- m[j, piv] / m[row.curr, piv]
m <- replacerow(m, row.curr, j, -k)
}
piv <- piv + 1
}
}
return(m)
}
#' @rdname refmatrix
#' @export
rrefmatrix <- function(m) {
count.rows <- nrow(m)
count.cols <- ncol(m)
piv <- 1
for(row.curr in 1:count.rows) {
if(piv <= count.cols) {
i <- row.curr
while(m[i, piv] == 0 && i < count.rows) {
i <- i + 1
if(i > count.rows) {
i <- row.curr
piv <- piv + 1
if(piv > count.cols)
return(m)
}
}
if(i != row.curr)
m <- swaprows(m, i, row.curr)
piv.val <- m[row.curr, piv]
m <- scalerow(m, row.curr, 1 / piv.val)
for(j in 1:count.rows)
if(j != row.curr) {
k <- m[j, piv] / m[row.curr, piv]
m <- replacerow(m, row.curr, j, -k)
}
piv <- piv + 1
}
}
return(m)
}
#' @rdname refmatrix
#' @export
solvematrix <- function(A, b) {
m <- cbind(A, b)
m <- rrefmatrix(m)
x <- m[, ncol(m)]
return(x)
}
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.