# R/Gaussian_Elimination.R In restriktor: Restricted Statistical Estimation and Inference for Linear Models

#### Defines functions GaussianElimination

```GaussianElimination <- function(A, B, tol=sqrt(.Machine\$double.eps),
verbose = FALSE){
# A: coefficient matrix
# B: right-hand side vector or matrix
# tol: tolerance for checking for 0 pivot
# verbose: if TRUE, print intermediate steps
# If B is absent returns the reduced row-echelon form of A.
# If B is present, reduces A to RREF carrying B along.

## routine by John Fox modified to output pivot column numbers
## by Ulrike Groemping (ic.infer package)
pivot.num <- integer(0)
if ((!is.matrix(A)) || (!is.numeric(A)))
stop("argument must be a numeric matrix")
n <- nrow(A)
m <- ncol(A)
if (!missing(B)){
B <- as.matrix(B)
if (!(nrow(B) == nrow(A)) || !is.numeric(B))
stop("argument must be numeric and must match the number of row of A")
A <- cbind(A, B)
}
i <- j <- k <- 1
while (i <= n && j <= m){
while (j <= m){
currentColumn <- A[,j]
currentColumn[1:n < i] <- 0
# find maximum pivot in current column at or below current row
which <- which.max(abs(currentColumn))
pivot <- currentColumn[which]
if (abs(pivot) <= tol) { # check for 0 pivot
j <- j + 1
next
}
if (which > i) A[c(i, which),] <- A[c(which, i),] # exchange rows
A[i,] <- A[i,]/pivot # pivot
pivot.num <- c(pivot.num, j)
k <- k + 1
row <- A[i,]
A <- A - outer(A[,j], row) # sweep
A[i,] <- row # restore current row
if (verbose) print(round(A, round(abs(log(tol,10)))))
j <- j + 1
break
}
i <- i + 1
}
# 0 rows to bottom
zeros <- which(apply(matrix(A[,1:m],nrow(A),m), 1, function(x) max(abs(x)) <= tol))
if (length(zeros) > 0){
zeroRows <- A[zeros,]
A <- A[-zeros,]
A <- rbind(A, zeroRows)
}
rownames(A) <- NULL
list(E=round(A, round(abs(log(tol, 10)))), pivot=pivot.num, rank=length(pivot.num))
}
```

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restriktor documentation built on Feb. 25, 2020, 5:08 p.m.