R/Gaussian_Elimination.R

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.