Julia operations.

row_simple.jl

function swap_row!{T}(X::Array{T,2}, i, j)
  if i != j
    @inbounds for k in 1:size(X, 2)
        X[i, k], X[j, k] = X[j, k], X[i, k]
    end
  end
  return X
end

function swap_column!{T}(X::Array{T,2}, i, j)
  if i != j
    @inbounds for k in 1:size(X, 1)
        X[k, i], X[k, j] = X[k, j], X[k, i]
    end
  end
  return X
end

function row_simple!{T}(X::Array{T,2})
  column_ptr = 1
  height, width = size(X)
  # result=
  @printf("%d, %d", width, height)
  finished = false
  @inbounds for i=1:height
    @inbounds for j=i+1:height
      # Ensure that this line starts with a non-zero element.
      while X[i,column_ptr] == 0
        i_,j_=first_nonzero(X,i,column_ptr)
        if i_==-1
          finished = true
          break
        else
          swap_row!(X, i, i_)
          swap_column!(X, column_ptr, j_)
        end
      end
      if finished
        break
      end
      # Do the subtrXction
      @printf("Doing with row %d, %d, column %d\n", i, j, column_ptr)
      X[j,:]=X[j,:] - X[j,column_ptr]/X[i,column_ptr]*X[i,:]
      println(X)
    end
    if finished
      break
    end
    column_ptr += 1
  end
  return X
end

function row_simple{T}(mat::Array{T,2})
  X = copy(mat)
  return row_simple!(X)
end

function row_simple{T<:Int}(X::Array{T,2})
  return row_simple!(convert(Array{Float64,2},X))
end

function first_nonzero{T}(mat::Array{T,2}, i_offset=1, j_offset=1)
  @printf("Offsets: %d, %d", i_offset, j_offset)
  @inbounds for i=i_offset:size(mat,1)
    @inbounds for j=j_offset:size(mat,2)
      @printf("Checking %d, %d", i, j)
      if (mat[i,j] != 0)
        return i,j
      end
    end
  end
  return -1,-1
end