Julia: swap gives errors - julia

Question

I'm using Julia 0.3.4
I'm trying to write LU-decomposition using Gaussian elimination. So I have to swap rows. And here's my problem:
If I'm using a,b = b,a I get an error,
but if I'm using:
function swapRows(row1, row2)
temp = row1
row1 = row2
row2 = temp
end
then everything works just fine.
Am I doing something wrong or it's a bug?
Here's my source code:
function lu_t(A::Matrix)
# input value: (A), where A is a matrix
# return value: (L,U), where L,U are matrices
function swapRows(row1, row2)
temp = row1
row1 = row2
row2 = temp
return null
end
if size(A)[1] != size(A)[2]
throw(DimException())
end
n = size(A)[1] # matrix dimension
U = copy(A) # upper triangular matrix
L = eye(n) # lower triangular matrix
for k = 1:n-1 # direct Gaussian elimination for each column `k`
(val,id) = findmax(U[k:end,k]) # find max pivot element and it's row `id`
if val == 0 # check matrix for singularity
throw(SingularException())
end
swapRows(U[k,k:end],U[id,k:end]) # swap row `k` and `id`
# U[k,k:end],U[id,k:end] = U[id,k:end],U[k,k:end] - error
for i = k+1:n # for each row `i` > `k`
μ = U[i,k] / U[k,k] # find elimination coefficient `μ`
L[i,k] = μ # save to an appropriate position in lower triangular matrix `L`
for j = k:n # update each value of the row `i`
U[i,j] = U[i,j] - μ⋅U[k,j]
end
end
end
return (L,U)
end
###### main code ######
A = rand(4,4)
#time (L,U) = lu_t(A)
#test_approx_eq(L*U, A)

Answer 1

The swapRows function is a no-op and has no effect whatsoever – all it does is swap around some local variable names. See various discussions of the difference between assignment and mutation:
https://groups.google.com/d/msg/julia-users/oSW5hH8vxAo/llAHRvvFVhMJ
http://julia.readthedocs.org/en/latest/manual/faq/#i-passed-an-argument-x-to-a-function-modified-it-inside-that-function-but-on-the-outside-the-variable-x-is-still-unchanged-why
http://julia.readthedocs.org/en/latest/manual/faq/#why-does-x-y-allocate-memory-when-x-and-y-are-arrays
The constant null doesn't mean what you think it does – in Julia v0.3 it's a function that computes the null space of a linear transformation; in Julia v0.4 it still means this but has been deprecated and renamed to nullspace. The "uninteresting" value in Julia is called nothing.
I'm not sure what's wrong with your commented out row swapping code, but this general approach does work:
julia> X = rand(3,4)
3x4 Array{Float64,2}:
0.149066 0.706264 0.983477 0.203822
0.478816 0.0901912 0.810107 0.675179
0.73195 0.756805 0.345936 0.821917
julia> X[1,:], X[2,:] = X[2,:], X[1,:]
(
1x4 Array{Float64,2}:
0.478816 0.0901912 0.810107 0.675179,
1x4 Array{Float64,2}:
0.149066 0.706264 0.983477 0.203822)
julia> X
3x4 Array{Float64,2}:
0.478816 0.0901912 0.810107 0.675179
0.149066 0.706264 0.983477 0.203822
0.73195 0.756805 0.345936 0.821917
Since this creates a pair of temporary arrays that we can't yet eliminate the allocation of, this isn't the most efficient approach. If you want the most efficient code here, looping over the two rows and swapping pairs of scalar values will be faster:
function swapRows!(X, i, j)
for k = 1:size(X,2)
X[i,k], X[j,k] = X[j,k], X[i,k]
end
end
Note that it is conventional in Julia to name functions that mutate one or more of their arguments with a trailing !. Currently, closures (i.e. inner functions) have some performance issues, so you'll want such a helper function to be defined at the top-level scope instead of inside of another function the way you've got it.
Finally, I assume this is an exercise since Julia ships with carefully tuned generic (i.e. it works for arbitrary numeric types) LU decomposition: http://docs.julialang.org/en/release-0.3/stdlib/linalg/#Base.lu.
-

Answer 2

It's quite simple
julia> A = rand(3,4)
3×4 Array{Float64,2}:
0.241426 0.283391 0.201864 0.116797
0.457109 0.138233 0.346372 0.458742
0.0940065 0.358259 0.260923 0.578814
julia> A[[1,2],:] = A[[2,1],:]
2×4 Array{Float64,2}:
0.457109 0.138233 0.346372 0.458742
0.241426 0.283391 0.201864 0.116797
julia> A
3×4 Array{Float64,2}:
0.457109 0.138233 0.346372 0.458742
0.241426 0.283391 0.201864 0.116797
0.0940065 0.358259 0.260923 0.578814