Lower triangular matrix in julia

Question

I have the number of columns equals the number of rows. And the the diagonal is is equal to zero. How can I build this matrix?

#mat
#     [,1] [,2] [,3] [,4]
#[1,]   0   NA   NA   NA
#[2,]    1   0   NA   NA
#[3,]    2    4   0   NA
#[4,]    3    5    6   0

I tried this

x=rand(4,4)
4x4 Array{Float64,2}:
 0.60064   0.917443  0.561744   0.135717 
 0.106728  0.72391   0.0894174  0.0656103
 0.410262  0.953857  0.844697   0.0375045
 0.476771  0.778106  0.469514   0.398846 

c=LowerTriangular(x)

4x4 LowerTriangular{Float64,Array{Float64,2}}:
 0.60064   0.0       0.0       0.0     
 0.106728  0.72391   0.0       0.0     
 0.410262  0.953857  0.844697  0.0     
 0.476771  0.778106  0.469514  0.398846

but l'm looking for something like this

c=LowerTriangular(x)
4x4 LowerTriangular{Float64,Array{Float64,2}}:
 0.0   NA      NA       NA    
 0.106728  0.0    NA      NA    
 0.410262  0.953857  0.0 NA     
 0.476771  0.778106  0.469514  0

The diagonal should be equal to zero.

Answer 1

You might want to use a list comprehension. But it would be good if you could give more information in the question about what you are trying to do.

numrows =4
numcols = 4
[ x>y ? 1 : (x == y ? 0 : NaN) for x in 1:numrows, y in 1:numcols]

which will give:

 0  NaN  NaN  NaN
 1    0  NaN  NaN
 1    1    0  NaN
 1    1    1    0

For any number of rows and columns. And then you can work from there.

See docs for list comprehensions & conditionals:

http://docs.julialang.org/en/release-0.4/manual/arrays/#comprehensions

http://docs.julialang.org/en/release-0.4/manual/control-flow/#man-conditional-evaluation

Answer 2

Here is something taking inspiration from Code by Stefan Karpinski on the Julia User's list:

function vec2ltri_alt{T}(v::AbstractVector{T}, z::T=zero(T))
    n = length(v)
    v1 = vcat(0,v)
    s = round(Int,(sqrt(8n+1)-1)/2)
    s*(s+1)/2 == n || error("vec2utri: length of vector is not triangular")
    s+=1
    [ i>j ? v1[round(Int, j*(j-1)/2+i)] : (i == j ? z : NaN) for i=1:s, j=1:s ]
end

julia> vec2ltri_alt(collect(1:6))
4x4 Array{Any,2}:
 0  NaN  NaN  NaN
 1    0  NaN  NaN
 2    3    0  NaN
 3    4    6    0

Note: If desired, check out the official documentation on the ternary operator for a bit more clarity on what is going on with the ? ... : syntax here.

For those looking for a more "standard" diagonal matrix solution:

Here is a version that creates a more standard solution:

function vec2ltri{T}(v::AbstractVector{T}, z::T=zero(T))
    n = length(v)
    s = round(Int,(sqrt(8n+1)-1)/2)
    s*(s+1)/2 == n || error("vec2utri: length of vector is not triangular")
    [ i>=j ? v[round(Int, j*(j-1)/2+i)] : z for i=1:s, j=1:s ]
end

a = vec2ltri(collect(1:6))

julia> a = vec2ltri(collect(1:6))
3x3 Array{Int64,2}:
 1  0  0
 2  3  0
 3  4  6

julia> istril(a)  ## verify matrix is lower triangular
true

If you want upper triangular: instead of lower, just change the i<=j to i>=j.

Other random tools Note also functions like tril!(a) which will convert in place a given matrix to lower triangular, replacing everything above the main diagonal with zeros. See the Julia documentation for more info on this function, as well as various other related tools.