QR-like factorization preserving type?

General Usage
2

I don’t think the LinearAlgebra package has such a function; perhaps the following will work:

julia> function gs(H::Matrix{Td}) where {Td}
           Q = copy(H)
           n = size(H,2)
           R = Matrix{Td}(I,n,n)
           for i=1:n
               for j=1:i-1
                   R[j,i] = H[:,i]'*Q[:,j]
                   Q[:,i]-= R[j,i]*Q[:,j]
               end
           end
           return Q,R
       end
gs (generic function with 1 method)

julia> N=2; a=rand(0:10,N,N);   Q,R = gs(a);   Q*R-a
2×2 Array{Int64,2}:
 0  0
 0  0

julia> N=2; a=rand(0:10,N,N).//rand(1:10,N,N); Q,R = gs(a); Q*R-a
2×2 Array{Rational{Int64},2}:
 0//1  0//1
 0//1  0//1
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