herm.jl

function isnothermitian(A::SparseMatrixCSC)
    m, n = size(A)
    if m != n; return false; end

    CHECK_PERCENTAGE = 0.001

    colptr = A.colptr
    rowval = A.rowval
    nzval = A.nzval
    nrnzval = length(nzval)
    nrvals_check = trunc(Int, nrnzval * CHECK_PERCENTAGE)
    c = 0
    @inbounds for col = 1 : A.n, j = colptr[col] : colptr[col+1]-1
        c += 1
        if c > nrvals_check
            break
        end
        row = rowval[j]
        nz = nzval[j]
        if nz != ctranspose(A[col, row])
            return true
        end
    end
    false
end

function ishermitian_fast(A::SparseMatrixCSC)
    if isnothermitian(A)
        return false
    end
    return countnz(A - A') == 0
end

 function is_prob_hermitian{Tv, Ti}(A::SparseMatrixCSC{Tv, Ti}, tol = 10e-13)
    if isnothermitian(A)
        return false
    end

   # Heuristic check if <Ax, y> = <x, Ay>
   # for random x and y
   x = rand(Tv, A.n)
   y = rand(Tv, A.n)

   Axy = ((A*x)' * y)[1]
   xAy = (x' * (A*y))[1]
   res = abs(Axy - xAy) / sqrt(abs2(Axy) + abs2(xAy))
   if res < tol
       return true
   end
   return false
end




A = sprand(10^5,10^5, 0.001);
Aherm = A + A';

julia> @time ishermitian_fast(A)
# elapsed time: 1.8951e-5 seconds (160 bytes allocated)
# false

julia> @time ishermitian(A)
# elapsed time: 1.937657887 seconds (460 MB allocated, 4.44% gc time in 3 pauses with 1 full sweep)
# false

julia> @time is_prob_hermitian(A)
# elapsed time: 8.826e-6 seconds (160 bytes allocated)
# false

julia> @time ishermitian_fast(Aherm)
# elapsed time: 3.885827524 seconds (918 MB allocated, 2.94% gc time in 4 pauses with 2 full sweep)
# true

julia> @time ishermitian(Aherm)
# elapsed time: 4.004578854 seconds (918 MB allocated, 2.62% gc time in 4 pauses with 2 full sweep)
# true

julia> @time is_prob_hermitian(Aherm)
# elapsed time: 0.266606414 seconds (3 MB allocated)
# true