Hello.
I am working with a pentadiagonal sparse matrix that represents a 2D
Schrodinger's time-independent equation. I first work the laplacian
expressed in Finite Differences form and then I apply the potential on the
same matrix.
So far I've been able to validate my results for both an electron in a box
as well as a harmonic oscillator, but when I change to the following
potential of a dipole, Julia pretty much quits on me when I try to obtain
the eigenvalues and eigenvectors:
O = [round(L/2)-hx round(L/2)-hy]# --el ORIGEN (centro -- x,y)
del potencial.
Eps_o = 8.854187817e10-12# --F*m^-1
C = 1/(4*pi*Eps_o)
D = 1e-21#C*m^2/s# --Debyes)
pe = 1.8*D
*P(X,Y) = -(C)*pe*(Y/X)*(1/( (X)^2 + (Y)^2 ) )*# --How the
potential gets described.
#--I'm aware there's singularities in the potential.
#--and here's how I apply the potential to my sparse matrix.
Vi = Float64[]# --container for the potential.
for j=Y for i=X push!(Vi,P(i,j)) end end@ --applying the potential.
I use this command: *l, v = eigs(M,nev=15,which = :SM ,ritzvec=true)*
My problem seems to be that there's an error that I can't get past:
ERROR: LoadError: ArgumentError: matrix has one or more zero pivots
>>
>> in #ldltfact!#10(::Float64, ::Function,
>>> ::Base.SparseArrays.CHOLMOD.Factor{Float64},
>>> ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./sparse/cholmod.jl:1350
>>
>> in (::Base.LinAlg.#kw##ldltfact!)(::Array{Any,1},
>>> ::Base.LinAlg.#ldltfact!, ::Base.SparseArrays.CHOLMOD.Factor{Float64},
>>> ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./<missing>:0
>>
>> in #ldltfact#12(::Float64, ::Array{Int64,1}, ::Function,
>>> ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./sparse/cholmod.jl:1386
>>
>> in #ldltfact#13(::Array{Any,1}, ::Function,
>>> ::Hermitian{Float64,SparseMatrixCSC{Float64,Int64}}) at
>>> ./sparse/cholmod.jl:1426
>>
>> in factorize(::SparseMatrixCSC{Float64,Int64}) at ./sparse/linalg.jl:897
>>
>> in #_eigs#62(::Int64, ::Int64, ::Symbol, ::Float64, ::Int64, ::Void,
>>> ::Array{Float64,1}, ::Bool, ::Base.LinAlg.#_eigs,
>>> ::SparseMatrixCSC{Float64,Int64}, ::UniformScaling{Int64}) at
>>> ./linalg/arnoldi.jl:251
>>
>> in (::Base.LinAlg.#kw##_eigs)(::Array{Any,1}, ::Base.LinAlg.#_eigs,
>>> ::SparseMatrixCSC{Float64,Int64}, ::UniformScaling{Int64}) at ./<missing>:0
>>
>> in #eigs#55(::Array{Any,1}, ::Function,
>>> ::SparseMatrixCSC{Float64,Int64}, ::UniformScaling{Int64}) at
>>> ./linalg/arnoldi.jl:78
>>
>> in (::Base.LinAlg.#kw##eigs)(::Array{Any,1}, ::Base.LinAlg.#eigs,
>>> ::SparseMatrixCSC{Float64,Int64}, ::UniformScaling{Int64}) at ./<missing>:0
>>
>> in #eigs#54(::Array{Any,1}, ::Function,
>>> ::SparseMatrixCSC{Float64,Int64}) at ./linalg/arnoldi.jl:77
>>
>> in (::Base.LinAlg.#kw##eigs)(::Array{Any,1}, ::Base.LinAlg.#eigs,
>>> ::SparseMatrixCSC{Float64,Int64}) at ./<missing>:0
>>
>> in include_from_node1(::String) at ./loading.jl:488
>>
>> while loading /home/alejandro/Desktop/ACAD/PROG/ACADEMIC_PROGRAMMING/FDM
>>> (Finite_Difference_Method)/2D/SCHROD_DIP_2D/SCRATCH-2D-SI-DIPOLO2.jl, in
>>> expression starting on line 106
>>
>>
>> My question is, is there a way to work around it, or, am I completely
screwed?
Thanks so much in advance.
