pcg demanding more memory than direct solver ?

[jmbeckers]

using SparseArrays
using LinearAlgebra
using DIVAnd
using Plots
using Statistics
using Random
using BenchmarkTools

Random.seed!(1234)
ND=10^3
NX=45
NY=46
NZ=47
len=0.1
# obs. error variance normalized by the background error variance
epsilon2 = 1.0

fun(x,y,z) = 2*(sin.(6x) * cos.(6y).* cos.(6z)) .+ (0 .- 1) .* x .* y .*z
x = 0.5.+0.25.*randn(ND);
y = 0.5  .+ 0.25 .* randn(ND);
z= 0.5  .+ 0.25 .* randn(ND);
f = fun.(x,y,z)+0.5*randn(ND)

x=[0.5]
y=[0.5]
z=[0.5]
f=[1.0]

# final grid
xi,yi,zi= ndgrid(range(0,stop=1,length=NX),range(0,stop=1,length=NY),range(0,stop=1,length=NZ));

# all points are valid points
mask = trues(size(xi));
#mask[:,:,1].=false
#mask[15:30,15:30,1:end].=false

pm = ones(size(xi)) / (xi[2,1,1]-xi[1,1,1]);
pn = ones(size(xi)) / (yi[1,2,1]-yi[1,1,1]);
po = ones(size(xi)) / (zi[1,1,2]-zi[1,1,1]);

pmn=(pm,pn,po)
xyi=(xi,yi,zi)
xy=(x,y,z)

fi,s= DIVAndrun(mask,pmn,xyi,xy,f,len,epsilon2);

#fi,s=DIVAndrun(mask,pmn,xyi,xy,f,len,epsilon2;inversion=:pcg,maxit=0)

If I replace the direct solver (which fits into memory), by an iterative solver with no iteration (and hence immediate warning of non-convergence), there seems to be, after the warning on non-convergence, a huge increase in memory demand and out of memory in my case:

Julia 1.8.5 and 1.7.1

[1] Array @ .\boot.jl:457 [inlined] [2] Array @ .\boot.jl:466 [inlined] [3] zeros @ .\array.jl:525 [inlined] [4] zeros @ .\array.jl:521 [inlined] [5] getindex(C::CovarIS{Float64, SparseMatrixCSC{Float64, Int64}}, i::Int64, j::Int64) @ DIVAnd C:\Users\jmbeckers.julia\packages\DIVAnd\MV3j9\src\special_matrices.jl:104 [6] isassigned(::CovarIS{Float64, SparseMatrixCSC{Float64, Int64}}, ::Int64, ::Int64) @ Base .\abstractarray.jl:553 [7] _show_nonempty(io::IOContext{IOBuffer}, X::AbstractMatrix, prefix::String, drop_brackets::Bool, axs::Tuple{Base.OneTo{Int64}, Base.OneTo{Int64}}) @ Base .\arrayshow.jl:438 [8] _show_nonempty(io::IOContext{IOBuffer}, X::CovarIS{Float64, SparseMatrixCSC{Float64, Int64}}, prefix::String) @ Base .\arrayshow.jl:410 [9] show(io::IOContext{IOBuffer}, X::CovarIS{Float64, SparseMatrixCSC{Float64, Int64}}) @ Base .\arrayshow.jl:486 [10] _show_default(io::IOContext{IOBuffer}, x::Any) @ Base .\show.jl:413 [11] show_default @ .\show.jl:396 [inlined] [12] show @ .\show.jl:391 [inlined] [13] show_delim_array(io::IOContext{IOBuffer}, itr::Tuple{Array{Float64, 3}, DIVAnd.DIVAnd_struct{Float64, Int64, 3, SparseMatrixCSC{Float64, Int64}}}, op::Char, delim::Char, cl::Char, delim_one::Bool, i1::Int64, n::Int64) @ Base .\show.jl:1244 [14] show_delim_array @ .\show.jl:1229 [inlined] [15] show @ .\show.jl:1262 [inlined] [16] show @ .\multimedia.jl:47 [inlined] [17] limitstringmime(mime::MIME{Symbol("text/plain")}, x::Tuple{Array{Float64, 3}, DIVAnd.DIVAnd_struct{Float64, Int64, 3, SparseMatrixCSC{Float64, Int64}}}) @ IJulia C:\Users\jmbeckers.julia\packages\IJulia\e8kqU\src\inline.jl:43 [18] display_mimestring @ C:\Users\jmbeckers.julia\packages\IJulia\e8kqU\src\display.jl:71 [inlined] [19] display_dict(x::Tuple{Array{Float64, 3}, DIVAnd.DIVAnd_struct{Float64, Int64, 3, SparseMatrixCSC{Float64, Int64}}}) @ IJulia C:\Users\jmbeckers.julia\packages\IJulia\e8kqU\src\display.jl:102 [20] #invokelatest#2 @ .\essentials.jl:716 [inlined] [21] invokelatest @ .\essentials.jl:714 [inlined] [22] execute_request(socket::ZMQ.Socket, msg::IJulia.Msg) @ IJulia C:\Users\jmbeckers.julia\packages\IJulia\e8kqU\src\execute_request.jl:112 [23] #invokelatest#2 @ .\essentials.jl:716 [inlined] [24] invokelatest @ .\essentials.jl:714 [inlined] [25] eventloop(socket::ZMQ.Socket) @ IJulia C:\Users\jmbeckers.julia\packages\IJulia\e8kqU\src\eventloop.jl:8 [26] (::IJulia.var"#15#18")() @ IJulia .\task.jl:423

[jmbeckers]

Actually, if you suppress the output on screen by adding a ";" at the end, the problem disappears. It seems it is the screen showing that causes the problem.

[ctroupin]

Same here, indeed it seems the display saturates the memory in gnome-terminal