[blegat]

Extracted from #2788

[odow]

I'm going to say no to this one. It seems reasonable that common subexpressions could be supported only in direct_mode without copies.

[blegat]

Direct mode and non-direct mode shouldn't produce different results like this. For the user, direct_model should be the same as Model except the model transfer should be faster and lighter in memory. So from that perspective, it makes sense that we add this Dict in the IndexMap. We could make it so that when the variables indices map is trivial, we don't do any copy so that most of the time, this dictionary does not get filled.

[odow]

This needs tests, and a benchmark.

[blegat]

Benchmark

import MathOptInterface as MOI
using BenchmarkTools

# f_{k+1} = sin(f_k) * f_k + f_k with f_0 = sin(x): the tree has O(3^n) nodes
# but the DAG has O(n) nodes.
function build(n)
    x = MOI.VariableIndex(1)
    f = MOI.ScalarNonlinearFunction(:sin, Any[x])
    for _ in 1:n
        sin_f = MOI.ScalarNonlinearFunction(:sin, Any[f])
        prod = MOI.ScalarNonlinearFunction(:*, Any[sin_f, f])
        f = MOI.ScalarNonlinearFunction(:+, Any[prod, f])
    end
    return f
end

# A non-identity map so that `map_indices` does not return `f` directly.
function swap_map()
    map = MOI.Utilities.IndexMap()
    map[MOI.VariableIndex(1)] = MOI.VariableIndex(2)
    return map
end

function bench(n)
    f = build(n)
    map = swap_map()
    println("n = $n, no cache:")
    @btime MOI.Utilities.map_indices(Base.Fix1(getindex, $map), $f)
    println("n = $n, cache:")
    # `setup` with `evals = 1` gives each run an empty cache.
    @btime MOI.Utilities.map_indices(m, $f) setup = (m = swap_map()) evals = 1
    return
end

n	no cache (μs)	cache (μs)	no cache (bytes)	cache (bytes)
4	4.54	1.16	25008	3728
8	383	3.0	1994928	7216
12	47200	5.4	161559936	12736