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geoffroylecontegeoffroyleconte
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Presolve fixed variables (#49)
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‎src/QuadraticModels.jl‎

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -29,9 +29,10 @@ import NLPModels:
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SlackModel,
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slack_meta
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export QuadraticModel
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export AbstractQuadraticModel, QuadraticModel, presolve, postsolve!
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include("qpmodel.jl")
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include("presolve/presolve.jl")
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function __init__()
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@require QPSReader = "10f199a5-22af-520b-b891-7ce84a7b1bd0" include("qps.jl")

‎src/presolve/presolve.jl‎

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@@ -0,0 +1,92 @@
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include("remove_ifix.jl")
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mutable struct PresolvedQuadraticModel{T, S} <: AbstractQuadraticModel{T, S}
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meta::NLPModelMeta{T, S}
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counters::Counters
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data::QPData{T, S}
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xrm::S
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end
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"""
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psqm = presolve(qm::QuadraticModel{T, S}; kwargs...)
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Apply a presolve routine to `qm` and returns a `PresolvedQuadraticModel{T, S} <: AbstractQuadraticModel{T, S}`.
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The presolve operations currently implemented are:
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- [`remove_ifix!`](@ref)
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"""
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function presolve(qm::QuadraticModel{T, S}; kwargs...) where {T <: Real, S}
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psqm = deepcopy(qm)
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psdata = psqm.data
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lvar, uvar = psqm.meta.lvar, psqm.meta.uvar
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lcon, ucon = psqm.meta.lcon, psqm.meta.ucon
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nvar, ncon = psqm.meta.nvar, psqm.meta.ncon
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ifix = qm.meta.ifix
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if length(ifix) > 0
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xrm, psdata.c0, nvarps = remove_ifix!(
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ifix,
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psdata.Hrows,
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psdata.Hcols,
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psdata.Hvals,
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nvar,
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psdata.Arows,
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psdata.Acols,
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psdata.Avals,
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psdata.c,
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psdata.c0,
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lvar,
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uvar,
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lcon,
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ucon,
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)
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else
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nvarps = nvar
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xrm = S(undef, 0)
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end
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# form meta
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nnzh = length(psdata.Hvals)
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if !(nnzh == length(psdata.Hrows) == length(psdata.Hcols))
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error("The length of Hrows, Hcols and Hvals must be the same")
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end
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nnzj = length(psdata.Avals)
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if !(nnzj == length(psdata.Arows) == length(psdata.Acols))
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error("The length of Arows, Acols and Avals must be the same")
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end
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psmeta = NLPModelMeta{T, S}(
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nvarps,
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lvar = lvar,
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uvar = uvar,
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ncon = ncon,
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lcon = lcon,
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ucon = ucon,
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nnzj = nnzj,
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nnzh = nnzh,
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lin = 1:ncon,
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nln = Int[],
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islp = (ncon == 0);
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minimize = qm.meta.minimize,
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kwargs...,
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)
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ps = PresolvedQuadraticModel(psmeta, Counters(), psdata, xrm)
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return ps
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end
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"""
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postsolve!(qm::QuadraticModel{T, S}, psqm::PresolvedQuadraticModel{T, S},
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x_in::S, x_out::S) where {T, S}
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Retrieve the solution `x_out` of the original QP `qm` given the solution of the presolved QP (`psqm`)
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`x_in`.
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"""
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function postsolve!(qm::QuadraticModel{T, S}, psqm::PresolvedQuadraticModel{T, S}, x_in::S, x_out::S) where {T, S}
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if length(qm.meta.ifix) > 0
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restore_ifix!(qm.meta.ifix, psqm.xrm, x_in, x_out)
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else
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x_out .= @views x_in[1: qm.meta.nvar]
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end
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end

‎src/presolve/remove_ifix.jl‎

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# ̃xᵀ̃Hx̃ + ̃ĉᵀx̃ + lⱼ²Hⱼⱼ + cⱼxⱼ + c₀
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# ̂c = ̃c + 2lⱼΣₖHⱼₖxₖ , k ≂̸ j
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"""
5+
xrm, c0ps, nvarrm = remove_ifix!(ifix, Hrows, Hcols, Hvals, nvar,
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Arows, Acols, Avals, c, c0,
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lvar, uvar, lcon, ucon)
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9+
Remove rows and columns in H, columns in A, and elements in lcon and ucon
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corresponding to fixed variables, that are in `ifix`
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(They should be the indices `i` where `lvar[i] == uvar[i]`).
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Returns the removed elements of `lvar` (or `uvar`), the constant term in the QP
14+
objective `c0ps` resulting from the fixed variables, and the new number of variables `nvarrm`.
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`Hrows`, `Hcols`, `Hvals`, `Arows`, `Acols`, `Avals`, `c`, `lvar`, `uvar`,
16+
`lcon` and `ucon` are updated in-place.
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"""
18+
function remove_ifix!(
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ifix,
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Hrows,
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Hcols,
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Hvals,
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nvar,
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Arows,
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Acols,
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Avals,
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c::AbstractVector{T},
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c0,
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lvar,
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uvar,
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lcon,
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ucon,
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) where {T}
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# assume Hcols is sorted
36+
c0_offset = zero(T)
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Hnnz = length(Hrows)
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Hrm = 0
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Annz = length(Arows)
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Arm = 0
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# assume ifix is sorted and length(ifix) > 0
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nfix = length(ifix)
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# remove ifix 1 by 1 in H and A and update QP data
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for idxfix = 1:nfix
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currentifix = ifix[idxfix]
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xifix = lvar[currentifix]
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# index of the current fixed variable that takes the number of
49+
# already removed variables into account:
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newcurrentifix = currentifix - idxfix + 1
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Hwritepos = 1
53+
# shift corresponding to the already removed fixed variables to update c:
54+
shiftHj = 1
55+
if Hnnz > 0
56+
oldHj = Hrows[1]
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end
58+
# remove ifix in H and update data
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k = 1
60+
while k <= Hnnz && Hcols[k] <= (nvar - idxfix + 1)
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Hi, Hj, Hx = Hrows[k], Hcols[k], Hvals[k] # Hj sorted
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63+
while (Hj == oldHj) && shiftHj <= idxfix - 1 && Hj + shiftHj - 1 >= ifix[shiftHj]
64+
shiftHj += 1
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end
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shiftHi = 1
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while shiftHi <= idxfix - 1 && Hi + shiftHi - 1 >= ifix[shiftHi]
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shiftHi += 1
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end
70+
if Hi == Hj == newcurrentifix
71+
Hrm += 1
72+
c0_offset += xifix^2 * Hx / 2
73+
elseif Hi == newcurrentifix
74+
Hrm += 1
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c[Hj + shiftHj - 1] += xifix * Hx
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elseif Hj == newcurrentifix
77+
Hrm += 1
78+
c[Hi + shiftHi - 1] += xifix * Hx
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else # keep Hi, Hj, Hx
80+
Hrows[Hwritepos] = (Hi < newcurrentifix) ? Hi : Hi - 1
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Hcols[Hwritepos] = (Hj < newcurrentifix) ? Hj : Hj - 1
82+
Hvals[Hwritepos] = Hx
83+
Hwritepos += 1
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end
85+
k += 1
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end
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# remove ifix in A cols
89+
Awritepos = 1
90+
currentAn = nvar - idxfix + 1 # remove rows if uplo == :U
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k = 1
92+
while k <= Annz && Acols[k] <= currentAn
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Ai, Aj, Ax = Arows[k], Acols[k], Avals[k]
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if Aj == newcurrentifix
95+
Arm += 1
96+
lcon[Ai] -= Ax * xifix
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ucon[Ai] -= Ax * xifix
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else
99+
if Awritepos != k
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Arows[Awritepos] = Ai
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Acols[Awritepos] = (Aj < newcurrentifix) ? Aj : Aj - 1
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Avals[Awritepos] = Ax
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end
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Awritepos += 1
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end
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k += 1
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end
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# update c0 with c[currentifix] coeff
110+
c0_offset += c[currentifix] * xifix
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end
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# resize Q and A
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if nfix > 0
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Hnnz -= Hrm
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Annz -= Arm
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resize!(Hrows, Hnnz)
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resize!(Hcols, Hnnz)
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resize!(Hvals, Hnnz)
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resize!(Arows, Annz)
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resize!(Acols, Annz)
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resize!(Avals, Annz)
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end
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# store removed x values
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xrm = lvar[ifix]
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# remove coefs in lvar, uvar, c
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deleteat!(c, ifix)
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deleteat!(lvar, ifix)
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deleteat!(uvar, ifix)
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# update c0
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c0ps = c0 + c0_offset
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nvarrm = nvar - nfix
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return xrm, c0ps, nvarrm
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end
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function restore_ifix!(ifix, xrm, x, xout)
142+
# put x and xrm inside xout
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cfix, cx = 1, 1
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nfix = length(ifix)
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for i = 1:length(xout)
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if cfix <= nfix && i == ifix[cfix]
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xout[i] = xrm[cfix]
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cfix += 1
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else
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xout[i] = x[cx]
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cx += 1
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end
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end
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end

‎test/runtests.jl‎

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Original file line numberDiff line numberDiff line change
@@ -71,3 +71,5 @@ end
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SlackModel!(qp)
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testSM(qp)
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end
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include("test_presolve.jl")

‎test/test_presolve.jl‎

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@@ -0,0 +1,58 @@
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@testset "presolve ifix" begin
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H = [
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6.0 2.0 1.0
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2.0 5.0 2.0
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1.0 2.0 4.0
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]
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c = [-8.0; -3; -3]
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A = [
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1.0 0.0 1.0
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0.0 2.0 1.0
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]
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b = [0.0; 3]
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l = [0.0; 2.0; 0]
14+
u = [Inf; 2.0; Inf]
15+
T = eltype(c)
16+
qp = QuadraticModel(
17+
c,
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H,
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A = A,
20+
lcon = [-3.0; -4.0],
21+
ucon = [-2.0; Inf],
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lvar = l,
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uvar = u,
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c0 = 0.0,
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name = "QM1",
26+
)
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psqp = presolve(qp)
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c_true = [-4.0; 1.0]
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c0_true = 4.0
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Hps_true = [
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6.0 1.0
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1.0 4.0
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]
36+
Aps_true = [
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1.0 1.0
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0.0 1.0
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]
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lvarps_true, uvarps_true = [0. ; 0.], [Inf; Inf]
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@test psqp.data.c == [-4.0; 1.0]
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@test psqp.data.c0 == 4.0
44+
Hps = sparse(psqp.data.Hrows, psqp.data.Hcols, psqp.data.Hvals, psqp.meta.ncon, psqp.meta.nvar)
45+
@test norm(Symmetric(Hps, :L) - sparse(Hps_true)) ≤ sqrt(eps(T))
46+
Aps = sparse(psqp.data.Arows, psqp.data.Acols, psqp.data.Avals, psqp.meta.ncon, psqp.meta.nvar)
47+
@test norm(Aps - sparse(Aps_true)) ≤ sqrt(eps(T))
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@test psqp.meta.lvar == lvarps_true
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@test psqp.meta.uvar == uvarps_true
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@test psqp.xrm == [2.0]
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@test psqp.meta.ifix == Int[]
52+
@test psqp.meta.nvar == 2
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x_in = [4.0; 7.0]
55+
x_out = zeros(3)
56+
postsolve!(qp, psqp, x_in, x_out)
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@test x_out == [4.0; 2.0; 7.0]
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end

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