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nlp.jl
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nlp.jl
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# Copyright 2017, Iain Dunning, Joey Huchette, Miles Lubin, and contributors
# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at http://mozilla.org/MPL/2.0/.
type NonlinearExprData
nd::Vector{NodeData}
const_values::Vector{Float64}
end
include("parsenlp.jl")
const NonlinearConstraint = GenericRangeConstraint{NonlinearExprData}
type NLPData
nlobj
nlconstr::Vector{NonlinearConstraint}
nlexpr::Vector{NonlinearExprData}
nlconstrDuals::Vector{Float64}
nlparamvalues::Vector{Float64}
user_operators::ReverseDiffSparse.UserOperatorRegistry
largest_user_input_dimension::Int
evaluator
end
function NonlinearExpression(m::Model,ex::NonlinearExprData)
initNLP(m)
nldata::NLPData = m.nlpdata
push!(nldata.nlexpr, ex)
return NonlinearExpression(m, length(nldata.nlexpr))
end
function newparameter(m::Model,value::Number)
initNLP(m)
nldata::NLPData = m.nlpdata
push!(nldata.nlparamvalues, value)
return NonlinearParameter(m, length(nldata.nlparamvalues))
end
getvalue(p::NonlinearParameter) = p.m.nlpdata.nlparamvalues[p.index]::Float64
setvalue(p::NonlinearParameter,v::Number) = (p.m.nlpdata.nlparamvalues[p.index] = v)
NLPData() = NLPData(nothing, NonlinearConstraint[], NonlinearExprData[], Float64[], Float64[], ReverseDiffSparse.UserOperatorRegistry(), 0, nothing)
Base.copy(::NLPData) = error("Copying nonlinear problems not yet implemented")
function initNLP(m::Model)
if m.nlpdata === nothing
m.nlpdata = NLPData()
end
end
function getdual(c::ConstraintRef{Model,NonlinearConstraint})
initNLP(c.m)
nldata::NLPData = c.m.nlpdata
if length(nldata.nlconstrDuals) != length(nldata.nlconstr)
getdualwarn(c)
NaN
else
nldata.nlconstrDuals[c.idx]
end
end
type FunctionStorage
nd::Vector{NodeData}
adj::SparseMatrixCSC{Bool,Int}
const_values::Vector{Float64}
forward_storage::Vector{Float64}
partials_storage::Vector{Float64}
reverse_storage::Vector{Float64}
grad_sparsity::Vector{Int}
hess_I::Vector{Int} # nonzero pattern of hessian
hess_J::Vector{Int}
rinfo::Coloring.RecoveryInfo # coloring info for hessians
seed_matrix::Matrix{Float64}
linearity::Linearity
dependent_subexpressions::Vector{Int} # subexpressions which this function depends on, ordered for forward pass
end
type SubexpressionStorage
nd::Vector{NodeData}
adj::SparseMatrixCSC{Bool,Int}
const_values::Vector{Float64}
forward_storage::Vector{Float64}
partials_storage::Vector{Float64}
reverse_storage::Vector{Float64}
forward_storage_ϵ::Vector{Float64}
partials_storage_ϵ::Vector{Float64}
reverse_storage_ϵ::Vector{Float64}
linearity::Linearity
end
type NLPEvaluator <: MathProgBase.AbstractNLPEvaluator
m::Model
A::SparseMatrixCSC{Float64,Int} # linear constraint matrix
parameter_values::Vector{Float64}
has_nlobj::Bool
linobj::Vector{Float64}
objective::FunctionStorage
constraints::Vector{FunctionStorage}
subexpressions::Vector{SubexpressionStorage}
subexpression_order::Vector{Int}
subexpression_forward_values::Vector{Float64}
subexpression_reverse_values::Vector{Float64}
subexpression_linearity::Vector{ReverseDiffSparse.Linearity}
subexpressions_as_julia_expressions::Vector{Any}
last_x::Vector{Float64}
jac_storage::Vector{Float64} # temporary storage for computing jacobians
user_output_buffer::Vector{Float64} # temporary storage for user-defined functions
# storage for computing hessians
# these Float64 vectors are reinterpreted to hold multiple epsilon components
# so the length should be multiplied by the maximum number of epsilon components
disable_2ndorder::Bool # don't offer Hess or HessVec
want_hess::Bool
forward_storage_ϵ::Vector{Float64} # (longest expression)
partials_storage_ϵ::Vector{Float64} # (longest expression)
reverse_storage_ϵ::Vector{Float64} # (longest expression)
input_ϵ::Vector{Float64} # (number of variables)
output_ϵ::Vector{Float64}# (number of variables)
subexpression_forward_values_ϵ::Vector{Float64} # (number of subexpressions)
subexpression_reverse_values_ϵ::Vector{Float64} # (number of subexpressions)
# hessian sparsity pattern
hess_I::Vector{Int}
hess_J::Vector{Int}
max_chunk::Int # chunk size for which we've allocated storage
# timers
eval_f_timer::Float64
eval_g_timer::Float64
eval_grad_f_timer::Float64
eval_jac_g_timer::Float64
eval_hesslag_timer::Float64
function NLPEvaluator(m::Model)
d = new(m)
numVar = m.numCols
d.A = prepConstrMatrix(m)
# check if we have any user-defined operators, in which case we need to
# disable hessians.
if isa(m.nlpdata,NLPData)
nldata::NLPData = m.nlpdata
has_nlobj = isa(nldata.nlobj, NonlinearExprData)
has_user_mv_operator = false
for nlexpr in nldata.nlexpr
has_user_mv_operator |= ReverseDiffSparse.has_user_multivariate_operators(nlexpr.nd)
end
if has_nlobj
has_user_mv_operator |= ReverseDiffSparse.has_user_multivariate_operators(nldata.nlobj.nd)
end
for nlconstr in nldata.nlconstr
has_user_mv_operator |= ReverseDiffSparse.has_user_multivariate_operators(nlconstr.terms.nd)
end
d.disable_2ndorder = has_user_mv_operator
d.user_output_buffer = Array{Float64}(m.nlpdata.largest_user_input_dimension)
d.jac_storage = Array{Float64}(max(numVar,m.nlpdata.largest_user_input_dimension))
else
d.disable_2ndorder = false
d.user_output_buffer = Array{Float64}(0)
d.jac_storage = Array{Float64}(numVar)
end
d.eval_f_timer = 0
d.eval_g_timer = 0
d.eval_grad_f_timer = 0
d.eval_jac_g_timer = 0
d.eval_hesslag_timer = 0
return d
end
end
function simplify_expression(nd::Vector{NodeData}, const_values, subexpression_linearity, fixed_variables, parameter_values, x_values, subexpression_values)
adj = adjmat(nd)
forward_storage = zeros(length(nd))
partials_storage = zeros(length(nd))
linearity = classify_linearity(nd, adj, subexpression_linearity, fixed_variables)
forward_eval(forward_storage, partials_storage, nd, adj, const_values, parameter_values, x_values, subexpression_values)
nd_new = simplify_constants(forward_storage, nd, adj, const_values, linearity)
return nd_new, forward_storage[1], linearity[1]
end
function FunctionStorage(nd::Vector{NodeData}, const_values,numVar, coloring_storage, want_hess::Bool, subexpr::Vector{Vector{NodeData}}, dependent_subexpressions, subexpression_linearity, subexpression_edgelist, subexpression_variables, fixed_variables)
adj = adjmat(nd)
forward_storage = zeros(length(nd))
partials_storage = zeros(length(nd))
reverse_storage = zeros(length(nd))
empty!(coloring_storage)
compute_gradient_sparsity!(coloring_storage, nd)
for k in dependent_subexpressions
compute_gradient_sparsity!(coloring_storage,subexpr[k])
end
grad_sparsity = sort!(collect(coloring_storage))
empty!(coloring_storage)
if want_hess
# compute hessian sparsity
linearity = classify_linearity(nd, adj, subexpression_linearity, fixed_variables)
edgelist = compute_hessian_sparsity(nd, adj, linearity, coloring_storage, subexpression_edgelist, subexpression_variables)
hess_I, hess_J, rinfo = Coloring.hessian_color_preprocess(edgelist, numVar, coloring_storage)
seed_matrix = Coloring.seed_matrix(rinfo)
if linearity[1] == NONLINEAR
@assert length(hess_I) > 0
end
else
hess_I = hess_J = Int[]
rinfo = Coloring.RecoveryInfo()
seed_matrix = Array{Float64}(0,0)
linearity = [NONLINEAR]
end
return FunctionStorage(nd, adj, const_values, forward_storage, partials_storage, reverse_storage, grad_sparsity, hess_I, hess_J, rinfo, seed_matrix, linearity[1],dependent_subexpressions)
end
function SubexpressionStorage(nd::Vector{NodeData}, const_values,numVar, fixed_variables,subexpression_linearity)
adj = adjmat(nd)
forward_storage = zeros(length(nd))
partials_storage = zeros(length(nd))
reverse_storage = zeros(length(nd))
linearity = classify_linearity(nd, adj, subexpression_linearity, fixed_variables)
empty_arr = Array{Float64}(0)
return SubexpressionStorage(nd, adj, const_values, forward_storage, partials_storage, reverse_storage, empty_arr, empty_arr, empty_arr, linearity[1])
end
function MathProgBase.initialize(d::NLPEvaluator, requested_features::Vector{Symbol})
for feat in requested_features
if !(feat in MathProgBase.features_available(d))
error("Unsupported feature $feat")
# TODO: implement Jac-vec products
# for solvers that need them
end
end
if d.eval_f_timer != 0
# we've already been initialized
# assume no new features are being requested.
return
end
initNLP(d.m) #in case the problem is purely linear/quadratic thus far
nldata::NLPData = d.m.nlpdata
d.constraints = FunctionStorage[]
d.last_x = fill(NaN, d.m.numCols)
SIMPLIFY = d.m.simplify_nonlinear_expressions
fixed_variables = SIMPLIFY ? d.m.colLower .== d.m.colUpper : d.m.colLower .== NaN
d.m.colVal[fixed_variables] = d.m.colLower[fixed_variables]
d.parameter_values = nldata.nlparamvalues
tic()
d.linobj = prepAffObjective(d.m)
linrowlb, linrowub = prepConstrBounds(d.m)
numVar = length(d.linobj)
d.want_hess = (:Hess in requested_features)
want_hess_storage = (:HessVec in requested_features) || d.want_hess
coloring_storage = ReverseDiffSparse.Coloring.IndexedSet(numVar)
d.has_nlobj = isa(nldata.nlobj, NonlinearExprData)
max_expr_length = 0
main_expressions = Array{Vector{NodeData}}(0)
subexpr = Array{Vector{NodeData}}(0)
for nlexpr in nldata.nlexpr
push!(subexpr, nlexpr.nd)
end
if d.has_nlobj
push!(main_expressions,nldata.nlobj.nd)
end
for nlconstr in nldata.nlconstr
push!(main_expressions,nlconstr.terms.nd)
end
d.subexpression_order, individual_order = order_subexpressions(main_expressions,subexpr)
d.subexpression_linearity = Array{Linearity}(length(nldata.nlexpr))
subexpression_variables = Array{Vector{Int}}(length(nldata.nlexpr))
subexpression_edgelist = Array{Set{Tuple{Int,Int}}}(length(nldata.nlexpr))
d.subexpressions = Array{SubexpressionStorage}(length(nldata.nlexpr))
d.subexpression_forward_values = Array{Float64}(length(d.subexpressions))
d.subexpression_reverse_values = Array{Float64}(length(d.subexpressions))
empty_edgelist = Set{Tuple{Int,Int}}()
for k in d.subexpression_order # only load expressions which actually are used
if SIMPLIFY
nd_new, forward_value, simplified_linearity = simplify_expression(nldata.nlexpr[k].nd, nldata.nlexpr[k].const_values,d.subexpression_linearity, fixed_variables, d.parameter_values, d.m.colVal, d.subexpression_forward_values)
else
nd_new = nldata.nlexpr[k].nd
forward_value = NaN
simplified_linearity = NONLINEAR
end
d.subexpression_forward_values[k] = forward_value
if simplified_linearity != CONSTANT
d.subexpressions[k] = SubexpressionStorage(nd_new, nldata.nlexpr[k].const_values, numVar, fixed_variables, d.subexpression_linearity)
subex = d.subexpressions[k]
d.subexpression_linearity[k] = subex.linearity
@assert !SIMPLIFY || subex.linearity != CONSTANT
if d.want_hess
empty!(coloring_storage)
compute_gradient_sparsity!(coloring_storage,subex.nd)
# union with all dependent expressions
for idx in list_subexpressions(subex.nd)
union!(coloring_storage, subexpression_variables[idx])
end
subexpression_variables[k] = collect(coloring_storage)
empty!(coloring_storage)
linearity = classify_linearity(subex.nd, subex.adj, d.subexpression_linearity, fixed_variables)
edgelist = compute_hessian_sparsity(subex.nd, subex.adj, linearity,coloring_storage,subexpression_edgelist, subexpression_variables)
subexpression_edgelist[k] = edgelist
end
else
d.subexpression_linearity[k] = simplified_linearity
subexpression_edgelist[k] = empty_edgelist
end
end
if :ExprGraph in requested_features
d.subexpressions_as_julia_expressions = Array{Any}(length(subexpr))
for k in d.subexpression_order
if d.subexpression_linearity[k] != CONSTANT || !SIMPLIFY
ex = d.subexpressions[k]
d.subexpressions_as_julia_expressions[k] = tapeToExpr(d.m, 1, ex.nd, ex.adj, ex.const_values, d.parameter_values, d.subexpressions_as_julia_expressions, nldata.user_operators, true, true)
else
d.subexpressions_as_julia_expressions[k] = d.subexpression_forward_values[k]
end
end
end
if SIMPLIFY
main_expressions = Array{Vector{NodeData}}(0)
# simplify objective and constraint expressions
if d.has_nlobj
nd_new, forward_value = simplify_expression(nldata.nlobj.nd, nldata.nlobj.const_values,d.subexpression_linearity, fixed_variables, d.parameter_values, d.m.colVal, d.subexpression_forward_values)
push!(main_expressions,nd_new)
end
for k in 1:length(nldata.nlconstr)
nd_new, forward_value = simplify_expression(nldata.nlconstr[k].terms.nd, nldata.nlconstr[k].terms.const_values,d.subexpression_linearity, fixed_variables, d.parameter_values, d.m.colVal, d.subexpression_forward_values)
push!(main_expressions,nd_new)
end
# recompute dependencies after simplification
d.subexpression_order, individual_order = order_subexpressions(main_expressions,subexpr)
subexpr = Array{Vector{NodeData}}(length(d.subexpressions))
for k in d.subexpression_order
subexpr[k] = d.subexpressions[k].nd
end
end
max_chunk = 1
if d.has_nlobj
@assert length(d.m.obj.qvars1) == 0 && length(d.m.obj.aff.vars) == 0
nd = main_expressions[1]
d.objective = FunctionStorage(nd, nldata.nlobj.const_values, numVar, coloring_storage, d.want_hess, subexpr, individual_order[1], d.subexpression_linearity, subexpression_edgelist, subexpression_variables, fixed_variables)
max_expr_length = max(max_expr_length, length(d.objective.nd))
max_chunk = max(max_chunk, size(d.objective.seed_matrix,2))
end
for k in 1:length(nldata.nlconstr)
nlconstr = nldata.nlconstr[k]
idx = (d.has_nlobj) ? k+1 : k
nd = main_expressions[idx]
push!(d.constraints, FunctionStorage(nd, nlconstr.terms.const_values, numVar, coloring_storage, d.want_hess, subexpr, individual_order[idx], d.subexpression_linearity, subexpression_edgelist, subexpression_variables, fixed_variables))
max_expr_length = max(max_expr_length, length(d.constraints[end].nd))
max_chunk = max(max_chunk, size(d.constraints[end].seed_matrix,2))
end
max_chunk = min(max_chunk, 10) # 10 is hardcoded upper bound to avoid excess memory allocation
if d.want_hess || want_hess_storage # storage for Hess or HessVec
d.input_ϵ = Array{Float64}(max_chunk*d.m.numCols)
d.output_ϵ = Array{Float64}(max_chunk*d.m.numCols)
d.forward_storage_ϵ = Array{Float64}(max_chunk*max_expr_length)
d.partials_storage_ϵ = Array{Float64}(max_chunk*max_expr_length)
d.reverse_storage_ϵ = Array{Float64}(max_chunk*max_expr_length)
d.subexpression_forward_values_ϵ = Array{Float64}(max_chunk*length(d.subexpressions))
d.subexpression_reverse_values_ϵ = Array{Float64}(max_chunk*length(d.subexpressions))
for k in d.subexpression_order
subex = d.subexpressions[k]
subex.forward_storage_ϵ = zeros(Float64,max_chunk*length(subex.nd))
subex.partials_storage_ϵ = zeros(Float64,max_chunk*length(subex.nd))
subex.reverse_storage_ϵ = zeros(Float64,max_chunk*length(subex.nd))
end
d.max_chunk = max_chunk
if d.want_hess
d.hess_I, d.hess_J = _hesslag_structure(d)
# JIT warm-up
MathProgBase.eval_hesslag(d, Array{Float64}(length(d.hess_I)), d.m.colVal, 1.0, ones(MathProgBase.numconstr(d.m)))
end
end
# JIT warm-up
if :Grad in requested_features
MathProgBase.eval_grad_f(d, zeros(numVar), d.m.colVal)
MathProgBase.eval_g(d, zeros(MathProgBase.numconstr(d.m)), d.m.colVal)
end
tprep = toq()
#println("Prep time: $tprep")
# reset timers
d.eval_f_timer = 0
d.eval_grad_f_timer = 0
d.eval_g_timer = 0
d.eval_jac_g_timer = 0
d.eval_hesslag_timer = 0
nothing
end
function MathProgBase.features_available(d::NLPEvaluator)
features = [:Grad, :Jac, :ExprGraph]
if !d.disable_2ndorder
push!(features,:Hess)
push!(features,:HessVec)
end
return features
end
function forward_eval_all(d::NLPEvaluator,x)
# do a forward pass on all expressions at x
subexpr_values = d.subexpression_forward_values
user_operators = d.m.nlpdata.user_operators::ReverseDiffSparse.UserOperatorRegistry
user_input_buffer = d.jac_storage
user_output_buffer = d.user_output_buffer
SIMPLIFY = d.m.simplify_nonlinear_expressions
for k in d.subexpression_order
if SIMPLIFY && d.subexpression_linearity[k] == CONSTANT
continue
end
ex = d.subexpressions[k]
subexpr_values[k] = forward_eval(ex.forward_storage,ex.partials_storage,ex.nd,ex.adj,ex.const_values,d.parameter_values,x,subexpr_values,user_input_buffer,user_output_buffer, user_operators=user_operators)
end
if d.has_nlobj
ex = d.objective
forward_eval(ex.forward_storage,ex.partials_storage,ex.nd,ex.adj,ex.const_values,d.parameter_values,x,subexpr_values,user_input_buffer,user_output_buffer,user_operators=user_operators)
end
for ex in d.constraints
forward_eval(ex.forward_storage,ex.partials_storage,ex.nd,ex.adj,ex.const_values,d.parameter_values,x,subexpr_values,user_input_buffer,user_output_buffer,user_operators=user_operators)
end
end
function reverse_eval_all(d::NLPEvaluator,x)
# do a reverse pass on all expressions at x
subexpr_reverse_values = d.subexpression_reverse_values
subexpr_values = d.subexpression_forward_values
grad_storage = d.jac_storage
SIMPLIFY = d.m.simplify_nonlinear_expressions
for k in d.subexpression_order
if SIMPLIFY && d.subexpression_linearity[k] == CONSTANT
continue
end
ex = d.subexpressions[k]
reverse_eval(ex.reverse_storage,ex.partials_storage,ex.nd,ex.adj)
end
if d.has_nlobj
ex = d.objective
reverse_eval(ex.reverse_storage,ex.partials_storage,ex.nd,ex.adj)
end
for ex in d.constraints
reverse_eval(ex.reverse_storage,ex.partials_storage,ex.nd,ex.adj)
end
copy!(d.last_x,x)
end
function MathProgBase.eval_f(d::NLPEvaluator, x)
tic()
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
val = zero(eltype(x))
if d.has_nlobj
val = d.objective.forward_storage[1]
else
qobj = d.m.obj::QuadExpr
val = dot(x,d.linobj) + qobj.aff.constant
for k in 1:length(qobj.qvars1)
val += qobj.qcoeffs[k]*x[qobj.qvars1[k].col]*x[qobj.qvars2[k].col]
end
end
d.eval_f_timer += toq()
return val
end
function MathProgBase.eval_grad_f(d::NLPEvaluator, g, x)
tic()
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
SIMPLIFY = d.m.simplify_nonlinear_expressions
if d.has_nlobj
fill!(g,0.0)
ex = d.objective
subexpr_reverse_values = d.subexpression_reverse_values
subexpr_reverse_values[ex.dependent_subexpressions] = 0.0
reverse_extract(g,ex.reverse_storage,ex.nd,ex.adj,subexpr_reverse_values,1.0)
for i in length(ex.dependent_subexpressions):-1:1
k = ex.dependent_subexpressions[i]
if SIMPLIFY && d.subexpression_linearity[k] == CONSTANT
continue
end
subexpr = d.subexpressions[k]
reverse_extract(g,subexpr.reverse_storage,subexpr.nd,subexpr.adj,subexpr_reverse_values,subexpr_reverse_values[k])
end
else
copy!(g,d.linobj)
qobj::QuadExpr = d.m.obj
for k in 1:length(qobj.qvars1)
coef = qobj.qcoeffs[k]
g[qobj.qvars1[k].col] += coef*x[qobj.qvars2[k].col]
g[qobj.qvars2[k].col] += coef*x[qobj.qvars1[k].col]
end
end
d.eval_grad_f_timer += toq()
return
end
function MathProgBase.eval_g(d::NLPEvaluator, g, x)
tic()
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
A = d.A
for i in 1:size(A,1); g[i] = 0.0; end
#fill!(view(g,1:size(A,1)), 0.0)
A_mul_B!(view(g,1:size(A,1)),A,x)
idx = size(A,1)+1
quadconstr = d.m.quadconstr::Vector{QuadConstraint}
for c::QuadConstraint in quadconstr
aff = c.terms.aff
v = aff.constant
for k in 1:length(aff.vars)
v += aff.coeffs[k]*x[aff.vars[k].col]
end
for k in 1:length(c.terms.qvars1)
v += c.terms.qcoeffs[k]*x[c.terms.qvars1[k].col]*x[c.terms.qvars2[k].col]
end
g[idx] = v
idx += 1
end
for ex in d.constraints
g[idx] = ex.forward_storage[1]
idx += 1
end
d.eval_g_timer += toq()
#print("x = ");show(x);println()
#println(size(A,1), " g(x) = ");show(g);println()
return
end
function MathProgBase.eval_jac_g(d::NLPEvaluator, J, x)
tic()
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
fill!(J,0.0)
idx = 1
A = d.A
for col = 1:size(A,2)
for pos = nzrange(A,col)
J[idx] = A.nzval[pos]
idx += 1
end
end
quadconstr = d.m.quadconstr::Vector{QuadConstraint}
for c::QuadConstraint in quadconstr
aff = c.terms.aff
for k in 1:length(aff.vars)
J[idx] = aff.coeffs[k]
idx += 1
end
for k in 1:length(c.terms.qvars1)
coef = c.terms.qcoeffs[k]
qidx1 = c.terms.qvars1[k].col
qidx2 = c.terms.qvars2[k].col
J[idx] = coef*x[qidx2]
J[idx+1] = coef*x[qidx1]
idx += 2
end
end
grad_storage = d.jac_storage
subexpr_reverse_values = d.subexpression_reverse_values
SIMPLIFY = d.m.simplify_nonlinear_expressions
for ex in d.constraints
nzidx = ex.grad_sparsity
grad_storage[nzidx] = 0.0
subexpr_reverse_values[ex.dependent_subexpressions] = 0.0
reverse_extract(grad_storage,ex.reverse_storage,ex.nd,ex.adj,subexpr_reverse_values,1.0)
for i in length(ex.dependent_subexpressions):-1:1
k = ex.dependent_subexpressions[i]
if SIMPLIFY && d.subexpression_linearity[k] == CONSTANT
continue
end
subexpr = d.subexpressions[k]
reverse_extract(grad_storage,subexpr.reverse_storage,subexpr.nd,subexpr.adj,subexpr_reverse_values,subexpr_reverse_values[k])
end
for k in 1:length(nzidx)
J[idx+k-1] = grad_storage[nzidx[k]]
end
idx += length(nzidx)
end
d.eval_jac_g_timer += toq()
#print("x = ");show(x);println()
#print("V ");show(J);println()
return
end
function MathProgBase.eval_hesslag_prod(
d::NLPEvaluator,
h::Vector{Float64}, # output vector
x::Vector{Float64}, # current solution
v::Vector{Float64}, # rhs vector
σ::Float64, # multiplier for objective
μ::Vector{Float64}) # multipliers for each constraint
nldata = d.m.nlpdata::NLPData
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
fill!(h, 0.0)
# quadratic objective
qobj::QuadExpr = d.m.obj
for k in 1:length(qobj.qvars1)
col1 = qobj.qvars1[k].col
col2 = qobj.qvars2[k].col
coef = qobj.qcoeffs[k]
if col1 == col2
h[col1] += σ*2*coef*v[col1]
else
h[col1] += σ*coef*v[col2]
h[col2] += σ*coef*v[col1]
end
end
# quadratic constraints
row = size(d.A,1)+1
quadconstr = d.m.quadconstr::Vector{QuadConstraint}
for c in quadconstr
l = μ[row]
for k in 1:length(c.terms.qvars1)
col1 = c.terms.qvars1[k].col
col2 = c.terms.qvars2[k].col
coef = c.terms.qcoeffs[k]
if col1 == col2
h[col1] += l*2*coef*v[col1]
else
h[col1] += l*coef*v[col2]
h[col2] += l*coef*v[col1]
end
end
row += 1
end
input_ϵ = reinterpret(ForwardDiff.Partials{1,Float64}, d.input_ϵ)
output_ϵ = reinterpret(ForwardDiff.Partials{1,Float64}, d.output_ϵ)
for i in 1:length(x)
input_ϵ[i] = ForwardDiff.Partials((v[i],))
end
# forward evaluate all subexpressions once
subexpr_forward_values_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},d.subexpression_forward_values_ϵ)
subexpr_reverse_values_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},d.subexpression_reverse_values_ϵ)
forward_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},d.forward_storage_ϵ)
reverse_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},d.reverse_storage_ϵ)
partials_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},d.partials_storage_ϵ)
SIMPLIFY = d.m.simplify_nonlinear_expressions
for expridx in d.subexpression_order
if SIMPLIFY && d.subexpression_linearity[expridx] == CONSTANT
continue
end
subexpr = d.subexpressions[expridx]
sub_forward_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},subexpr.forward_storage_ϵ)
sub_partials_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},subexpr.partials_storage_ϵ)
subexpr_forward_values_ϵ[expridx] = forward_eval_ϵ(subexpr.forward_storage,sub_forward_storage_ϵ, subexpr.partials_storage, sub_partials_storage_ϵ, subexpr.nd, subexpr.adj, input_ϵ, subexpr_forward_values_ϵ,user_operators=nldata.user_operators)
end
# we only need to do one reverse pass through the subexpressions as well
zero_ϵ = zero(ForwardDiff.Partials{1,Float64})
fill!(subexpr_reverse_values_ϵ,zero_ϵ)
fill!(d.subexpression_reverse_values,0.0)
fill!(reverse_storage_ϵ,zero_ϵ)
fill!(output_ϵ,zero_ϵ)
if d.has_nlobj
ex = d.objective
forward_eval_ϵ(ex.forward_storage, forward_storage_ϵ, ex.partials_storage, partials_storage_ϵ, ex.nd,ex.adj,input_ϵ, subexpr_forward_values_ϵ,user_operators=nldata.user_operators)
reverse_eval_ϵ(output_ϵ,ex.reverse_storage, reverse_storage_ϵ,ex.partials_storage, partials_storage_ϵ,ex.nd,ex.adj,d.subexpression_reverse_values,subexpr_reverse_values_ϵ, σ, zero_ϵ)
end
for i in 1:length(d.constraints)
ex = d.constraints[i]
l = μ[row]
forward_eval_ϵ(ex.forward_storage, forward_storage_ϵ, ex.partials_storage, partials_storage_ϵ, ex.nd,ex.adj, input_ϵ,subexpr_forward_values_ϵ,user_operators=nldata.user_operators)
reverse_eval_ϵ(output_ϵ, ex.reverse_storage, reverse_storage_ϵ, ex.partials_storage, partials_storage_ϵ, ex.nd,ex.adj,d.subexpression_reverse_values,subexpr_reverse_values_ϵ, l, zero_ϵ)
row += 1
end
for i in length(ex.dependent_subexpressions):-1:1
expridx = ex.dependent_subexpressions[i]
if SIMPLIFY && d.subexpression_linearity[expridx] == CONSTANT
continue
end
subexpr = d.subexpressions[expridx]
sub_reverse_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},subexpr.reverse_storage_ϵ)
sub_partials_storage_ϵ = reinterpret(ForwardDiff.Partials{1,Float64},subexpr.partials_storage_ϵ)
reverse_eval_ϵ(output_ϵ,subexpr.reverse_storage,sub_reverse_storage_ϵ, subexpr.partials_storage, sub_partials_storage_ϵ,subexpr.nd,subexpr.adj,d.subexpression_reverse_values,subexpr_reverse_values_ϵ,d.subexpression_reverse_values[expridx],subexpr_reverse_values_ϵ[expridx])
end
for i in 1:length(x)
h[i] += output_ϵ[i].values[1]
end
end
function MathProgBase.eval_hesslag(
d::NLPEvaluator,
H::Vector{Float64}, # Sparse hessian entry vector
x::Vector{Float64}, # Current solution
obj_factor::Float64, # Lagrangian multiplier for objective
lambda::Vector{Float64}) # Multipliers for each constraint
qobj = d.m.obj::QuadExpr
nldata = d.m.nlpdata::NLPData
d.want_hess || error("Hessian computations were not requested on the call to MathProgBase.initialize.")
if d.last_x != x
forward_eval_all(d,x)
reverse_eval_all(d,x)
end
tic()
# quadratic objective
nzcount = 1
for k in 1:length(qobj.qvars1)
if qobj.qvars1[k].col == qobj.qvars2[k].col
H[nzcount] = obj_factor*2*qobj.qcoeffs[k]
else
H[nzcount] = obj_factor*qobj.qcoeffs[k]
end
nzcount += 1
end
# quadratic constraints
quadconstr = d.m.quadconstr::Vector{QuadConstraint}
for i in 1:length(quadconstr)
c = quadconstr[i]
l = lambda[length(d.m.linconstr)+i]
for k in 1:length(c.terms.qvars1)
if c.terms.qvars1[k].col == c.terms.qvars2[k].col
H[nzcount] = l*2*c.terms.qcoeffs[k]
else
H[nzcount] = l*c.terms.qcoeffs[k]
end
nzcount += 1
end
end
fill!(d.input_ϵ,0.0)
recovery_tmp_storage = d.output_ϵ
nzcount -= 1
if d.has_nlobj
ex = d.objective
chunk = min(size(ex.seed_matrix,2),d.max_chunk)
if chunk == 1
# skip dynamic dispatch
nzthis = hessian_slice(d, ex, x, H, obj_factor, nzcount, recovery_tmp_storage, Val{1})::Int
else
nzthis = hessian_slice(d, ex, x, H, obj_factor, nzcount, recovery_tmp_storage, Val{chunk})::Int
end
nzcount += nzthis
end
for i in 1:length(d.constraints)
ex = d.constraints[i]
chunk = min(size(ex.seed_matrix,2),d.max_chunk)
if chunk == 1
nzthis = hessian_slice(d, ex, x, H, lambda[i+length(quadconstr)+length(d.m.linconstr)], nzcount, recovery_tmp_storage, Val{1})::Int
else
nzthis = hessian_slice(d, ex, x, H, lambda[i+length(quadconstr)+length(d.m.linconstr)], nzcount, recovery_tmp_storage, Val{chunk})::Int
end
nzcount += nzthis
end
d.eval_hesslag_timer += toq()
return
end
function hessian_slice_inner{CHUNK}(d, ex, R, input_ϵ, output_ϵ, ::Type{Val{CHUNK}})
subexpr_forward_values_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},d.subexpression_forward_values_ϵ)
subexpr_reverse_values_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},d.subexpression_reverse_values_ϵ)
forward_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},d.forward_storage_ϵ)
reverse_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},d.reverse_storage_ϵ)
partials_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},d.partials_storage_ϵ)
zero_ϵ = zero(ForwardDiff.Partials{CHUNK,Float64})
user_operators = d.m.nlpdata.user_operators::ReverseDiffSparse.UserOperatorRegistry
SIMPLIFY = d.m.simplify_nonlinear_expressions
# do a forward pass
for expridx in ex.dependent_subexpressions
if SIMPLIFY && d.subexpression_linearity[expridx] == CONSTANT
continue
end
subexpr = d.subexpressions[expridx]
sub_forward_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},subexpr.forward_storage_ϵ)
sub_partials_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},subexpr.partials_storage_ϵ)
subexpr_forward_values_ϵ[expridx] = forward_eval_ϵ(subexpr.forward_storage,sub_forward_storage_ϵ,subexpr.partials_storage,sub_partials_storage_ϵ, subexpr.nd, subexpr.adj, input_ϵ, subexpr_forward_values_ϵ,user_operators=user_operators)
end
forward_eval_ϵ(ex.forward_storage,forward_storage_ϵ,ex.partials_storage, partials_storage_ϵ,ex.nd,ex.adj,input_ϵ, subexpr_forward_values_ϵ,user_operators=user_operators)
# do a reverse pass
subexpr_reverse_values_ϵ[ex.dependent_subexpressions] = zero_ϵ
d.subexpression_reverse_values[ex.dependent_subexpressions] = 0.0
reverse_eval_ϵ(output_ϵ, ex.reverse_storage, reverse_storage_ϵ,ex.partials_storage, partials_storage_ϵ,ex.nd,ex.adj,d.subexpression_reverse_values,subexpr_reverse_values_ϵ, 1.0, zero_ϵ)
for i in length(ex.dependent_subexpressions):-1:1
expridx = ex.dependent_subexpressions[i]
if SIMPLIFY && d.subexpression_linearity[expridx] == CONSTANT
continue
end
subexpr = d.subexpressions[expridx]
sub_reverse_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},subexpr.reverse_storage_ϵ)
sub_partials_storage_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64},subexpr.partials_storage_ϵ)
reverse_eval_ϵ(output_ϵ, subexpr.reverse_storage, sub_reverse_storage_ϵ,subexpr.partials_storage,sub_partials_storage_ϵ,subexpr.nd,subexpr.adj,d.subexpression_reverse_values,subexpr_reverse_values_ϵ,d.subexpression_reverse_values[expridx],subexpr_reverse_values_ϵ[expridx])
end
end
function hessian_slice{CHUNK}(d, ex, x, H, scale, nzcount, recovery_tmp_storage,::Type{Val{CHUNK}})
nzthis = length(ex.hess_I)
if ex.linearity == LINEAR
@assert nzthis == 0
return 0
end
R = ex.seed_matrix
Coloring.prepare_seed_matrix!(R,ex.rinfo)
local_to_global_idx = ex.rinfo.local_indices
zero_ϵ = zero(ForwardDiff.Partials{CHUNK,Float64})
input_ϵ_raw = d.input_ϵ
output_ϵ_raw = d.output_ϵ
input_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64}, input_ϵ_raw)
output_ϵ = reinterpret_unsafe(ForwardDiff.Partials{CHUNK,Float64}, output_ϵ_raw)
# compute hessian-vector products
num_products = size(R,2) # number of hessian-vector products
num_chunks = div(num_products, CHUNK)
@assert size(R,1) == length(local_to_global_idx)
numVar = length(x)
for k in 1:CHUNK:CHUNK*num_chunks
for r in 1:length(local_to_global_idx)
# set up directional derivatives
@inbounds idx = local_to_global_idx[r]
# load up R[r,k,k+1,...,k+CHUNK-1] into input_ϵ
for s in 1:CHUNK
input_ϵ_raw[(idx-1)*CHUNK + s] = R[r,k+s-1]
end
@inbounds output_ϵ[idx] = zero_ϵ
end
hessian_slice_inner(d, ex, R, input_ϵ, output_ϵ, Val{CHUNK})
# collect directional derivatives
for r in 1:length(local_to_global_idx)
idx = local_to_global_idx[r]
# load output_ϵ into R[r,k,k+1,...,k+CHUNK-1]
for s in 1:CHUNK
R[r,k+s-1] = output_ϵ_raw[(idx-1)*CHUNK + s]
end
@inbounds input_ϵ[idx] = zero_ϵ
end
end
# leftover chunk
remaining = num_products - CHUNK*num_chunks
if remaining > 0
k = CHUNK*num_chunks+1
for r in 1:length(local_to_global_idx)
# set up directional derivatives
@inbounds idx = local_to_global_idx[r]
# load up R[r,k,k+1,...,k+remaining-1] into input_ϵ
for s in 1:remaining
# leave junk in the unused components
input_ϵ_raw[(idx-1)*CHUNK + s] = R[r,k+s-1]
end
@inbounds output_ϵ[idx] = zero_ϵ
end
hessian_slice_inner(d, ex, R, input_ϵ, output_ϵ, Val{CHUNK})
# collect directional derivatives
for r in 1:length(local_to_global_idx)
idx = local_to_global_idx[r]
# load output_ϵ into R[r,k,k+1,...,k+remaining-1]
for s in 1:remaining
R[r,k+s-1] = output_ϵ_raw[(idx-1)*CHUNK + s]
end
@inbounds input_ϵ[idx] = zero_ϵ
end
end
# Output is in R, now recover
#output_slice = view(H, (nzcount+1):(nzcount+nzthis))
output_slice = VectorView(nzcount, nzthis, pointer(H))
Coloring.recover_from_matmat!(output_slice, R, ex.rinfo, recovery_tmp_storage)
scale!(output_slice, scale)
return nzthis
end
MathProgBase.isobjlinear(d::NLPEvaluator) = !d.has_nlobj && (length(d.m.obj.qvars1) == 0)
# interpret quadratic to include purely linear
MathProgBase.isobjquadratic(d::NLPEvaluator) = !d.has_nlobj
MathProgBase.isconstrlinear(d::NLPEvaluator, i::Integer) = (i <= length(d.m.linconstr))
function MathProgBase.jac_structure(d::NLPEvaluator)
# Jacobian structure
jac_I = Int[]
jac_J = Int[]
A = d.A
for col = 1:size(A,2)
for pos = nzrange(A,col)
push!(jac_I, A.rowval[pos])
push!(jac_J, col)
end
end
rowoffset = size(A,1)+1
for c::QuadConstraint in d.m.quadconstr
aff = c.terms.aff
for k in 1:length(aff.vars)
push!(jac_I, rowoffset)
push!(jac_J, aff.vars[k].col)
end
for k in 1:length(c.terms.qvars1)
push!(jac_I, rowoffset)
push!(jac_I, rowoffset)
push!(jac_J, c.terms.qvars1[k].col)
push!(jac_J, c.terms.qvars2[k].col)
end
rowoffset += 1
end
for ex in d.constraints
idx = ex.grad_sparsity
for i in 1:length(idx)
push!(jac_I, rowoffset)
push!(jac_J, idx[i])
end
rowoffset += 1
end
return jac_I, jac_J
end
function MathProgBase.hesslag_structure(d::NLPEvaluator)
d.want_hess || error("Hessian computations were not requested on the call to MathProgBase.initialize.")
return d.hess_I,d.hess_J
end
function _hesslag_structure(d::NLPEvaluator)
hess_I = Int[]
hess_J = Int[]
qobj::QuadExpr = d.m.obj
for k in 1:length(qobj.qvars1)
qidx1 = qobj.qvars1[k].col
qidx2 = qobj.qvars2[k].col
if qidx2 > qidx1