[Nonlinear] add support for univariate sign (#2444)

src/FileFormats/NL/NLExpr.jl

@@ -247,6 +247,7 @@ const _UNARY_SPECIAL_CASES = Dict{Symbol,Function}(
     :asech => (x) -> :(acosh(1 / $x)),
     :acsch => (x) -> :(asinh(1 / $x)),
     :acoth => (x) -> :(atanh(1 / $x)),
+    :sign => (x) -> :(ifelse($x >= 0, 1, -1)),
 )
 
 """

src/Nonlinear/operators.jl

@@ -81,17 +81,17 @@ The list of univariate operators that are supported by default.
 julia> import MathOptInterface as MOI
 
 julia> MOI.Nonlinear.DEFAULT_UNIVARIATE_OPERATORS
-72-element Vector{Symbol}:
+73-element Vector{Symbol}:
  :+
  :-
  :abs
+ :sign
  :sqrt
  :cbrt
  :abs2
  :inv
  :log
  :log10
- :log2
  ⋮
  :airybi
  :airyaiprime

src/Nonlinear/univariate_expressions.jl

@@ -12,6 +12,7 @@ const SYMBOLIC_UNIVARIATE_EXPRESSIONS = Tuple{Symbol,Expr,Any}[
     (:+, :(one(x)), :(zero(x))),
     (:-, :(-one(x)), :(zero(x))),
     (:abs, :(ifelse(x >= 0, one(x), -one(x))), :(zero(x))),
+    (:sign, :(zero(x)), :(zero(x))),
     (:sqrt, :(0.5 / sqrt(x)), :((0.5 * -(0.5 / sqrt(x))) / sqrt(x) ^ 2)),
     (:cbrt, :(0.3333333333333333 / cbrt(x) ^ 2), :((0.3333333333333333 * -(2 * (0.3333333333333333 / cbrt(x) ^ 2) * cbrt(x))) / (cbrt(x) ^ 2) ^ 2)),
     (:abs2, :(2x), :((typeof(x))(2))),

src/Nonlinear/univariate_expressions_generator.jl

@@ -42,7 +42,8 @@ open("univariate_expressions.jl", "w") do io
 const SYMBOLIC_UNIVARIATE_EXPRESSIONS = Tuple{Symbol,Expr,Any}[
     (:+, :(one(x)), :(zero(x))),
     (:-, :(-one(x)), :(zero(x))),
-    (:abs, :(ifelse(x >= 0, one(x), -one(x))), :(zero(x))),""",
+    (:abs, :(ifelse(x >= 0, one(x), -one(x))), :(zero(x))),
+    (:sign, :(zero(x)), :(zero(x))),""",
     )
     for (op, deriv) in Calculus.symbolic_derivatives_1arg()
         f = Expr(:call, op, :x)

test/FileFormats/NL/NL.jl

@@ -151,6 +151,14 @@ function test_nlexpr_scalarnonlinearfunction_unary_special_case()
     return
 end
 
+function test_nlexpr_scalarnonlinearfunction_unary_special_case_sign()
+    x = MOI.VariableIndex(1)
+    f = MOI.ScalarNonlinearFunction(:sign, Any[x])
+    expr = NL._NLExpr(:(ifelse($x >= 0, 1, -1)))
+    _test_nlexpr(f, expr.nonlinear_terms, Dict(x => 0.0), 0.0)
+    return
+end
+
 function test_nlexpr_scalarnonlinearfunction_binary_special_case()
     x = MOI.VariableIndex(1)
     f = MOI.ScalarNonlinearFunction(:\, Any[x, 1])

test/Nonlinear/Nonlinear.jl

@@ -1163,6 +1163,32 @@ function test_automatic_differentiation_backend()
     return
 end
 
+function test_univariate_sign()
+    f(y, p) = sign(y) * abs(y)^p
+    ∇f(y, p) = p * abs(y)^(p - 1)
+    ∇²f(y, p) = sign(y) * p * (p - 1) * abs(y)^(p - 2)
+    for p in (-0.5, 0.5, 2.0)
+        x = MOI.VariableIndex(1)
+        model = MOI.Nonlinear.Model()
+        MOI.Nonlinear.set_objective(model, :(sign($x) * abs($x)^$p))
+        evaluator = MOI.Nonlinear.Evaluator(
+            model,
+            MOI.Nonlinear.SparseReverseMode(),
+            [x],
+        )
+        MOI.initialize(evaluator, [:Grad, :Hess])
+        for y in (-10.0, -1.2, 1.2, 10.0)
+            @test MOI.eval_objective(evaluator, [y]) ≈ f(y, p)
+            g = [NaN]
+            MOI.eval_objective_gradient(evaluator, g, [y])
+            @test g[1] ≈ ∇f(y, p)
+            H = zeros(length(MOI.hessian_objective_structure(evaluator)))
+            MOI.eval_hessian_objective(evaluator, H, [y])
+            @test H[1] ≈ ∇²f(y, p)
+        end
+    end
+end
+
 end  # TestNonlinear
 
 TestNonlinear.runtests()