Merge pull request #643 from JuliaOpt/bl/iszero

✨ Add iszero

Author: blegat

src/Utilities/functions.jl

@@ -353,11 +353,22 @@ function test_constraintnames_equal(model, constraintnames)
     end
 end
 
-isapprox_zero(α::AbstractFloat, tol) = -tol < α < tol
-isapprox_zero(α::Union{Integer, Rational}, tol) = iszero(α)
-function isapprox_zero(t::Union{MOI.ScalarAffineTerm,
-                                MOI.ScalarQuadraticTerm}, tol)
-    isapprox_zero(MOI.coefficient(t), tol)
+"""
+    all_coefficients(p::Function, f::MOI.AbstractFunction)
+
+Determine whether predicate `p` returns `true` for all coefficients of `f`,
+returning `false` as soon as the first coefficient of `f` for which `p`
+returns `false` is encountered (short-circuiting). Similar to `all`.
+"""
+function all_coefficients end
+
+function all_coefficients(p::Function, f::MOI.ScalarAffineFunction)
+    return p(f.constant) && all(t -> p(MOI.coefficient(t)), f.terms)
+end
+function all_coefficients(p::Function, f::MOI.ScalarQuadraticFunction)
+    return p(f.constant) &&
+        all(t -> p(MOI.coefficient(t)), f.affine_terms) &&
+        all(t -> p(MOI.coefficient(t)), f.quadratic_terms)
 end
 
 """
@@ -379,16 +390,15 @@ then `isapprox_zero(f)` is `false` but `isapprox_zero(MOIU.canonical(f))` is
 """
 function isapprox_zero end
 
-function isapprox_zero(f::MOI.ScalarAffineFunction, tol)
-    isapprox_zero(f.constant, tol) && all(t -> isapprox_zero(t, tol),
-                                           f.terms)
+isapprox_zero(α::AbstractFloat, tol) = -tol <= α <= tol
+isapprox_zero(α::Union{Integer, Rational}, tol) = iszero(α)
+function isapprox_zero(f::MOI.AbstractFunction, tol)
+    return all_coefficients(α -> isapprox_zero(α, tol), f)
 end
-function isapprox_zero(f::MOI.ScalarQuadraticFunction, tol)
-    isapprox_zero(f.constant, tol) &&
-        all(t -> isapprox_zero(t, tol),
-            f.affine_terms) &&
-        all(t -> isapprox_zero(t, tol),
-            f.quadratic_terms)
+
+function Base.iszero(f::Union{MOI.ScalarAffineFunction{T},
+                              MOI.ScalarQuadraticFunction{T}}) where T
+    return all_coefficients(iszero, canonical(f))
 end
 
 """

test/Utilities/functions.jl

@@ -175,6 +175,7 @@ const MOIU = MOI.Utilities
         @testset "Affine" begin
             @testset "zero" begin
                 f = @inferred MOIU.zero(MOI.ScalarAffineFunction{Float64})
+                @test iszero(f)
                 @test MOIU.isapprox_zero(f, 1e-16)
             end
             @testset "promote_operation" begin
@@ -187,17 +188,24 @@ const MOIU = MOI.Utilities
                                              MOI.ScalarAffineFunction{Int},
                                              MOI.ScalarAffineFunction{Int}) == MOI.ScalarAffineFunction{Int}
             end
-            @testset "Comparison tolerance" begin
+            @testset "Comparison" begin
                 @test MOIU.operate(+, Float64, MOI.SingleVariable(x),
                                    MOI.SingleVariable(z)) + 1.0 ≈
                       MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1, 1e-7, 1], [x, y, z]), 1.0) atol=1e-6
                 f1 = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x), MOI.ScalarAffineTerm(1e-7, y)], 1.0)
                 f2 = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 1.0)
                 @test f1 ≈ f2 atol=1e-6
                 fdiff = f1 - f2
-                MOIU.canonicalize!(fdiff)
-                @test !MOIU.isapprox_zero(fdiff, 1e-8)
-                @test MOIU.isapprox_zero(fdiff, 1e-6)
+                @testset "With iszero" begin
+                    @test !iszero(fdiff)
+                    @test iszero(f1 - f1)
+                    @test iszero(f2 - f2)
+                end
+                @testset "With tolerance" begin
+                    MOIU.canonicalize!(fdiff)
+                    @test !MOIU.isapprox_zero(fdiff, 1e-8)
+                    @test MOIU.isapprox_zero(fdiff, 1e-6)
+                end
             end
             @testset "canonical" begin
                 f = MOIU.canonical(MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([2, 1, 3, -2, -3], [y, x, z, x, z]), 5))
@@ -290,14 +298,21 @@ const MOIU = MOI.Utilities
             f = 7 + 3fx + 1fx * fx + 2fy * fy + 3fx * fy
             MOIU.canonicalize!(f)
             @test MOI.output_dimension(f) == 1
-            @testset "isapprox_zero" begin
-                @test !MOIU.isapprox_zero(f, 1e-8)
-                # Test isapprox_zero with zero terms
-                @test MOIU.isapprox_zero(0 * f, 1e-8)
-                g = 1.0fx * fy - (1 + 1e-6) * fy * fx
-                MOIU.canonicalize!(g)
-                @test MOIU.isapprox_zero(g, 1e-5)
-                @test !MOIU.isapprox_zero(g, 1e-7)
+            @testset "Comparison" begin
+                @testset "With iszero" begin
+                    @test !iszero(f)
+                    @test iszero(0 * f)
+                    @test iszero(f - f)
+                end
+                @testset "With tolerance" begin
+                    @test !MOIU.isapprox_zero(f, 1e-8)
+                    # Test isapprox_zero with zero terms
+                    @test MOIU.isapprox_zero(0 * f, 1e-8)
+                    g = 1.0fx * fy - (1 + 1e-6) * fy * fx
+                    MOIU.canonicalize!(g)
+                    @test MOIU.isapprox_zero(g, 1e-5)
+                    @test !MOIU.isapprox_zero(g, 1e-7)
+                end
             end
             @testset "convert" begin
                 @test_throws InexactError convert(MOI.SingleVariable, f)