Add conversions in variable substitution (#1181)

* Add conversions in variable substitution

* Add convert for substitute_variable of quad terms

Author: blegat

src/Utilities/functions.jl

@@ -161,8 +161,11 @@ end
 
 function substitute_variables(variable_map::Function,
                               term::MOI.ScalarQuadraticTerm{T}) where T
-    f1 = variable_map(term.variable_index_1)
-    f2 = variable_map(term.variable_index_2)
+    # We could have `T = Complex{Float64}` and `variable_map(term.variable_index)`
+    # be a `MOI.ScalarAffineFunction{Float64}` with the Hermitian to PSD bridge.
+    # We convert to `MOI.ScalarAffineFunction{T}` to avoid any issue.
+    f1::MOI.ScalarAffineFunction{T} = variable_map(term.variable_index_1)
+    f2::MOI.ScalarAffineFunction{T} = variable_map(term.variable_index_2)
     f12 = operate(*, T, f1, f2)::MOI.ScalarQuadraticFunction{T}
     coef = term.coefficient
     # The quadratic terms are evaluated as x'Qx/2 so a diagonal term should
@@ -175,8 +178,9 @@ function substitute_variables(variable_map::Function,
 end
 function substitute_variables(variable_map::Function,
                               term::MOI.ScalarAffineTerm{T}) where T
-    return operate(*, T, term.coefficient,
-                       variable_map(term.variable_index))::MOI.ScalarAffineFunction{T}
+    # See comment for `term::MOI.ScalarQuadraticTerm` for the conversion.
+    func::MOI.ScalarAffineFunction{T} = variable_map(term.variable_index)
+    return operate(*, T, term.coefficient, func)::MOI.ScalarAffineFunction{T}
 end
 function substitute_variables(
     variable_map::Function,

test/Utilities/functions.jl

@@ -169,6 +169,17 @@ end
     @test MOIU.eval_variables(vi -> subs_vals[vi], fvq) == MOIU.eval_variables(vi -> vals[vi], subs_vq)
     @test MOIU.substitute_variables(vi -> subs[vi], fvq) ≈ subs_vq
     @test MOIU.substitute_variables(vi -> subs[vi], fvq) ≈ subs_vq
+
+    complex_aff = 2.0im * fy
+    # Test that variables can be substituted for `MOI.ScalarAffineFunction{S}`
+    # in a `MOI.ScalarAffineFunction{T}` where `S != T`.
+    @test MOIU.substitute_variables(vi -> 1.5fx, complex_aff) ≈ 3.0im * fx
+    float_aff = 2.0 * fy
+    @test MOIU.substitute_variables(vi -> 3fx, float_aff) ≈ 6.0 * fx
+    complex_quad = 1.5im * fy * fy
+    @test MOIU.substitute_variables(vi -> 2fx, complex_quad) ≈ 6.0im * fx * fx
+    int_quad = 3 * fy * fx
+    @test MOIU.substitute_variables(vi -> true * fy, int_quad) ≈ 3 * fy * fy
 end
 @testset "map_indices" begin
     fsq = MOI.ScalarQuadraticFunction(MOI.ScalarAffineTerm.(1.0, [x, y]),