[Nonlinear] parse x*x as x^2 in Nonlinear.Model (#2799)

Author: odow

src/Nonlinear/parse.jl

@@ -345,18 +345,40 @@ function parse_expression(
     x::MOI.ScalarQuadraticTerm,
     parent_index::Int,
 )
-    id_mul = data.operators.multivariate_operator_to_id[:*]
-    push!(expr.nodes, Node(NODE_CALL_MULTIVARIATE, id_mul, parent_index))
-    mul_parent = length(expr.nodes)
-    coef = x.coefficient
+    # There are four cases:
+    #   (1): 1 * x * x  -->  ^(x, 2)
+    #   (2): a * x * x  -->  *(a, ^(x, 2))
+    #   (3): a * x * y  -->  *(a, x, y)
+    #   (4): 1 * x * y  -->  *(x, y)
     if x.variable_1 == x.variable_2
-        coef /= 2
-    end
-    if !isone(coef)
-        parse_expression(data, expr, coef, mul_parent)
+        # Case (1): 1 * x * x  -->  ^(x, 2)
+        # Case (2): a * x * x  -->  *(a, ^(x, 2))
+        coef = x.coefficient / 2
+        parent = parent_index
+        if !isone(coef)
+            id = data.operators.multivariate_operator_to_id[:*]
+            push!(expr.nodes, Node(NODE_CALL_MULTIVARIATE, id, parent_index))
+            parent = length(expr.nodes)
+            parse_expression(data, expr, coef, parent)
+            parent
+        end
+        id = data.operators.multivariate_operator_to_id[:^]
+        push!(expr.nodes, Node(NODE_CALL_MULTIVARIATE, id, parent))
+        pow_parent = length(expr.nodes)
+        parse_expression(data, expr, x.variable_1, pow_parent)
+        parse_expression(data, expr, 2, pow_parent)
+    else
+        # Case (3): a * x * y  -->  *(a, x, y)
+        # Case (4): 1 * x * y  -->  *(x, y)
+        id_mul = data.operators.multivariate_operator_to_id[:*]
+        push!(expr.nodes, Node(NODE_CALL_MULTIVARIATE, id_mul, parent_index))
+        mul_parent = length(expr.nodes)
+        if !isone(x.coefficient)
+            parse_expression(data, expr, x.coefficient, mul_parent)
+        end
+        parse_expression(data, expr, x.variable_1, mul_parent)
+        parse_expression(data, expr, x.variable_2, mul_parent)
     end
-    parse_expression(data, expr, x.variable_1, mul_parent)
-    parse_expression(data, expr, x.variable_2, mul_parent)
     return
 end
 

test/Nonlinear/Nonlinear.jl

@@ -1167,13 +1167,13 @@ function test_scalar_nonlinear_function_parse_scalarquadraticfunction()
         MOI.ScalarQuadraticFunction(qterms, terms, 0.0) => :(0.0),
         MOI.ScalarQuadraticFunction(qterms, terms, 1.0) => :(1.0),
         MOI.ScalarQuadraticFunction(qterms, [aterm], 0.0) => :(2.0 * $x),
-        (1.0 * x * x + 1.0 * x + 1.0) => :($x * $x + $x + 1),
-        (1.0 * x * x + 1.0 * x) => :($x * $x + $x),
-        (1.0 * x * x + 2.0 * x) => :($x * $x + 2.0 * $x),
-        (2.0 * x * x + 2.0 * x) => :(2.0 * $x * $x + 2.0 * $x),
-        (1.0 * x * x) => :($x * $x),
+        (1.0 * x * x + 1.0 * x + 1.0) => :($x^2 + $x + 1),
+        (1.0 * x * x + 1.0 * x) => :($x^2 + $x),
+        (1.0 * x * x + 2.0 * x) => :($x^2 + 2.0 * $x),
+        (2.0 * x * x + 2.0 * x) => :(2.0 * $x^2 + 2.0 * $x),
+        (1.0 * x * x) => :($x^2),
         (1.5 * x * x + 2.5 * x * y + 3.5 * x + 2.0) =>
-            :(1.5 * $x * $x + 2.5 * $x * $y + 3.5 * $x + 2.0),
+            :(1.5 * $x^2 + 2.5 * $x * $y + 3.5 * $x + 2.0),
     )
         nlp_model = MOI.Nonlinear.Model()
         f1 = MOI.Nonlinear.add_expression(nlp_model, f)