Fix Bug in How LinearConstraint Representations handle w.r.t. variables for scalar case (#17)

* Fixed bug in how scalar constraint computes linear constraint representations (make sure that we always include the wrt variable)

* Fixed a few more cases that were needed to make the bug's tests work

---------

Co-authored-by: Kwesi Rutledge <[email protected]>

Author: kwesiRutledge

symbolic/constant_vector.go

@@ -160,19 +160,18 @@ func (kv KVector) Plus(rightIn interface{}) Expression {
 
 		// Add the values
 		return kv.Plus(VecDenseToKVector(eAsVec))
-	case K:
-		// Return Addition
-		return kv.Plus(float64(right))
-	case Variable:
+	case K, Variable, Monomial, Polynomial:
 		// Create a new polynomial vector
-		var pvOut PolynomialVector
+		var out []ScalarExpression
 		for _, element := range kv {
-			pvOut = append(pvOut, element.Plus(right).(Polynomial))
+			out = append(out, element.Plus(right).(ScalarExpression))
 		}
-		return pvOut
+		return ConcretizeVectorExpression(out)
 
 	case *mat.VecDense:
 		return kv.Plus(VecDenseToKVector(*right)) // Convert to KVector
+	case mat.VecDense:
+		return kv.Plus(VecDenseToKVector(right)) // Convert to KVector
 
 	case KVector:
 		// Compute Addition
@@ -234,6 +233,9 @@ func (kv KVector) Minus(e interface{}) Expression {
 		return kv.Minus(VecDenseToKVector(right)) // Convert to KVector
 	case *mat.VecDense:
 		return kv.Minus(VecDenseToKVector(*right)) // Convert to KVector
+	case K, Variable, Monomial, Polynomial:
+		rightAsSE := right.(ScalarExpression)
+		return kv.Plus(rightAsSE.Multiply(-1.0)) // Reuse K case
 	case KVector, VariableVector, MonomialVector, PolynomialVector:
 		// Force the right hand side to be a VectorExpression
 		rhsAsVE := right.(VectorExpression)

symbolic/polynomial_like_vector.go

@@ -30,7 +30,7 @@ type PolynomialLikeVector interface {
 	// Variables returns the number of variables in the expression.
 	Variables() []Variable
 
-	// Coeffs returns a slice of the coefficients in the expression
+	// LinearCoeff returns a slice of the coefficients in the expression
 	LinearCoeff(wrt ...[]Variable) mat.Dense
 
 	// Constant returns the constant additive value in the expression

symbolic/scalar_constraint.go

@@ -137,7 +137,7 @@ func (sc ScalarConstraint) LinearInequalityConstraintRepresentation(wrt ...[]Var
 	newLHS := sc.Left().(ScalarExpression)
 	newLHS = newLHS.Minus(sc.Right()).(ScalarExpression)
 
-	A = newLHS.LinearCoeff()
+	A = newLHS.LinearCoeff(wrt...)
 
 	if sc.Sense == SenseGreaterThanEqual {
 		A.ScaleVec(-1, &A)
@@ -199,7 +199,7 @@ func (sc ScalarConstraint) LinearEqualityConstraintRepresentation(wrt ...[]Varia
 	// Create C
 	newLHS := sc.Left().(ScalarExpression)
 	newLHS = newLHS.Minus(sc.Right()).(ScalarExpression)
-	C = newLHS.LinearCoeff()
+	C = newLHS.LinearCoeff(wrt...)
 
 	// Create d
 	newRHS := sc.Right().(ScalarExpression).Constant() - sc.Left().(ScalarExpression).Constant()

symbolic/variable.go

@@ -121,6 +121,9 @@ func (v Variable) Plus(rightIn interface{}) Expression {
 		return right.Plus(v)
 	case *mat.VecDense:
 		return v.Plus(VecDenseToKVector(*right))
+	case mat.VecDense:
+		// Convert to KVector
+		return v.Plus(VecDenseToKVector(right))
 	case KVector, VariableVector, MonomialVector, PolynomialVector:
 		ve, _ := ToVectorExpression(rightIn)
 		return ve.Plus(v)

symbolic/vector_expression.go

@@ -30,8 +30,8 @@ type VectorExpression interface {
 	// Variables returns the number of variables in the expression.
 	Variables() []Variable
 
-	//// Coeffs returns a slice of the coefficients in the expression
-	//LinearCoeff() mat.Dense
+	// LinearCoeffs returns a slice of the coefficients in the expression
+	LinearCoeff(wrt ...[]Variable) mat.Dense
 
 	// Constant returns the constant additive value in the expression
 	Constant() mat.VecDense

testing/symbolic/scalar_constraint_test.go

@@ -652,6 +652,53 @@ func TestScalarConstraint_LinearInequalityConstraintRepresentation5(t *testing.T
 	sc.(symbolic.ScalarConstraint).LinearInequalityConstraintRepresentation()
 }
 
+/*
+TestScalarConstraint_LinearInequalityConstraintRepresentation6
+Description:
+
+	Tests the LinearInequalityConstraintRepresentation() method of a scalar
+	constraint. This test verifies that the method correctly produces a vector with
+	length 2 and a constant of value 2.1 when using a small cosntraint:
+	x1 <= 2.1
+	but when calculating the representation with respect to a vector of 2 variables.
+*/
+func TestScalarConstraint_LinearInequalityConstraintRepresentation6(t *testing.T) {
+	// Constants
+	x := symbolic.NewVariableVector(2)
+	c2 := symbolic.K(2.1)
+
+	// Create constraint
+	sc := x.AtVec(0).LessEq(c2)
+
+	// Verify that the constraint is linear
+	if !sc.IsLinear() {
+		t.Errorf(
+			"Expected sc to be linear; received %v",
+			sc.IsLinear(),
+		)
+	}
+
+	// Get linear representation
+	A, b := sc.(symbolic.ScalarConstraint).LinearInequalityConstraintRepresentation(x)
+
+	// Verify that the vector is all ones
+	if A.AtVec(0) != 1 {
+		t.Errorf("Expected A[0] to be 1; received %v", A.AtVec(0))
+	}
+
+	if A.AtVec(1) != 0 {
+		t.Errorf("Expected A[1] to be 0; received %v", A.AtVec(1))
+	}
+
+	// Verify that the constant is 2.5
+	if b != 2.1 {
+		t.Errorf(
+			"Expected b to be 2.5; received %v",
+			b,
+		)
+	}
+}
+
 /*
 TestScalarConstraint_LinearEqualityConstraintRepresentation1
 Description:
@@ -847,3 +894,50 @@ func TestScalarConstraint_LinearEqualityConstraintRepresentation4(t *testing.T)
 
 	sc.(symbolic.ScalarConstraint).LinearEqualityConstraintRepresentation()
 }
+
+/*
+TestScalarConstraint_LinearEqualityConstraintRepresentation5
+Description:
+
+	Tests the LinearEqualityConstraintRepresentation() method of a scalar
+	constraint. This test verifies that the method correctly produces a vector with
+	length 2 and a constant of value 2.1 when using a small cosntraint:
+	x1 = 2.1
+	but when calculating the representation with respect to a vector of 2 variables.
+*/
+func TestScalarConstraint_LinearEqualityConstraintRepresentation5(t *testing.T) {
+	// Constants
+	x := symbolic.NewVariableVector(2)
+	c2 := symbolic.K(2.1)
+
+	// Create constraint
+	sc := x.AtVec(0).Eq(c2)
+
+	// Verify that the constraint is linear
+	if !sc.IsLinear() {
+		t.Errorf(
+			"Expected sc to be linear; received %v",
+			sc.IsLinear(),
+		)
+	}
+
+	// Get linear representation
+	A, b := sc.(symbolic.ScalarConstraint).LinearEqualityConstraintRepresentation(x)
+
+	// Verify that the vector is all ones
+	if A.AtVec(0) != 1 {
+		t.Errorf("Expected A[0] to be 1; received %v", A.AtVec(0))
+	}
+
+	if A.AtVec(1) != 0 {
+		t.Errorf("Expected A[1] to be 0; received %v", A.AtVec(1))
+	}
+
+	// Verify that the constant is 2.5
+	if b != 2.1 {
+		t.Errorf(
+			"Expected b to be 2.5; received %v",
+			b,
+		)
+	}
+}

testing/symbolic/vector_constraint_test.go

@@ -564,6 +564,52 @@ func TestVectorConstraint_LinearInequalityConstraintRepresentation7(t *testing.T
 	vc.LinearInequalityConstraintRepresentation()
 }
 
+/*
+TestVectorConstraint_LinearInequalityConstraintRepresentation8
+Description:
+
+	This function tests that the LinearInequalityConstraintRepresentation method
+	properly returns a matrix of shape (2, 2) and a vector of shape (2, 1)
+	for a well-defined, lienar vector constraint. This constraint will only contain
+	1 variable, but the w.r.t. variable will contain 2 variables.
+*/
+func TestVectorConstraint_LinearInequalityConstraintRepresentation8(t *testing.T) {
+	// Constants
+	N := 2
+	x := symbolic.NewVariableVector(N)
+	left := x.AtVec(0).Plus(symbolic.ZerosVector(N))
+	right := mat.NewVecDense(N, []float64{1, 2})
+	vc := left.LessEq(right).(symbolic.VectorConstraint)
+
+	// Test
+	A, b := vc.LinearInequalityConstraintRepresentation(x)
+
+	nRowsA, nColsA := A.Dims()
+	if nRowsA != N || nColsA != 2 {
+		t.Errorf(
+			"Expected vc.LinearInequalityConstraintRepresentation() to return a matrix of dimension %v; received dimension (%v, %v)",
+			[]int{N, 2},
+			nRowsA, nColsA,
+		)
+	}
+
+	if b.AtVec(0) != 1 {
+		t.Errorf(
+			"Expected vc.LinearEqualityConstraintRepresentation()'s b vector to contain a 1 at the %v-th index; received %v",
+			0,
+			b.AtVec(0),
+		)
+	}
+
+	if b.AtVec(1) != 2 {
+		t.Errorf(
+			"Expected vc.LinearEqualityConstraintRepresentation()'s b vector to contain a 2 at the %v-th index; received %v",
+			1,
+			b.AtVec(1),
+		)
+	}
+}
+
 /*
 TestVectorConstraint_LinearEqualityConstraintRepresentation1
 Description: