/// <summary>
/// Adds a ray to the frame of "this" and updates Constraints accordingly, see
/// Cousot and Halbwachs, section 3.3.1.1. However, this method does not simplify
/// Constraints after the operation; that remains the caller's responsibility (which
/// gives the caller the opportunity to make multiple calls to AddVertex, AddRay,
/// and AddLine before calling SimplifyConstraints).
/// Assumes Constraints (and the frame fields) to be non-null.
/// </summary>
/// <param name="ray"></param>
void AddRay(FrameElement/*!*/ ray) {
Contract.Requires(ray != null);
Contract.Requires(this.FrameRays != null);
#if DEBUG_PRINT
Console.WriteLine("DEBUG: AddRay called on {0}", ray);
Console.WriteLine(" Initial constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
FrameRays.Add(ray.Clone());
#if FIXED_DESERIALIZER
Contract.Assert(Contract.ForAll(ray.GetDefinedDimensions() , var=> FrameDimensions.Contains(var)));
#endif
// We use a new temporary dimension.
IVariable/*!*/ lambda = new LambdaDimension();
// We change the constraints A*X <= B into
// A*X - (A*ray)*lambda <= B.
// That means that each row k in A (which corresponds to one LinearConstraint
// in Constraints) is changed by subtracting
// (A*ray)[k] * lambda
// from row k.
// Note:
// (A*ray)[k]
// = { A*ray is a row vector whose every row i is the dot-product of
// row i of A with the column vector "ray" }
// A[k]*ray
foreach (LinearConstraint/*!*/ cc in cce.NonNull(Constraints)) {
Contract.Assert(cc != null);
Rational d = cc.EvaluateLhs(ray);
cc.SetCoefficient(lambda, -d);
}
// We also add the constraints that lambda is at least 0.
LinearConstraint la = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
la.SetCoefficient(lambda, Rational.MINUS_ONE);
la.rhs = Rational.ZERO;
Constraints.Add(la);
#if DEBUG_PRINT
Console.WriteLine(" Constraints after addition:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
// Finally, project out the dummy dimension.
Constraints = Project(lambda, Constraints);
#if DEBUG_PRINT
Console.WriteLine(" Resulting constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
}
/// <summary>
/// Adds a line to the frame of "this" and updates Constraints accordingly, see
/// Cousot and Halbwachs, section 3.3.1.1. However, this method does not simplify
/// Constraints after the operation; that remains the caller's responsibility (which
/// gives the caller the opportunity to make multiple calls to AddVertex, AddRay,
/// and AddLine before calling SimplifyConstraints).
/// Assumes Constraints (and the frame fields) to be non-null.
/// </summary>
/// <param name="line"></param>
void AddLine(FrameElement/*!*/ line) {
Contract.Requires(line != null);
Contract.Requires(this.FrameLines != null);
// Note: The code for AddLine is identical to that of AddRay, except the AddLine
// does not introduce the constraint 0 <= lambda. (One could imagine sharing the
// code between AddRay and AddLine.)
#if DEBUG_PRINT
Console.WriteLine("DEBUG: AddLine called on {0}", line);
Console.WriteLine(" Initial constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
FrameLines.Add(line.Clone());
#if FIXED_DESERIALIZER
Contract.Assert(Contract.ForAll(line.GetDefinedDimensions() , var=> FrameDimensions.Contains(var)));
#endif
// We use a new temporary dimension.
IVariable/*!*/ lambda = new LambdaDimension();
// We change the constraints A*X <= B into
// A*X - (A*line)*lambda <= B.
// That means that each row k in A (which corresponds to one LinearConstraint
// in Constraints) is changed by subtracting
// (A*line)[k] * lambda
// from row k.
// Note:
// (A*line)[k]
// = { A*line is a row vector whose every row i is the dot-product of
// row i of A with the column vector "line" }
// A[k]*line
foreach (LinearConstraint/*!*/ cc in cce.NonNull(Constraints)) {
Contract.Assert(cc != null);
Rational d = cc.EvaluateLhs(line);
cc.SetCoefficient(lambda, -d);
}
#if DEBUG_PRINT
Console.WriteLine(" Constraints after addition:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
// Finally, project out the dummy dimension.
Constraints = Project(lambda, Constraints);
#if DEBUG_PRINT
Console.WriteLine(" Resulting constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
}
/// <summary>
/// Adds a vertex to the frame of "this" and updates Constraints accordingly, see
/// Cousot and Halbwachs, section 3.3.1.1. However, this method does not simplify
/// Constraints after the operation; that remains the caller's responsibility (which
/// gives the caller the opportunity to make multiple calls to AddVertex, AddRay,
/// and AddLine before calling SimplifyConstraints).
/// Assumes Constraints (and the frame fields) to be non-null.
/// </summary>
/// <param name="vertex"></param>
void AddVertex(FrameElement/*!*/ vertex) {
Contract.Requires(vertex != null);
Contract.Requires(this.FrameVertices != null);
#if DEBUG_PRINT
Console.WriteLine("DEBUG: AddVertex called on {0}", vertex);
Console.WriteLine(" Initial constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
FrameVertices.Add(vertex.Clone());
#if FIXED_DESERIALIZER
Contract.Assert(Contract.ForAll(vertex.GetDefinedDimensions() , var=> FrameDimensions.Contains(var)));
#endif
// We use a new temporary dimension.
IVariable/*!*/ lambda = new LambdaDimension();
// We change the constraints A*X <= B into
// A*X + (A*vector - B)*lambda <= A*vector.
// That means that each row k in A (which corresponds to one LinearConstraint
// in Constraints) is changed by adding
// (A*vector - B)[k] * lambda
// to row k and changing the right-hand side of row k to
// (A*vector)[k]
// Note:
// (A*vector - B)[k]
// = { vector subtraction is pointwise }
// (A*vector)[k] - B[k]
// = { A*vector is a row vector whose every row i is the dot-product of
// row i of A with the column vector "vector" }
// A[k]*vector - B[k]
foreach (LinearConstraint/*!*/ cc in cce.NonNull(Constraints)) {
Contract.Assert(cc != null);
Rational d = cc.EvaluateLhs(vertex);
cc.SetCoefficient(lambda, d - cc.rhs);
cc.rhs = d;
}
// We also add the constraints that lambda lies between 0 ...
LinearConstraint la = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
la.SetCoefficient(lambda, Rational.MINUS_ONE);
la.rhs = Rational.ZERO;
Constraints.Add(la);
// ... and 1.
la = new LinearConstraint(LinearConstraint.ConstraintRelation.LE);
la.SetCoefficient(lambda, Rational.ONE);
la.rhs = Rational.ONE;
Constraints.Add(la);
#if DEBUG_PRINT
Console.WriteLine(" Constraints after addition:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
// Finally, project out the dummy dimension.
Constraints = Project(lambda, Constraints);
#if DEBUG_PRINT
Console.WriteLine(" Resulting constraints:");
foreach (LinearConstraint cc in Constraints) {
Console.WriteLine(" {0}", cc);
}
#endif
}
