void centerMatrix(DenseMatrix& matrix)
{
DenseVector col_means = matrix.colwise().mean().transpose();
DenseMatrix::Scalar grand_mean = matrix.mean();
matrix.array() += grand_mean;
matrix.rowwise() -= col_means.transpose();
matrix.colwise() -= col_means;
}
bool ConstraintBSpline::controlPointBoundsDeduction() const
{
// Get variable bounds
auto xlb = bspline.getDomainLowerBound();
auto xub = bspline.getDomainUpperBound();
// Use these instead?
// for (unsigned int i = 0; i < bspline.getNumVariables(); i++)
// {
// xlb.at(i) = variables.at(i)->getLowerBound();
// xub.at(i) = variables.at(i)->getUpperBound();
// }
double lowerBound = variables.back()->getLowerBound(); // f(x) = y > lowerBound
double upperBound = variables.back()->getUpperBound(); // f(x) = y < upperBound
// Get knot vectors and basis degrees
auto knotVectors = bspline.getKnotVectors();
auto basisDegrees = bspline.getBasisDegrees();
// Compute n value for each variable
// Total number of control points is ns(0)*...*ns(d-1)
std::vector<unsigned int> numBasisFunctions = bspline.getNumBasisFunctions();
// Get matrix of coefficients
DenseMatrix cps = controlPoints;
DenseMatrix coeffs = cps.block(bspline.getNumVariables(), 0, 1, cps.cols());
for (unsigned int d = 0; d < bspline.getNumVariables(); d++)
{
if (assertNear(xlb.at(d), xub.at(d)))
continue;
auto n = numBasisFunctions.at(d);
auto p = basisDegrees.at(d);
std::vector<double> knots = knotVectors.at(d);
assert(knots.size() == n+p+1);
// Tighten lower bound
unsigned int i = 1;
for (; i <= n; i++)
{
// Knot interval of interest: [t_0, t_i]
// Selection matrix
DenseMatrix S = DenseMatrix::Ones(1,1);
for (unsigned int d2 = 0; d2 < bspline.getNumVariables(); d2++)
{
DenseMatrix temp(S);
DenseMatrix Sd_full = DenseMatrix::Identity(numBasisFunctions.at(d2),numBasisFunctions.at(d2));
DenseMatrix Sd(Sd_full);
if (d == d2)
Sd = Sd_full.block(0,0,n,i);
S = kroneckerProduct(temp, Sd);
}
// Control points that have support in [t_0, t_i]
DenseMatrix selc = coeffs*S;
DenseVector minCP = selc.rowwise().minCoeff();
DenseVector maxCP = selc.rowwise().maxCoeff();
double minv = minCP(0);
double maxv = maxCP(0);
// Investigate feasibility
if (minv > upperBound || maxv < lowerBound)
continue; // infeasible
else
break; // feasible
}
// New valid lower bound on x(d) is knots(i-1)
if (i > 1)
{
if (!variables.at(d)->updateLowerBound(knots.at(i-1)))
return false;
}
// Tighten upper bound
i = 1;
for (; i <= n; i++)
{
// Knot interval of interest: [t_{n+p-i}, t_{n+p}]
// Selection matrix
DenseMatrix S = DenseMatrix::Ones(1,1);
for (unsigned int d2 = 0; d2 < bspline.getNumVariables(); d2++)
{
DenseMatrix temp(S);
DenseMatrix Sd_full = DenseMatrix::Identity(numBasisFunctions.at(d2),numBasisFunctions.at(d2));
DenseMatrix Sd(Sd_full);
if (d == d2)
Sd = Sd_full.block(0,n-i,n,i);
S = kroneckerProduct(temp, Sd);
}
// Control points that have support in [t_{n+p-i}, t_{n+p}]
DenseMatrix selc = coeffs*S;
DenseVector minCP = selc.rowwise().minCoeff();
DenseVector maxCP = selc.rowwise().maxCoeff();
double minv = minCP(0);
double maxv = maxCP(0);
// Investigate feasibility
if (minv > upperBound || maxv < lowerBound)
continue; // infeasible
else
break; // feasible
}
// New valid lower bound on x(d) is knots(n+p-(i-1))
if (i > 1)
{
if (!variables.at(d)->updateUpperBound(knots.at(n+p-(i-1))))
return false;
// NOTE: the upper bound seems to not be tight! can we use knots.at(n+p-i)?
}
}
return true;
}