// Old implementation of Jacobian
DenseMatrix BSplineBasis::evalBasisJacobianOld(DenseVector &x) const
{
// Jacobian basis matrix
DenseMatrix J; J.setZero(getNumBasisFunctions(), numVariables);
// Calculate partial derivatives
for (unsigned int i = 0; i < numVariables; i++)
{
// One column in basis jacobian
DenseVector bi; bi.setOnes(1);
for (unsigned int j = 0; j < numVariables; j++)
{
DenseVector temp = bi;
DenseVector xi;
if (j == i)
{
// Differentiated basis
xi = bases.at(j).evaluateFirstDerivative(x(j));
}
else
{
// Normal basis
xi = bases.at(j).evaluate(x(j));
}
bi = kroneckerProduct(temp, xi);
}
// Fill out column
J.block(0,i,bi.rows(),1) = bi.block(0,0,bi.rows(),1);
}
return J;
}
void BSpline::setControlPoints(const DenseMatrix &controlPoints)
{
if (controlPoints.cols() != numVariables + 1)
throw Exception("BSpline::setControlPoints: Incompatible size of control point matrix.");
int nc = controlPoints.rows();
knotaverages = controlPoints.block(0, 0, nc, numVariables);
coefficients = controlPoints.block(0, numVariables, nc, 1);
checkControlPoints();
}
SparseMatrix BSplineBasis1D::reduceSupport(double lb, double ub)
{
// Check bounds
if (lb < knots.front() || ub > knots.back())
throw Exception("BSplineBasis1D::reduceSupport: Cannot increase support!");
unsigned int k = degree + 1;
int index_lower = indexSupportedBasisfunctions(lb).front();
int index_upper = indexSupportedBasisfunctions(ub).back();
// Check lower bound index
if (k != knotMultiplicity(knots.at(index_lower)))
{
int suggested_index = index_lower - 1;
if (0 <= suggested_index)
{
index_lower = suggested_index;
}
else
{
throw Exception("BSplineBasis1D::reduceSupport: Suggested index is negative!");
}
}
// Check upper bound index
if (knotMultiplicity(ub) == k && knots.at(index_upper) == ub)
{
index_upper -= k;
}
// New knot vector
std::vector<double> si;
si.insert(si.begin(), knots.begin()+index_lower, knots.begin()+index_upper+k+1);
// Construct selection matrix A
int numOld = knots.size()-k; // Current number of basis functions
int numNew = si.size()-k; // Number of basis functions after update
if (numOld < numNew)
throw Exception("BSplineBasis1D::reduceSupport: Number of basis functions is increased instead of reduced!");
DenseMatrix Ad = DenseMatrix::Zero(numOld, numNew);
Ad.block(index_lower, 0, numNew, numNew) = DenseMatrix::Identity(numNew, numNew);
SparseMatrix A = Ad.sparseView();
// Update knots
knots = si;
return A;
}
template<typename SparseMatrixType> void sparse_block(const SparseMatrixType& ref)
{
const Index rows = ref.rows();
const Index cols = ref.cols();
const Index inner = ref.innerSize();
const Index outer = ref.outerSize();
typedef typename SparseMatrixType::Scalar Scalar;
typedef typename SparseMatrixType::StorageIndex StorageIndex;
double density = (std::max)(8./(rows*cols), 0.01);
typedef Matrix<Scalar,Dynamic,Dynamic,SparseMatrixType::IsRowMajor?RowMajor:ColMajor> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
typedef SparseVector<Scalar> SparseVectorType;
Scalar s1 = internal::random<Scalar>();
{
SparseMatrixType m(rows, cols);
DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
initSparse<Scalar>(density, refMat, m);
VERIFY_IS_APPROX(m, refMat);
// test InnerIterators and Block expressions
for (int t=0; t<10; ++t)
{
Index j = internal::random<Index>(0,cols-2);
Index i = internal::random<Index>(0,rows-2);
Index w = internal::random<Index>(1,cols-j);
Index h = internal::random<Index>(1,rows-i);
VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
}
}
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
}
}
VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));
VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));
for(Index r=0; r<h; r++)
{
VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));
VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));
VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));
VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));
VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
if(m.middleCols(j,w).coeff(r,c) != Scalar(0))
{
VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));
}
if(m.middleRows(i,h).coeff(r,c) != Scalar(0))
{
VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
}
}
}
for(Index c=0; c<w; c++)
{
VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));
VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));
}
}
for(Index c=0; c<cols; c++)
{
VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
}
for(Index r=0; r<rows; r++)
{
VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
}
}
// test innerVector()
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
Index j0 = internal::random<Index>(0,outer-1);
Index j1 = internal::random<Index>(0,outer-1);
Index r0 = internal::random<Index>(0,rows-1);
Index c0 = internal::random<Index>(0,cols-1);
VERIFY_IS_APPROX(m2.innerVector(j0), innervec(refMat2,j0));
VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), innervec(refMat2,j0)+innervec(refMat2,j1));
m2.innerVector(j0) *= Scalar(2);
innervec(refMat2,j0) *= Scalar(2);
VERIFY_IS_APPROX(m2, refMat2);
m2.row(r0) *= Scalar(3);
refMat2.row(r0) *= Scalar(3);
VERIFY_IS_APPROX(m2, refMat2);
m2.col(c0) *= Scalar(4);
refMat2.col(c0) *= Scalar(4);
VERIFY_IS_APPROX(m2, refMat2);
m2.row(r0) /= Scalar(3);
refMat2.row(r0) /= Scalar(3);
VERIFY_IS_APPROX(m2, refMat2);
m2.col(c0) /= Scalar(4);
refMat2.col(c0) /= Scalar(4);
VERIFY_IS_APPROX(m2, refMat2);
SparseVectorType v1;
VERIFY_IS_APPROX(v1 = m2.col(c0) * 4, refMat2.col(c0)*4);
VERIFY_IS_APPROX(v1 = m2.row(r0) * 4, refMat2.row(r0).transpose()*4);
SparseMatrixType m3(rows,cols);
m3.reserve(VectorXi::Constant(outer,int(inner/2)));
for(Index j=0; j<outer; ++j)
for(Index k=0; k<(std::min)(j,inner); ++k)
m3.insertByOuterInner(j,k) = internal::convert_index<StorageIndex>(k+1);
for(Index j=0; j<(std::min)(outer, inner); ++j)
{
VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
if(j>0)
VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
}
m3.makeCompressed();
for(Index j=0; j<(std::min)(outer, inner); ++j)
{
VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
if(j>0)
VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
}
VERIFY(m3.innerVector(j0).nonZeros() == m3.transpose().innerVector(j0).nonZeros());
// m2.innerVector(j0) = 2*m2.innerVector(j1);
// refMat2.col(j0) = 2*refMat2.col(j1);
// VERIFY_IS_APPROX(m2, refMat2);
}
// test innerVectors()
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
if(internal::random<float>(0,1)>0.5f) m2.makeCompressed();
Index j0 = internal::random<Index>(0,outer-2);
Index j1 = internal::random<Index>(0,outer-2);
Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));
else
VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));
else
VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
VERIFY_IS_APPROX(m2, refMat2);
VERIFY(m2.innerVectors(j0,n0).nonZeros() == m2.transpose().innerVectors(j0,n0).nonZeros());
m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
if(SparseMatrixType::IsRowMajor)
refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();
else
refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();
VERIFY_IS_APPROX(m2, refMat2);
}
// test generic blocks
{
DenseMatrix refMat2 = DenseMatrix::Zero(rows, cols);
SparseMatrixType m2(rows, cols);
initSparse<Scalar>(density, refMat2, m2);
Index j0 = internal::random<Index>(0,outer-2);
Index j1 = internal::random<Index>(0,outer-2);
Index n0 = internal::random<Index>(1,outer-(std::max)(j0,j1));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));
else
VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));
if(SparseMatrixType::IsRowMajor)
VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),
refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));
else
VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),
refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
Index i = internal::random<Index>(0,m2.outerSize()-1);
if(SparseMatrixType::IsRowMajor) {
m2.innerVector(i) = m2.innerVector(i) * s1;
refMat2.row(i) = refMat2.row(i) * s1;
VERIFY_IS_APPROX(m2,refMat2);
} else {
m2.innerVector(i) = m2.innerVector(i) * s1;
refMat2.col(i) = refMat2.col(i) * s1;
VERIFY_IS_APPROX(m2,refMat2);
}
Index r0 = internal::random<Index>(0,rows-2);
Index c0 = internal::random<Index>(0,cols-2);
Index r1 = internal::random<Index>(1,rows-r0);
Index c1 = internal::random<Index>(1,cols-c0);
VERIFY_IS_APPROX(DenseVector(m2.col(c0)), refMat2.col(c0));
VERIFY_IS_APPROX(m2.col(c0), refMat2.col(c0));
VERIFY_IS_APPROX(RowDenseVector(m2.row(r0)), refMat2.row(r0));
VERIFY_IS_APPROX(m2.row(r0), refMat2.row(r0));
VERIFY_IS_APPROX(m2.block(r0,c0,r1,c1), refMat2.block(r0,c0,r1,c1));
VERIFY_IS_APPROX((2*m2).block(r0,c0,r1,c1), (2*refMat2).block(r0,c0,r1,c1));
if(m2.nonZeros()>0)
{
VERIFY_IS_APPROX(m2, refMat2);
SparseMatrixType m3(rows, cols);
DenseMatrix refMat3(rows, cols); refMat3.setZero();
Index n = internal::random<Index>(1,10);
for(Index k=0; k<n; ++k)
{
Index o1 = internal::random<Index>(0,outer-1);
Index o2 = internal::random<Index>(0,outer-1);
if(SparseMatrixType::IsRowMajor)
{
m3.innerVector(o1) = m2.row(o2);
refMat3.row(o1) = refMat2.row(o2);
}
else
{
m3.innerVector(o1) = m2.col(o2);
refMat3.col(o1) = refMat2.col(o2);
}
if(internal::random<bool>())
m3.makeCompressed();
}
if(m3.nonZeros()>0)
VERIFY_IS_APPROX(m3, refMat3);
}
}
}
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;
}
bool BSplineBasis1D::reduceSupport(double lb, double ub, SparseMatrix &A)
{
// Check bounds
if(lb < knots.front() || ub > knots.back())
{
return false;
}
unsigned int k = degree + 1;
int index_lower = indexSupportedBasisfunctions(lb).front();
int index_upper = indexSupportedBasisfunctions(ub).back();
// Check lower bound index
unsigned int count = knotMultiplicity(knots.at(index_lower));
bool is_p_regular = (k == count);
if(!is_p_regular)
{
int suggested_index = index_lower - 1;
if(0 <= suggested_index)
{
index_lower = suggested_index;
}
else
{
#ifndef NDEBUG
std::cout << "\n\n----------------adjust_index_for_domain_reduction-----------------" << std::endl;
std::cout << "Error: not enough knots to guarantee controlpoint convergence" << std::endl;
std::cout << "----------------adjust_index_for_domain_reduction-----------------\n\n" << std::endl;
#endif // NDEBUG
return false;
}
}
// Check upper bound index
if(knotMultiplicity(ub) == k && knots.at(index_upper) == ub)
{
index_upper -= k;
}
// New knot vector
std::vector<double> si;
si.insert(si.begin(), knots.begin()+index_lower, knots.begin()+index_upper+k+1);
// Construct selection matrix A
int n_old = knots.size()-k; // Current number of basis functions
int n_new = si.size()-k; // Number of basis functions after update
if (n_old < n_new) return false;
DenseMatrix Ad = DenseMatrix::Zero(n_old, n_new);
Ad.block(index_lower, 0, n_new, n_new) = DenseMatrix::Identity(n_new, n_new);
A = Ad.sparseView();
// Update knots
knots = si;
return true;
}