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;
}
/*
* Calculate coefficients of B-spline representing a multivariate polynomial
*
* The polynomial f(x), with x in R^n, has m terms on the form
* f(x) = c(0)*x(0)^E(0,0)*x(1)^E(0,1)*...*x(n-1)^E(0,n-1)
* +c(1)*x(0)^E(1,0)*x(1)^E(1,1)*...*x(n-1)^E(1,n-1)
* +...
* +c(m-1)*x(0)^E(m-1,0)*x(1)^E(m-1,1)*...*x(n-1)^E(m-1,n-1)
* where c in R^m is a vector with coefficients for each of the m terms,
* and E in N^(mxn) is a matrix with the exponents of each variable in each of the m terms,
* e.g. the first row of E defines the first term with variable exponents E(0,0) to E(0,n-1).
*
* Note: E must be a matrix of nonnegative integers
*/
DenseMatrix getBSplineBasisCoefficients(DenseVector c, DenseMatrix E, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = E.cols();
unsigned int terms = E.rows();
assert(dim >= 1); // At least one variable
assert(terms >= 1); // At least one term (assumes that c is a column vector)
assert(terms == c.rows());
assert(dim == lb.size());
assert(dim == ub.size());
// Get highest power of each variable
DenseVector powers = E.colwise().maxCoeff();
// Store in std vector
std::vector<unsigned int> powers2;
for (unsigned int i = 0; i < powers.size(); ++i)
powers2.push_back(powers(i));
// Calculate tensor product transformation matrix T
DenseMatrix T = getTransformationMatrix(powers2, lb, ub);
// Compute power basis coefficients (lambda vector)
SparseMatrix L(T.cols(),1);
L.setZero();
for (unsigned int i = 0; i < terms; i++)
{
SparseMatrix Li(1,1);
Li.insert(0,0) = 1;
for (unsigned int j = 0; j < dim; j++)
{
int e = E(i,j);
SparseVector li(powers(j)+1);
li.reserve(1);
li.insert(e) = 1;
SparseMatrix temp = Li;
Li = kroneckerProduct(temp, li);
}
L += c(i)*Li;
}
// Compute B-spline coefficients
DenseMatrix C = T*L;
return C;
}