MathUtils.C File Reference

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Namespaces
namespace	MathUtils

Functions
void	MathUtils::kron (RealEigenMatrix &product, const RealEigenMatrix &mat_A, const RealEigenMatrix &mat_B)
	Computes the Kronecker product of two matrices.
Real	MathUtils::plainLog (Real x, unsigned int derivative_order)
Real	MathUtils::poly1Log (Real x, Real tol, unsigned int derivative_order)
Real	MathUtils::poly2Log (Real x, Real tol, unsigned int derivative_order)
Real	MathUtils::poly3Log (Real x, Real tol, unsigned int derivative_order)
Real	MathUtils::poly4Log (Real x, Real tol, unsigned int derivative_order)
Real	MathUtils::taylorLog (Real x)
std::vector< std::vector< unsigned int > >	MathUtils::multiIndex (unsigned int dim, unsigned int order)
	generate a complete multi index table for given dimension and order i.e.
Point	MathUtils::barycentricToCartesian2D (const Point &p0, const Point &p1, const Point &p2, const Real b0, const Real b1, const Real b2)
	Evaluate Cartesian coordinates of any center point of a triangle given Barycentric coordinates of center point and Cartesian coordinates of triangle's vertices.
Point	MathUtils::barycentricToCartesian3D (const Point &p0, const Point &p1, const Point &p2, const Point &p3, const Real b0, const Real b1, const Real b2, const Real b3)
	Evaluate Cartesian coordinates of any center point of a tetrahedron given Barycentric coordinates of center point and Cartesian coordinates of tetrahedon's vertices.
Point	MathUtils::circumcenter2D (const Point &p0, const Point &p1, const Point &p2)
	Evaluate circumcenter of a triangle given three arbitrary points.
Point	MathUtils::circumcenter3D (const Point &p0, const Point &p1, const Point &p2, const Point &p3)
	Evaluate circumcenter of a tetrahedrom given four arbitrary points.
std::vector< std::vector< unsigned int > >	multiIndexHelper (unsigned int N, unsigned int K)
	A helper function for MathUtils::multiIndex.

Function Documentation

multiIndexHelper()

std::vector< std::vector< unsigned int > > multiIndexHelper	(	unsigned int	N,
		unsigned int	K
	)

A helper function for MathUtils::multiIndex.

Definition at line 333 of file MathUtils.C.

{
  std::vector<std::vector<unsigned int>> n_choose_k;
  std::vector<unsigned int> row;
  std::string bitmask(K, 1); // K leading 1's
  bitmask.resize(N, 0);      // N-K trailing 0's
 
  do
  {
    row.clear();
    row.push_back(0);
    for (unsigned int i = 0; i < N; ++i) // [0..N-1] integers
      if (bitmask[i])
        row.push_back(i + 1);
    row.push_back(N + 1);
    n_choose_k.push_back(row);
  } while (std::prev_permutation(bitmask.begin(), bitmask.end()));
 
  return n_choose_k;
}

Referenced by MathUtils::multiIndex().