DGMSolver.hpp

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#ifndef DGMSOLVER_HPP
#define DGMSOLVER_HPP
#include <vector>
 
namespace moab
{
 
class DGMSolver
{
    DGMSolver(){};
    ~DGMSolver(){};
 
  public:
    //! \brief compute combinational number, n choose k, maximum output is
    //! std::numeric_limits<unsigned int>::max();
    // If overflows, return 0
    static unsigned int nchoosek( unsigned int n, unsigned int k );
 
    //! \brief compute the number of columns for a multivariate vandermonde matrix, given certen
    //! degree
    /** If degree = 0, out put is 1;
     *If kvars = 1, degree = k, output is k+1;
     *If kvars = 2, degree = k, output is (k+2)*(k+1)/2;
     */
    static unsigned int compute_numcols_vander_multivar( unsigned int kvars, unsigned int degree );
 
    //! \brief compute the monomial basis of mutiple variables, up to input degree,
    //! lexicographically ordered
    /** if degree = 0, output basis = {1}
     *If kvars = 1, vars = {u}, degree = k, basis = {1,u,...,u^k}
     *If kvars = 2, vars = {u,v}, degree = k, basis =
     *{1,u,v,u^2,uv,v^2,u^3,u^2*v,uv^2,v^3,...,u^k,u^k-1*v,...,uv^k-1,v^k} If kvars = 3, vars =
     *{u,v,w}, degree = k, basis =
     *{1,u,v,w,u^2,uv,uw,v^2,v*w,w^2,...,u^k,u^k-1v,u^k-1w,...,v^k,v^k-1w,...,vw^k-1,w^k} \param
     *kvars Integer, number of variables \param vars Pointer to array of doubles, size = kvars,
     *variable values \param degree Integer, maximum degree \param basis Reference to vector, user
     *input container to hold output which is appended to existing data; users don't have to
     *preallocate for basis, this function will allocate interally
     */
    static void gen_multivar_monomial_basis( const int kvars,
                                             const double* vars,
                                             const int degree,
                                             std::vector< double >& basis );
 
    //! \brief compute multivariate vandermonde matrix, monomial basis ordered in the same way as
    //! gen_multivar_monomial_basis
    /** if degree = 0, V = {1,...,1}';
        *If kvars = 1, us = {u1;u2;..,;um}, degree = k, V = {1 u1 u1^2 ... u1^k;1 u2 u2^2 ...
       u2^k;...;1 um um^2 ... um^k}; *If kvars = 2, us = {u1 v1;u2 v2;...;um vm}, degree = k, V = {1
       u1 v1 u1^2 u1v1 v1^2;...;1 um vm um^2 umvm vm^2};
        * \param mrows Integer, number of points to evaluate Vandermonde matrix
        * \param kvars Integer, number of variables
        * \param us Pointer to array of doubles, size = mrow*kvars, variable values for all points.
       Stored in row-wise, like {u1 v1 u2 v2 ...}
        * \param degree Integer, maximum degree
        * \param basis Reference to vector, user input container to hold Vandermonde matrix which is
       appended to existing data; users don't have to preallocate for basis, this function will
       allocate interally; the Vandermonde matrix is stored in an array, columnwise, like {1 ... 1
       u1 ...um u1^2 ... um^2 ...}
    */
    static void gen_vander_multivar( const int mrows,
                                     const int kvars,
                                     const double* us,
                                     const int degree,
                                     std::vector< double >& V );
 
    static void rescale_matrix( int mrows, int ncols, double* V, double* ts );
 
    static void compute_qtransposeB( int mrows, int ncols, const double* Q, int bncols, double* bs );
 
    static void qr_polyfit_safeguarded( const int mrows, const int ncols, double* V, double* D, int* rank );
 
    static void backsolve( int mrows, int ncols, double* R, int bncols, double* bs, double* ws );
 
    static void backsolve_polyfit_safeguarded( int dim,
                                               int degree,
                                               const bool interp,
                                               int mrows,
                                               int ncols,
                                               double* R,
                                               int bncols,
                                               double* bs,
                                               const double* ws,
                                               int* degree_out );
 
    static void vec_dotprod( const int len, const double* a, const double* b, double* c );
 
    static void vec_scalarprod( const int len, const double* a, const double c, double* b );
 
    static void vec_crossprod( const double a[3], const double b[3], double ( &c )[3] );
 
    static double vec_innerprod( const int len, const double* a, const double* b );
 
    static double vec_2norm( const int len, const double* a );
 
    static double vec_normalize( const int len, const double* a, double* b );
 
    static double vec_distance( const int len, const double* a, const double* b );
 
    static void vec_projoff( const int len, const double* a, const double* b, double* c );
 
    static void vec_linear_operation( const int len,
                                      const double mu,
                                      const double* a,
                                      const double psi,
                                      const double* b,
                                      double* c );
 
    static void get_tri_natural_coords( const int dim,
                                        const double* cornercoords,
                                        const int npts,
                                        const double* currcoords,
                                        double* naturalcoords );
};
 
}  // namespace moab
#endif