Mesh Oriented datABase  (version 5.5.1)
An array-based unstructured mesh library
DGMSolver.hpp
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1 #ifndef DGMSOLVER_HPP
2 #define DGMSOLVER_HPP
3 #include <vector>
4 
5 namespace moab
6 {
7 
8 class DGMSolver
9 {
10  DGMSolver(){};
11  ~DGMSolver(){};
12 
13  public:
14  //! \brief compute combinational number, n choose k, maximum output is
15  //! std::numeric_limits<unsigned int>::max();
16  // If overflows, return 0
17  static unsigned int nchoosek( unsigned int n, unsigned int k );
18 
19  //! \brief compute the number of columns for a multivariate vandermonde matrix, given certen
20  //! degree
21  /** If degree = 0, out put is 1;
22  *If kvars = 1, degree = k, output is k+1;
23  *If kvars = 2, degree = k, output is (k+2)*(k+1)/2;
24  */
25  static unsigned int compute_numcols_vander_multivar( unsigned int kvars, unsigned int degree );
26 
27  //! \brief compute the monomial basis of mutiple variables, up to input degree,
28  //! lexicographically ordered
29  /** if degree = 0, output basis = {1}
30  *If kvars = 1, vars = {u}, degree = k, basis = {1,u,...,u^k}
31  *If kvars = 2, vars = {u,v}, degree = k, basis =
32  *{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 =
33  *{u,v,w}, degree = k, basis =
34  *{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
35  *kvars Integer, number of variables \param vars Pointer to array of doubles, size = kvars,
36  *variable values \param degree Integer, maximum degree \param basis Reference to vector, user
37  *input container to hold output which is appended to existing data; users don't have to
38  *preallocate for basis, this function will allocate interally
39  */
40  static void gen_multivar_monomial_basis( const int kvars,
41  const double* vars,
42  const int degree,
43  std::vector< double >& basis );
44 
45  //! \brief compute multivariate vandermonde matrix, monomial basis ordered in the same way as
46  //! gen_multivar_monomial_basis
47  /** if degree = 0, V = {1,...,1}';
48  *If kvars = 1, us = {u1;u2;..,;um}, degree = k, V = {1 u1 u1^2 ... u1^k;1 u2 u2^2 ...
49  u2^k;...;1 um um^2 ... um^k}; *If kvars = 2, us = {u1 v1;u2 v2;...;um vm}, degree = k, V = {1
50  u1 v1 u1^2 u1v1 v1^2;...;1 um vm um^2 umvm vm^2};
51  * \param mrows Integer, number of points to evaluate Vandermonde matrix
52  * \param kvars Integer, number of variables
53  * \param us Pointer to array of doubles, size = mrow*kvars, variable values for all points.
54  Stored in row-wise, like {u1 v1 u2 v2 ...}
55  * \param degree Integer, maximum degree
56  * \param basis Reference to vector, user input container to hold Vandermonde matrix which is
57  appended to existing data; users don't have to preallocate for basis, this function will
58  allocate interally; the Vandermonde matrix is stored in an array, columnwise, like {1 ... 1
59  u1 ...um u1^2 ... um^2 ...}
60  */
61  static void gen_vander_multivar( const int mrows,
62  const int kvars,
63  const double* us,
64  const int degree,
65  std::vector< double >& V );
66 
67  static void rescale_matrix( int mrows, int ncols, double* V, double* ts );
68 
69  static void compute_qtransposeB( int mrows, int ncols, const double* Q, int bncols, double* bs );
70 
71  static void qr_polyfit_safeguarded( const int mrows, const int ncols, double* V, double* D, int* rank );
72 
73  static void backsolve( int mrows, int ncols, double* R, int bncols, double* bs, double* ws );
74 
75  static void backsolve_polyfit_safeguarded( int dim,
76  int degree,
77  const bool interp,
78  int mrows,
79  int ncols,
80  double* R,
81  int bncols,
82  double* bs,
83  const double* ws,
84  int* degree_out );
85 
86  static void vec_dotprod( const int len, const double* a, const double* b, double* c );
87 
88  static void vec_scalarprod( const int len, const double* a, const double c, double* b );
89 
90  static void vec_crossprod( const double a[3], const double b[3], double ( &c )[3] );
91 
92  static double vec_innerprod( const int len, const double* a, const double* b );
93 
94  static double vec_2norm( const int len, const double* a );
95 
96  static double vec_normalize( const int len, const double* a, double* b );
97 
98  static double vec_distance( const int len, const double* a, const double* b );
99 
100  static void vec_projoff( const int len, const double* a, const double* b, double* c );
101 
102  static void vec_linear_operation( const int len,
103  const double mu,
104  const double* a,
105  const double psi,
106  const double* b,
107  double* c );
108 
109  static void get_tri_natural_coords( const int dim,
110  const double* cornercoords,
111  const int npts,
112  const double* currcoords,
113  double* naturalcoords );
114 };
115 
116 } // namespace moab
117 #endif