Intrepid
Intrepid_Polylib.hpp
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48 // File: Intrepid_Polylib.hpp
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77 // Description:
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86 
87 
95 #ifndef INTREPID_POLYLIB_HPP
96 #define INTREPID_POLYLIB_HPP
97 
98 #include "Intrepid_ConfigDefs.hpp"
99 #include "Intrepid_Types.hpp"
100 #include "Teuchos_Assert.hpp"
101 
102 namespace Intrepid {
103 
197  enum EIntrepidPLPoly {
198  PL_GAUSS=0,
199  PL_GAUSS_RADAU_LEFT,
200  PL_GAUSS_RADAU_RIGHT,
201  PL_GAUSS_LOBATTO,
202  PL_MAX
203  };
204 
205  inline EIntrepidPLPoly & operator++(EIntrepidPLPoly &type) {
206  return type = static_cast<EIntrepidPLPoly>(type+1);
207  }
208 
209  inline EIntrepidPLPoly operator++(EIntrepidPLPoly &type, int) {
210  EIntrepidPLPoly oldval = type;
211  ++type;
212  return oldval;
213  }
214 
215 
223  class IntrepidPolylib {
224 
225  public:
226 
227  /* Points and weights */
228 
236  template<class Scalar>
237  static void zwgj (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
238 
239 
247  template<class Scalar>
248  static void zwgrjm (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
249 
250 
258  template<class Scalar>
259  static void zwgrjp (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
260 
261 
269  template<class Scalar>
270  static void zwglj (Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta);
271 
272 
273 
274  /* Derivative operators */
275 
284  template<class Scalar>
285  static void Dgj (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
286 
287 
296  template<class Scalar>
297  static void Dgrjm (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
298 
299 
308  template<class Scalar>
309  static void Dgrjp (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
310 
311 
320  template<class Scalar>
321  static void Dglj (Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta);
322 
323 
324 
325  /* Lagrangian interpolants */
326 
346  template<class Scalar>
347  static Scalar hgj (const int i, const Scalar z, const Scalar *zgj,
348  const int np, const Scalar alpha, const Scalar beta);
349 
350 
370  template<class Scalar>
371  static Scalar hgrjm (const int i, const Scalar z, const Scalar *zgrj,
372  const int np, const Scalar alpha, const Scalar beta);
373 
374 
394  template<class Scalar>
395  static Scalar hgrjp (const int i, const Scalar z, const Scalar *zgrj,
396  const int np, const Scalar alpha, const Scalar beta);
397 
398 
418  template<class Scalar>
419  static Scalar hglj (const int i, const Scalar z, const Scalar *zglj,
420  const int np, const Scalar alpha, const Scalar beta);
421 
422 
423 
424  /* Interpolation operators */
425 
436  template<class Scalar>
437  static void Imgj (Scalar *im, const Scalar *zgj, const Scalar *zm, const int nz,
438  const int mz, const Scalar alpha, const Scalar beta);
439 
440 
451  template<class Scalar>
452  static void Imgrjm(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
453  const int mz, const Scalar alpha, const Scalar beta);
454 
455 
466  template<class Scalar>
467  static void Imgrjp(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz,
468  const int mz, const Scalar alpha, const Scalar beta);
469 
470 
481  template<class Scalar>
482  static void Imglj (Scalar *im, const Scalar *zglj, const Scalar *zm, const int nz,
483  const int mz, const Scalar alpha, const Scalar beta);
484 
485 
486  /* Polynomial functions */
487 
527  template<class Scalar>
528  static void jacobfd (const int np, const Scalar *z, Scalar *poly_in, Scalar *polyd,
529  const int n, const Scalar alpha, const Scalar beta);
530 
531 
545  template<class Scalar>
546  static void jacobd (const int np, const Scalar *z, Scalar *polyd, const int n,
547  const Scalar alpha, const Scalar beta);
548 
549 
550 
551  /* Helper functions. */
552 
559  template<class Scalar>
560  static void Jacobz (const int n, Scalar *z, const Scalar alpha, const Scalar beta);
561 
562 
585  template<class Scalar>
586  static void JacZeros (const int n, Scalar *a, const Scalar alpha, const Scalar beta);
587 
588 
612  template<class Scalar>
613  static void TriQL (const int n, Scalar *d, Scalar *e);
614 
615 
625  template<class Scalar>
626  static Scalar gammaF (const Scalar x);
627 
628 
629  }; // class IntrepidPolylib
630 
631 } // end of Intrepid namespace
632 
633 // include templated definitions
634 #include <Intrepid_PolylibDef.hpp>
635 
636 #endif
Intrepid::IntrepidPolylib::Dgrjp
static void Dgrjp(Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta)
Compute the Derivative Matrix associated with the Gauss-Radau-Jacobi zeros with a zero at z=1.
Definition: Intrepid_PolylibDef.hpp:287
Intrepid::IntrepidPolylib::zwgj
static void zwgj(Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta)
Gauss-Jacobi zeros and weights.
Definition: Intrepid_PolylibDef.hpp:117
Intrepid::IntrepidPolylib::hgrjm
static Scalar hgrjm(const int i, const Scalar z, const Scalar *zgrj, const int np, const Scalar alpha, const Scalar beta)
Compute the value of the i th Lagrangian interpolant through the np Gauss-Radau-Jacobi points zgrj at...
Definition: Intrepid_PolylibDef.hpp:390
Intrepid_Types.hpp
Contains definitions of custom data types in Intrepid.
Intrepid::EIntrepidPLPoly
EIntrepidPLPoly
Enumeration of coordinate frames (reference/ambient) for geometrical entities (cells,...
Definition: Intrepid_Polylib.hpp:197
Intrepid::IntrepidPolylib::Imgrjm
static void Imgrjm(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz, const int mz, const Scalar alpha, const Scalar beta)
Interpolation Operator from Gauss-Radau-Jacobi points (including z=-1) to an arbitrary distrubtion at...
Definition: Intrepid_PolylibDef.hpp:484
Intrepid::IntrepidPolylib::zwgrjm
static void zwgrjm(Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta)
Gauss-Radau-Jacobi zeros and weights with end point at z=-1.
Definition: Intrepid_PolylibDef.hpp:134
Intrepid::IntrepidPolylib::Imgj
static void Imgj(Scalar *im, const Scalar *zgj, const Scalar *zm, const int nz, const int mz, const Scalar alpha, const Scalar beta)
Interpolation Operator from Gauss-Jacobi points to an arbitrary distribution at points zm.
Definition: Intrepid_PolylibDef.hpp:456
Intrepid::IntrepidPolylib::jacobd
static void jacobd(const int np, const Scalar *z, Scalar *polyd, const int n, const Scalar alpha, const Scalar beta)
Calculate the derivative of Jacobi polynomials.
Definition: Intrepid_PolylibDef.hpp:661
Intrepid::IntrepidPolylib
Providing orthogonal polynomial calculus and interpolation, created by Spencer Sherwin,...
Definition: Intrepid_Polylib.hpp:223
Intrepid::IntrepidPolylib::Dglj
static void Dglj(Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta)
Compute the Derivative Matrix associated with the Gauss-Lobatto-Jacobi zeros.
Definition: Intrepid_PolylibDef.hpp:328
Intrepid::IntrepidPolylib::Imglj
static void Imglj(Scalar *im, const Scalar *zglj, const Scalar *zm, const int nz, const int mz, const Scalar alpha, const Scalar beta)
Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points zm.
Definition: Intrepid_PolylibDef.hpp:540
Intrepid::IntrepidPolylib::Imgrjp
static void Imgrjp(Scalar *im, const Scalar *zgrj, const Scalar *zm, const int nz, const int mz, const Scalar alpha, const Scalar beta)
Interpolation Operator from Gauss-Radau-Jacobi points (including z=1) to an arbitrary distrubtion at ...
Definition: Intrepid_PolylibDef.hpp:512
Intrepid::IntrepidPolylib::hgj
static Scalar hgj(const int i, const Scalar z, const Scalar *zgj, const int np, const Scalar alpha, const Scalar beta)
Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi points zgj at the ar...
Definition: Intrepid_PolylibDef.hpp:371
Intrepid::IntrepidPolylib::zwgrjp
static void zwgrjp(Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta)
Gauss-Radau-Jacobi zeros and weights with end point at z=1.
Definition: Intrepid_PolylibDef.hpp:160
Intrepid::IntrepidPolylib::Jacobz
static void Jacobz(const int n, Scalar *z, const Scalar alpha, const Scalar beta)
Calculate the n zeros, z, of the Jacobi polynomial, i.e. .
Definition: Intrepid_PolylibDef.hpp:678
Intrepid::IntrepidPolylib::hgrjp
static Scalar hgrjp(const int i, const Scalar z, const Scalar *zgrj, const int np, const Scalar alpha, const Scalar beta)
Compute the value of the i th Lagrangian interpolant through the np Gauss-Radau-Jacobi points zgrj at...
Definition: Intrepid_PolylibDef.hpp:412
Intrepid::IntrepidPolylib::Dgj
static void Dgj(Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta)
Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.
Definition: Intrepid_PolylibDef.hpp:214
Intrepid::IntrepidPolylib::TriQL
static void TriQL(const int n, Scalar *d, Scalar *e)
QL algorithm for symmetric tridiagonal matrix.
Definition: Intrepid_PolylibDef.hpp:748
Intrepid::IntrepidPolylib::JacZeros
static void JacZeros(const int n, Scalar *a, const Scalar alpha, const Scalar beta)
Zero determination through the eigenvalues of a tridiagonal matrix from the three term recursion rela...
Definition: Intrepid_PolylibDef.hpp:709
Intrepid::IntrepidPolylib::hglj
static Scalar hglj(const int i, const Scalar z, const Scalar *zglj, const int np, const Scalar alpha, const Scalar beta)
Compute the value of the i th Lagrangian interpolant through the np Gauss-Lobatto-Jacobi points zglj ...
Definition: Intrepid_PolylibDef.hpp:434
Intrepid::IntrepidPolylib::gammaF
static Scalar gammaF(const Scalar x)
Calculate the Gamma function , , for integer values x and halves.
Definition: Intrepid_PolylibDef.hpp:814
Intrepid::IntrepidPolylib::Dgrjm
static void Dgrjm(Scalar *D, const Scalar *z, const int np, const Scalar alpha, const Scalar beta)
Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a z...
Definition: Intrepid_PolylibDef.hpp:247
Intrepid::IntrepidPolylib::zwglj
static void zwglj(Scalar *z, Scalar *w, const int np, const Scalar alpha, const Scalar beta)
Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1.
Definition: Intrepid_PolylibDef.hpp:186
Intrepid_PolylibDef.hpp
Definition file for a set of functions providing orthogonal polynomial polynomial calculus and interp...
Intrepid::IntrepidPolylib::jacobfd
static void jacobfd(const int np, const Scalar *z, Scalar *poly_in, Scalar *polyd, const int n, const Scalar alpha, const Scalar beta)
Routine to calculate Jacobi polynomials, , and their first derivative, .
Definition: Intrepid_PolylibDef.hpp:570
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