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Nektar++
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#include "Polylib.h"#include <cfloat>#include <cmath>#include <complex>#include <cstdio>#include <LibUtilities/BasicConst/NektarUnivTypeDefs.hpp>Go to the source code of this file.
Namespaces | |
| namespace | Polylib |
| The namespace associated with the the Polylib library (Polylib introduction) | |
Macros | |
| #define | STOP 30 |
| Maximum number of iterations in polynomial defalation routine Jacobz. More... | |
| #define | EPS 100 * DBL_EPSILON |
| Precision tolerance for two points to be similar. More... | |
| #define | sign(a, b) ((b) < 0 ? -fabs(a) : fabs(a)) |
| return the sign(b)*a More... | |
| #define | POLYNOMIAL_DEFLATION 0 |
| Define whether to use polynomial deflation (1) or tridiagonal solver (0). More... | |
| #define | jacobz(n, z, alpha, beta) Jacobz(n, z, alpha, beta) |
| zero determination using Newton iteration with polynomial deflation More... | |
Functions | |
| double | Polylib::optdiff (double xl, double xr) |
| The following function is used to circumvent/reduce "Subtractive
Cancellation" The expression 1/dz is replaced by optinvsub(.,.) Added on 26 April 2017. More... | |
| double | Polylib::laginterp (double z, int j, const double *zj, int np) |
| double | Polylib::laginterpderiv (double z, int k, const double *zj, int np) |
| static void | Polylib::Jacobz (const int n, double *z, const double alpha, const double beta) |
| Calculate the n zeros, z, of the Jacobi polynomial, i.e. \( P_n^{\alpha,\beta}(z) = 0 \). More... | |
| static void | Polylib::RecCoeff (const int n, double *a, double *b, const double alpha, const double beta) |
| The routine finds the recurrence coefficients a and b of the orthogonal polynomials. More... | |
| static void | Polylib::TriQL (const int n, double *d, double *e, double **z) |
| QL algorithm for symmetric tridiagonal matrix. More... | |
| void | Polylib::JKMatrix (int n, double *a, double *b) |
| Calcualtes the Jacobi-kronrod matrix by determining the a and coefficients. More... | |
| void | Polylib::chri1 (int n, double *a, double *b, double *a0, double *b0, double z) |
| Given a weight function \(w(t)\) through the first n+1 coefficients a and b of its orthogonal polynomials this routine generates the first n recurrence coefficients for the orthogonal polynomials relative to the modified weight function \((t-z)w(t)\). More... | |
| void | Polylib::zwgj (double *z, double *w, const int np, const double alpha, const double beta) |
| Gauss-Jacobi zeros and weights. More... | |
| void | Polylib::zwgrjm (double *z, double *w, const int np, const double alpha, const double beta) |
| Gauss-Radau-Jacobi zeros and weights with end point at z=-1. More... | |
| void | Polylib::zwgrjp (double *z, double *w, const int np, const double alpha, const double beta) |
| Gauss-Radau-Jacobi zeros and weights with end point at z=1. More... | |
| void | Polylib::zwglj (double *z, double *w, const int np, const double alpha, const double beta) |
| Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1. More... | |
| void | Polylib::zwgk (double *z, double *w, const int npt, const double alpha, const double beta) |
| Gauss-Kronrod-Jacobi zeros and weights. More... | |
| void | Polylib::zwrk (double *z, double *w, const int npt, const double alpha, const double beta) |
| Gauss-Radau-Kronrod-Jacobi zeros and weights. More... | |
| void | Polylib::zwlk (double *z, double *w, const int npt, const double alpha, const double beta) |
| Gauss-Lobatto-Kronrod-Jacobi zeros and weights. More... | |
| void | Polylib::Qg (double *Q, const double *z, const int np) |
| Compute the Integration Matrix. More... | |
| void | Polylib::Dgj (double *D, const double *z, const int np, const double alpha, const double beta) |
| Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros. More... | |
| void | Polylib::Dgrjm (double *D, const double *z, const int np, const double alpha, const double beta) |
| Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=-1. More... | |
| void | Polylib::Dgrjp (double *D, const double *z, const int np, const double alpha, const double beta) |
| Compute the Derivative Matrix associated with the Gauss-Radau-Jacobi zeros with a zero at z=1. More... | |
| void | Polylib::Dglj (double *D, const double *z, const int np, const double alpha, const double beta) |
| Compute the Derivative Matrix associated with the Gauss-Lobatto-Jacobi zeros. More... | |
| double | Polylib::hgj (const int i, const double z, const double *zgj, const int np, const double alpha, const double beta) |
| Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi points zgj at the arbitrary location z. More... | |
| double | Polylib::hgrjm (const int i, const double z, const double *zgrj, const int np, const double alpha, const double beta) |
| Compute the value of the i th Lagrangian interpolant through the np Gauss-Radau-Jacobi points zgrj at the arbitrary location z. This routine assumes zgrj includes the point -1. More... | |
| double | Polylib::hgrjp (const int i, const double z, const double *zgrj, const int np, const double alpha, const double beta) |
| Compute the value of the i th Lagrangian interpolant through the np Gauss-Radau-Jacobi points zgrj at the arbitrary location z. This routine assumes zgrj includes the point +1. More... | |
| double | Polylib::hglj (const int i, const double z, const double *zglj, const int np, const double alpha, const double beta) |
| Compute the value of the i th Lagrangian interpolant through the np Gauss-Lobatto-Jacobi points zgrj at the arbitrary location z. More... | |
| void | Polylib::Imgj (double *im, const double *zgj, const double *zm, const int nz, const int mz, const double alpha, const double beta) |
| Interpolation Operator from Gauss-Jacobi points to an arbitrary distribution at points zm. More... | |
| void | Polylib::Imgrjm (double *im, const double *zgrj, const double *zm, const int nz, const int mz, const double alpha, const double beta) |
| Interpolation Operator from Gauss-Radau-Jacobi points (including z=-1) to an arbitrary distrubtion at points zm. More... | |
| void | Polylib::Imgrjp (double *im, const double *zgrj, const double *zm, const int nz, const int mz, const double alpha, const double beta) |
| Interpolation Operator from Gauss-Radau-Jacobi points (including z=1) to an arbitrary distrubtion at points zm. More... | |
| void | Polylib::Imglj (double *im, const double *zglj, const double *zm, const int nz, const int mz, const double alpha, const double beta) |
| Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points zm. More... | |
| void | Polylib::polycoeffs (double *c, const double *z, const int i, const int np) |
| Compute the coefficients of Lagrange interpolation polynomials. More... | |
| void | Polylib::jacobfd (const int np, const double *z, double *poly_in, double *polyd, const int n, const double alpha, const double beta) |
| Routine to calculate Jacobi polynomials, \(
P^{\alpha,\beta}_n(z) \), and their first derivative, \(
\frac{d}{dz} P^{\alpha,\beta}_n(z) \). More... | |
| void | Polylib::jacobd (const int np, const double *z, double *polyd, const int n, const double alpha, const double beta) |
| Calculate the derivative of Jacobi polynomials. More... | |
| double | Polylib::gammaF (const double x) |
| Calculate the Gamma function , \( \Gamma(n)\), for integer values and halves. More... | |
| double | Polylib::gammaFracGammaF (const int x, const double alpha, const int y, const double beta) |
| Calculate fraction of two Gamma functions, \(
\Gamma(x+\alpha)/\Gamma(y+\beta) \), for integer values and halves. More... | |
| std::complex< Nektar::NekDouble > | Polylib::ImagBesselComp (int n, std::complex< Nektar::NekDouble > y) |
| Calcualte the bessel function of the first kind with complex double input y. Taken from Numerical Recipies in C. More... | |
| void | Polylib::JacZeros (const int n, double *a, double *b, const double alpha, const double beta) |
| Zero and Weight determination through the eigenvalues and eigenvectors of a tridiagonal matrix from the three term recurrence relationship. More... | |
| #define EPS 100 * DBL_EPSILON |
Precision tolerance for two points to be similar.
Definition at line 45 of file Polylib.cpp.
| #define jacobz | ( | n, | |
| z, | |||
| alpha, | |||
| beta | |||
| ) | Jacobz(n, z, alpha, beta) |
zero determination using Newton iteration with polynomial deflation
Definition at line 128 of file Polylib.cpp.
| #define POLYNOMIAL_DEFLATION 0 |
Define whether to use polynomial deflation (1) or tridiagonal solver (0).
Definition at line 124 of file Polylib.cpp.
| #define sign | ( | a, | |
| b | |||
| ) | ((b) < 0 ? -fabs(a) : fabs(a)) |
return the sign(b)*a
Definition at line 47 of file Polylib.cpp.
| #define STOP 30 |
Maximum number of iterations in polynomial defalation routine Jacobz.
Definition at line 43 of file Polylib.cpp.
1.9.4