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| void | Polylib::zwgj (double *z, double *w, const int np, const double alpha, const double beta) |
| | Gauss-Jacobi zeros and weights. More...
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| 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...
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| 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...
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| 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...
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| void | Polylib::zwgk (double *z, double *w, const int npt, const double alpha, const double beta) |
| | Gauss-Kronrod-Jacobi zeros and weights. More...
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| void | Polylib::zwrk (double *z, double *w, const int npt, const double alpha, const double beta) |
| | Gauss-Radau-Kronrod-Jacobi zeros and weights. More...
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| void | Polylib::zwlk (double *z, double *w, const int npt, const double alpha, const double beta) |
| | Gauss-Lobatto-Kronrod-Jacobi zeros and weights. More...
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| 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...
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| void | Polylib::Qg (double *Q, const double *z, const int np) |
| | Compute the Integration Matrix. More...
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| 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...
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| 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...
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| 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...
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| 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...
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| double | Polylib::laginterp (double z, int j, const double *zj, int np) |
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| double | Polylib::laginterpderiv (double z, int k, const double *zj, int np) |
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| 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...
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| 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...
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| 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...
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| 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...
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| 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...
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| 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...
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| 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...
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| 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...
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| void | Polylib::polycoeffs (double *c, const double *z, const int i, const int np) |
| | Compute the coefficients of Lagrange interpolation polynomials. More...
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| 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...
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| 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...
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| double | Polylib::gammaF (const double x) |
| | Calculate the Gamma function , \( \Gamma(n)\), for integer values and halves. More...
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| 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...
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| 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...
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