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polylib.h File Reference

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Defines

#define zwgl(z, w, np)   zwgj (z,w,np,0.0,0.0);

#define zwgrlm(z, w, np)   zwgrjm(z,w,np,0.0,0.0);

#define zwgrlp(z, w, np)   zwgrjp(z,w,np,0.0,0.0);

#define zwgll(z, w, np)   zwglj (z,w,np,0.0,0.0);

#define zwgc(z, w, np)   zwgj (z,w,np,-0.5,-0.5);

#define zwgrcm(z, w, np)   zwgrjm(z,w,np,-0.5,-0.5);

#define zwgrcp(z, w, np)   zwgrjp(z,w,np,-0.5,-0.5);

#define zwglc(z, w, np)   zwglj (z,w,np,-0.5,-0.5);

#define Dgl(d, dt, z, np)   Dgj (*d,*dt,z,np,0.0,0.0);

#define Dgrlm(d, dt, z, np)   Dgrjm(*d,*dt,z,np,0.0,0.0);

#define Dgrlp(d, dt, z, np)   Dgrjp(*d,*dt,z,np,0.0,0.0);

#define Dgll(d, dt, z, np)   Dglj (*d,*dt,z,np,0.0,0.0);

#define Dgc(d, dt, z, np)   Dgj (*d,*dt,z,np,-0.5,-0.5);

#define Dgrcm(d, dt, z, np)   Dgrjm(*d,*dt,z,np,-0.5,-0.5);

#define Dgrcp(d, dt, z, np)   Dgrjp(*d,*dt,z,np,-0.5,-0.5);

#define Dglc(d, dt, z, np)   Dglj (*d,*dt,z,np,-0.5,-0.5);

#define hgl(i, z, zgj,np)   hgj ( i,z,zgj ,np,0.0,0.0);

#define hgrlm(i, z, zgrj, np)   hgrjm(i,z,zgrj,np,0.0,0.0);

#define hgrlp(i, z, zgrj, np)   hgrjp(i,z,zgrj,np,0.0,0.0);

#define hgll(i, z, zglj, np)   hglj (i,z,zglj,np,0.0,0.0);

#define hgc(i, z, zgj,np)   hgj( i,z,zgj ,np,-0.5,-0.5);

#define hgrc(i, z, zgrj, np)   hgrjm(i,z,zgrj,np,-0.5,-0.5);

#define hglc(i, z, zglj, np)   hglj( i,z,zglj,np,-0.5,-0.5);

#define Imgl(im, zgl,zm, nz, mz)   Imgj (im,zgl ,zm,nz,mz,0.0,0.0)

#define Imgrlm(im, zgrl, zm, nz, mz)   Imgrjm(im,zgrl,zm,nz,mz,0.0,0.0)

#define Imgrlp(im, zgrl, zm, nz, mz)   Imgrjp(im,zgrl,zm,nz,mz,0.0,0.0)

#define Imgll(im, zgll, zm, nz, mz)   Imglj (im,zgll,zm,nz,mz,0.0,0.0)

#define Imgc(im, zgl,zm, nz, mz)   Imgj (im,zgl ,zm,nz,mz,-0.5,-0.5)

#define Imgrcm(im, zgrl, zm, nz, mz)   Imgrjm(im,zgrl,zm,nz,mz,-0.5,-0.5)

#define Imgrcp(im, zgrl, zm, nz, mz)   Imgrjp(im,zgrl,zm,nz,mz,-0.5,-0.5)

#define Imglc(im, zgll, zm, nz, mz)   Imglj (im,zgll,zm,nz,mz,-0.5,-0.5)

#define zwgrj(z, w, np, alpha, beta)   zwgrjm (z,w,np,alpha,beta)

#define zwgrl(z, w, np)   zwgrjm (z,w,np,0.0,0.0);

#define hgrj(i, z, zgrj, np, alpha, beta)   hgrjm (i,z,zgrj,np,alpha,beta)

#define hgrl(i, z, zgrj, np)   hgrjm(i,z,zgrj,np,0.0,0.0);

#define jacobf(np, z, p,n, alpha, beta)   jacobfd(np,z,p,NULL ,n,alpha,beta)

#define igjm(im, zgl, zm, nz, mz, alpha, beta)   Imgj (*im,zgl ,zm,nz,mz,alpha,beta)

#define igrjm(im, zgrl, zm, nz, mz, alpha, beta)   Imgrjm(*im,zgrl,zm,nz,mz,alpha,beta)

#define igljm(im, zgll, zm, nz, mz, alpha, beta)   Imglj (*im,zgll,zm,nz,mz,alpha,beta)

#define iglm(im, zgl,zm, nz, mz)   Imgj (*im,zgl ,zm,nz,mz,0.0,0.0)

#define igrlm(im, zgrl, zm, nz, mz)   Imgrjm(*im,zgrl,zm,nz,mz,0.0,0.0)

#define igllm(im, zgll, zm, nz, mz)   Imglj (*im,zgll,zm,nz,mz,0.0,0.0)

#define dgj(d, dt, z, np, alpha, beta)   Dgj (*d,*dt,z,np,alpha,beta)

#define dgrj(d, dt, z, np, alpha, beta)   Dgrjm(*d,*dt,z,np,alpha,beta)

#define dglj(d, dt, z, np, alpha, beta)   Dglj (*d,*dt,z,np,alpha,beta)

#define dgll(d, dt, z, np)   Dglj (*d,*dt,z,np,0.0,0.0);

#define dgrl(d, dt, z, np)   Dgrjm(*d,*dt,z,np,0.0,0.0);

Functions

void zwgj (double *, double *, int, double, double)

Gauss-Jacobi zeros and weights.

void zwgrjm (double *, double *, int, double, double)

Gauss-Radau-Jacobi zeros and weights with end point at z=-1.

void zwgrjp (double *, double *, int, double, double)

Gauss-Radau-Jacobi zeros and weights with end point at z=1.

void zwglj (double *, double *, int, double, double)

Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1.

void Dgj (double *, double *, double *, int, double, double)

Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.

void Dgrjm (double *, double *, double *, int, double, double)

Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=-1.

void Dgrjp (double *, double *, double *, int, double, double)

Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=1.

void Dglj (double *, double *, double *, int, double, double)

Compute the Derivative Matrix and its transpose associated with the Gauss-Lobatto-Jacobi zeros.

double hgj (int, double, double *, int, double, double)

Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi points zgj at the arbitrary location z.

double hgrjm (int, double, double *, int, double, double)

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.

double hgrjp (int, double, double *, int, double, double)

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.

double hglj (int, double, double *, int, double, double)

Compute the value of the i th Lagrangian interpolant through the np Gauss-Lobatto-Jacobi points zgrj at the arbitrary location z.

void Imgj (double *, double *, double *, int, int, double, double)

Interpolation Operator from Gauss-Jacobi points to an arbitrary distrubtion at points zm.

void Imgrjm (double *, double *, double *, int, int, double, double)

Interpolation Operator from Gauss-Radau-Jacobi points (including z=-1) to an arbitrary distrubtion at points zm.

void Imgrjp (double *, double *, double *, int, int, double, double)

Interpolation Operator from Gauss-Radau-Jacobi points (including z=1) to an arbitrary distrubtion at points zm.

void Imglj (double *, double *, double *, int, int, double, double)

Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points zm.

void jacobfd (int, double *, double *, double *, int, double, double)

Routine to calculate Jacobi polynomials, , and their first derivative, .

void jacobd (int, double *, double *, int, double, double)

Calculate the derivative of Jacobi polynomials.

Define Documentation

#define Dgc ( d,
dt,
z,
np ) Dgj (*d,*dt,z,np,-0.5,-0.5);

Definition at line 71 of file polylib.h.

#define dgj ( d,
dt,
z,
np,
alpha,
beta ) Dgj (*d,*dt,z,np,alpha,beta)

Definition at line 116 of file polylib.h.

#define Dgl ( d,
dt,
z,
np ) Dgj (*d,*dt,z,np,0.0,0.0);

Definition at line 66 of file polylib.h.

#define Dglc ( d,
dt,
z,
np ) Dglj (*d,*dt,z,np,-0.5,-0.5);

Definition at line 74 of file polylib.h.

#define dglj ( d,
dt,
z,
np,
alpha,
beta ) Dglj (*d,*dt,z,np,alpha,beta)

Definition at line 118 of file polylib.h.

#define dgll ( d,
dt,
z,
np ) Dglj (*d,*dt,z,np,0.0,0.0);

Definition at line 120 of file polylib.h.

#define Dgll ( d,
dt,
z,
np ) Dglj (*d,*dt,z,np,0.0,0.0);

Definition at line 69 of file polylib.h.

#define Dgrcm ( d,
dt,
z,
np ) Dgrjm(*d,*dt,z,np,-0.5,-0.5);

Definition at line 72 of file polylib.h.

#define Dgrcp ( d,
dt,
z,
np ) Dgrjp(*d,*dt,z,np,-0.5,-0.5);

Definition at line 73 of file polylib.h.

#define dgrj ( d,
dt,
z,
np,
alpha,
beta ) Dgrjm(*d,*dt,z,np,alpha,beta)

Definition at line 117 of file polylib.h.

#define dgrl ( d,
dt,
z,
np ) Dgrjm(*d,*dt,z,np,0.0,0.0);

Definition at line 121 of file polylib.h.

#define Dgrlm ( d,
dt,
z,
np ) Dgrjm(*d,*dt,z,np,0.0,0.0);

Definition at line 67 of file polylib.h.

#define Dgrlp ( d,
dt,
z,
np ) Dgrjp(*d,*dt,z,np,0.0,0.0);

Definition at line 68 of file polylib.h.

#define hgc ( i,
z,
zgj,
np ) hgj( i,z,zgj ,np,-0.5,-0.5);

Definition at line 83 of file polylib.h.

#define hgl ( i,
z,
zgj,
np ) hgj ( i,z,zgj ,np,0.0,0.0);

Definition at line 78 of file polylib.h.

#define hglc ( i,
z,
zglj,
np ) hglj( i,z,zglj,np,-0.5,-0.5);

Definition at line 85 of file polylib.h.

#define hgll ( i,
z,
zglj,
np ) hglj (i,z,zglj,np,0.0,0.0);

Definition at line 81 of file polylib.h.

#define hgrc ( i,
z,
zgrj,
np ) hgrjm(i,z,zgrj,np,-0.5,-0.5);

Definition at line 84 of file polylib.h.

#define hgrj ( i,
z,
zgrj,
np,
alpha,
beta ) hgrjm (i,z,zgrj,np,alpha,beta)

Definition at line 103 of file polylib.h.

#define hgrl ( i,
z,
zgrj,
np ) hgrjm(i,z,zgrj,np,0.0,0.0);

Definition at line 104 of file polylib.h.

#define hgrlm ( i,
z,
zgrj,
np ) hgrjm(i,z,zgrj,np,0.0,0.0);

Definition at line 79 of file polylib.h.

#define hgrlp ( i,
z,
zgrj,
np ) hgrjp(i,z,zgrj,np,0.0,0.0);

Definition at line 80 of file polylib.h.

#define igjm ( im,
zgl,
zm,
nz,
mz,
alpha,
beta ) Imgj (*im,zgl ,zm,nz,mz,alpha,beta)

Definition at line 108 of file polylib.h.

#define igljm ( im,
zgll,
zm,
nz,
mz,
alpha,
beta ) Imglj (*im,zgll,zm,nz,mz,alpha,beta)

Definition at line 110 of file polylib.h.

#define igllm ( im,
zgll,
zm,
nz,
mz ) Imglj (*im,zgll,zm,nz,mz,0.0,0.0)

Definition at line 114 of file polylib.h.

#define iglm ( im,
zgl,
zm,
nz,
mz ) Imgj (*im,zgl ,zm,nz,mz,0.0,0.0)

Definition at line 112 of file polylib.h.

#define igrjm ( im,
zgrl,
zm,
nz,
mz,
alpha,
beta ) Imgrjm(*im,zgrl,zm,nz,mz,alpha,beta)

Definition at line 109 of file polylib.h.

#define igrlm ( im,
zgrl,
zm,
nz,
mz ) Imgrjm(*im,zgrl,zm,nz,mz,0.0,0.0)

Definition at line 113 of file polylib.h.

#define Imgc ( im,
zgl,
zm,
nz,
mz ) Imgj (im,zgl ,zm,nz,mz,-0.5,-0.5)

Definition at line 94 of file polylib.h.

#define Imgl ( im,
zgl,
zm,
nz,
mz ) Imgj (im,zgl ,zm,nz,mz,0.0,0.0)

Definition at line 89 of file polylib.h.

#define Imglc ( im,
zgll,
zm,
nz,
mz ) Imglj (im,zgll,zm,nz,mz,-0.5,-0.5)

Definition at line 97 of file polylib.h.

#define Imgll ( im,
zgll,
zm,
nz,
mz ) Imglj (im,zgll,zm,nz,mz,0.0,0.0)

Definition at line 92 of file polylib.h.

#define Imgrcm ( im,
zgrl,
zm,
nz,
mz ) Imgrjm(im,zgrl,zm,nz,mz,-0.5,-0.5)

Definition at line 95 of file polylib.h.

#define Imgrcp ( im,
zgrl,
zm,
nz,
mz ) Imgrjp(im,zgrl,zm,nz,mz,-0.5,-0.5)

Definition at line 96 of file polylib.h.

#define Imgrlm ( im,
zgrl,
zm,
nz,
mz ) Imgrjm(im,zgrl,zm,nz,mz,0.0,0.0)

Definition at line 90 of file polylib.h.

#define Imgrlp ( im,
zgrl,
zm,
nz,
mz ) Imgrjp(im,zgrl,zm,nz,mz,0.0,0.0)

Definition at line 91 of file polylib.h.

#define jacobf ( np,
z,
p,
n,
alpha,
beta ) jacobfd(np,z,p,NULL ,n,alpha,beta)

Definition at line 106 of file polylib.h.

#define zwgc ( z,
w,
np ) zwgj (z,w,np,-0.5,-0.5);

Definition at line 59 of file polylib.h.

#define zwgl ( z,
w,
np ) zwgj (z,w,np,0.0,0.0);

Definition at line 54 of file polylib.h.

#define zwglc ( z,
w,
np ) zwglj (z,w,np,-0.5,-0.5);

Definition at line 62 of file polylib.h.

#define zwgll ( z,
w,
np ) zwglj (z,w,np,0.0,0.0);

Definition at line 57 of file polylib.h.

#define zwgrcm ( z,
w,
np ) zwgrjm(z,w,np,-0.5,-0.5);

Definition at line 60 of file polylib.h.

#define zwgrcp ( z,
w,
np ) zwgrjp(z,w,np,-0.5,-0.5);

Definition at line 61 of file polylib.h.

#define zwgrj ( z,
w,
np,
alpha,
beta ) zwgrjm (z,w,np,alpha,beta)

Definition at line 101 of file polylib.h.

#define zwgrl ( z,
w,
np ) zwgrjm (z,w,np,0.0,0.0);

Definition at line 102 of file polylib.h.

#define zwgrlm ( z,
w,
np ) zwgrjm(z,w,np,0.0,0.0);

Definition at line 55 of file polylib.h.

#define zwgrlp ( z,
w,
np ) zwgrjp(z,w,np,0.0,0.0);

Definition at line 56 of file polylib.h.

Function Documentation

void Dgj ( double * D,

double * Dt,

double * z,

int np,

double alpha,

double beta

)

Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.

Compute the derivative matrix, d, and its transpose, dt, associated with the n_th order Lagrangian interpolants through the np Gauss-Jacobi points z such that

d and dt are both square matrices.

Definition at line 321 of file polylib.c.
References jacobd().

void Dglj ( double * D,

double * Dt,

double * z,

int np,

double alpha,

double beta

)

Compute the Derivative Matrix and its transpose associated with the Gauss-Lobatto-Jacobi zeros.

Compute the derivative matrix, d, and its transpose, dt, associated with the n_th order Lagrangian interpolants through the np Gauss-Lobatto-Jacobi points z such that

d and dt are both square matrices.

Definition at line 469 of file polylib.c.
References gammaF(), and jacobd().

void Dgrjm ( double * D,

double * Dt,

double * z,

int np,

double alpha,

double beta

)

Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=-1.

Compute the derivative matrix, d, and its transpose, dt, associated with the n_th order Lagrangian interpolants through the np Gauss-Radau-Jacobi points z such that

d and dt are both square matrices.

Definition at line 365 of file polylib.c.
References gammaF(), and jacobd().

void Dgrjp ( double * D,

double * Dt,

double * z,

int np,

double alpha,

double beta

)

Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=1.

Compute the derivative matrix, d, and its transpose, dt, associated with the n_th order Lagrangian interpolants through the np Gauss-Radau-Jacobi points z such that

d and dt are both square matrices.

Definition at line 417 of file polylib.c.
References gammaF(), and jacobd().

double hgj ( int i,

double z,

double * zgj,

int np,

double alpha,

double beta

)

Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi points zgj at the arbitrary location z.

Uses the defintion of the Lagrangian interpolant:

Definition at line 532 of file polylib.c.
References EPS, jacobd(), and jacobfd().
Referenced by Imgj().

double hglj ( int i,

double z,

double * zglj,

int np,

double alpha,

double beta

)

Compute the value of the i th Lagrangian interpolant through the np Gauss-Lobatto-Jacobi points zgrj at the arbitrary location z.

Uses the defintion of the Lagrangian interpolant:

Definition at line 651 of file polylib.c.
References EPS, jacobd(), and jacobfd().
Referenced by Imglj().

double hgrjm ( int i,

double z,

double * zgrj,

int np,

double alpha,

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.

Uses the defintion of the Lagrangian interpolant:

Definition at line 569 of file polylib.c.
References EPS, jacobd(), and jacobfd().
Referenced by Imgrjm().

double hgrjp ( int i,

double z,

double * zgrj,

int np,

double alpha,

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.

Uses the defintion of the Lagrangian interpolant:

Definition at line 610 of file polylib.c.
References EPS, jacobd(), and jacobfd().
Referenced by Imgrjp().

void Imgj ( double * im,

double * zgj,

double * zm,

int nz,

int mz,

double alpha,

double beta

)

Interpolation Operator from Gauss-Jacobi points to an arbitrary distrubtion at points zm.

Computes the one-dimensional interpolation matrix, im, to interpolate a function from at Gauss-Jacobi distribution of nz zeros zgrj to an arbitrary distribution of mz points zm, i.e.

Definition at line 684 of file polylib.c.
References hgj().

void Imglj ( double * im,

double * zglj,

double * zm,

int nz,

int mz,

double alpha,

double beta

)

Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points zm.

Computes the one-dimensional interpolation matrix, im, to interpolate a function from at Gauss-Lobatto-Jacobi distribution of nz zeros zgrj (where zgrj[0]=-1) to an arbitrary distribution of mz points zm, i.e.

Definition at line 766 of file polylib.c.
References hglj().

void Imgrjm ( double * im,

double * zgrj,

double * zm,

int nz,

int mz,

double alpha,

double beta

)

Interpolation Operator from Gauss-Radau-Jacobi points (including z=-1) to an arbitrary distrubtion at points zm.

Computes the one-dimensional interpolation matrix, im, to interpolate a function from at Gauss-Radau-Jacobi distribution of nz zeros zgrj (where zgrj[0]=-1) to an arbitrary distribution of mz points zm, i.e.

Definition at line 711 of file polylib.c.
References hgrjm().

void Imgrjp ( double * im,

double * zgrj,

double * zm,

int nz,

int mz,

double alpha,

double beta

)

Interpolation Operator from Gauss-Radau-Jacobi points (including z=1) to an arbitrary distrubtion at points zm.

Computes the one-dimensional interpolation matrix, im, to interpolate a function from at Gauss-Radau-Jacobi distribution of nz zeros zgrj (where zgrj[nz-1]=1) to an arbitrary distribution of mz points zm, i.e.

Definition at line 738 of file polylib.c.
References hgrjp().

void jacobd ( int np,

double * z,

double * polyd,

int n,

double alpha,

double beta

)

Calculate the derivative of Jacobi polynomials.

Generates a vector poly of values of the derivative of the n th order Jacobi polynomial at the np points z.

To do this we have used the relation

This formulation is valid for

Definition at line 921 of file polylib.c.
References jacobfd().
Referenced by Dgj(), Dglj(), Dgrjm(), Dgrjp(), hgj(), hglj(), hgrjm(), hgrjp(), and zwgj().

void jacobfd ( int np,

double * z,

double * poly_in,

double * polyd,

int n,

double alpha,

double beta

)

Routine to calculate Jacobi polynomials, , and their first derivative, .

This function returns the vectors poly_in and poly_d containing the value of the order Jacobi polynomial and its derivative at the np points in z[i]

If poly_in = NULL then only calculate derivatice

If polyd = NULL then only calculate polynomial

To calculate the polynomial this routine uses the recursion relationship (see appendix A ref [4]) :

To calculate the derivative of the polynomial this routine uses the relationship (see appendix A ref [4]) :

Note the derivative from this routine is only valid for -1 < z < 1.

Definition at line 821 of file polylib.c.
Referenced by hgj(), hglj(), hgrjm(), hgrjp(), jacobd(), Jacobz(), zwglj(), zwgrjm(), and zwgrjp().

void zwgj ( double * z,

double * w,

int np,

double alpha,

double beta

)

Gauss-Jacobi zeros and weights.

Generate np Gauss Jacobi zeros, z, and weights,w, associated with the Jacobi polynomial ,

Exact for polynomials of order 2np-1 or less

Definition at line 186 of file polylib.c.
References gammaF(), jacobd(), and jacobz.

void zwglj ( double * z,

double * w,

int np,

double alpha,

double beta

)

Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1.

Generate np Gauss-Lobatto-Jacobi points, z, and weights, w, associated with polynomial

Exact for polynomials of order 2np-3 or less

Definition at line 282 of file polylib.c.
References gammaF(), jacobfd(), and jacobz.

void zwgrjm ( double * z,

double * w,

int np,

double alpha,

double beta

)

Gauss-Radau-Jacobi zeros and weights with end point at z=-1.

Generate np Gauss-Radau-Jacobi zeros, z, and weights,w, associated with the polynomial .

Exact for polynomials of order 2np-2 or less

Definition at line 212 of file polylib.c.
References gammaF(), jacobfd(), and jacobz.

void zwgrjp ( double * z,

double * w,

int np,

double alpha,

double beta

)

Gauss-Radau-Jacobi zeros and weights with end point at z=1.

Generate np Gauss-Radau-Jacobi zeros, z, and weights,w, associated with the polynomial .

Exact for polynomials of order 2np-2 or less

Definition at line 248 of file polylib.c.
References gammaF(), jacobfd(), and jacobz.

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1.3


Defines
#define	zwgl(z, w, np) zwgj (z,w,np,0.0,0.0);
#define	zwgrlm(z, w, np) zwgrjm(z,w,np,0.0,0.0);
#define	zwgrlp(z, w, np) zwgrjp(z,w,np,0.0,0.0);
#define	zwgll(z, w, np) zwglj (z,w,np,0.0,0.0);
#define	zwgc(z, w, np) zwgj (z,w,np,-0.5,-0.5);
#define	zwgrcm(z, w, np) zwgrjm(z,w,np,-0.5,-0.5);
#define	zwgrcp(z, w, np) zwgrjp(z,w,np,-0.5,-0.5);
#define	zwglc(z, w, np) zwglj (z,w,np,-0.5,-0.5);
#define	Dgl(d, dt, z, np) Dgj (d,dt,z,np,0.0,0.0);
#define	Dgrlm(d, dt, z, np) Dgrjm(d,dt,z,np,0.0,0.0);
#define	Dgrlp(d, dt, z, np) Dgrjp(d,dt,z,np,0.0,0.0);
#define	Dgll(d, dt, z, np) Dglj (d,dt,z,np,0.0,0.0);
#define	Dgc(d, dt, z, np) Dgj (d,dt,z,np,-0.5,-0.5);
#define	Dgrcm(d, dt, z, np) Dgrjm(d,dt,z,np,-0.5,-0.5);
#define	Dgrcp(d, dt, z, np) Dgrjp(d,dt,z,np,-0.5,-0.5);
#define	Dglc(d, dt, z, np) Dglj (d,dt,z,np,-0.5,-0.5);
#define	hgl(i, z, zgj,np) hgj ( i,z,zgj ,np,0.0,0.0);
#define	hgrlm(i, z, zgrj, np) hgrjm(i,z,zgrj,np,0.0,0.0);
#define	hgrlp(i, z, zgrj, np) hgrjp(i,z,zgrj,np,0.0,0.0);
#define	hgll(i, z, zglj, np) hglj (i,z,zglj,np,0.0,0.0);
#define	hgc(i, z, zgj,np) hgj( i,z,zgj ,np,-0.5,-0.5);
#define	hgrc(i, z, zgrj, np) hgrjm(i,z,zgrj,np,-0.5,-0.5);
#define	hglc(i, z, zglj, np) hglj( i,z,zglj,np,-0.5,-0.5);
#define	Imgl(im, zgl,zm, nz, mz) Imgj (im,zgl ,zm,nz,mz,0.0,0.0)
#define	Imgrlm(im, zgrl, zm, nz, mz) Imgrjm(im,zgrl,zm,nz,mz,0.0,0.0)
#define	Imgrlp(im, zgrl, zm, nz, mz) Imgrjp(im,zgrl,zm,nz,mz,0.0,0.0)
#define	Imgll(im, zgll, zm, nz, mz) Imglj (im,zgll,zm,nz,mz,0.0,0.0)
#define	Imgc(im, zgl,zm, nz, mz) Imgj (im,zgl ,zm,nz,mz,-0.5,-0.5)
#define	Imgrcm(im, zgrl, zm, nz, mz) Imgrjm(im,zgrl,zm,nz,mz,-0.5,-0.5)
#define	Imgrcp(im, zgrl, zm, nz, mz) Imgrjp(im,zgrl,zm,nz,mz,-0.5,-0.5)
#define	Imglc(im, zgll, zm, nz, mz) Imglj (im,zgll,zm,nz,mz,-0.5,-0.5)
#define	zwgrj(z, w, np, alpha, beta) zwgrjm (z,w,np,alpha,beta)
#define	zwgrl(z, w, np) zwgrjm (z,w,np,0.0,0.0);
#define	hgrj(i, z, zgrj, np, alpha, beta) hgrjm (i,z,zgrj,np,alpha,beta)
#define	hgrl(i, z, zgrj, np) hgrjm(i,z,zgrj,np,0.0,0.0);
#define	jacobf(np, z, p,n, alpha, beta) jacobfd(np,z,p,NULL ,n,alpha,beta)
#define	igjm(im, zgl, zm, nz, mz, alpha, beta) Imgj (*im,zgl ,zm,nz,mz,alpha,beta)
#define	igrjm(im, zgrl, zm, nz, mz, alpha, beta) Imgrjm(*im,zgrl,zm,nz,mz,alpha,beta)
#define	igljm(im, zgll, zm, nz, mz, alpha, beta) Imglj (*im,zgll,zm,nz,mz,alpha,beta)
#define	iglm(im, zgl,zm, nz, mz) Imgj (*im,zgl ,zm,nz,mz,0.0,0.0)
#define	igrlm(im, zgrl, zm, nz, mz) Imgrjm(*im,zgrl,zm,nz,mz,0.0,0.0)
#define	igllm(im, zgll, zm, nz, mz) Imglj (*im,zgll,zm,nz,mz,0.0,0.0)
#define	dgj(d, dt, z, np, alpha, beta) Dgj (d,dt,z,np,alpha,beta)
#define	dgrj(d, dt, z, np, alpha, beta) Dgrjm(d,dt,z,np,alpha,beta)
#define	dglj(d, dt, z, np, alpha, beta) Dglj (d,dt,z,np,alpha,beta)
#define	dgll(d, dt, z, np) Dglj (d,dt,z,np,0.0,0.0);
#define	dgrl(d, dt, z, np) Dgrjm(d,dt,z,np,0.0,0.0);
Functions
void	zwgj (double , double , int, double, double)
	Gauss-Jacobi zeros and weights.
void	zwgrjm (double , double , int, double, double)
	Gauss-Radau-Jacobi zeros and weights with end point at z=-1.
void	zwgrjp (double , double , int, double, double)
	Gauss-Radau-Jacobi zeros and weights with end point at z=1.
void	zwglj (double , double , int, double, double)
	Gauss-Lobatto-Jacobi zeros and weights with end point at z=-1,1.
void	Dgj (double , double , double *, int, double, double)
	Compute the Derivative Matrix and its transpose associated with the Gauss-Jacobi zeros.
void	Dgrjm (double , double , double *, int, double, double)
	Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=-1.
void	Dgrjp (double , double , double *, int, double, double)
	Compute the Derivative Matrix and its transpose associated with the Gauss-Radau-Jacobi zeros with a zero at z=1.
void	Dglj (double , double , double *, int, double, double)
	Compute the Derivative Matrix and its transpose associated with the Gauss-Lobatto-Jacobi zeros.
double	hgj (int, double, double *, int, double, double)
	Compute the value of the i th Lagrangian interpolant through the np Gauss-Jacobi points zgj* at the arbitrary location z.*
double	hgrjm (int, double, double *, int, double, double)
	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.*
double	hgrjp (int, double, double *, int, double, double)
	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.*
double	hglj (int, double, double *, int, double, double)
	Compute the value of the i th Lagrangian interpolant through the np Gauss-Lobatto-Jacobi points zgrj* at the arbitrary location z.*
void	Imgj (double , double , double *, int, int, double, double)
	Interpolation Operator from Gauss-Jacobi points to an arbitrary distrubtion at points zm.
void	Imgrjm (double , double , double *, int, int, double, double)
	Interpolation Operator from Gauss-Radau-Jacobi points (including z=-1) to an arbitrary distrubtion at points zm.
void	Imgrjp (double , double , double *, int, int, double, double)
	Interpolation Operator from Gauss-Radau-Jacobi points (including z=1) to an arbitrary distrubtion at points zm.
void	Imglj (double , double , double *, int, int, double, double)
	Interpolation Operator from Gauss-Lobatto-Jacobi points to an arbitrary distrubtion at points zm.
void	jacobfd (int, double , double , double *, int, double, double)
	Routine to calculate Jacobi polynomials, , and their first derivative, .
void	jacobd (int, double , double , int, double, double)
	Calculate the derivative of Jacobi polynomials.