nubspline_eval_std_z.h File Reference

#include <math.h>
#include <stdio.h>
#include "nubspline_structs.h"

Go to the source code of this file.

Macros
#define	C(i, j)   coefs[(ix+(i))*xs+iy+(j)]
#define	C(i, j)   coefs[(ix+(i))*xs+iy+(j)]
#define	C(i, j)   coefs[(ix+(i))*xs+iy+(j)]
#define	C(i, j)   coefs[(ix+(i))*xs+iy+(j)]
#define	P(i, j, k)   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
#define	P(i, j, k)   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
#define	P(i, j, k)   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
#define	P(i, j, k)   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]

Functions
void	eval_NUBspline_1d_z (NUBspline_1d_z *restrict spline, double x, complex_double *restrict val)
void	eval_NUBspline_1d_z_vg (NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad)
void	eval_NUBspline_1d_z_vgh (NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess)
void	eval_NUBspline_1d_z_vgl (NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl)
void	eval_NUBspline_2d_z (NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val)
void	eval_NUBspline_2d_z_vg (NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad)
void	eval_NUBspline_2d_z_vgh (NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess)
void	eval_NUBspline_2d_z_vgl (NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl)
void	eval_NUBspline_3d_z (NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val)
void	eval_NUBspline_3d_z_vg (NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad)
void	eval_NUBspline_3d_z_vgh (NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess)
void	eval_NUBspline_3d_z_vgl (NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl)

Macro Definition Documentation

C [1/4]

#define C	(		i,
			j )   coefs[(ix+(i))*xs+iy+(j)]

C [2/4]

#define C	(		i,
			j )   coefs[(ix+(i))*xs+iy+(j)]

C [3/4]

#define C	(		i,
			j )   coefs[(ix+(i))*xs+iy+(j)]

C [4/4]

#define C	(		i,
			j )   coefs[(ix+(i))*xs+iy+(j)]

P [1/4]

#define P	(		i,
			j,
			k )   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]

P [2/4]

#define P	(		i,
			j,
			k )   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]

P [3/4]

#define P	(		i,
			j,
			k )   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]

P [4/4]

#define P	(		i,
			j,
			k )   coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]

Function Documentation

eval_NUBspline_1d_z()

void eval_NUBspline_1d_z ( NUBspline_1d_z *restrict spline, double x, complex_double *restrict val )

inline

Definition at line 34 of file nubspline_eval_std_z.h.

{
  double bfuncs[4];
  int i = get_NUBasis_funcs_d (spline->x_basis, x, bfuncs);
  complex_double* restrict coefs = spline->coefs;
  *val = (coefs[i+0]*bfuncs[0] +coefs[i+1]*bfuncs[1] +
      coefs[i+2]*bfuncs[2] +coefs[i+3]*bfuncs[3]);
}

References get_NUBasis_funcs_d(), and restrict.

eval_NUBspline_1d_z_vg()

void eval_NUBspline_1d_z_vg ( NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad )

inline

Definition at line 46 of file nubspline_eval_std_z.h.

{
  double bfuncs[4], dbfuncs[4];
  int i = get_NUBasis_dfuncs_d (spline->x_basis, x, bfuncs, dbfuncs);
  complex_double* restrict coefs = spline->coefs;
  *val =  (coefs[i+0]* bfuncs[0] + coefs[i+1]* bfuncs[1] +
       coefs[i+2]* bfuncs[2] + coefs[i+3]* bfuncs[3]);
  *grad = (coefs[i+0]*dbfuncs[0] + coefs[i+1]*dbfuncs[1] +
       coefs[i+2]*dbfuncs[2] + coefs[i+3]*dbfuncs[3]);
}

References get_NUBasis_dfuncs_d(), and restrict.

eval_NUBspline_1d_z_vgh()

void eval_NUBspline_1d_z_vgh ( NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess )

inline

Definition at line 77 of file nubspline_eval_std_z.h.

{
  eval_NUBspline_1d_z_vgl (spline, x, val, grad, hess);
}

References eval_NUBspline_1d_z_vgl().

eval_NUBspline_1d_z_vgl()

void eval_NUBspline_1d_z_vgl ( NUBspline_1d_z *restrict spline, double x, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl )

inline

Definition at line 60 of file nubspline_eval_std_z.h.

{
  double bfuncs[4], dbfuncs[4], d2bfuncs[4];
  int i = get_NUBasis_d2funcs_d (spline->x_basis, x, bfuncs, dbfuncs, d2bfuncs);
  complex_double* restrict coefs = spline->coefs;
  *val =  (coefs[i+0]*  bfuncs[0] + coefs[i+1]*  bfuncs[1] +
       coefs[i+2]*  bfuncs[2] + coefs[i+3]*  bfuncs[3]);
  *grad = (coefs[i+0]* dbfuncs[0] + coefs[i+1]* dbfuncs[1] +
       coefs[i+2]* dbfuncs[2] + coefs[i+3]* dbfuncs[3]);
  *lapl = (coefs[i+0]*d2bfuncs[0] + coefs[i+1]*d2bfuncs[1] +
       coefs[i+2]*d2bfuncs[2] + coefs[i+3]*d2bfuncs[3]);
 
}

References get_NUBasis_d2funcs_d(), and restrict.

eval_NUBspline_2d_z()

void eval_NUBspline_2d_z ( NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val )

inline

Definition at line 90 of file nubspline_eval_std_z.h.

{
  double a[4], b[4];
  int ix = get_NUBasis_funcs_d (spline->x_basis, x, a);
  int iy = get_NUBasis_funcs_d (spline->y_basis, y, b);
  
  complex_double* restrict coefs = spline->coefs;
 
  int xs = spline->x_stride;
#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
  *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
      a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
      a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
      a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
#undef C
 
}

References C, get_NUBasis_funcs_d(), and restrict.

eval_NUBspline_2d_z_vg()

void eval_NUBspline_2d_z_vg ( NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad )

inline

Definition at line 112 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], da[4], db[4];
  int ix = get_NUBasis_dfuncs_d (spline->x_basis, x, a, da);
  int iy = get_NUBasis_dfuncs_d (spline->y_basis, y, b, db);
  
  complex_double* restrict coefs = spline->coefs;
 
  int xs = spline->x_stride;
#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
  *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
      a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
      a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
      a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
  grad[0] = (da[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
         da[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
         da[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
         da[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
  grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
         a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
         a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
         a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
#undef C
}

References C, get_NUBasis_dfuncs_d(), and restrict.

eval_NUBspline_2d_z_vgh()

void eval_NUBspline_2d_z_vgh ( NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess )

inline

Definition at line 175 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], da[4], db[4], d2a[4], d2b[4];
  complex_double bc[4];
  int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
  int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
  
  complex_double* restrict coefs = spline->coefs;
 
  int xs = spline->x_stride;
#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
  bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
  bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
  bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
  bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
  *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
  grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
  grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
         a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
         a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
         a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
  hess[0] = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]);
  hess[1] = (da[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
         da[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
         da[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
         da[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
  hess[3] = (a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
         a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
         a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
         a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
  hess[2] = hess[1];
  
#undef C
}

References C, get_NUBasis_d2funcs_d(), and restrict.

eval_NUBspline_2d_z_vgl()

void eval_NUBspline_2d_z_vgl ( NUBspline_2d_z *restrict spline, double x, double y, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl )

inline

Definition at line 141 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], da[4], db[4], d2a[4], d2b[4];
  complex_double bc[4];
  int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
  int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
  
  complex_double* restrict coefs = spline->coefs;
 
  int xs = spline->x_stride;
#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
  bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
  bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
  bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
  bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
  *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
  grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
  grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
         a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
         a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
         a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
  *lapl   = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]+
         a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
         a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
         a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
         a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
  
#undef C
}

References C, get_NUBasis_d2funcs_d(), and restrict.

eval_NUBspline_3d_z()

void eval_NUBspline_3d_z ( NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val )

inline

Definition at line 219 of file nubspline_eval_std_z.h.

{
 
  double a[4], b[4], c[4];
  int ix = get_NUBasis_funcs_d (spline->x_basis, x, a);
  int iy = get_NUBasis_funcs_d (spline->y_basis, y, b);
  int iz = get_NUBasis_funcs_d (spline->z_basis, z, c);
  complex_double* restrict coefs = spline->coefs;
  
  int xs = spline->x_stride;
  int ys = spline->y_stride;
#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
  *val = (a[0]*(b[0]*(P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3])+
        b[1]*(P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3])+
        b[2]*(P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3])+
        b[3]*(P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]))+
      a[1]*(b[0]*(P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3])+
        b[1]*(P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3])+
        b[2]*(P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3])+
        b[3]*(P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]))+
      a[2]*(b[0]*(P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3])+
        b[1]*(P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3])+
        b[2]*(P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3])+
        b[3]*(P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]))+
      a[3]*(b[0]*(P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3])+
        b[1]*(P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3])+
        b[2]*(P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3])+
        b[3]*(P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3])));
#undef P
 
}

References get_NUBasis_funcs_d(), P, and restrict.

eval_NUBspline_3d_z_vg()

void eval_NUBspline_3d_z_vg ( NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad )

inline

Definition at line 255 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], c[4], da[4], db[4], dc[4];
  complex_double cP[16], bcP[4], dbcP[4];
  int ix = get_NUBasis_dfuncs_d (spline->x_basis, x, a, da);
  int iy = get_NUBasis_dfuncs_d (spline->y_basis, y, b, db);
  int iz = get_NUBasis_dfuncs_d (spline->z_basis, z, c, dc);
  complex_double* restrict coefs = spline->coefs;
  
  int xs = spline->x_stride;
  int ys = spline->y_stride;
#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
  cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
  cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
  cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
  cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
  cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
  cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
  cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
  cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
  cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
  cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
  cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
  cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
  cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
  cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
  cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
  cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
 
  bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
  bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
  bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
  bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
 
  dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
  dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
  dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
  dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
 
  *val    = ( a[0]*bcP[0] +  a[1]*bcP[1] +  a[2]*bcP[2] +  a[3]*bcP[3]);
  grad[0] = (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
  grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
  grad[2] = 
    (a[0]*(b[0]*(P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3])+
       b[1]*(P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3])+
       b[2]*(P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3])+
       b[3]*(P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]))+
     a[1]*(b[0]*(P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3])+
       b[1]*(P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3])+
       b[2]*(P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3])+
       b[3]*(P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]))+
     a[2]*(b[0]*(P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3])+
       b[1]*(P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3])+
       b[2]*(P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3])+
       b[3]*(P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]))+
     a[3]*(b[0]*(P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3])+
       b[1]*(P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3])+
       b[2]*(P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3])+
       b[3]*(P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3])));
#undef P
 
}

References get_NUBasis_dfuncs_d(), P, and restrict.

eval_NUBspline_3d_z_vgh()

void eval_NUBspline_3d_z_vgh ( NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict hess )

inline

Definition at line 434 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], c[4], da[4], db[4], dc[4], 
    d2a[4], d2b[4], d2c[4];
  complex_double cP[16], dcP[16], d2cP[16], bcP[4], dbcP[4],
    d2bcP[4], dbdcP[4], bd2cP[4], bdcP[4];
  int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
  int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
  int iz = get_NUBasis_d2funcs_d (spline->z_basis, z, c, dc, d2c);
 
  int xs = spline->x_stride;
  int ys = spline->y_stride;
  complex_double* restrict coefs = spline->coefs;
#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
  cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
  cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
  cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
  cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
  cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
  cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
  cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
  cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
  cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
  cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
  cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
  cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
  cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
  cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
  cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
  cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
 
  dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
  dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
  dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
  dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
  dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
  dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
  dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
  dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
  dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
  dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
  dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
  dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
  dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
  dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
  dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
  dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
 
  d2cP[ 0] = (P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3]);
  d2cP[ 1] = (P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3]);
  d2cP[ 2] = (P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3]);
  d2cP[ 3] = (P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]);
  d2cP[ 4] = (P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3]);
  d2cP[ 5] = (P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3]);
  d2cP[ 6] = (P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3]);
  d2cP[ 7] = (P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]);
  d2cP[ 8] = (P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3]);
  d2cP[ 9] = (P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3]);
  d2cP[10] = (P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3]);
  d2cP[11] = (P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]);
  d2cP[12] = (P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3]);
  d2cP[13] = (P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3]);
  d2cP[14] = (P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3]);
  d2cP[15] = (P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3]);
 
  bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
  bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
  bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
  bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
 
  dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
  dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
  dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
  dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
 
  bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
  bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
  bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
  bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
 
  bd2cP[0] = ( b[0]*d2cP[ 0] + b[1]*d2cP[ 1] + b[2]*d2cP[ 2] + b[3]*d2cP[ 3]);
  bd2cP[1] = ( b[0]*d2cP[ 4] + b[1]*d2cP[ 5] + b[2]*d2cP[ 6] + b[3]*d2cP[ 7]);
  bd2cP[2] = ( b[0]*d2cP[ 8] + b[1]*d2cP[ 9] + b[2]*d2cP[10] + b[3]*d2cP[11]);
  bd2cP[3] = ( b[0]*d2cP[12] + b[1]*d2cP[13] + b[2]*d2cP[14] + b[3]*d2cP[15]);
 
  d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
  d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
  d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
  d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
  
  dbdcP[0] = ( db[0]*dcP[ 0] + db[1]*dcP[ 1] + db[2]*dcP[ 2] + db[3]*dcP[ 3]);
  dbdcP[1] = ( db[0]*dcP[ 4] + db[1]*dcP[ 5] + db[2]*dcP[ 6] + db[3]*dcP[ 7]);
  dbdcP[2] = ( db[0]*dcP[ 8] + db[1]*dcP[ 9] + db[2]*dcP[10] + db[3]*dcP[11]);
  dbdcP[3] = ( db[0]*dcP[12] + db[1]*dcP[13] + db[2]*dcP[14] + db[3]*dcP[15]);
 
  *val = a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3];
  grad[0] = (da[0] *bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
  grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
  grad[2] = (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
  // d2x
  hess[0] = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3]);
  // dx dy
  hess[1] = (da[0]*dbcP[0] + da[1]*dbcP[1] + da[1]*dbcP[1] + da[1]*dbcP[1]);
  hess[3] = hess[1];
  // dx dz;
  hess[2] = (da[0]*bdcP[0] + da[1]*bdcP[1] + da[1]*bdcP[1] + da[1]*bdcP[1]);
  hess[6] = hess[2];
  // d2y
  hess[4] = (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]);
  // dy dz
  hess[5] = (a[0]*dbdcP[0] + a[1]*dbdcP[1] + a[2]*dbdcP[2] + a[3]*dbdcP[3]);
  hess[7] = hess[5];
  // d2z
  hess[8] = (a[0]*bd2cP[0] + a[1]*bd2cP[1] + a[2]*bd2cP[2] + a[3]*bd2cP[3]);
#undef P
 
}

References get_NUBasis_d2funcs_d(), P, and restrict.

eval_NUBspline_3d_z_vgl()

void eval_NUBspline_3d_z_vgl ( NUBspline_3d_z *restrict spline, double x, double y, double z, complex_double *restrict val, complex_double *restrict grad, complex_double *restrict lapl )

inline

Definition at line 324 of file nubspline_eval_std_z.h.

{
  double a[4], b[4], c[4], da[4], db[4], dc[4], 
    d2a[4], d2b[4], d2c[4];
  complex_double cP[16], dcP[16], bcP[4], dbcP[4], d2bcP[4], bdcP[4];
 
  int ix = get_NUBasis_d2funcs_d (spline->x_basis, x, a, da, d2a);
  int iy = get_NUBasis_d2funcs_d (spline->y_basis, y, b, db, d2b);
  int iz = get_NUBasis_d2funcs_d (spline->z_basis, z, c, dc, d2c);
 
  complex_double* restrict coefs = spline->coefs;
  int xs = spline->x_stride;
  int ys = spline->y_stride;
#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
  cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
  cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
  cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
  cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
  cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
  cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
  cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
  cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
  cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
  cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
  cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
  cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
  cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
  cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
  cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
  cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
 
  dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
  dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
  dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
  dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
  dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
  dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
  dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
  dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
  dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
  dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
  dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
  dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
  dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
  dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
  dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
  dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
 
  bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
  bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
  bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
  bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
 
  dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
  dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
  dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
  dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
 
  bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
  bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
  bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
  bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
 
  d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
  d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
  d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
  d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
 
 
  *val    = 
    ( a[0]*bcP[0] +  a[1]*bcP[1] +  a[2]*bcP[2] +  a[3]*bcP[3]);
 
  grad[0] = 
    (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
  grad[1] = 
    (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
  grad[2] = 
    (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
 
  *lapl = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3])
    +     (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]) +
    (a[0]*(b[0]*(P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3])+    
       b[1]*(P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3])+
       b[2]*(P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3])+
       b[3]*(P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]))+
     a[1]*(b[0]*(P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3])+
       b[1]*(P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3])+
       b[2]*(P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3])+
       b[3]*(P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]))+
     a[2]*(b[0]*(P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3])+
       b[1]*(P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3])+
       b[2]*(P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3])+
       b[3]*(P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]))+
     a[3]*(b[0]*(P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3])+
       b[1]*(P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3])+
       b[2]*(P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3])+
       b[3]*(P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3])));
#undef P
 
}

References get_NUBasis_d2funcs_d(), P, and restrict.