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kernel.h
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/* this file contains the definitions for the kernel functions */
/*
* This file was originally part of the GADGET3 code developed by
* Volker Springel. The code has been modified
* substantially by Phil Hopkins (phopkins@caltech.edu) for GIZMO (added the
* calls to this for other uses of the kernel in-code in areas like gravity;
* also added new kernels here)
*/
#if !defined(KERNEL_FUNCTION)
#define KERNEL_FUNCTION 3 // default to cubic spline kernel
#endif
#if (KERNEL_FUNCTION == 1) // linear ramp (not a good kernel for many numerical reasons; here for testing purposes)
#define KERNEL_CORE_SIZE (2.0/3.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (1.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 2 // minimum number of neighbors for this kernel and dimension
#define KERNEL_NMAX 8 // maximum number of neighbors for this kernel and dimension
#elif (NUMDIMS==2)
#define KERNEL_NORM (3.0/M_PI) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 12
#define KERNEL_NMAX 24
#else
#define KERNEL_NORM (3.0/M_PI) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 30
#define KERNEL_NMAX 64
#endif
#endif
#if (KERNEL_FUNCTION == 2) // quadratic 'peak' kernel
#define KERNEL_CORE_SIZE (1.0/2.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (3.0/2.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 2 // minimum number of neighbors for this kernel and dimension
#define KERNEL_NMAX 8 // maximum number of neighbors for this kernel and dimension
#elif (NUMDIMS==2)
#define KERNEL_NORM (6.0/M_PI) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 12
#define KERNEL_NMAX 24
#else
#define KERNEL_NORM (15.0/(2.0*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 30
#define KERNEL_NMAX 64
#endif
#endif
#if (KERNEL_FUNCTION == 3) // Morris 1996 cubic spline kernel
#define KERNEL_CORE_SIZE (1.0/2.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (4.0/3.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 2 // minimum number of neighbors for this kernel and dimension
#define KERNEL_NMAX 8 // maximum number of neighbors for this kernel and dimension
#elif (NUMDIMS==2)
#define KERNEL_NORM (40.0/(7.0*M_PI)) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 12
#define KERNEL_NMAX 24
#else
#define KERNEL_NORM (8.0/M_PI) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 30
#define KERNEL_NMAX 64
#endif
#endif
#if (KERNEL_FUNCTION == 4) // Morris 1996 quartic spline kernel
#define KERNEL_CORE_SIZE (2.0/5.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (243.0/40.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 3
#define KERNEL_NMAX 8
#elif (NUMDIMS==2)
#define KERNEL_NORM (15309.0/(478.0*M_PI)) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 16
#define KERNEL_NMAX 32
#else
#define KERNEL_NORM (2187.0/(40.0*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 40
#define KERNEL_NMAX 125
#endif
#endif
#if (KERNEL_FUNCTION == 5) // Morris 1996 quintic spline kernel
#define KERNEL_CORE_SIZE (1.0/3.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (3125.0/768.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 4
#define KERNEL_NMAX 12
#elif (NUMDIMS==2)
#define KERNEL_NORM (46875.0/(2398.0*M_PI)) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 20
#define KERNEL_NMAX 50
#else
#define KERNEL_NORM (15625.0/(512.0*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 60
#define KERNEL_NMAX 180
#endif
#endif
#if (KERNEL_FUNCTION == 6) // Wendland C2 kernel
#define KERNEL_CORE_SIZE (2.0/5.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (5.0/4.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 3
#define KERNEL_NMAX 8
#elif (NUMDIMS==2)
#define KERNEL_NORM (7.0/M_PI) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 16
#define KERNEL_NMAX 32
#else
#define KERNEL_NORM (21.0/(2.0*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 40
#define KERNEL_NMAX 125
#endif
#endif
#if (KERNEL_FUNCTION == 7) // Wendland C4 kernel
#define KERNEL_CORE_SIZE (1.0/3.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (3.0/2.0) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 4
#define KERNEL_NMAX 12
#elif (NUMDIMS==2)
#define KERNEL_NORM (9.0/M_PI) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 20
#define KERNEL_NMAX 50
#else
#define KERNEL_NORM (495.0/(32.0*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 60
#define KERNEL_NMAX 180
#endif
#endif
#if (KERNEL_FUNCTION == 8) // quadratic 2-step kernel ('magic kernel' for image filtering is this in 2d with KERNEL_U0=1/3)
#define KERNEL_CORE_SIZE (1.0/2.0)
#if !defined(KERNEL_U0)
#define KERNEL_U0 (0.2) // set to anything between 0 (most 'peaked') to 1 ('flattest'): values ~0.55-0.59 minimize second derivative
#endif
#if (NUMDIMS==1)
#define KERNEL_NORM (3.0/(2.0 + KERNEL_U0)) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 2 // minimum number of neighbors for this kernel and dimension
#define KERNEL_NMAX 8 // maximum number of neighbors for this kernel and dimension
#elif (NUMDIMS==2)
#define KERNEL_NORM (6.0/(M_PI*(1 + KERNEL_U0 + KERNEL_U0*KERNEL_U0))) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 12
#define KERNEL_NMAX 24
#else
#define KERNEL_NORM (15.0/(2.0*M_PI*(1+KERNEL_U0)*(1+KERNEL_U0*KERNEL_U0))) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 30
#define KERNEL_NMAX 64
#endif
#endif
#if (KERNEL_FUNCTION == 9) // Wendland C6 kernel
#define KERNEL_CORE_SIZE (3.0/10.0)
#if (NUMDIMS==1)
#define KERNEL_NORM (55./32.) /*!< For 1D-normalized kernel */
#define KERNEL_NMIN 12
#define KERNEL_NMAX 50
#elif (NUMDIMS==2)
#define KERNEL_NORM (78./(7.*M_PI)) /*!< For 2D-normalized kernel */
#define KERNEL_NMIN 50
#define KERNEL_NMAX 150
#else
#define KERNEL_NORM (1365./(64.*M_PI)) /*!< For 3D-normalized kernel */
#define KERNEL_NMIN 180
#define KERNEL_NMAX 600
#endif
#endif
static inline void kernel_hinv(double h, double *hinv, double *hinv3, double *hinv4)
{
*hinv = 1.0 / h;
#if (NUMDIMS==1)
*hinv3 = *hinv;
#elif (NUMDIMS==2)
*hinv3 = *hinv * *hinv;
#else // THREEDIMS
*hinv3 = *hinv * *hinv * *hinv;
#endif
*hinv4 = *hinv3 * *hinv;
return;
}
/* Attention: Here we assume that kernel is only called
with range 0..1 for u as done in hydra or density !!
Call with mode 0 to calculate dwk and wk
Call with mode -1 to calculate only wk
Call with mode +1 to calculate only dwk */
static inline void kernel_main(double u, double hinv3, double hinv4, double *wk, double *dwk, int mode)
{
if(u>=1) {*wk=0; *dwk=0; return;} /* currently fully-redundant, but better safety for various subroutines calling this */
#if (KERNEL_FUNCTION == 1) /* linear ramp */
if(mode >= 0)
*dwk = -1;
if(mode <= 0)
*wk = 1-u;
#endif
#if (KERNEL_FUNCTION == 2) /* quadratic */
double t1 = 1-u;
if(mode >= 0)
*dwk = -2*t1;
if(mode <= 0)
*wk = t1*t1;
#endif
#if (KERNEL_FUNCTION == 3) /* cubic spline */
if(u < 0.5)
{
if(mode >= 0)
*dwk = u * (18.0 * u - 12.0);
if(mode <= 0)
*wk = (1.0 + 6.0 * (u - 1.0) * u * u);
}
else
{
double t1 = (1.0 - u);
double t2 = t1 * t1;
if(mode >= 0)
*dwk = -6.0 * t2;
if(mode <= 0)
*wk = 2.0 * t2 * t1;
}
#endif /* cubic spline */
#if (KERNEL_FUNCTION == 4) /* quartic spline */
double t1 = (1.0 - u);
double t2 = t1 * t1;
double t4 = t2 * t2;
if(mode >= 0)
*dwk = -5.0 * t4;
if(mode <= 0)
*wk = t4 * t1;
if (u < 2.0/3.0)
{
t1 = (2.0/3.0 - u);
t2 = t1 * t1;
t4 = t2 * t2;
if(mode >= 0)
*dwk += 30.0 * t4;
if(mode <= 0)
*wk -= 6.0 * t4 * t1;
}
if (u < 1.0/3.0)
{
t1 = (1.0/3.0 - u);
t2 = t1 * t1;
t4 = t2 * t2;
if(mode >= 0)
*dwk -= 75.0 * t4;
if(mode <= 0)
*wk += 15.0 * t4 * t1;
}
#endif /* quartic spline */
#if (KERNEL_FUNCTION == 5) /* quintic spline */
double t1 = (1.0 - u);
double t2 = t1 * t1;
if(mode >= 0)
*dwk = -4.0 * t2 * t1;
if(mode <= 0)
*wk = t2 * t2;
if (u < 0.6)
{
t1 = (0.6 - u);
t2 = t1 * t1;
if(mode >= 0)
*dwk += 20.0 * t2 * t1;
if(mode <= 0)
*wk -= 5.0 * t2 * t2;
}
if (u < 0.2)
{
t1 = (0.2 - u);
t2 = t1 * t1;
if(mode >= 0)
*dwk -= 40.0 * t2 * t1;
if(mode <= 0)
*wk += 10.0 * t2 * t2;
}
#endif /* quintic spline */
#if (KERNEL_FUNCTION == 6) /* Wendland C2 */
double t1 = (1 - u);
double t3 = t1*t1*t1;
#if (NUMDIMS == 1)
if(mode >= 0)
*dwk = -12.0 * u * t1*t1;
if(mode <= 0)
*wk = t3 * (1.0 + 3.0*u);
#else
if(mode >= 0)
*dwk = -20.0 * u * t3;
if(mode <= 0)
*wk = t3 * t1 * (1.0 + 4.0*u);
#endif
#endif
#if (KERNEL_FUNCTION == 7) /* Wendland C4 */
double t1 = (1 - u);
double t5 = t1*t1; t5 *= t5*t1;
#if (NUMDIMS == 1)
if(mode >= 0)
*dwk = -14.0 * (t5/t1) * u * (1.0 + 4.0*u);
if(mode <= 0)
*wk = t5 * (1.0 + 5.0*u + 8.0*u*u);
#else
if(mode >= 0)
*dwk = -(56.0/3.0) * t5 * u * (1.0 + 5.0*u);
if(mode <= 0)
*wk = t5 * t1 * (1.0 + 6.0*u + (35.0/3.0)*u*u);
#endif
#endif
#if (KERNEL_FUNCTION == 8) /* quadratic '2-part' kernel */
if(u < KERNEL_U0)
{
if(mode >= 0)
*dwk = -2*u/KERNEL_U0;
if(mode <= 0)
*wk = 1-u*u/KERNEL_U0;
} else {
if(mode >= 0)
*dwk = -2*(1-u)/(1-KERNEL_U0);
if(mode <= 0)
*wk = (1-u)*(1-u)/(1-KERNEL_U0);
}
#endif
#if (KERNEL_FUNCTION == 9) /* Wendland C6 */
double t1 = (1 - u);
double t7 = t1*t1*t1; t7 *= t7*t1;
#if (NUMDIMS == 1)
if(mode >= 0)
*dwk = -6.0 * (t7/t1) * u * (3.0 + 18.0*u + 35.0*u*u);
if(mode <= 0)
*wk = t7 * (1.0 + 7.0*u + 19.0*u*u + 21.0*u*u*u);
#else
if(mode >= 0)
*dwk = -22.0 * t7 * u * (1.0 + 7.0*u + 16.0*u*u);
if(mode <= 0)
*wk = t7 * t1 * (1.0 + 8.0*u + 25.0*u*u + 32.0*u*u*u);
#endif
#endif
if(mode >= 0) {*dwk *= KERNEL_NORM * hinv4;}
if(mode <= 0) {*wk *= KERNEL_NORM * hinv3;}
return;
}
/* this defines the kernel for the short-range gravitational softening,
which does not have to correspond to that of the gas (although for the gas
itself, it should). dwk is the force kernel, wk is the potential kernel
mode= 0 to calculate dphi_dh (for zeta correction to adaptive forces)
mode= -1 to calculate phi (for potential)
mode= 1 to calculate (1/u)*dphi_du (for acceleration/force)
mode= 2 to calculate -(1/u)*d[(1/u)*dphi_du]/du (for tidal tensor)
*/
static inline double kernel_gravity(double u, double hinv, double hinv3, int mode)
{
/* here everything is newtonian, add this as a check just in case */
if(u >= 1)
{
if(mode == 0) {return 0;}
if(mode == 1) {return hinv3/(u*u*u);}
if(mode == -1) {return -hinv/u;}
if(mode == 2) {return 3.*hinv3*hinv*hinv/(u*u*u*u*u);}
}
double wk;
#if (KERNEL_FUNCTION == 1) /* linear ramp */
if(mode == 1)
{
wk = 4 - 3*u;
return wk * hinv3;
}
else if(mode == -1)
{
wk = -2 + u*u*(2-u);
return wk * hinv;
}
else if(mode == 0)
{
wk = 2*(1-u)*(1-u)*(1+2*u);
return wk * hinv * hinv;
}
else if(mode == 2)
{
wk = 3./u;
return wk * hinv3*hinv*hinv;
}
#endif
#if (KERNEL_FUNCTION == 2) /* quadratic */
if(mode == 1)
{
wk = 10. + 3.*u * (-5. + 2.*u);
return wk * hinv3;
}
else if(mode == -1)
{
double uu = u*u;
wk = -2.5 + 5.*uu*(1.-u) + 1.5*uu*uu;
return wk * hinv;
}
else if(mode == 0)
{
double uu = 1 - u;
wk = 2.5 * uu*uu*uu * (1. + 3.*u);
return wk * hinv * hinv;
}
else if(mode == 2)
{
wk = 15./u-12.;
return wk * hinv3*hinv*hinv;
}
#endif
#if (KERNEL_FUNCTION == 3) /* cubic spline */
if(mode == 1)
{
if(u < 0.5)
wk = (10.666666666667 + u * u * (32.0 * u - 38.4));
else
wk = (21.333333333333 - 48.0 * u +
38.4 * u * u - 10.666666666667 * u * u * u - 0.066666666667 / (u * u * u));
return wk * hinv3;
}
else if(mode == -1)
{
if(u < 0.5)
wk = -2.8 + u * u * (5.333333333333 + u * u * (6.4 * u - 9.6));
else
wk = -3.2 + 0.066666666667 / u + u * u * (10.666666666667 +
u * (-16.0 + u * (9.6 - 2.133333333333 * u)));
return wk * hinv;
}
else if(mode == 0)
{
if(u < 0.5)
wk = 2.8 + 16.0 * u * u * (-1.0 + 3.0 * u * u * (1.0 - 0.8 * u));
else
wk = 3.2 + 32.0 * u * u * (-1.0 + u * (2.0 - 1.5 * u + 0.4 * u * u));
return wk * hinv * hinv;
}
else if(mode == 2)
{
if(u < 0.5)
wk = 76.8 - 96.0 * u;
else
wk = -0.2 / (u*u*u*u*u) + 48.0 / u - 76.8 + 32.0 * u;
return wk * hinv3*hinv*hinv;
}
#endif /* cubic spline */
#if (KERNEL_FUNCTION == 4) /* quartic spline */
double u2=u*u;
if(mode == 1)
{
if(u < 0.2)
wk = 125.*(161. - 630.*u2 + 1125.*u2*u2) / 1344.;
else
if(u < 0.6)
wk = (1. - 625.*u2*u*(-154. + 5.*u*(-21. + 2.*u*(126. + 25.*u*(-7. + 3.*u))))) / (6720.*u2*u);
else
wk = (-437. + 3125.*u2*u*(35. + u*(-105. + u*(126. + 5.*u*(-14. + 3.*u))))) / (2688.*u2*u);
return wk * hinv3;
}
else if(mode == -1)
{
if(u < 0.2)
wk = (-8393. + 125.*u2 * (161. - 315.*u2 + 375.*u2*u2)) / 2688.;
else
if(u < 0.6)
wk = -(1. + 5.*u*(4193. + 125.*u2*(-77. + 5.*u*(-7. + u*(63. + 5.*u*(-14. + 5.*u)))))) / (6720.*u);
else
wk = (874. + 3125.*u*(-7. + u2*(35. + u*(-70. + u*(63. + u*(-28. + 5.*u)))))) / (5376.*u);
return wk * hinv;
}
else if(mode == 0)
{
if(u < 0.2)
wk = (1199. - 375.*u2*(23. - 75.*u2 + 125.*u2*u2)) / 384.;
else
if(u < 0.6)
wk = (599. + 125.*u2*(-33. + 5.*u*(-4. + 5.*u*(9. + u*(-12. + 5.*u))))) / 192.;
else
{
double um=1.0-u; u2=um*um;
wk = (3125./768.) * u2*u2*um * (1. + 5.*u);
}
return wk * hinv * hinv;
}
else if(mode == 2)
{
if(u < 0.2)
wk = 2500. * (63. - 225.*u2) / 1344.;
else
if(u < 0.6)
wk = (1. + 3125.*u2*u2*(-7.+2.*u*(84.+25.*u*(-7.+4.*u)))) / (2240.*u2*u2*u);
else
wk = -(437. + 3125.*u2*u2*(-35. + 2.*u*(42. + 5.*u*(-7. + 2.*u)))) / (896.*u2*u2*u);
return wk * hinv3*hinv*hinv;
}
#endif /* quartic spline */
#if (KERNEL_FUNCTION == 5) /* quintic spline */
double u2=u*u;
if(mode == 1)
{
if(u < 1./3.)
wk = -(9./280.)*(-616.+27.*u2*(112.+45.*u2*(-8.+7.*u)));
else
if(u < 2./3.)
wk = (5.+27.*u2*u*(952.+9.*u*(350.+3.*u*(-784.+5.*u*(280.+9.*u*(-24.+7.*u)))))) / (1680.*u2*u);
else
wk = -(169.+729.*u2*u*(-56.+u*(210.+u*(-336.+u*(280.+3.*u*(-40.+7.*u)))))) / (560.*u2*u);
return wk * hinv3;
}
else if(mode == -1)
{
if(u < 1./3.)
wk = (-956.-9.*u2*(-308.+27.*u2*(28.+15.*u2*(-4.+3.*u)))) / 280.;
else
if(u < 2./3.)
wk = (-5.+3.*u*(-1892.+9.*u2*(476.+3.*u*(350.+9.*u*(-196.+5.*u*(56.+9.*u*(-4.+u))))))) / (1680.*u);
else
wk = (169.-729*u*(4.+(-2.+u)*u2*(14.+u*(-28.+u*(28.+u*(-14.+3.*u)))))) / (560.*u);
return wk * hinv;
}
else if(mode == 0)
{
if(u < 1./3.)
wk = (239.+27.*u2*(-77.+45.*u2*(7.+3.*u2*(-7.+6.*u)))) / 70.;
else
if(u < 2./3.)
wk = (473.-27.*u2*(119.+5.*u*(70.+9*u*(-49.+3*u*(28.+3.*u*(-7.+2.*u)))))) / 140.;
else
{
double um=1.0-u; um*=um*um; um*=um;
wk = (729./140.) * um * (1.+6.*u);
}
return wk * hinv * hinv;
}
else if(mode == 2)
{
if(u < 1./3.)
wk = 972./5. + 2187.*u2*(35.*u-32.)/56.;
else
if(u < 2./3.)
wk = (5. - 81.*u2*u2*(350. + 3.*u*(-1568. + 15.*u*(280. + 3.*u*(-96. + 35.*u))))) / (560 * u2*u2*u);
else
wk = (-507. + 2187.*u2*u2*(70. + u*(-224. + 5.*u*(56. + u*(-32. + 7.*u))))) / (560 * u2*u2*u);
return wk * hinv3*hinv*hinv;
}
#endif /* quintic spline */
#if (KERNEL_FUNCTION == 6) /* Wendland C2 */
if(mode == 1)
{
wk = 14. + u*u * (-84. + u*(140. + 3.*u*(-30. + 7.*u)));
return wk * hinv3;
}
else if(mode == -1)
{
double uu = u*u;
wk = -3. + uu * (7. + uu * (-21. + u * (28. + 3. * (-5. + u) * u)));
return wk * hinv;
}
else if(mode == 0)
{
double t1 = 1 - u;
double t2 = t1*t1; t2 *= t2; t2 *= t1;
wk = 3. * t2 * (1. + u * (5. + 8. * u));
return wk * hinv * hinv;
}
else if(mode == 2)
{
wk = 168. + u * (-420. + (360. - 105. * u) * u);
return wk * hinv3*hinv*hinv;
}
#endif
#if (KERNEL_FUNCTION == 7) /* Wendland C4 */
if(mode == 1)
{
double uu = u*u;
wk = 0.125 * (165 + uu*(-924 + uu*(4950 + u*(-9240 + u*(7700 - 3168*u + 525*uu)))));
return wk * hinv3;
}
else if(mode == -1)
{
double uu = u*u;
wk = 0.0625 * (-55 + uu*(165 + uu*(-462 + uu*(1650 + u*(-2640 + u*(1925 + u*(-704 + 105*u)))))));
return wk * hinv;
}
else if(mode == 0)
{
double t1 = 1 - u;
double t2 = t1*t1*t1; t2 *= t2; t2 *= t1;
wk = (55./16.) * t2 * (1 + 3*u) * (1 + u*(4 + 7*u));
return wk * hinv * hinv;
}
else if(mode == 2)
{
double uu = u*u;
wk = 231. + uu * (-2475. + u * (5775. + u * (-5775. + (2772. - 525. * u) * u)));
return wk * hinv3*hinv*hinv;
}
#endif
#if (KERNEL_FUNCTION == 8) /* quadratic 2-step kernel */
if(mode == 1)
{
if(u < KERNEL_U0) {wk=4.*M_PI*(5.-3.*u*u/KERNEL_U0)/15.;} else {wk=-2.*M_PI*(KERNEL_U0*KERNEL_U0*KERNEL_U0*KERNEL_U0+u*u*u*(-10.+3.*u*(5.-2.*u)))/(15.*(1.-KERNEL_U0)*u*u*u);}
return KERNEL_NORM * wk * hinv3;
}
else if(mode == -1)
{
if(u < KERNEL_U0) {wk=M_PI*(-5.*KERNEL_U0*(1.+KERNEL_U0+KERNEL_U0*KERNEL_U0)+10.*KERNEL_U0*u*u-3.*u*u*u*u)/(15.*KERNEL_U0);} else {wk=M_PI*(2.*KERNEL_U0*KERNEL_U0*KERNEL_U0*KERNEL_U0-5.*u+u*u*u*(10.+u*(3.*u-10.)))/(15.*u*(1.-KERNEL_U0));}
return KERNEL_NORM * wk * hinv;
}
else if(mode == 0)
{
if(u < KERNEL_U0) {wk=M_PI*(1.+KERNEL_U0*(1.+KERNEL_U0)-6.*u*u+3.*u*u*u*u/KERNEL_U0)/3.;} else {wk=M_PI*(u-1.)*(u-1.)*(u-1.)*(1.+3.*u)/(3.*(KERNEL_U0-1.));}
return KERNEL_NORM * wk * hinv * hinv;
}
else if(mode == 2)
{
if(u < KERNEL_U0) {wk=8.*M_PI/(5.*KERNEL_U0);} else {wk=-2.*M_PI*(KERNEL_U0*KERNEL_U0*KERNEL_U0*KERNEL_U0+u*u*u*u*(4.*u-KERNEL_U0))/(5.*(1.-KERNEL_U0)*u*u*u*u*u);}
return KERNEL_NORM * wk * hinv3*hinv*hinv;
}
#endif
#if (KERNEL_FUNCTION == 9) /* Wendland C6 */
if(mode == 1)
{
double uu = u*u;
wk = 0.0625 * (455. - 3003.*uu + 12870.*uu*uu + uu*uu*uu * (-70070. + u * (144144. + 5.*u*(-28665. + u*(16016. - 4851.*u + 624.*uu)))));
return wk * hinv3;
}
else if(mode == -1)
{
double uu = u*u;
wk = (1./16.) * (-245. + 910.*uu - uu*uu * (3003. - 8580.*uu + 35035.*uu*uu - 64064.*uu*uu*u + 57330.*uu*uu*uu - 29120.*uu*uu*uu*u + 8085.*uu*uu*uu*uu - 960.*uu*uu*uu*uu*u));
return wk * hinv;
}
else if(mode == 0)
{
double t1 = 1 - u;
double t2 = t1*t1*t1*t1; t2 *= t2; t2 *= t1;
wk = (35./64.) * t2 * (7. + 3.*u * (21. + u * (79. + u * (151. + 128. * u))));
return wk * hinv * hinv;
}
else if(mode == 2)
{
double uu = u*u;
wk = -(3./8.) * (-1001. + 8580.*uu + uu*uu * (-70070. + u * (168168. + 5.*u * (-38220. + 11.*u * (2184. + u * (-735. + 104.*u))))));
return wk * hinv3*hinv*hinv;
}
#endif
return 0;
}
#define KERNEL_FAC_FROM_FORCESOFT_TO_PLUMMER ((-1./kernel_gravity(0,1,1,-1))) /* factor which defines the plummer-equivalent radius for any kernel. multiplying ForceSoftening [radius of compact support] by this number gives the standard Plummer-equivalent definition: e.g. for a cubic spline, this returns 1./2.8, which is the desired conversion factor */