small edits for reformatting

This commit is contained in:
Steve Plimpton
2020-01-13 14:26:22 -07:00
parent 51efee43be
commit aa70f8cc6b
5 changed files with 623 additions and 629 deletions

View File

@ -19,40 +19,40 @@
#include "update.h" #include "update.h"
#include "modify.h" #include "modify.h"
#include "domain.h" #include "domain.h"
#include "force.h"
#include "lattice.h" #include "lattice.h"
#include "input.h" #include "input.h"
#include "variable.h" #include "variable.h"
#include "error.h"
#include "force.h"
#include "random_mars.h" #include "random_mars.h"
#include "error.h"
using namespace LAMMPS_NS; using namespace LAMMPS_NS;
using namespace FixConst; using namespace FixConst;
enum{NONE=0,DIFFUSIVE=1,MAXWELL=2,CERCIGNANILAMPIS=3}; enum{NONE=0,DIFFUSIVE=1,MAXWELL=2,CERCIGNANILAMPIS=3};
/* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */
FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char **arg) : FixWallReflectStochastic::
FixWallReflectStochastic(LAMMPS *lmp, int narg, char **arg) :
FixWallReflect(lmp, narg, arg), random(NULL) FixWallReflect(lmp, narg, arg), random(NULL)
{ {
int arginc,dir;
if (narg < 8) error->all(FLERR,"Illegal fix wall/reflect/stochastic command"); if (narg < 8) error->all(FLERR,"Illegal fix wall/reflect/stochastic command");
if (domain->triclinic != 0) error->all(FLERR, "This fix wall/reflect/stochastic is not incompatible with triclinic simulation box"); if (domain->triclinic != 0)
error->all(FLERR, "Fix wall/reflect/stochastic cannot be used with "
"triclinic simulation box");
dynamic_group_allow = 1; dynamic_group_allow = 1;
// parse args // parse args
int arginc;
nwall = 0; nwall = 0;
int scaleflag = 1; int scaleflag = 1;
reflectionstyle = NONE; reflectionstyle = NONE;
if (strcmp(arg[3],"diffusive") == 0) { if (strcmp(arg[3],"diffusive") == 0) {
reflectionstyle = DIFFUSIVE; reflectionstyle = DIFFUSIVE;
arginc = 6; arginc = 6;
@ -66,15 +66,15 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
seedfix = force->inumeric(FLERR,arg[4]); seedfix = force->inumeric(FLERR,arg[4]);
if (seedfix <=0) error->all(FLERR,"Random seed must be a postive number"); if (seedfix <= 0) error->all(FLERR,"Random seed must be a postive number");
random = new RanMars(lmp,seedfix + comm->me);
int iarg = 5; int iarg = 5;
while (iarg < narg) { while (iarg < narg) {
if ((strcmp(arg[iarg],"xlo") == 0) || (strcmp(arg[iarg],"xhi") == 0) || if ((strcmp(arg[iarg],"xlo") == 0) || (strcmp(arg[iarg],"xhi") == 0) ||
(strcmp(arg[iarg],"ylo") == 0) || (strcmp(arg[iarg],"yhi") == 0) || (strcmp(arg[iarg],"ylo") == 0) || (strcmp(arg[iarg],"yhi") == 0) ||
(strcmp(arg[iarg],"zlo") == 0) || (strcmp(arg[iarg],"zhi") == 0)) { (strcmp(arg[iarg],"zlo") == 0) || (strcmp(arg[iarg],"zhi") == 0)) {
if (iarg+2 > narg) error->all(FLERR,"Illegal fix wall/reflect/stochastic command"); if (iarg+2 > narg)
error->all(FLERR,"Illegal fix wall/reflect/stochastic command");
int newwall; int newwall;
if (strcmp(arg[iarg],"xlo") == 0) newwall = XLO; if (strcmp(arg[iarg],"xlo") == 0) newwall = XLO;
@ -86,7 +86,8 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
for (int m = 0; (m < nwall) && (m < 6); m++) for (int m = 0; (m < nwall) && (m < 6); m++)
if (newwall == wallwhich[m]) if (newwall == wallwhich[m])
error->all(FLERR,"Wall defined twice in fix wall/reflect/stochastic command"); error->all(FLERR,
"Fix wall/reflect/stochastic command wall defined twice");
wallwhich[nwall] = newwall; wallwhich[nwall] = newwall;
if (strcmp(arg[iarg+1],"EDGE") == 0) { if (strcmp(arg[iarg+1],"EDGE") == 0) {
@ -100,18 +101,19 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
coord0[nwall] = force->numeric(FLERR,arg[iarg+1]); coord0[nwall] = force->numeric(FLERR,arg[iarg+1]);
} }
walltemp[nwall]= force->numeric(FLERR,arg[iarg+2]); walltemp[nwall]= force->numeric(FLERR,arg[iarg+2]);
for (dir = 0; dir < 3; dir++) { for (int dir = 0; dir < 3; dir++) {
wallvel[nwall][dir]= force->numeric(FLERR,arg[iarg+dir+3]); wallvel[nwall][dir]= force->numeric(FLERR,arg[iarg+dir+3]);
int dim = wallwhich[nwall] / 2; int dim = wallwhich[nwall] / 2;
if ((wallvel[nwall][dir] !=0) & (dir == dim)) error->all(FLERR,"The wall velocity must be tangential"); if ((wallvel[nwall][dir] !=0) & (dir == dim))
error->all(FLERR,"The wall velocity must be tangential");
if (reflectionstyle == CERCIGNANILAMPIS) { if (reflectionstyle == CERCIGNANILAMPIS) {
wallaccom[nwall][dir]= force->numeric(FLERR,arg[iarg+dir+6]); wallaccom[nwall][dir]= force->numeric(FLERR,arg[iarg+dir+6]);
} else if (reflectionstyle == MAXWELL) { } else if (reflectionstyle == MAXWELL) {
wallaccom[nwall][dir]= force->numeric(FLERR,arg[iarg+6]);// One accommodation coefficient for all directions // one accommodation coefficient for all directions
wallaccom[nwall][dir]= force->numeric(FLERR,arg[iarg+6]);
} }
} }
@ -119,7 +121,8 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
iarg += arginc; iarg += arginc;
} else if (strcmp(arg[iarg],"units") == 0) { } else if (strcmp(arg[iarg],"units") == 0) {
if (iarg+2 > narg) error->all(FLERR,"Illegal wall/reflect/stochastic command"); if (iarg+2 > narg)
error->all(FLERR,"Illegal wall/reflect/stochastic command");
if (strcmp(arg[iarg+1],"box") == 0) scaleflag = 0; if (strcmp(arg[iarg+1],"box") == 0) scaleflag = 0;
else if (strcmp(arg[iarg+1],"lattice") == 0) scaleflag = 1; else if (strcmp(arg[iarg+1],"lattice") == 0) scaleflag = 1;
else error->all(FLERR,"Illegal fix wall/reflect/stochastic command"); else error->all(FLERR,"Illegal fix wall/reflect/stochastic command");
@ -133,17 +136,21 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
for (int m = 0; m < nwall; m++) { for (int m = 0; m < nwall; m++) {
if ((wallwhich[m] == XLO || wallwhich[m] == XHI) && domain->xperiodic) if ((wallwhich[m] == XLO || wallwhich[m] == XHI) && domain->xperiodic)
error->all(FLERR,"Cannot use fix wall/reflect/stochastic in periodic dimension"); error->all(FLERR,"Cannot use fix wall/reflect/stochastic "
"in periodic dimension");
if ((wallwhich[m] == YLO || wallwhich[m] == YHI) && domain->yperiodic) if ((wallwhich[m] == YLO || wallwhich[m] == YHI) && domain->yperiodic)
error->all(FLERR,"Cannot use fix wall/reflect/stochastic in periodic dimension"); error->all(FLERR,"Cannot use fix wall/reflect/stochastic "
"in periodic dimension");
if ((wallwhich[m] == ZLO || wallwhich[m] == ZHI) && domain->zperiodic) if ((wallwhich[m] == ZLO || wallwhich[m] == ZHI) && domain->zperiodic)
error->all(FLERR,"Cannot use fix wall/reflect/stochastic in periodic dimension"); error->all(FLERR,"Cannot use fix wall/reflect/stochastic "
"in periodic dimension");
} }
for (int m = 0; m < nwall; m++) for (int m = 0; m < nwall; m++)
if ((wallwhich[m] == ZLO || wallwhich[m] == ZHI) && domain->dimension == 2) if ((wallwhich[m] == ZLO || wallwhich[m] == ZHI) && domain->dimension == 2)
error->all(FLERR, error->all(FLERR,
"Cannot use fix wall/reflect/stochastic zlo/zhi for a 2d simulation"); "Cannot use fix wall/reflect/stochastic zlo/zhi "
"for a 2d simulation");
// scale factors for CONSTANT walls, VARIABLE wall is not allowed // scale factors for CONSTANT walls, VARIABLE wall is not allowed
@ -167,14 +174,16 @@ FixWallReflectStochastic::FixWallReflectStochastic(LAMMPS *lmp, int narg, char *
} }
} }
} // random number generator
random = new RanMars(lmp,seedfix + comm->me);
}
/* ---------------------------------------------------------------------- */
FixWallReflectStochastic::~FixWallReflectStochastic() FixWallReflectStochastic::~FixWallReflectStochastic()
{ {
delete random;
delete random ;
} }
/* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */
@ -188,7 +197,6 @@ void FixWallReflectStochastic::wall_particle(int m, int which, double coord)
double *mass = atom->mass; double *mass = atom->mass;
// coord = current position of wall // coord = current position of wall
// evaluate variable if necessary, wrap with clear/add
double **x = atom->x; double **x = atom->x;
double **v = atom->v; double **v = atom->v;
@ -200,67 +208,67 @@ void FixWallReflectStochastic::wall_particle(int m, int which, double coord)
side = which % 2; side = which % 2;
for (i = 0; i < nlocal; i++) { for (i = 0; i < nlocal; i++) {
if (mask[i] & groupbit) { if (!(mask[i] & groupbit)) continue;
sign = 0; sign = 0;
if ((side == 0) & (x[i][dim] < coord)) sign = 1;
else if ((side == 1) & (x[i][dim] > coord)) sign = -1;
if (sign == 0) continue;
if ((side == 0) & (x[i][dim] < coord)){ // theta = kT/m
sign = 1;
} else if ((side == 1) & (x[i][dim] > coord)){
sign = -1;
}
if (rmass) theta = force->boltz*walltemp[m]/(rmass[i]*force->mvv2e);
if (sign != 0) {
if (rmass) theta = force->boltz*walltemp[m]/(rmass[i]*force->mvv2e);// theta = kT/m
else theta = force->boltz*walltemp[m]/(mass[type[i]]*force->mvv2e); else theta = force->boltz*walltemp[m]/(mass[type[i]]*force->mvv2e);
factor = sqrt(theta); factor = sqrt(theta);
timecol= (x[i][dim] - coord)/v[i][dim]; // time travelling after collision // time travelling after collision
if (reflectionstyle == MAXWELL) {difftest = random->uniform(); }// for Maxwell model only timecol = (x[i][dim]-coord) / v[i][dim];
// only needed for Maxwell model
if (reflectionstyle == MAXWELL) difftest = random->uniform();
for (dir = 0; dir < 3; dir++) { for (dir = 0; dir < 3; dir++) {
x[i][dir] -= v[i][dir]*timecol; // pushing back atoms to the wall position and assign new reflected velocity // pushing back atoms to wall position, assign new reflected velocity
// Diffusive reflection x[i][dir] -= v[i][dir]*timecol;
if (reflectionstyle == DIFFUSIVE){
if (dir != dim) { // diffusive reflection
if (reflectionstyle == DIFFUSIVE) {
if (dir != dim)
v[i][dir] = wallvel[m][dir] + random->gaussian(0,factor); v[i][dir] = wallvel[m][dir] + random->gaussian(0,factor);
} else { v[i][dir] = sign*random->rayleigh(factor) ; } else v[i][dir] = sign*random->rayleigh(factor);
}
// Maxwell reflection // Maxwell reflection
if (reflectionstyle == MAXWELL){
} else if (reflectionstyle == MAXWELL) {
if (difftest < wallaccom[m][dir]) { if (difftest < wallaccom[m][dir]) {
if (dir != dim) { if (dir != dim)
v[i][dir] = wallvel[m][dir] + random->gaussian(0,factor); v[i][dir] = wallvel[m][dir] + random->gaussian(0,factor);
} else { v[i][dir] = sign*random->rayleigh(factor) ; } else v[i][dir] = sign*random->rayleigh(factor);
} else { } else {
if (dir == dim) {v[i][dir] = -v[i][dir]; if (dir == dim) v[i][dir] = -v[i][dir];
} }
}
}
// Cercignani Lampis reflection // Cercignani Lampis reflection
if (reflectionstyle == CERCIGNANILAMPIS){
if (dir != dim) {
v[i][dir] = wallvel[m][dir] + random->gaussian((1-wallaccom[m][dir])*(v[i][dir]-wallvel[m][dir]),sqrt((2-wallaccom[m][dir])*wallaccom[m][dir]*theta)) ;
} else { v[i][dir] = random->besselexp(theta, wallaccom[m][dir], v[i][dir]) ; }
} else if (reflectionstyle == CERCIGNANILAMPIS) {
if (dir != dim)
v[i][dir] = wallvel[m][dir] +
random->gaussian((1-wallaccom[m][dir]) *
(v[i][dir] - wallvel[m][dir]),
sqrt((2-wallaccom[m][dir]) *
wallaccom[m][dir]*theta));
else v[i][dir] = random->besselexp(theta,wallaccom[m][dir],v[i][dir]);
} }
// update new position due to the new velocity // update new position due to the new velocity
if (dir != dim) {
x[i][dir] += v[i][dir]*timecol; } if (dir != dim) x[i][dir] += v[i][dir]*timecol;
else {x[i][dir] = coord + v[i][dir]*timecol;} else x[i][dir] = coord + v[i][dir]*timecol;
}// for loop }
}// if sign
}// if mask
} }
} }

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@ -20,7 +20,6 @@ FixStyle(wall/reflect/stochastic,FixWallReflectStochastic)
#ifndef LMP_FIX_WALL_REFLECT_STOCHASTIC_H #ifndef LMP_FIX_WALL_REFLECT_STOCHASTIC_H
#define LMP_FIX_WALL_REFLECT_STOCHASTIC_H #define LMP_FIX_WALL_REFLECT_STOCHASTIC_H
#include "random_mars.h" #include "random_mars.h"
#include "fix_wall_reflect.h" #include "fix_wall_reflect.h"
@ -29,20 +28,16 @@ namespace LAMMPS_NS {
class FixWallReflectStochastic : public FixWallReflect { class FixWallReflectStochastic : public FixWallReflect {
public: public:
FixWallReflectStochastic(class LAMMPS *, int, char **); FixWallReflectStochastic(class LAMMPS *, int, char **);
void wall_particle(int m,int which, double coord);
virtual ~FixWallReflectStochastic(); virtual ~FixWallReflectStochastic();
private:
protected:
class RanMars *random;
int seedfix; int seedfix;
double walltemp[6],wallvel[6][3],wallaccom[6][3]; double walltemp[6],wallvel[6][3],wallaccom[6][3];
int reflectionstyle; int reflectionstyle;
class RanMars *random;
void wall_particle(int m,int which, double coord);
}; };
} }

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@ -18,30 +18,26 @@
#include "update.h" #include "update.h"
#include "modify.h" #include "modify.h"
#include "domain.h" #include "domain.h"
#include "force.h"
#include "lattice.h" #include "lattice.h"
#include "input.h" #include "input.h"
#include "variable.h" #include "variable.h"
#include "error.h" #include "error.h"
#include "force.h"
using namespace LAMMPS_NS; using namespace LAMMPS_NS;
using namespace FixConst; using namespace FixConst;
/* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */
FixWallReflect::FixWallReflect(LAMMPS *lmp, int narg, char **arg) : FixWallReflect::FixWallReflect(LAMMPS *lmp, int narg, char **arg) :
Fix(lmp, narg, arg), Fix(lmp, narg, arg),
nwall(0) nwall(0)
{ {
if (narg < 4) error->all(FLERR,"Illegal fix wall/reflect command"); if (narg < 4) error->all(FLERR,"Illegal fix wall/reflect command");
if (strcmp(arg[2],"wall/reflect/stochastic") == 0) return;// child class can be stochastic // let child class process all args
if (strcmp(arg[2],"wall/reflect/stochastic") == 0) return;
dynamic_group_allow = 1; dynamic_group_allow = 1;
@ -89,13 +85,13 @@ FixWallReflect::FixWallReflect(LAMMPS *lmp, int narg, char **arg) :
nwall++; nwall++;
iarg += 2; iarg += 2;
} else if (strcmp(arg[iarg],"units") == 0) { } else if (strcmp(arg[iarg],"units") == 0) {
if (iarg+2 > narg) error->all(FLERR,"Illegal wall/reflect command"); if (iarg+2 > narg) error->all(FLERR,"Illegal wall/reflect command");
if (strcmp(arg[iarg+1],"box") == 0) scaleflag = 0; if (strcmp(arg[iarg+1],"box") == 0) scaleflag = 0;
else if (strcmp(arg[iarg+1],"lattice") == 0) scaleflag = 1; else if (strcmp(arg[iarg+1],"lattice") == 0) scaleflag = 1;
else error->all(FLERR,"Illegal fix wall/reflect command"); else error->all(FLERR,"Illegal fix wall/reflect command");
iarg += 2; iarg += 2;
} else error->all(FLERR,"Illegal fix wall/reflect command"); } else error->all(FLERR,"Illegal fix wall/reflect command");
} }
@ -146,8 +142,6 @@ FixWallReflect::FixWallReflect(LAMMPS *lmp, int narg, char **arg) :
if (wallstyle[m] == VARIABLE) varflag = 1; if (wallstyle[m] == VARIABLE) varflag = 1;
} }
/* ---------------------------------------------------------------------- */ /* ---------------------------------------------------------------------- */
FixWallReflect::~FixWallReflect() FixWallReflect::~FixWallReflect()
@ -194,14 +188,11 @@ void FixWallReflect::init()
void FixWallReflect::post_integrate() void FixWallReflect::post_integrate()
{ {
//int m;
double coord; double coord;
// coord = current position of wall // coord = current position of wall
// evaluate variable if necessary, wrap with clear/add // evaluate variable if necessary, wrap with clear/add
if (varflag) modify->clearstep_compute(); if (varflag) modify->clearstep_compute();
for (int m = 0; m < nwall; m++) { for (int m = 0; m < nwall; m++) {
@ -212,17 +203,19 @@ void FixWallReflect::post_integrate()
else coord *= zscale; else coord *= zscale;
} else coord = coord0[m]; } else coord = coord0[m];
wall_particle(m,wallwhich[m],coord); wall_particle(m,wallwhich[m],coord);
}
if (varflag) modify->addstep_compute(update->ntimestep + 1); if (varflag) modify->addstep_compute(update->ntimestep + 1);
} }
}
/* ----------------------------------------------------------------------
this method may be overwritten by a child class
------------------------------------------------------------------------- */
void FixWallReflect::wall_particle(int m, int which, double coord) void FixWallReflect::wall_particle(int m, int which, double coord)
{ {
int i, dim, side,sign; int i,dim,side;
double **x = atom->x; double **x = atom->x;
double **v = atom->v; double **v = atom->v;
@ -232,9 +225,8 @@ void FixWallReflect::wall_particle(int m, int which, double coord)
dim = which / 2; dim = which / 2;
side = which % 2; side = which % 2;
for (i = 0; i < nlocal; i++) for (i = 0; i < nlocal; i++) {
if (mask[i] & groupbit) { if (mask[i] & groupbit) {
if (side == 0) { if (side == 0) {
if (x[i][dim] < coord) { if (x[i][dim] < coord) {
x[i][dim] = coord + (coord - x[i][dim]); x[i][dim] = coord + (coord - x[i][dim]);
@ -247,4 +239,5 @@ void FixWallReflect::wall_particle(int m, int which, double coord)
} }
} }
} }
}
} }

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@ -26,14 +26,14 @@ namespace LAMMPS_NS {
class FixWallReflect : public Fix { class FixWallReflect : public Fix {
public: public:
enum{XLO=0,XHI=1,YLO=2,YHI=3,ZLO=4,ZHI=5};
enum{NONE=0,EDGE,CONSTANT,VARIABLE};
FixWallReflect(class LAMMPS *, int, char **); FixWallReflect(class LAMMPS *, int, char **);
virtual ~FixWallReflect(); virtual ~FixWallReflect();
virtual void wall_particle(int m, int which, double coord);
int setmask(); int setmask();
void init(); void init();
void post_integrate(); void post_integrate();
enum{XLO=0,XHI=1,YLO=2,YHI=3,ZLO=4,ZHI=5};
enum{NONE=0,EDGE,CONSTANT,VARIABLE};
protected: protected:
int nwall; int nwall;
@ -43,6 +43,8 @@ class FixWallReflect : public Fix {
int varindex[6]; int varindex[6];
int varflag; int varflag;
double xscale,yscale,zscale; double xscale,yscale,zscale;
virtual void wall_particle(int m, int which, double coord);
}; };
} }

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@ -90,7 +90,6 @@ double RanMars::uniform()
return uni; return uni;
} }
/* ---------------------------------------------------------------------- /* ----------------------------------------------------------------------
gaussian RN gaussian RN
------------------------------------------------------------------------- */ ------------------------------------------------------------------------- */
@ -127,7 +126,6 @@ double RanMars::gaussian(double mu, double sigma)
return v1; return v1;
} }
/* ---------------------------------------------------------------------- /* ----------------------------------------------------------------------
Rayleigh RN Rayleigh RN
------------------------------------------------------------------------- */ ------------------------------------------------------------------------- */
@ -136,16 +134,13 @@ double RanMars::rayleigh(double sigma)
{ {
double first,v1; double first,v1;
if (sigma <= 0) { if (sigma <= 0) error->all(FLERR,"Invalid Rayleigh parameter");
error->all(FLERR,"Invalid Rayleigh parameter");
} else {
v1 = uniform(); v1 = uniform();
first = sigma*sqrt(-2.0*log(v1)); first = sigma*sqrt(-2.0*log(v1));
return first; return first;
}
} }
/* ---------------------------------------------------------------------- /* ----------------------------------------------------------------------
Bessel exponential RN Bessel exponential RN
------------------------------------------------------------------------- */ ------------------------------------------------------------------------- */
@ -153,20 +148,21 @@ double RanMars::rayleigh(double sigma)
double RanMars::besselexp(double theta, double alpha, double cp) double RanMars::besselexp(double theta, double alpha, double cp)
{ {
double first,v1,v2; double first,v1,v2;
if ((theta < 0) || (alpha < 0) || (alpha >1)) {
if (theta < 0.0 || alpha < 0.0 || alpha < 1.0)
error->all(FLERR,"Invalid Bessel exponential distribution parameters"); error->all(FLERR,"Invalid Bessel exponential distribution parameters");
} else {
v1 = uniform(); v1 = uniform();
v2 = uniform(); v2 = uniform();
if (cp < 0) {
first = sqrt((1.0-alpha)*cp*cp - 2.0*alpha*theta*log(v1) if (cp < 0.0)
+ 2.0*sqrt(-2.0*theta*(1.0-alpha)*alpha*log(v1)) first = sqrt((1.0-alpha)*cp*cp - 2.0*alpha*theta*log(v1) +
* cos(2.0*MathConst::MY_PI*v2)*cp); 2.0*sqrt(-2.0*theta*(1.0-alpha)*alpha*log(v1)) *
} else { cos(2.0*MathConst::MY_PI*v2)*cp);
first = -sqrt((1.0-alpha)*cp*cp - 2.0*alpha*theta*log(v1) else
- 2.0*sqrt(-2.0*theta*(1.0-alpha)*alpha*log(v1)) first = -sqrt((1.0-alpha)*cp*cp - 2.0*alpha*theta*log(v1) -
* cos(2.0*MathConst::MY_PI*v2)*cp); 2.0*sqrt(-2.0*theta*(1.0-alpha)*alpha*log(v1)) *
} cos(2.0*MathConst::MY_PI*v2)*cp);
return first; return first;
}
} }