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KernelFunction.cpp
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KernelFunction.cpp
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#include "KernelFunction.h"
#include "math.h"
#include <vector>
#include "ATC_Error.h"
#include "Quadrature.h"
#include "Utility.h"
using namespace std;
using namespace ATC_Utility;
static const double tol = 1.0e-8;
static const int line_ngauss = 10;
static double line_xg[line_ngauss], line_wg[line_ngauss];
namespace ATC {
//========================================================================
// KernelFunctionMgr
//========================================================================
KernelFunctionMgr * KernelFunctionMgr::myInstance_ = NULL;
//------------------------------------------------------------------------
// instance
//------------------------------------------------------------------------
KernelFunctionMgr * KernelFunctionMgr::instance()
{
if (myInstance_ == NULL) {
myInstance_ = new KernelFunctionMgr();
}
return myInstance_;
}
//------------------------------------------------------------------------
// get function from args
//------------------------------------------------------------------------
KernelFunction* KernelFunctionMgr::function(char ** arg, int narg)
{
/*! \page man_kernel_function fix_modify AtC kernel
\section syntax
fix_modify AtC kernel <type> <parameters>
- type (keyword) = step, cell, cubic_bar, cubic_cylinder, cubic_sphere,
quartic_bar, quartic_cylinder, quartic_sphere \n
- parameters :\n
step = radius (double) \n
cell = hx, hy, hz (double) or h (double) \n
cubic_bar = half-width (double) \n
cubic_cylinder = radius (double) \n
cubic_sphere = radius (double) \n
quartic_bar = half-width (double) \n
quartic_cylinder = radius (double) \n
quartic_sphere = radius (double) \n
\section examples
fix_modify AtC kernel cell 1.0 1.0 1.0
fix_modify AtC kernel quartic_sphere 10.0
\section description
\section restrictions
Must be used with the hardy AtC fix \n
For bar kernel types, half-width oriented along x-direction \n
For cylinder kernel types, cylindrical axis is assumed to be in z-direction \n
( see \ref man_fix_atc )
\section related
\section default
No default
*/
int argIdx = 0;
KernelFunction * ptr = NULL;
char* type = arg[argIdx++];
if (strcmp(type,"step")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff radius
ptr = new KernelFunctionStep(1,parameters);
}
else if (strcmp(type,"cell")==0) {
double parameters[3];
parameters[0] = parameters[1] = parameters[2] = atof(arg[argIdx++]);
if (narg > argIdx) { // L_x, L_y, L_z
for (int i = 1; i < 3; i++) { parameters[i] = atof(arg[argIdx++]); }
}
ptr = new KernelFunctionCell(2,parameters);
}
else if (strcmp(type,"cubic_bar")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff half-length
ptr = new KernelFunctionCubicBar(1,parameters);
}
else if (strcmp(type,"linear_bar")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff half-length
ptr = new KernelFunctionLinearBar(1,parameters);
}
else if (strcmp(type,"cubic_cylinder")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff radius
ptr = new KernelFunctionCubicCyl(1,parameters);
}
else if (strcmp(type,"cubic_sphere")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff radius
ptr = new KernelFunctionCubicSphere(1,parameters);
}
else if (strcmp(type,"quartic_bar")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff half-length
ptr = new KernelFunctionQuarticBar(1,parameters);
}
else if (strcmp(type,"quartic_cylinder")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff radius
ptr = new KernelFunctionQuarticCyl(1,parameters);
}
else if (strcmp(type,"quartic_sphere")==0) {
double parameters[1] = {atof(arg[argIdx])}; // cutoff radius
ptr = new KernelFunctionQuarticSphere(1,parameters);
}
pointerSet_.insert(ptr);
return ptr;
}
// Destructor
KernelFunctionMgr::~KernelFunctionMgr()
{
set<KernelFunction * >::iterator it;
for (it = pointerSet_.begin(); it != pointerSet_.end(); it++)
if (*it) delete *it;
}
//------------------------------------------------------------------------
// KernelFunction
//------------------------------------------------------------------------
// constructor
KernelFunction::KernelFunction(int nparameters, double* parameters):
Rc_(0),invRc_(0),nsd_(3),
lammpsInterface_(LammpsInterface::instance())
{
Rc_ = parameters[0];
invRc_ = 1.0/Rc_;
Rc_ = parameters[0];
invRc_ = 1.0/Rc_;
invVol_ = 1.0/(4.0/3.0*Pi_*pow(Rc_,3));
ATC::Quadrature::instance()->set_line_quadrature(line_ngauss,line_xg,line_wg);
// get periodicity and box bounds/lengths
lammpsInterface_->box_periodicity(periodicity[0],
periodicity[1],periodicity[2]);
lammpsInterface_->box_bounds(box_bounds[0][0],box_bounds[1][0],
box_bounds[0][1],box_bounds[1][1],
box_bounds[0][2],box_bounds[1][2]);
for (int k = 0; k < 3; k++) {
box_length[k] = box_bounds[1][k] - box_bounds[0][k];
}
}
// does an input node's kernel intersect bonds on this processor
bool KernelFunction::node_contributes(DENS_VEC node) const
{
DENS_VEC ghostNode = node;
bool contributes = true;
bool ghostContributes = lammpsInterface_->nperiodic();
double kernel_bounds[2][3];
lammpsInterface_->sub_bounds(kernel_bounds[0][0],kernel_bounds[1][0],
kernel_bounds[0][1],kernel_bounds[1][1],
kernel_bounds[0][2],kernel_bounds[1][2]);
for (int i=0; i<3; ++i) {
if (i < nsd_) {
kernel_bounds[0][i] -= (Rc_+lammpsInterface_->pair_cutoff());
kernel_bounds[1][i] += (Rc_+lammpsInterface_->pair_cutoff());
contributes = contributes && (node(i) >= kernel_bounds[0][i])
&& (node(i) < kernel_bounds[1][i]);
if (periodicity[i]) {
if (node[i] <= box_bounds[0][i] + box_length[i]/2) {
ghostNode[i] += box_length[i];
} else {
ghostNode[i] -= box_length[i];
}
ghostContributes = ghostContributes
&& ((ghostNode(i) >= kernel_bounds[0][i]) ||
(node(i) >= kernel_bounds[0][i]))
&& ((ghostNode(i) < kernel_bounds[1][i]) ||
(node(i) < kernel_bounds[1][i]));
}
}
if (!(contributes || ghostContributes)) break;
}
return true;
}
bool KernelFunction::in_support(DENS_VEC dx) const
{
if (dx.norm() > Rc_) return false;
return true;
}
// bond function value via quadrature
double KernelFunction::bond(DENS_VEC& xa, DENS_VEC&xb, double lam1, double lam2) const
{
DENS_VEC xab(nsd_), q(nsd_);
double lamg;
double bhsum=0.0;
xab = xa - xb;
for (int i = 0; i < line_ngauss; i++) {
lamg=0.5*((lam2-lam1)*line_xg[i]+(lam2+lam1));
q = lamg*xab + xb;
double locg_value=this->value(q);
bhsum+=locg_value*line_wg[i];
}
return 0.5*(lam2-lam1)*bhsum;
}
// localization-volume intercepts for bond calculation
// bond intercept values assuming spherical support
void KernelFunction::bond_intercepts(DENS_VEC& xa,
DENS_VEC& xb, double &lam1, double &lam2) const
{
if (nsd_ == 2) {// for cylinders, axis is always z!
const int iaxis = 2;
xa[iaxis] = 0.0;
xb[iaxis] = 0.0;
} else if (nsd_ == 1) {// for bars, analysis is 1D in x
xa[1] = 0.0;
xa[2] = 0.0;
xb[1] = 0.0;
xb[2] = 0.0;
}
lam1 = lam2 = -1;
double ra_n = invRc_*xa.norm(); // lambda = 1
double rb_n = invRc_*xb.norm(); // lambda = 0
bool a_in = (ra_n <= 1.0);
bool b_in = (rb_n <= 1.0);
if (a_in && b_in) {
lam1 = 0.0;
lam2 = 1.0;
return;
}
DENS_VEC xab = xa - xb;
double rab_n = invRc_*xab.norm();
double a = rab_n*rab_n; // always at least an interatomic distance
double b = 2.0*invRc_*invRc_*xab.dot(xb);
double c = rb_n*rb_n - 1.0;
double discrim = b*b - 4.0*a*c; // discriminant
if (discrim < 0) return; // no intersection
// num recipes:
double s1, s2;
if (b < 0.0) {
double aux = -0.5*(b-sqrt(discrim));
s1 = c/aux;
s2 = aux/a;
}
else {
double aux = -0.5*(b+sqrt(discrim));
s1 = aux/a;
s2 = c/aux;
}
if (a_in && !b_in) {
lam1 = s1;
lam2 = 1.0;
}
else if (!a_in && b_in) {
lam1 = 0.0;
lam2 = s2;
}
else {
if (s1 >= 0.0 && s2 <= 1.0) {
lam1 = s1;
lam2 = s2;
}
}
}
//------------------------------------------------------------------------
// constructor
KernelFunctionStep::KernelFunctionStep
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
}
}
}
}
// function value
double KernelFunctionStep::value(DENS_VEC& x_atom) const
{
double rn=invRc_*x_atom.norm();
if (rn <= 1.0) { return 1.0; }
else { return 0.0; }
}
// function derivative value
void KernelFunctionStep::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
/** a step with rectangular support suitable for a rectangular grid */
// constructor
KernelFunctionCell::KernelFunctionCell
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
hx = parameters[0];
hy = parameters[1];
hz = parameters[2];
invVol_ = 1.0/8.0/(hx*hy*hz);
cellBounds_.reset(6);
cellBounds_(0) = -hx;
cellBounds_(1) = hx;
cellBounds_(2) = -hy;
cellBounds_(3) = hy;
cellBounds_(4) = -hz;
cellBounds_(5) = hz;
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (parameters[k] > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
}
}
}
}
// does an input node's kernel intersect bonds on this processor
bool KernelFunctionCell::node_contributes(DENS_VEC node) const
{
DENS_VEC ghostNode = node;
bool contributes = true;
bool ghostContributes = lammpsInterface_->nperiodic();
double kernel_bounds[2][3];
lammpsInterface_->sub_bounds(kernel_bounds[0][0],kernel_bounds[1][0],
kernel_bounds[0][1],kernel_bounds[1][1],
kernel_bounds[0][2],kernel_bounds[1][2]);
for (int i=0; i<3; ++i) {
kernel_bounds[0][i] -= (cellBounds_(i*2+1) +
lammpsInterface_->pair_cutoff());
kernel_bounds[1][i] += (cellBounds_(i*2+1) +
lammpsInterface_->pair_cutoff());
contributes = contributes && (node(i) >= kernel_bounds[0][i])
&& (node(i) < kernel_bounds[1][i]);
if (periodicity[i]) {
if (node[i] <= box_bounds[0][i] + box_length[i]/2) {
ghostNode[i] += box_length[i];
} else {
ghostNode[i] -= box_length[i];
}
ghostContributes = ghostContributes
&& ((ghostNode(i) >= kernel_bounds[0][i]) ||
(node(i) >= kernel_bounds[0][i]))
&& ((ghostNode(i) < kernel_bounds[1][i]) ||
(node(i) < kernel_bounds[1][i]));
}
if (!(contributes || ghostContributes)) break;
}
return true;
}
bool KernelFunctionCell::in_support(DENS_VEC dx) const
{
if (dx(0) < cellBounds_(0)
|| dx(0) > cellBounds_(1)
|| dx(1) < cellBounds_(2)
|| dx(1) > cellBounds_(3)
|| dx(2) < cellBounds_(4)
|| dx(2) > cellBounds_(5) ) return false;
return true;
}
// function value
double KernelFunctionCell::value(DENS_VEC& x_atom) const
{
if ((cellBounds_(0) <= x_atom(0)) && (x_atom(0) < cellBounds_(1))
&& (cellBounds_(2) <= x_atom(1)) && (x_atom(1) < cellBounds_(3))
&& (cellBounds_(4) <= x_atom(2)) && (x_atom(2) < cellBounds_(5))) {
return 1.0;
}
else {
return 0.0;
}
}
// function derivative value
void KernelFunctionCell::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
// bond intercept values for rectangular region : origin is the node position
void KernelFunctionCell::bond_intercepts(DENS_VEC& xa,
DENS_VEC& xb, double &lam1, double &lam2) const
{
lam1 = 0.0; // start
lam2 = 1.0; // end
bool a_in = (value(xa) > 0.0);
bool b_in = (value(xb) > 0.0);
// (1) both in, no intersection needed
if (a_in && b_in) {
return;
}
// (2) for one in & one out -> one plane intersection
// determine the points of intersection between the line joining
// atoms a and b and the bounding planes of the localization volume
else if (a_in || b_in) {
DENS_VEC xab = xa - xb;
for (int i = 0; i < nsd_; i++) {
// check if segment is parallel to face
if (fabs(xab(i)) > tol) {
for (int j = 0; j < 2; j++) {
double s = (cellBounds_(2*i+j) - xb(i))/xab(i);
// check if between a & b
if (s >= 0 && s <= 1) {
bool in_bounds = false;
DENS_VEC x = xb + s*xab;
if (i == 0) {
if ((cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
in_bounds = true;
}
}
else if (i == 1) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
in_bounds = true;
}
}
else if (i == 2) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))) {
in_bounds = true;
}
}
if (in_bounds) {
if (a_in) { lam1 = s;}
else { lam2 = s;}
return;
}
}
}
}
}
throw ATC_Error("logic failure in HardyKernel Cell for single intersection\n");
}
// (3) both out -> corner intersection
else {
lam2 = lam1; // default to no intersection
DENS_VEC xab = xa - xb;
double ss[6] = {-1,-1,-1,-1,-1,-1};
int is = 0;
for (int i = 0; i < nsd_; i++) {
// check if segment is parallel to face
if (fabs(xab(i)) > tol) {
for (int j = 0; j < 2; j++) {
double s = (cellBounds_(2*i+j) - xb(i))/xab(i);
// check if between a & b
if (s >= 0 && s <= 1) {
// check if in face
DENS_VEC x = xb + s*xab;
if (i == 0) {
if ((cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
ss[is++] = s;
}
}
else if (i == 1) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(4) <= x(2)) && (x(2) <= cellBounds_(5))) {
ss[is++] = s;
}
}
else if (i == 2) {
if ((cellBounds_(0) <= x(0)) && (x(0) <= cellBounds_(1))
&& (cellBounds_(2) <= x(1)) && (x(1) <= cellBounds_(3))) {
ss[is++] = s;
}
}
}
}
}
}
if (is == 1) {
// intersection occurs at a box edge - leave lam1 = lam2
}
else if (is == 2) {
lam1 = min(ss[0],ss[1]);
lam2 = max(ss[0],ss[1]);
}
else if (is == 3) {
// intersection occurs at a box vertex - leave lam1 = lam2
}
else {
if (is != 0) throw ATC_Error("logic failure in HardyKernel Cell for corner intersection\n");
}
}
}
//------------------------------------------------------------------------
// constructor
KernelFunctionCubicSphere::KernelFunctionCubicSphere
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double KernelFunctionCubicSphere::value(DENS_VEC& x_atom) const
{
double r=x_atom.norm();
double rn=r/Rc_;
if (rn < 1.0) { return 5.0*(1.0-3.0*rn*rn+2.0*rn*rn*rn); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionCubicSphere::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
// constructor
KernelFunctionQuarticSphere::KernelFunctionQuarticSphere
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double KernelFunctionQuarticSphere::value(DENS_VEC& x_atom) const
{
double r=x_atom.norm();
double rn=r/Rc_;
if (rn < 1.0) { return 35.0/8.0*pow((1.0-rn*rn),2); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionQuarticSphere::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
// constructor
KernelFunctionCubicCyl::KernelFunctionCubicCyl
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
nsd_ = 2;
double Lz = box_length[2];
invVol_ = 1.0/(Pi_*pow(Rc_,2)*Lz);
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double KernelFunctionCubicCyl::value(DENS_VEC& x_atom) const
{
double r=sqrt(pow(x_atom(0),2)+pow(x_atom(1),2));
double rn=r/Rc_;
if (rn < 1.0) { return 10.0/3.0*(1.0-3.0*rn*rn+2.0*rn*rn*rn); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionCubicCyl::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
// constructor
KernelFunctionQuarticCyl::KernelFunctionQuarticCyl
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
nsd_ = 2;
double Lz = box_length[2];
invVol_ = 1.0/(Pi_*pow(Rc_,2)*Lz);
for (int k = 0; k < nsd_; k++ ) {
if ((bool) periodicity[k]) {
if (Rc_ > 0.5*box_length[k]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
};
}
// function value
double KernelFunctionQuarticCyl::value(DENS_VEC& x_atom) const
{
double r=sqrt(pow(x_atom(0),2)+pow(x_atom(1),2));
double rn=r/Rc_;
if (rn < 1.0) { return 3.0*pow((1.0-rn*rn),2); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionQuarticCyl::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
// constructor
KernelFunctionCubicBar::KernelFunctionCubicBar
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
// Note: Bar is assumed to be oriented in the x(0) direction
nsd_ = 1;
double Ly = box_length[1];
double Lz = box_length[2];
invVol_ = 1.0/(2*Rc_*Ly*Lz);
if ((bool) periodicity[0]) {
if (Rc_ > 0.5*box_length[0]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
}
// function value
double KernelFunctionCubicBar::value(DENS_VEC& x_atom) const
{
double r=abs(x_atom(0));
double rn=r/Rc_;
if (rn < 1.0) { return 2.0*(1.0-3.0*rn*rn+2.0*rn*rn*rn); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionCubicBar::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
//------------------------------------------------------------------------
// constructor
KernelFunctionLinearBar::KernelFunctionLinearBar
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
// Note: Bar is assumed to be oriented in the z(0) direction
double Lx = box_length[0];
double Ly = box_length[1];
invVol_ = 1.0/(Lx*Ly*Rc_);
if ((bool) periodicity[2]) {
if (Rc_ > 0.5*box_length[2]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
}
// function value
double KernelFunctionLinearBar::value(DENS_VEC& x_atom) const
{
double r=abs(x_atom(2));
double rn=r/Rc_;
if (rn < 1.0) { return 1.0-rn; }
else { return 0.0; }
}
// function derivative value
void KernelFunctionLinearBar::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
deriv(0) = 0.0;
deriv(1) = 0.0;
double r=abs(x_atom(2));
double rn=r/Rc_;
if (rn < 1.0 && x_atom(2) <= 0.0) { deriv(2) = 1.0/Rc_; }
else if (rn < 1.0 && x_atom(2) > 0.0) { deriv(2) = -1.0/Rc_; }
else { deriv(2) = 0.0; }
}
//------------------------------------------------------------------------
// constructor
KernelFunctionQuarticBar::KernelFunctionQuarticBar
(int nparameters, double* parameters):
KernelFunction(nparameters, parameters)
{
// Note: Bar is assumed to be oriented in the x(0) direction
nsd_ = 1;
double Ly = box_length[1];
double Lz = box_length[2];
invVol_ = 1.0/(2*Rc_*Ly*Lz);
if ((bool) periodicity[0]) {
if (Rc_ > 0.5*box_length[0]) {
throw ATC_Error("Size of localization volume is too large for periodic boundary condition");
};
};
}
// function value
double KernelFunctionQuarticBar::value(DENS_VEC& x_atom) const
{
double r=abs(x_atom(0));
double rn=r/Rc_;
// if (rn < 1.0) { return 5.0/2.0*(1.0-6*rn*rn+8*rn*rn*rn-3*rn*rn*rn*rn); } - alternative quartic
if (rn < 1.0) { return 15.0/8.0*pow((1.0-rn*rn),2); }
else { return 0.0; }
}
// function derivative value
void KernelFunctionQuarticBar::derivative(const DENS_VEC& x_atom, DENS_VEC& deriv) const
{
deriv.reset(nsd_);
}
};

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