forked from lijiext/lammps
Merge pull request #553 from Pakketeretet2/USER-MANIFOLD-gaussian-bump
Update to USER-MANIFOLD gaussian bump
This commit is contained in:
sjplimp
GitHub
commit
3bf2c60276
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@ -1,138 +1,374 @@
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#include "manifold_gaussian_bump.h"
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#include "comm.h"
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#include "error.h"
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using namespace LAMMPS_NS;
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using namespace user_manifold;
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// This manifold comes with some baggage;
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// it needs a taper function that is sufficiently smooth
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// so we use a cubic Hermite interpolation and then for
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// efficiency we construct a lookup table for that....
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class cubic_hermite
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{
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public:
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// Represent x-polynomial as a * t^3 + b * t^2 + c*t + d.
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double a, b, c, d;
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// And y-polynomial as s * t^3 + u * t^2 + v * t + w.
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double s, u, v, w;
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double x0, x1, y0, y1, yp0, yp1;
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LAMMPS_NS::Error *err;
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cubic_hermite( double x0, double x1, double y0, double y1,
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double yp0, double yp1, LAMMPS_NS::Error *err ) :
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x0(x0), x1(x1), y0(y0), y1(y1), yp0(yp0), yp1(yp1),
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a( 2*x0 + 2 - 2*x1 ),
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b( -3*x0 - 3 + 3*x1 ),
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c( 1.0 ),
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d( x0 ),
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s( 2*y0 - 2*y1 + yp0 + yp1 ),
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u( -3*y0 + 3*y1 - 2*yp0 - yp1 ),
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v( yp0 ),
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w( y0 ),
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err(err)
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{
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test();
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}
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void test()
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{
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if( fabs( x(0) - x0 ) > 1e-8 ) err->one(FLERR, "x0 wrong");
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if( fabs( x(1) - x1 ) > 1e-8 ) err->one(FLERR, "x1 wrong");
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if( fabs( y(0) - y0 ) > 1e-8 ) err->one(FLERR, "y0 wrong");
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if( fabs( y(1) - y1 ) > 1e-8 ) err->one(FLERR, "y1 wrong");
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}
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double get_t_from_x( double xx ) const
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{
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if( xx < x0 || xx > x1 ){
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char msg[2048];
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sprintf(msg, "x ( %g ) out of bounds [%g, %g]", xx, x0, x1 );
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err->one(FLERR, msg);
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}
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// Newton iterate to get right t.
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double t = xx - x0;
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double dx = x1 - x0;
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// Reasonable initial guess I hope:
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t /= dx;
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double tol = 1e-8;
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int maxit = 500;
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double ff = x(t) - xx;
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double ffp = xp(t);
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// double l = 1.0 / ( 1 + res*res );
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for( int i = 0; i < maxit; ++i ){
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t -= ff / ffp;
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ff = x(t) - xx;
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ffp = xp(t);
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double res = ff;
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if( fabs( res ) < tol ){
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return t;
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}
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}
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err->warning(FLERR, "Convergence failed");
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return t;
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}
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double x( double t ) const
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{
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double t2 = t*t;
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double t3 = t2*t;
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return a*t3 + b*t2 + c*t + d;
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}
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double y_from_x( double x ) const
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{
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double t = get_t_from_x( x );
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return y(t);
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}
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double yp_from_x( double x ) const
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{
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double t = get_t_from_x( x );
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return yp(t);
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}
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double y( double t ) const
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{
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double t2 = t*t;
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double t3 = t2*t;
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return s*t3 + u*t2 + v*t + w;
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}
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void xy( double t, double &xx, double &yy ) const
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{
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xx = x(t);
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yy = y(t);
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}
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double xp( double t ) const
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{
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double t2 = t*t;
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return 3*a*t2 + 2*b*t + c;
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}
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double yp( double t ) const
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{
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double t2 = t*t;
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return 3*t2*s + 2*u*t + v;
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}
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double xpp( double t ) const
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{
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return 6*a*t + 2*b;
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}
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};
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// Manifold itself:
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manifold_gaussian_bump::manifold_gaussian_bump(class LAMMPS* lmp,
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int narg, char **arg)
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: manifold(lmp), lut_z(NULL), lut_zp(NULL) {}
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manifold_gaussian_bump::~manifold_gaussian_bump()
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{
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if( lut_z ) delete lut_z;
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if( lut_zp ) delete lut_zp;
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}
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// The constraint is z = f(r = sqrt( x^2 + y^2) )
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// f(x) = A*exp( -x^2 / 2 l^2 ) if x < rc1
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// = a + b*x + c*x**2 + d*x**3 if rc1 <= x < rc2
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// = Some interpolation if rc1 <= rc2
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// = 0 if x >= rc2
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//
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double manifold_gaussian_bump::g( const double *x )
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{
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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return x[2] - gaussian_bump_x2( x2 );
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}else if( x2 < rc22 ){
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double rr = sqrt(x2);
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double xi = rr - rc1;
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xi *= inv_dr;
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double xi2 = x2 * inv_dr*inv_dr;
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double xi3 = xi*xi2;
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return x[2] - ( aa + bb*xi + cc*xi2 + dd*xi3 );
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}else{
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return x[2];
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}
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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return x[2] - gaussian_bump_x2( x2 );
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}else if( x2 < rc22 ){
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double rr = sqrt( x2 );
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double z_taper_func = lut_get_z( rr );
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return x[2] - z_taper_func;
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}else{
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return x[2];
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}
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}
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void manifold_gaussian_bump::n( const double *x, double *nn )
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{
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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nn[2] = 1.0;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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double factor = gaussian_bump_x2(x2);
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factor /= (ll*ll);
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nn[0] = factor * x[0];
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nn[1] = factor * x[1];
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}else if( x2 < rc22 ){
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double rr = sqrt(x2);
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double xi = rr - rc1;
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xi *= inv_dr;
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double xi2 = x2 * inv_dr*inv_dr;
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double der = bb + 2*cc*xi + 3*dd*xi2;
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nn[0] = -der * x[0] / rr;
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nn[1] = -der * x[1] / rr;
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}else{
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nn[0] = nn[1] = 0.0;
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}
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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nn[2] = 1.0;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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double factor = gaussian_bump_x2(x2);
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factor /= (ll*ll);
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nn[0] = factor * x[0];
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nn[1] = factor * x[1];
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}else if( x2 < rc22 ){
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double rr = sqrt( x2 );
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double zp_taper_func = lut_get_zp( rr );
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double inv_r = 1.0 / rr;
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double der_part = zp_taper_func * inv_r;
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nn[0] = der_part * x[0];
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nn[1] = der_part * x[1];
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}else{
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nn[0] = nn[1] = 0.0;
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}
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}
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double manifold_gaussian_bump::g_and_n( const double *x, double *nn )
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{
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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nn[2] = 1.0;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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double gb = gaussian_bump_x2(x2);
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double factor = gb / (ll*ll);
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nn[0] = factor * x[0];
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nn[1] = factor * x[1];
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return x[2] - gb;
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}else if( x2 < rc22 ){
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double rr = sqrt(x2);
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double xi = rr - rc1;
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xi *= inv_dr;
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double xi2 = x2 * inv_dr*inv_dr;
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double xi3 = xi*xi2;
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double xf[3];
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xf[0] = x[0];
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xf[1] = x[1];
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xf[2] = 0.0;
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nn[2] = 1.0;
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double der = bb + 2*cc*xi + 3*dd*xi2;
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nn[0] = -der * x[0] / rr;
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nn[1] = -der * x[1] / rr;
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double x2 = dot(xf,xf);
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if( x2 < rc12 ){
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double gb = gaussian_bump_x2(x2);
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double factor = gb / (ll*ll);
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nn[0] = factor * x[0];
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nn[1] = factor * x[1];
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return x[2] - gb;
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}else if( x2 < rc22 ){
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double z_taper_func, zp_taper_func;
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double rr = sqrt( x2 );
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lut_get_z_and_zp( rr, z_taper_func, zp_taper_func );
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double inv_r = 1.0 / rr;
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double der_part = zp_taper_func * inv_r;
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nn[0] = der_part * x[0];
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nn[1] = der_part * x[1];
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return x[2] - z_taper_func;
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}else{
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nn[0] = nn[1] = 0.0;
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return x[2];
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}
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return x[2] - ( aa + bb*xi + cc*xi2 + dd*xi3 );
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}else{
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nn[0] = nn[1] = 0.0;
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return x[2];
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}
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}
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void manifold_gaussian_bump::post_param_init()
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{
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// Read in the params:
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AA = params[0];
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ll = params[1];
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rc1 = params[2];
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rc2 = params[3];
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// Read in the params:
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AA = params[0];
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ll = params[1];
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rc1 = params[2];
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rc2 = params[3];
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ll2 = 2.0*ll*ll;
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ll2 = 2.0*ll*ll;
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f_at_rc = gaussian_bump_x2 ( rc12 );
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fp_at_rc = gaussian_bump_der( rc12 );
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rc12 = rc1*rc1;
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rc22 = rc2*rc2;
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dr = rc2 - rc1;
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inv_dr = 1.0 / dr;
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rc12 = rc1*rc1;
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rc22 = rc2*rc2;
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dr = rc2 - rc1;
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inv_dr = 1.0 / dr;
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f_at_rc = gaussian_bump_x2 ( rc12 );
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fp_at_rc = gaussian_bump_der( rc1 );
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make_lut();
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// test_lut();
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}
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double manifold_gaussian_bump::gaussian_bump( double x )
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double manifold_gaussian_bump::gaussian_bump( double x ) const
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{
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double x2 = x*x;
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return gaussian_bump_x2( x2 );
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double x2 = x*x;
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return gaussian_bump_x2( x2 );
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}
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double manifold_gaussian_bump::gaussian_bump_x2( double x2 )
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double manifold_gaussian_bump::gaussian_bump_x2( double x2 ) const
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{
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return AA*exp( -x2 / ll2 );
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return AA*exp( -x2 / ll2 );
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}
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double manifold_gaussian_bump::gaussian_bump_der( double x )
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double manifold_gaussian_bump::gaussian_bump_der( double x ) const
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{
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double x2 = x*x;
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return gaussian_bump_x2( x2 )*( -x/(ll*ll) );
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double x2 = x*x;
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return gaussian_bump_x2( x2 )*( -x/(ll*ll) );
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}
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void manifold_gaussian_bump::make_lut()
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{
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lut_x0 = rc1;
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lut_x1 = rc2;
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lut_Nbins = 1024; // Don't make it too big, it should fit in cache.
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lut_z = new double[lut_Nbins+1];
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lut_zp = new double[lut_Nbins+1];
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lut_dx = (lut_x1 - lut_x0) / lut_Nbins;
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cubic_hermite pchip( lut_x0, lut_x1, f_at_rc, 0.0, fp_at_rc, 0.0, error );
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double xx = lut_x0;
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for( int i = 0; i <= lut_Nbins; ++i ){
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lut_z[i] = pchip.y_from_x( xx );
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lut_zp[i] = pchip.yp_from_x( xx );
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xx += lut_dx;
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}
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}
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double manifold_gaussian_bump::lut_get_z ( double rr ) const
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{
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double xs = rr - lut_x0;
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double xss = xs / lut_dx;
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int bin = static_cast<int>(xss);
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double frac = xss - bin;
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double zleft = lut_z[bin];
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double zright = lut_z[bin+1];
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return zleft * ( 1 - frac ) + frac * zright;
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}
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double manifold_gaussian_bump::lut_get_zp( double rr ) const
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{
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double xs = rr - lut_x0;
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double xss = xs / lut_dx;
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int bin = static_cast<int>(xss);
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double frac = xss - bin;
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double zleft = lut_zp[bin];
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double zright = lut_zp[bin+1];
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return zleft * ( 1 - frac) + frac * zright;
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}
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void manifold_gaussian_bump::lut_get_z_and_zp( double rr, double &zz,
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double &zzp ) const
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{
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double xs = rr - lut_x0;
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double xss = xs / lut_dx;
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int bin = static_cast<int>(xss);
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double frac = xss - bin;
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double fmin = 1 - frac;
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double zleft = lut_z[bin];
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double zright = lut_z[bin+1];
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double zpleft = lut_zp[bin];
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double zpright = lut_zp[bin+1];
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zz = zleft * fmin + zright * frac;
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zzp = zpleft * fmin + zpright * frac;
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}
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void manifold_gaussian_bump::test_lut()
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{
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double x[3], nn[3];
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if( comm->me != 0 ) return;
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FILE *fp = fopen( "test_lut_gaussian.dat", "w" );
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double dx = 0.1;
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for( double xx = 0; xx < 20; xx += dx ){
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x[0] = xx;
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x[1] = 0.0;
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x[2] = 0.0;
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double gg = g( x );
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n( x, nn );
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double taper_z;
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if( xx <= rc1 ){
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taper_z = gaussian_bump(xx);
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}else if( xx < rc2 ){
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taper_z = lut_get_z( xx );
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}else{
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taper_z = 0.0;
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}
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fprintf( fp, "%g %g %g %g %g\n", xx, gaussian_bump(xx), taper_z,
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gg, nn[0], nn[1], nn[2] );
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}
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fclose(fp);
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}
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@ -1,4 +1,4 @@
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/* -*- c++ -*- ----------------------------------------------------------
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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http://lammps.sandia.gov, Sandia National Laboratories
|
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Steve Plimpton, sjplimp@sandia.gov
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|
|
@ -50,8 +50,8 @@ namespace user_manifold {
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class manifold_gaussian_bump : public manifold {
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public:
|
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enum { NPARAMS = 4 };
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manifold_gaussian_bump(class LAMMPS*, int, char **) : manifold(lmp) {}
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||||
virtual ~manifold_gaussian_bump(){}
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manifold_gaussian_bump(class LAMMPS*, int, char **);
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||||
virtual ~manifold_gaussian_bump();
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||||
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||||
virtual double g( const double * );
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||||
virtual void n( const double *, double * );
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|
|
@ -66,12 +66,29 @@ namespace user_manifold {
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|||
virtual void post_param_init();
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||||
private:
|
||||
// Some private constants:
|
||||
double aa, bb, cc, dd, AA, ll, ll2, f_at_rc, fp_at_rc;
|
||||
double AA, ll, ll2, f_at_rc, fp_at_rc;
|
||||
double rc1, rc2, rc12, rc22, dr, inv_dr;
|
||||
|
||||
double gaussian_bump ( double );
|
||||
double gaussian_bump_x2 ( double );
|
||||
double gaussian_bump_der( double );
|
||||
// Stuff for the look-up table:
|
||||
double lut_x0, lut_x1;
|
||||
int lut_Nbins;
|
||||
double lut_dx;
|
||||
double *lut_z;
|
||||
double *lut_zp;
|
||||
|
||||
double gaussian_bump ( double ) const;
|
||||
double gaussian_bump_x2 ( double ) const;
|
||||
double gaussian_bump_der( double ) const;
|
||||
|
||||
void make_lut();
|
||||
double lut_get_z ( double rr ) const;
|
||||
double lut_get_zp( double rr ) const;
|
||||
void lut_get_z_and_zp( double rr, double &zz, double &zzp ) const;
|
||||
|
||||
void test_lut();
|
||||
|
||||
double taper( double );
|
||||
double taper_der( double );
|
||||
|
||||
};
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue