/*
mg_operators.hh - This file is part of MUSIC -
a code to generate multi-scale initial conditions
for cosmological simulations
Copyright (C) 2010 Oliver Hahn
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see .
*/
#ifndef __MG_OPERATORS_HH
#define __MG_OPERATORS_HH
//! injection operator based Catmull-Rom splines with arbitrary refinement factor
class mg_cubic_mult
{
protected:
template< typename real_t >
inline double CUBE( real_t x ) const
{ return x*x*x; }
template< typename T >
inline T SQR( T x ) const
{ return x*x; }
public:
template
inline double interp_cubic( double dx, double dy, double dz, M& V, int ox, int oy, int oz ) const
{
register int i, j, k;
double u[4], v[4], w[4];
double r[4], q[4];
double vox = 0;
int sx=0,sy=0,sz=0;
if( dx > 0.0 ) sx=1;
if( dy > 0.0 ) sy=1;
if( dz > 0.0 ) sz=1;
if( dx > 0 )
{
w[0] = -0.5*CUBE(dx)+SQR(dx)-0.5*dx;
w[1] = 1.5*CUBE(dx)-2.5*SQR(dx)+1.0;
w[2] = -1.5*CUBE(dx)+2.0*SQR(dx)+0.5*dx;
w[3] = 0.5*CUBE(dx)-0.5*SQR(dx);
} else {
w[0] = -0.5*CUBE(dx)-0.5*SQR(dx);
w[1] = 1.5*CUBE(dx)+2.0*SQR(dx)-0.5*dx;
w[2] = -1.5*CUBE(dx)-2.5*SQR(dx)+1.0;
w[3] = 0.5*CUBE(dx)+SQR(dx)+0.5*dx;
}
if( dy > 0 )
{
v[0] = -0.5*CUBE(dy)+SQR(dy)-0.5*dy;
v[1] = 1.5*CUBE(dy)-2.5*SQR(dy)+1.0;
v[2] = -1.5*CUBE(dy)+2.0*SQR(dy)+0.5*dy;
v[3] = 0.5*CUBE(dy)-0.5*SQR(dy);
} else {
v[0] = -0.5*CUBE(dy)-0.5*SQR(dy);
v[1] = 1.5*CUBE(dy)+2.0*SQR(dy)-0.5*dy;
v[2] = -1.5*CUBE(dy)-2.5*SQR(dy)+1.0;
v[3] = 0.5*CUBE(dy)+SQR(dy)+0.5*dy;
}
if( dz > 0 )
{
u[0] = -0.5*CUBE(dz)+SQR(dz)-0.5*dz;
u[1] = 1.5*CUBE(dz)-2.5*SQR(dz)+1.0;
u[2] = -1.5*CUBE(dz)+2.0*SQR(dz)+0.5*dz;
u[3] = 0.5*CUBE(dz)-0.5*SQR(dz);
} else {
u[0] = -0.5*CUBE(dz)-0.5*SQR(dz);
u[1] = 1.5*CUBE(dz)+2.0*SQR(dz)-0.5*dz;
u[2] = -1.5*CUBE(dz)-2.5*SQR(dz)+1.0;
u[3] = 0.5*CUBE(dz)+SQR(dz)+0.5*dz;
}
for (k = 0; k < 4; k++)
{
q[k] = 0;
for (j = 0; j < 4; j++)
{
r[j] = 0;
for (i = 0; i < 4; i++)
{
r[j] += u[i] * V(ox+k-2+sx,oy+j-2+sy,oz+i-2+sz);
}
q[k] += v[j] * r[j];
}
vox += w[k] * q[k];
}
return vox;
}
template< typename m1, typename m2 >
inline void prolong( m1& V, m2& v, int oxc, int oyc, int ozc, int oxf, int oyf, int ozf, int R ) const
{
int N = (int)pow(2,R);
int Nl= -N/2+1;//, Nr=N/2;
double dx = 1.0/(double)N;
int nx = v.size(0), ny = v.size(1), nz = v.size(2);
double finemean = 0.0, coarsemean = 0.0;
unsigned finecount = 0, coarsecount = 0;
#pragma omp parallel for reduction(+:finemean,finecount,coarsemean,coarsecount)
for( int i=0; i
inline void prolong_add( m1& V, m2& v, int oxc, int oyc, int ozc, int oxf, int oyf, int ozf, int R ) const
{
int N = (int)pow(2,R);
int Nl= -N/2+1;//, Nr=N/2;
double dx = 1.0/(double)N;
int nx = v.size(0), ny = v.size(1), nz = v.size(2);
double finemean = 0.0, coarsemean = 0.0;
unsigned finecount = 0, coarsecount = 0;
#pragma omp parallel for reduction(+:finemean,finecount,coarsemean,coarsecount)
for( int i=0; i
inline double CUBE( real_t x ) const
{ return x*x*x; }
template< typename T >
inline T SQR( T x ) const
{ return x*x; }
public:
template< int sx, int sy, int sz, typename M >
inline double interp_cubic( int x, int y, int z, M& V, double s=1.0 ) const
{
int i, j, k;
//double dx, dy, dz;
double u[4], v[4], w[4];
double r[4], q[4];
double vox = 0;
//dx = 0.5*((double)sz - 0.5)*s;
//dy = 0.5*((double)sy - 0.5)*s;
//dz = 0.5*((double)sx - 0.5)*s;
if( sz == 1 )
{
u[0] = -4.5/64.0;
u[1] = 55.5/64.0;
u[2] = 14.5/64.0;
u[3] = -1.5/64.0;
} else {
u[0] = -1.5/64.0;
u[1] = 14.5/64.0;
u[2] = 55.5/64.0;
u[3] = -4.5/64.0;
}
if( sy == 1 )
{
v[0] = -4.5/64.0;
v[1] = 55.5/64.0;
v[2] = 14.5/64.0;
v[3] = -1.5/64.0;
} else{
v[0] = -1.5/64.0;
v[1] = 14.5/64.0;
v[2] = 55.5/64.0;
v[3] = -4.5/64.0;
}
if( sx == 1 )
{
w[0] = -4.5/64.0;
w[1] = 55.5/64.0;
w[2] = 14.5/64.0;
w[3] = -1.5/64.0;
} else {
w[0] = -1.5/64.0;
w[1] = 14.5/64.0;
w[2] = 55.5/64.0;
w[3] = -4.5/64.0;
}
for (k = 0; k < 4; k++)
{
q[k] = 0;
for (j = 0; j < 4; j++)
{
r[j] = 0;
for (i = 0; i < 4; i++)
{
r[j] += u[i] * V(x+k-2+sx,y+j-2+sy,z+i-2+sz);
}
q[k] += v[j] * r[j];
}
vox += w[k] * q[k];
}
return vox;
}
public:
//... restricts v to V
template< typename m1, typename m2 >
inline void restrict( m1& v, m2& V )
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i2,j2,k2,v)
+interp_cubic<0,1,0>(i2,j2,k2,v)
+interp_cubic<0,0,1>(i2,j2,k2,v)
+interp_cubic<1,1,0>(i2,j2,k2,v)
+interp_cubic<0,1,1>(i2,j2,k2,v)
+interp_cubic<1,0,1>(i2,j2,k2,v)
+interp_cubic<1,1,1>(i2,j2,k2,v)
+interp_cubic<0,0,0>(i2,j2,k2,v));
}
}
//... restricts v to V
template< typename m1, typename m2 >
inline void restrict_add( m1& v, m2& V )
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i2+1,j2,k2,v)
+interp_cubic<0,1,0>(i2,j2+1,k2,v)
+interp_cubic<0,0,1>(i2,j2,k2+1,v)
+interp_cubic<1,1,0>(i2+1,j2+1,k2,v)
+interp_cubic<0,1,1>(i2,j2+1,k2+1,v)
+interp_cubic<1,0,1>(i2+1,j2,k2+1,v)
+interp_cubic<1,1,1>(i2+1,j2+1,k2+1,v)
+interp_cubic<0,0,0>(i2,j2,k2,v));
}
}
//.. straight restriction on boundary
template< typename m1, typename m2 >
inline void restrict_bnd( const m1& v, m2& V ) const
{
unsigned
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
//... boundary points
for( int j=0,j2=0; j
inline void restrict_bnd_add( const m1& v, m2& V ) const
{
unsigned
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
//... boundary points
for( int j=0,j2=0; j
inline void prolong( m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2) = interp_cubic<0,1,0>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2+1) = interp_cubic<0,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2) = interp_cubic<1,1,0>(i+ox,j+oy,k+oz,V);
v(i2+1,j2,k2+1) = interp_cubic<1,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2+1) = interp_cubic<1,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2+1) = interp_cubic<0,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2) = interp_cubic<0,0,0>(i+ox,j+oy,k+oz,V);
}
}
}
template< typename m1, typename m2 >
inline void prolong_add( m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2) += interp_cubic<0,1,0>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2+1) += interp_cubic<0,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2) += interp_cubic<1,1,0>(i+ox,j+oy,k+oz,V);
v(i2+1,j2,k2+1) += interp_cubic<1,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2+1) += interp_cubic<1,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2+1) += interp_cubic<0,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2) += interp_cubic<0,0,0>(i+ox,j+oy,k+oz,V);
}
}
}
template< typename m1, typename m2 >
inline void prolong_bnd( m1& V, m2& v )
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
int nbnd = V.m_nbnd;
int nbndtop = nbnd/2;
#pragma omp parallel for
for( int i=-nbndtop; i=0&&i=0&&j=0&&k(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2) = interp_cubic<0,1,0>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2+1) = interp_cubic<0,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2) = interp_cubic<1,1,0>(i+ox,j+oy,k+oz,V);
v(i2+1,j2,k2+1) = interp_cubic<1,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2+1) = interp_cubic<1,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2+1) = interp_cubic<0,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2) = interp_cubic<0,0,0>(i+ox,j+oy,k+oz,V);
}
}
}
template< typename m1, typename m2 >
inline void prolong_add_bnd( m1& V, m2& v )
{
unsigned
nx = V.size(0),
ny = V.size(1),
nz = V.size(2);
#pragma omp parallel for
for( int i=-1; i<=nx; ++i )
{
int i2(2*i);
for( int j=-1,j2=-2; j<=ny; ++j,j2+=2 )
for( int k=-1,k2=-2; k<=nz; ++k,k2+=2 )
{
if( i>=0&&i=0&&j=0&&k(i,j,k,V);
v(i2,j2+1,k2) += interp_cubic<0,1,0>(i,j,k,V);
v(i2,j2,k2+1) += interp_cubic<0,0,1>(i,j,k,V);
v(i2+1,j2+1,k2) += interp_cubic<1,1,0>(i,j,k,V);
v(i2+1,j2,k2+1) += interp_cubic<1,0,1>(i,j,k,V);
v(i2+1,j2+1,k2+1) += interp_cubic<1,1,1>(i,j,k,V);
v(i2,j2+1,k2+1) += interp_cubic<0,1,1>(i,j,k,V);
v(i2,j2,k2) += interp_cubic<0,0,0>(i,j,k,V);
}
}
}
};
class mg_lin
{
public:
template< typename M >
inline double restr_lin( int x, int y, int z, M& V ) const
{
double w[4] = { 1.0/4.0, 3.0/4.0, 3.0/4.0, 1.0/4.0 };
double vox = 0.0;
int i,j,k;
for( i=0; i<4; ++i )
for( j=0; j<4; ++j )
for( k=0; k<4; ++k )
vox += w[i]*w[j]*w[k] * V(x+i-1,y+j-1,z+k-1);
return vox;
}
template< int sx, int sy, int sz, typename M >
inline double interp_lin( int x, int y, int z, M& V, double s=1.0 ) const
{
double u[2], v[2], w[2];
double vox = 0;
int i,j,k;
if( sx==0 ){
u[0] = 1.0/4.0;
u[1] = 3.0/4.0;
}else{
u[0] = 3.0/4.0;
u[1] = 1.0/4.0;
}
if( sy==0 ){
v[0] = 1.0/4.0;
v[1] = 3.0/4.0;
}else{
v[0] = 3.0/4.0;
v[1] = 1.0/4.0;
}
if( sz==0 ){
w[0] = 1.0/4.0;
w[1] = 3.0/4.0;
}else{
w[0] = 3.0/4.0;
w[1] = 1.0/4.0;
}
for( i=0; i<2; ++i )
for( j=0; j<2; ++j )
for( k=0; k<2; ++k )
vox += u[i]*v[j]*w[k] * V(x+i+sx-1,y+j+sy-1,z+k+sz-1);
return vox;
}
template< typename m1, typename m2 >
inline void prolong( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2) = interp_lin<0,1,0>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2+1) = interp_lin<0,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2) = interp_lin<1,1,0>(i+ox,j+oy,k+oz,V);
v(i2+1,j2,k2+1) = interp_lin<1,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2+1) = interp_lin<1,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2+1) = interp_lin<0,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2) = interp_lin<0,0,0>(i+ox,j+oy,k+oz,V);
}
}
}
template< typename m1, typename m2 >
inline void prolong_add( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2) += interp_lin<0,1,0>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2+1) += interp_lin<0,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2) += interp_lin<1,1,0>(i+ox,j+oy,k+oz,V);
v(i2+1,j2,k2+1) += interp_lin<1,0,1>(i+ox,j+oy,k+oz,V);
v(i2+1,j2+1,k2+1) += interp_lin<1,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2+1,k2+1) += interp_lin<0,1,1>(i+ox,j+oy,k+oz,V);
v(i2,j2,k2) += interp_lin<0,0,0>(i+ox,j+oy,k+oz,V);
}
}
}
template< typename m1, typename m2 >
inline void restrict( const m1& v, m2& V ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i
class mg_linear
{
public:
//typedef T real_t;
//inline void prolong_bnd( const MeshvarBnd& V, MeshvarBnd& v ) const
template< typename m1, typename m2 >
inline void prolong_bnd( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel
{
{
for(int q=0;q<2; ++q)
{
int i=nx;
if(q==0) i=-1;
int i2 = 2*i;
for( int j=0,j2=0; j
inline void prolong_add_bnd( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel
{
{
for(int q=0;q<2; ++q)
{
int i=nx;
if(q==0) i=-1;
int i2 = 2*i;
for( int j=0,j2=0; j
inline void prolong( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i
inline void prolong_add( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i
class mg_straight
{
public:
//typedef T real_t;
template< typename m1, typename m2 >
inline void restrict_bnd( const m1& v, m2& V ) const
{
unsigned
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
//... boundary points
for( int j=0,j2=0; j
inline void restrict( const m1& v, m2& V ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i
inline void restrict_add( const m1& v, m2& V ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i
inline void restrict_bnd_add( const m1& v, m2& V ) const
{
unsigned
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
//... boundary points
for( int j=0,j2=0; j
inline void prolong( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel
{
#pragma omp for nowait
for( int i=0; i
inline void prolong_bnd( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel
{
for( int j=0,j2=0; j
inline void prolong_add_bnd( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel
{
for( int j=0,j2=0; j
inline void prolong_add( const m1& V, m2& v ) const
{
int
nx = v.size(0)/2,
ny = v.size(1)/2,
nz = v.size(2)/2,
ox = v.offset(0),
oy = v.offset(1),
oz = v.offset(2);
#pragma omp parallel for
for( int i=0; i