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added an external tool to compute ellipsoids from point files

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Oliver Hahn 2013-11-22 20:01:02 +01:00
parent 1f7ba3bca3
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#include <vector>
/*
region_ellipsoid.cc - This file is part of MUSIC -
a code to generate multi-scale initial conditions
for cosmological simulations
Copyright (C) 2010-13 Oliver Hahn
*/
#include <iostream>
#include <cmath>
#include <cassert>
#include <fstream>
#include <sstream>
#include <cctype>
#include <algorithm>
#include <stdexcept>
#include <gsl/gsl_math.h>
#include <gsl/gsl_eigen.h>
#define LOGERR printf
#define LOGINFO printf
#define LOGUSER printf
/***** Math helper functions ******/
//! return square of argument
template <typename X>
inline X sqr( X x )
{ return x*x; }
//! Determinant of 3x3 matrix
inline double Determinant_3x3( const float *data )
{
float detS = data[0]*(data[4]*data[8]-data[7]*data[5])
- data[1]*(data[3]*data[8]-data[5]*data[6])
+ data[2]*(data[3]*data[7]-data[4]*data[6]);
return detS;
}
//! Inverse of 3x3 matrix
inline void Inverse_3x3( const float *data, float *m )
{
float invdet = 1.0f/Determinant_3x3( data );
m[0] = (data[4]*data[8]-data[7]*data[5])*invdet;
m[1] = -(data[1]*data[8]-data[2]*data[7])*invdet;
m[2] = (data[1]*data[5]-data[2]*data[4])*invdet;
m[3] = -(data[3]*data[8]-data[5]*data[6])*invdet;
m[4] = (data[0]*data[8]-data[2]*data[6])*invdet;
m[5] = -(data[0]*data[5]-data[2]*data[3])*invdet;
m[6] = (data[3]*data[7]-data[4]*data[6])*invdet;
m[7] = -(data[0]*data[7]-data[1]*data[6])*invdet;
m[8] = (data[0]*data[4]-data[1]*data[3])*invdet;
}
void Inverse_4x4( float *mat )
{
double tmp[12]; /* temp array for pairs */
double src[16]; /* array of transpose source matrix */
double det; /* determinant */
double dst[16];
/* transpose matrix */
for (int i = 0; i < 4; i++)
{
src[i] = mat[i*4];
src[i + 4] = mat[i*4 + 1];
src[i + 8] = mat[i*4 + 2];
src[i + 12] = mat[i*4 + 3];
}
tmp[0] = src[10] * src[15];
tmp[1] = src[11] * src[14];
tmp[2] = src[9] * src[15];
tmp[3] = src[11] * src[13];
tmp[4] = src[9] * src[14];
tmp[5] = src[10] * src[13];
tmp[6] = src[8] * src[15];
tmp[7] = src[11] * src[12];
tmp[8] = src[8] * src[14];
tmp[9] = src[10] * src[12];
tmp[10] = src[8] * src[13];
tmp[11] = src[9] * src[12];
/* calculate first 8 elements (cofactors) */
dst[0] = tmp[0]*src[5] + tmp[3]*src[6] + tmp[4]*src[7];
dst[0] -= tmp[1]*src[5] + tmp[2]*src[6] + tmp[5]*src[7];
dst[1] = tmp[1]*src[4] + tmp[6]*src[6] + tmp[9]*src[7];
dst[1] -= tmp[0]*src[4] + tmp[7]*src[6] + tmp[8]*src[7];
dst[2] = tmp[2]*src[4] + tmp[7]*src[5] + tmp[10]*src[7];
dst[2] -= tmp[3]*src[4] + tmp[6]*src[5] + tmp[11]*src[7];
dst[3] = tmp[5]*src[4] + tmp[8]*src[5] + tmp[11]*src[6];
dst[3] -= tmp[4]*src[4] + tmp[9]*src[5] + tmp[10]*src[6];
dst[4] = tmp[1]*src[1] + tmp[2]*src[2] + tmp[5]*src[3];
dst[4] -= tmp[0]*src[1] + tmp[3]*src[2] + tmp[4]*src[3];
dst[5] = tmp[0]*src[0] + tmp[7]*src[2] + tmp[8]*src[3];
dst[5] -= tmp[1]*src[0] + tmp[6]*src[2] + tmp[9]*src[3];
dst[6] = tmp[3]*src[0] + tmp[6]*src[1] + tmp[11]*src[3];
dst[6] -= tmp[2]*src[0] + tmp[7]*src[1] + tmp[10]*src[3];
dst[7] = tmp[4]*src[0] + tmp[9]*src[1] + tmp[10]*src[2];
dst[7] -= tmp[5]*src[0] + tmp[8]*src[1] + tmp[11]*src[2];
/* calculate pairs for second 8 elements (cofactors) */
tmp[0] = src[2]*src[7];
tmp[1] = src[3]*src[6];
tmp[2] = src[1]*src[7];
tmp[3] = src[3]*src[5];
tmp[4] = src[1]*src[6];
tmp[5] = src[2]*src[5];
tmp[6] = src[0]*src[7];
tmp[7] = src[3]*src[4];
tmp[8] = src[0]*src[6];
tmp[9] = src[2]*src[4];
tmp[10] = src[0]*src[5];
tmp[11] = src[1]*src[4];
/* calculate second 8 elements (cofactors) */
dst[8] = tmp[0]*src[13] + tmp[3]*src[14] + tmp[4]*src[15];
dst[8] -= tmp[1]*src[13] + tmp[2]*src[14] + tmp[5]*src[15];
dst[9] = tmp[1]*src[12] + tmp[6]*src[14] + tmp[9]*src[15];
dst[9] -= tmp[0]*src[12] + tmp[7]*src[14] + tmp[8]*src[15];
dst[10] = tmp[2]*src[12] + tmp[7]*src[13] + tmp[10]*src[15];
dst[10]-= tmp[3]*src[12] + tmp[6]*src[13] + tmp[11]*src[15];
dst[11] = tmp[5]*src[12] + tmp[8]*src[13] + tmp[11]*src[14];
dst[11]-= tmp[4]*src[12] + tmp[9]*src[13] + tmp[10]*src[14];
dst[12] = tmp[2]*src[10] + tmp[5]*src[11] + tmp[1]*src[9];
dst[12]-= tmp[4]*src[11] + tmp[0]*src[9] + tmp[3]*src[10];
dst[13] = tmp[8]*src[11] + tmp[0]*src[8] + tmp[7]*src[10];
dst[13]-= tmp[6]*src[10] + tmp[9]*src[11] + tmp[1]*src[8];
dst[14] = tmp[6]*src[9] + tmp[11]*src[11] + tmp[3]*src[8];
dst[14]-= tmp[10]*src[11] + tmp[2]*src[8] + tmp[7]*src[9];
dst[15] = tmp[10]*src[10] + tmp[4]*src[8] + tmp[9]*src[9];
dst[15]-= tmp[8]*src[9] + tmp[11]*src[10] + tmp[5]*src[8];
/* calculate determinant */
det=src[0]*dst[0]+src[1]*dst[1]+src[2]*dst[2]+src[3]*dst[3];
/* calculate matrix inverse */
det = 1/det;
for (int j = 0; j < 16; j++)
{ dst[j] *= det;
mat[j] = dst[j];
}
}
/***** Minimum Volume Bounding Ellipsoid Implementation ******/
/*
* Finds the minimum volume enclosing ellipsoid (MVEE) of a set of data
* points stored in matrix P. The following optimization problem is solved:
*
* minimize log(det(A))
* s.t. (P_i - c)'*A*(P_i - c)<= 1
*
* in variables A and c, where P_i is the i-th column of the matrix P.
* The solver is based on Khachiyan Algorithm, and the final solution is
* different from the optimal value by the pre-specified amount of 'tolerance'.
*
* The ellipsoid equation is given in the canonical form
* (x-c)' A (x-c) <= 1
*
* Code was adapted from the MATLAB version by Nima Moshtagh (nima@seas.upenn.edu)
*/
class min_ellipsoid
{
protected:
size_t N;
float X[16];
float c[3];
float A[9], Ainv[9];
float *Q;
float *u;
float detA, detA13;
float v1[3],v2[3],v3[3],r1,r2,r3;
float V[9], mu[3];
bool axes_computed, hold_point_data;
void compute_axes( void )
{
gsl_vector *eval;
gsl_matrix *evec;
gsl_eigen_symmv_workspace *w;
eval = gsl_vector_alloc(3);
evec = gsl_matrix_alloc(3, 3);
w = gsl_eigen_symmv_alloc(3);
// promote to double, GSL wants double
double dA[9];
for( int i=0; i<9; ++i ) dA[i] = (double)A[i];
gsl_matrix_view m = gsl_matrix_view_array( dA, 3, 3);
gsl_eigen_symmv( &m.matrix, eval, evec, w);
gsl_eigen_symmv_sort( eval, evec, GSL_EIGEN_SORT_VAL_ASC);
gsl_vector_view evec_i;
for( int i=0; i<3; ++i )
{
mu[i] = gsl_vector_get(eval, i);
evec_i = gsl_matrix_column (evec, i);
for( int j=0; j<3; ++j )
V[3*i+j] = gsl_vector_get(&evec_i.vector,j);
}
r1 = 1.0 / sqrt( gsl_vector_get(eval, 0) );
r2 = 1.0 / sqrt( gsl_vector_get(eval, 1) );
r3 = 1.0 / sqrt( gsl_vector_get(eval, 2) );
evec_i = gsl_matrix_column (evec, 0);
v1[0] = gsl_vector_get(&evec_i.vector,0);
v1[1] = gsl_vector_get(&evec_i.vector,1);
v1[2] = gsl_vector_get(&evec_i.vector,2);
evec_i = gsl_matrix_column (evec, 1);
v2[0] = gsl_vector_get(&evec_i.vector,0);
v2[1] = gsl_vector_get(&evec_i.vector,1);
v2[2] = gsl_vector_get(&evec_i.vector,2);
evec_i = gsl_matrix_column (evec, 2);
v3[0] = gsl_vector_get(&evec_i.vector,0);
v3[1] = gsl_vector_get(&evec_i.vector,1);
v3[2] = gsl_vector_get(&evec_i.vector,2);
gsl_vector_free(eval);
gsl_matrix_free(evec);
gsl_eigen_symmv_free (w);
axes_computed = true;
}
// use the Khachiyan Algorithm to find the minimum bounding ellipsoid
void compute( double tol = 0.001, int maxit = 10000 )
{
double err = 10.0 * tol;
float *unew = new float[N];
int count = 0;
double temp;
while( err > tol && count < maxit )
{
for( int i=0; i<4; ++i )
for( int j=0,i4=4*i; j<4; ++j )
{
const int k = i4+j;
temp = 0.0;
for( size_t l=0; l<N; ++l )
temp += (double)(Q[4*l+i] * u[l] * Q[4*l+j]);
X[k] = temp;
}
Inverse_4x4(X);
int imax = 0; float Mmax = -1e30;
double m;
for( size_t i=0; i<N; ++i )
{
m = 0.0;
for( int k=0; k<4; ++k )
for( int l=0; l<4; ++l )
m += (double)(Q[4*i+k] * X[4*l+k] * Q[4*i+l]);
if( m > Mmax )
{
imax = i;
Mmax = m;
}
}
float step_size = (Mmax-4.0f)/(4.0f*(Mmax-1.0f)), step_size1 = 1.0f-step_size;
for( size_t i=0; i<N; ++i )
unew[i] = u[i] * step_size1;
unew[imax] += step_size;
err = 0.0;
for( size_t i=0; i<N; ++i )
{
err += sqr(unew[i]-u[i]);
u[i] = unew[i];
}
err = sqrt(err);
++count;
}
if( count >= maxit )
LOGERR("No convergence in min_ellipsoid::compute: maximum number of iterations reached!");
delete[] unew;
}
public:
min_ellipsoid( size_t N_, double* P )
: N( N_ ), axes_computed( false ), hold_point_data( true )
{
// --- initialize ---
LOGINFO("computing minimum bounding ellipsoid from %lld points",N);
Q = new float[4*N];
u = new float[N];
for( size_t i=0; i<N; ++i )
u[i] = 1.0/N;
for( size_t i=0; i<N; ++i )
{
int i4=4*i, i3=3*i;
for( size_t j=0; j<3; ++j )
Q[i4+j] = P[i3+j];
Q[i4+3] = 1.0f;
}
//--- compute the actual ellipsoid using the Khachiyan Algorithm ---
compute();
//--- determine the ellipsoid A matrix ---
double Pu[3];
for( int j=0; j<3; ++j )
{
Pu[j] = 0.0;
for( size_t i=0; i<N; ++i )
Pu[j] += P[3*i+j] * u[i];
}
// determine center
c[0] = Pu[0]; c[1] = Pu[1]; c[2] = Pu[2];
// need to do summation in double precision due to
// possible catastrophic cancellation issues when
// using many input points
double Atmp[9];
for( int i=0; i<3; ++i )
for( int j=0,i3=3*i; j<3; ++j )
{
const int k = i3+j;
Atmp[k] = 0.0;
for( size_t l=0; l<N; ++l )
Atmp[k] += P[3*l+i] * u[l] * P[3*l+j];
Atmp[k] -= Pu[i]*Pu[j];
}
for( int i=0;i<9;++i)
Ainv[i] = Atmp[i];
Inverse_3x3( Ainv, A );
for( size_t i=0; i<9; ++i ){ A[i] /= 3.0; Ainv[i] *= 3.0; }
detA = Determinant_3x3( A );
detA13 = pow( detA, 1.0/3.0 );
}
min_ellipsoid( const double* A_, const double *c_ )
: N( 0 ), axes_computed( false ), hold_point_data( false )
{
for( int i=0; i<9; ++i )
{ A[i] = A_[i]; Ainv[i] = 0.0; }
for( int i=0; i<3; ++i )
c[i] = c_[i];
}
min_ellipsoid( const min_ellipsoid& e )
: N( 0 ), hold_point_data( false )
{
for( int i=0; i<16; ++i )
X[i] = e.X[i];
for( int i=0; i<3; ++i )
{
c[i] = e.c[i];
v1[i] = e.v1[i];
v2[i] = e.v2[i];
v3[i] = e.v3[i];
mu[i] = e.mu[i];
}
for( int i=0; i<9; ++i )
{
A[i] = e.A[i];
Ainv[i] = e.Ainv[i];
V[i] = e.V[i];
}
N = e.N;
detA = e.detA;
detA13 = e.detA13;
axes_computed = e.axes_computed;
}
~min_ellipsoid()
{
if( hold_point_data )
{
delete[] u;
delete[] Q;
}
}
template<typename T>
bool check_point( const T *x, double dist = 0.0 )
{
dist = (dist + 1.0) * detA13;
T q[3] = {x[0]-c[0],x[1]-c[1],x[2]-c[2]};
T r = 0.0;
for( int i=0; i<3; ++i )
for( int j=0; j<3; ++j )
r += q[i]*A[3*j+i]*q[j];
return r <= 1.0;
}
void print( void )
{
std::cout << "A = \n";
for( int i=0; i<9; ++i )
{
if( i%3==0 ) std::cout << std::endl;
std::cout << A[i] << " ";
}
std::cout << std::endl;
std::cout << "Ainv = \n";
for( int i=0; i<9; ++i )
{
if( i%3==0 ) std::cout << std::endl;
std::cout << Ainv[i] << " ";
}
std::cout << std::endl;
std::cout << "c = (" << c[0] << ", " << c[1] << ", " << c[2] << ")\n";
}
template<typename T>
void get_AABB( T *left, T *right )
{
for( int i=0; i<3; ++i )
{
left[i] = c[i] - sqrt(Ainv[3*i+i]);
right[i] = c[i] + sqrt(Ainv[3*i+i]);
}
}
void get_center( float* xc )
{
for( int i=0; i<3; ++i ) xc[i] = c[i];
}
void get_matrix( float* AA )
{
for( int i=0; i<9; ++i ) AA[i] = A[i];
}
double sgn( double x )
{
if( x < 0.0 ) return -1.0;
return 1.0;
}
void expand_ellipsoid( float dr )
{
if( !axes_computed )
{
LOGUSER("computing ellipsoid axes.....");
compute_axes();
}
float muold[3] = {mu[0],mu[1],mu[2]};
float munew[3];
for( int i=0; i<3; ++i )
munew[i] = sgn(mu[i])/sqr(1.0/sqrt(fabs(mu[i]))+dr);
float Anew[9];
for(int i=0; i<3; ++i )
for( int j=0; j<3; ++j )
{
Anew[3*i+j] = 0.0;
for( int k=0; k<3; ++k )
Anew[3*i+j] += V[3*k+i] * munew[k] * V[3*k+j];
}
for( int i=0; i<9; ++i )
A[i] = Anew[i];
Inverse_3x3( A, Ainv );
//LOGUSER("computing ellipsoid axes.....");
compute_axes();
//print();
}
};
#include "point_file_reader.hh"
void apply_shift( size_t Np, double *p, int *shift, int levelmin )
{
double dx = 1.0/(1<<levelmin);
printf("unapplying shift of previous zoom region to region particles :\n" \
"\t [%d,%d,%d] = (%f,%f,%f)",shift[0],shift[1],shift[2],shift[0]*dx,shift[1]*dx,shift[2]*dx);
for( size_t i=0,i3=0; i<Np; i++,i3+=3 )
for( size_t j=0; j<3; ++j )
p[i3+j] = p[i3+j]-shift[j]*dx;
}
int main( int argc, char **argv )
{
std::vector<double> pp;
int shift[3];
unsigned shift_level = 0;
min_ellipsoid* pellip = 0;
if( argc < 2 )
{
printf("Usage: %s <point file> [shift x] [shift y] [shift z] [shift levelmin]\n\n",argv[0]);
return 0;
}
std::string point_file( argv[1] );
point_reader pfr;
pfr.read_points_from_file( point_file, 1.0, pp );
// if file has more than three columns, just take first three
// at the moment...
if( pfr.num_columns > 3 )
{
std::vector<double> xx;
xx.reserve( 3 * pp.size()/pfr.num_columns );
for( size_t i=0; i<pp.size()/pfr.num_columns; ++i )
for( size_t j=0; j<3; ++j )
xx.push_back( pp[ pfr.num_columns * i + j ] );
pp.swap( xx );
}
if( argc > 2 )
{
assert(argc==6);
shift[0] = atoi( argv[2] );
shift[1] = atoi( argv[3] );
shift[2] = atoi( argv[4] );
unsigned point_levelmin = atoi( argv[5] );
apply_shift( pp.size()/3, &pp[0], shift, point_levelmin );
shift_level = point_levelmin;
}
pellip = new min_ellipsoid( pp.size()/3, &pp[0] );
// output the center
float c[3], A[9];
pellip->get_center( c );
pellip->get_matrix( A );
printf("Region center for ellipsoid determined at\n\t xc = ( %f %f %f )",c[0],c[1],c[2]);
printf("Ellipsoid matrix determined as\n\t ( %f %f %f )\n\t A = ( %f %f %f )\n\t ( %f %f %f )",
A[0], A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8] );
delete pellip;
return 1;
}

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#ifndef POINT_FILE_READER_HH
#define POINT_FILE_READER_HH
#include <fstream>
#include <sstream>
#include <string>
#include <vector>
struct point_reader{
int num_columns;
point_reader( void )
: num_columns( 0 )
{ }
bool isFloat( std::string myString )
{
std::istringstream iss(myString);
double f;
//iss >> std::noskipws >> f; // noskipws considers leading whitespace invalid
// Check the entire string was consumed and if either failbit or badbit is set
iss >> f;
return iss.eof() && !iss.fail();
}
template< typename real_t >
void read_points_from_file( std::string fname, float vfac_, std::vector<real_t>& p )
{
std::ifstream ifs(fname.c_str());
if( !ifs )
{
printf("region_ellipsoid_plugin::read_points_from_file : Could not open file \'%s\'",fname.c_str());
throw std::runtime_error("region_ellipsoid_plugin::read_points_from_file : cannot open point file.");
}
int colcount = 0, colcount1 = 0, row = 0;
p.clear();
while( ifs )
{
std::string s;
if( !getline(ifs,s) )break;
std::stringstream ss(s);
colcount1 = 0;
while(ss)
{
if( !getline(ss,s,' ') ) break;
if( !isFloat( s ) ) continue;
p.push_back( strtod(s.c_str(),NULL) );
if( row == 0 )
colcount++;
else
colcount1++;
}
++row;
if( row>1 && colcount != colcount1 )
printf("error on line %d of input file",row);
//std::cout << std::endl;
}
printf("region point file appears to contain %d columns",colcount);
if( p.size()%3 != 0 && p.size()%6 != 0 )
{
printf("Region point file \'%s\' does not contain triplets (%d elems)",fname.c_str(),p.size());
throw std::runtime_error("region_ellipsoid_plugin::read_points_from_file : file does not contain triplets.");
}
double x0[3] = { p[0],p[1],p[2] }, dx;
if( colcount == 3 )
{
// only positions are given
for( size_t i=3; i<p.size(); i+=3 )
{
for( size_t j=0; j<3; ++j )
{
dx = p[i+j]-x0[j];
if( dx < -0.5 ) dx += 1.0;
else if( dx > 0.5 ) dx -= 1.0;
p[i+j] = x0[j] + dx;
}
}
}
else if( colcount == 6 )
{
// positions and velocities are given
//... include the velocties to unapply Zeldovich approx.
for( size_t j=3; j<6; ++j )
{
dx = (p[j-3]-p[j]/vfac_)-x0[j-3];
if( dx < -0.5 ) dx += 1.0;
else if( dx > 0.5 ) dx -= 1.0;
p[j] = x0[j-3] + dx;
}
for( size_t i=6; i<p.size(); i+=6 )
{
for( size_t j=0; j<3; ++j )
{
dx = p[i+j]-x0[j];
if( dx < -0.5 ) dx += 1.0;
else if( dx > 0.5 ) dx -= 1.0;
p[i+j] = x0[j] + dx;
}
for( size_t j=3; j<6; ++j )
{
dx = (p[i+j-3]-p[i+j]/vfac_)-x0[j-3];
if( dx < -0.5 ) dx += 1.0;
else if( dx > 0.5 ) dx -= 1.0;
p[i+j] = x0[j-3] + dx;
}
}
}
else
printf("Problem interpreting the region point file \'%s\'", fname.c_str() );
num_columns = colcount;
}
};
#endif