1 | /*
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2 | * Project: MoleCuilder
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3 | * Description: creates and alters molecular systems
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4 | * Copyright (C) 2010 University of Bonn. All rights reserved.
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5 | * Please see the LICENSE file or "Copyright notice" in builder.cpp for details.
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6 | */
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7 |
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8 | /*
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9 | * ellipsoid.cpp
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10 | *
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11 | * Created on: Jan 20, 2009
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12 | * Author: heber
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13 | */
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14 |
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15 | // include config.h
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16 | #ifdef HAVE_CONFIG_H
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17 | #include <config.h>
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18 | #endif
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19 |
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20 | #include "Helpers/MemDebug.hpp"
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21 |
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22 | #include <gsl/gsl_multimin.h>
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23 | #include <gsl/gsl_vector.h>
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24 |
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25 | #include <iomanip>
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26 |
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27 | #include <set>
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28 |
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29 | #include "BoundaryPointSet.hpp"
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30 | #include "boundary.hpp"
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31 | #include "ellipsoid.hpp"
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32 | #include "linkedcell.hpp"
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33 | #include "Helpers/Log.hpp"
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34 | #include "tesselation.hpp"
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35 | #include "LinearAlgebra/Vector.hpp"
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36 | #include "LinearAlgebra/Matrix.hpp"
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37 | #include "Helpers/Verbose.hpp"
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38 |
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39 | /** Determines squared distance for a given point \a x to surface of ellipsoid.
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40 | * \param x given point
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41 | * \param EllipsoidCenter center of ellipsoid
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42 | * \param EllipsoidLength[3] three lengths of half axis of ellipsoid
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43 | * \param EllipsoidAngle[3] three rotation angles of ellipsoid
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44 | * \return squared distance from point to surface
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45 | */
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46 | double SquaredDistanceToEllipsoid(Vector &x, Vector &EllipsoidCenter, double *EllipsoidLength, double *EllipsoidAngle)
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47 | {
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48 | Vector helper, RefPoint;
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49 | double distance = -1.;
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50 | Matrix Matrix;
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51 | double InverseLength[3];
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52 | double psi,theta,phi; // euler angles in ZX'Z'' convention
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53 |
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54 | //Log() << Verbose(3) << "Begin of SquaredDistanceToEllipsoid" << endl;
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55 |
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56 | for(int i=0;i<3;i++)
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57 | InverseLength[i] = 1./EllipsoidLength[i];
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58 |
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59 | // 1. translate coordinate system so that ellipsoid center is in origin
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60 | RefPoint = helper = x - EllipsoidCenter;
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61 | //Log() << Verbose(4) << "Translated given point is at " << RefPoint << "." << endl;
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62 |
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63 | // 2. transform coordinate system by inverse of rotation matrix and of diagonal matrix
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64 | psi = EllipsoidAngle[0];
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65 | theta = EllipsoidAngle[1];
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66 | phi = EllipsoidAngle[2];
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67 | Matrix.set(0,0, cos(psi)*cos(phi) - sin(psi)*cos(theta)*sin(phi));
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68 | Matrix.set(1,0, -cos(psi)*sin(phi) - sin(psi)*cos(theta)*cos(phi));
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69 | Matrix.set(2,0, sin(psi)*sin(theta));
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70 | Matrix.set(0,1, sin(psi)*cos(phi) + cos(psi)*cos(theta)*sin(phi));
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71 | Matrix.set(1,1, cos(psi)*cos(theta)*cos(phi) - sin(psi)*sin(phi));
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72 | Matrix.set(2,1, -cos(psi)*sin(theta));
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73 | Matrix.set(0,2, sin(theta)*sin(phi));
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74 | Matrix.set(1,2, sin(theta)*cos(phi));
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75 | Matrix.set(2,2, cos(theta));
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76 | helper *= Matrix;
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77 | helper.ScaleAll(InverseLength);
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78 | //Log() << Verbose(4) << "Transformed RefPoint is at " << helper << "." << endl;
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79 |
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80 | // 3. construct intersection point with unit sphere and ray between origin and x
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81 | helper.Normalize(); // is simply normalizes vector in distance direction
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82 | //Log() << Verbose(4) << "Transformed intersection is at " << helper << "." << endl;
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83 |
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84 | // 4. transform back the constructed intersection point
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85 | psi = -EllipsoidAngle[0];
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86 | theta = -EllipsoidAngle[1];
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87 | phi = -EllipsoidAngle[2];
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88 | helper.ScaleAll(EllipsoidLength);
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89 | Matrix.set(0,0, cos(psi)*cos(phi) - sin(psi)*cos(theta)*sin(phi));
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90 | Matrix.set(1,0, -cos(psi)*sin(phi) - sin(psi)*cos(theta)*cos(phi));
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91 | Matrix.set(2,0, sin(psi)*sin(theta));
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92 | Matrix.set(0,1, sin(psi)*cos(phi) + cos(psi)*cos(theta)*sin(phi));
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93 | Matrix.set(1,1, cos(psi)*cos(theta)*cos(phi) - sin(psi)*sin(phi));
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94 | Matrix.set(2,1, -cos(psi)*sin(theta));
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95 | Matrix.set(0,2, sin(theta)*sin(phi));
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96 | Matrix.set(1,2, sin(theta)*cos(phi));
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97 | Matrix.set(2,2, cos(theta));
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98 | helper *= Matrix;
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99 | //Log() << Verbose(4) << "Intersection is at " << helper << "." << endl;
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100 |
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101 | // 5. determine distance between backtransformed point and x
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102 | distance = RefPoint.DistanceSquared(helper);
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103 | //Log() << Verbose(4) << "Squared distance between intersection and RefPoint is " << distance << "." << endl;
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104 |
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105 | return distance;
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106 | //Log() << Verbose(3) << "End of SquaredDistanceToEllipsoid" << endl;
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107 | };
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108 |
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109 | /** structure for ellipsoid minimisation containing points to fit to.
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110 | */
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111 | struct EllipsoidMinimisation {
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112 | int N; //!< dimension of vector set
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113 | Vector *x; //!< array of vectors
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114 | };
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115 |
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116 | /** Sum of squared distance to ellipsoid to be minimised.
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117 | * \param *x parameters for the ellipsoid
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118 | * \param *params EllipsoidMinimisation with set of data points to minimise distance to and dimension
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119 | * \return sum of squared distance, \sa SquaredDistanceToEllipsoid()
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120 | */
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121 | double SumSquaredDistance (const gsl_vector * x, void * params)
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122 | {
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123 | Vector *set= ((struct EllipsoidMinimisation *)params)->x;
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124 | int N = ((struct EllipsoidMinimisation *)params)->N;
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125 | double SumDistance = 0.;
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126 | double distance;
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127 | Vector Center;
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128 | double EllipsoidLength[3], EllipsoidAngle[3];
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129 |
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130 | // put parameters into suitable ellipsoid form
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131 | for (int i=0;i<3;i++) {
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132 | Center[i] = gsl_vector_get(x, i+0);
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133 | EllipsoidLength[i] = gsl_vector_get(x, i+3);
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134 | EllipsoidAngle[i] = gsl_vector_get(x, i+6);
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135 | }
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136 |
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137 | // go through all points and sum distance
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138 | for (int i=0;i<N;i++) {
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139 | distance = SquaredDistanceToEllipsoid(set[i], Center, EllipsoidLength, EllipsoidAngle);
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140 | if (!isnan(distance)) {
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141 | SumDistance += distance;
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142 | } else {
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143 | SumDistance = GSL_NAN;
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144 | break;
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145 | }
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146 | }
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147 |
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148 | //Log() << Verbose(0) << "Current summed distance is " << SumDistance << "." << endl;
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149 | return SumDistance;
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150 | };
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151 |
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152 | /** Finds best fitting ellipsoid parameter set in Least square sense for a given point set.
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153 | * \param *out output stream for debugging
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154 | * \param *set given point set
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155 | * \param N number of points in set
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156 | * \param EllipsoidParamter[3] three parameters in ellipsoid equation
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157 | * \return true - fit successful, false - fit impossible
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158 | */
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159 | bool FitPointSetToEllipsoid(Vector *set, int N, Vector *EllipsoidCenter, double *EllipsoidLength, double *EllipsoidAngle)
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160 | {
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161 | int status = GSL_SUCCESS;
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162 | DoLog(2) && (Log() << Verbose(2) << "Begin of FitPointSetToEllipsoid " << endl);
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163 | if (N >= 3) { // check that enough points are given (9 d.o.f.)
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164 | struct EllipsoidMinimisation par;
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165 | const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex;
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166 | gsl_multimin_fminimizer *s = NULL;
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167 | gsl_vector *ss, *x;
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168 | gsl_multimin_function minex_func;
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169 |
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170 | size_t iter = 0;
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171 | double size;
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172 |
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173 | /* Starting point */
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174 | x = gsl_vector_alloc (9);
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175 | for (int i=0;i<3;i++) {
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176 | gsl_vector_set (x, i+0, EllipsoidCenter->at(i));
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177 | gsl_vector_set (x, i+3, EllipsoidLength[i]);
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178 | gsl_vector_set (x, i+6, EllipsoidAngle[i]);
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179 | }
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180 | par.x = set;
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181 | par.N = N;
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182 |
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183 | /* Set initial step sizes */
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184 | ss = gsl_vector_alloc (9);
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185 | for (int i=0;i<3;i++) {
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186 | gsl_vector_set (ss, i+0, 0.1);
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187 | gsl_vector_set (ss, i+3, 1.0);
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188 | gsl_vector_set (ss, i+6, M_PI/20.);
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189 | }
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190 |
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191 | /* Initialize method and iterate */
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192 | minex_func.n = 9;
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193 | minex_func.f = &SumSquaredDistance;
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194 | minex_func.params = (void *)∥
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195 |
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196 | s = gsl_multimin_fminimizer_alloc (T, 9);
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197 | gsl_multimin_fminimizer_set (s, &minex_func, x, ss);
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198 |
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199 | do {
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200 | iter++;
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201 | status = gsl_multimin_fminimizer_iterate(s);
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202 |
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203 | if (status)
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204 | break;
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205 |
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206 | size = gsl_multimin_fminimizer_size (s);
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207 | status = gsl_multimin_test_size (size, 1e-2);
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208 |
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209 | if (status == GSL_SUCCESS) {
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210 | for (int i=0;i<3;i++) {
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211 | EllipsoidCenter->at(i) = gsl_vector_get (s->x,i+0);
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212 | EllipsoidLength[i] = gsl_vector_get (s->x, i+3);
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213 | EllipsoidAngle[i] = gsl_vector_get (s->x, i+6);
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214 | }
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215 | DoLog(4) && (Log() << Verbose(4) << setprecision(3) << "Converged fit at: " << *EllipsoidCenter << ", lengths " << EllipsoidLength[0] << ", " << EllipsoidLength[1] << ", " << EllipsoidLength[2] << ", angles " << EllipsoidAngle[0] << ", " << EllipsoidAngle[1] << ", " << EllipsoidAngle[2] << " with summed distance " << s->fval << "." << endl);
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216 | }
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217 |
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218 | } while (status == GSL_CONTINUE && iter < 1000);
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219 |
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220 | gsl_vector_free(x);
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221 | gsl_vector_free(ss);
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222 | gsl_multimin_fminimizer_free (s);
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223 |
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224 | } else {
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225 | DoLog(3) && (Log() << Verbose(3) << "Not enough points provided for fit to ellipsoid." << endl);
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226 | return false;
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227 | }
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228 | DoLog(2) && (Log() << Verbose(2) << "End of FitPointSetToEllipsoid" << endl);
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229 | if (status == GSL_SUCCESS)
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230 | return true;
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231 | else
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232 | return false;
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233 | };
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234 |
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235 | /** Picks a number of random points from a LC neighbourhood as a fitting set.
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236 | * \param *out output stream for debugging
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237 | * \param *T Tesselation containing boundary points
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238 | * \param *LC linked cell list of all atoms
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239 | * \param *&x random point set on return (not allocated!)
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240 | * \param PointsToPick number of points in set to pick
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241 | */
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242 | void PickRandomNeighbouredPointSet(class Tesselation *T, class LinkedCell *LC, Vector *&x, size_t PointsToPick)
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243 | {
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244 | size_t PointsLeft = 0;
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245 | size_t PointsPicked = 0;
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246 | int Nlower[NDIM], Nupper[NDIM];
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247 | set<int> PickedAtomNrs; // ordered list of picked atoms
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248 | set<int>::iterator current;
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249 | int index;
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250 | TesselPoint *Candidate = NULL;
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251 | DoLog(2) && (Log() << Verbose(2) << "Begin of PickRandomPointSet" << endl);
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252 |
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253 | // allocate array
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254 | if (x == NULL) {
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255 | x = new Vector[PointsToPick];
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256 | } else {
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257 | DoeLog(2) && (eLog()<< Verbose(2) << "Given pointer to vector array seems already allocated." << endl);
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258 | }
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259 |
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260 | do {
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261 | for(int i=0;i<NDIM;i++) // pick three random indices
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262 | LC->n[i] = (rand() % LC->N[i]);
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263 | DoLog(2) && (Log() << Verbose(2) << "INFO: Center cell is " << LC->n[0] << ", " << LC->n[1] << ", " << LC->n[2] << " ... ");
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264 | // get random cell
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265 | const LinkedCell::LinkedNodes *List = LC->GetCurrentCell();
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266 | if (List == NULL) { // set index to it
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267 | continue;
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268 | }
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269 | DoLog(2) && (Log() << Verbose(2) << "with No. " << LC->index << "." << endl);
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270 |
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271 | DoLog(2) && (Log() << Verbose(2) << "LC Intervals:");
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272 | for (int i=0;i<NDIM;i++) {
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273 | Nlower[i] = ((LC->n[i]-1) >= 0) ? LC->n[i]-1 : 0;
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274 | Nupper[i] = ((LC->n[i]+1) < LC->N[i]) ? LC->n[i]+1 : LC->N[i]-1;
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275 | DoLog(0) && (Log() << Verbose(0) << " [" << Nlower[i] << "," << Nupper[i] << "] ");
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276 | }
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277 | DoLog(0) && (Log() << Verbose(0) << endl);
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278 |
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279 | // count whether there are sufficient atoms in this cell+neighbors
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280 | PointsLeft=0;
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281 | for (LC->n[0] = Nlower[0]; LC->n[0] <= Nupper[0]; LC->n[0]++)
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282 | for (LC->n[1] = Nlower[1]; LC->n[1] <= Nupper[1]; LC->n[1]++)
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283 | for (LC->n[2] = Nlower[2]; LC->n[2] <= Nupper[2]; LC->n[2]++) {
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284 | const LinkedCell::LinkedNodes *List = LC->GetCurrentCell();
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285 | PointsLeft += List->size();
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286 | }
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287 | DoLog(2) && (Log() << Verbose(2) << "There are " << PointsLeft << " atoms in this neighbourhood." << endl);
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288 | if (PointsLeft < PointsToPick) { // ensure that we can pick enough points in its neighbourhood at all.
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289 | continue;
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290 | }
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291 |
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292 | // pre-pick a fixed number of atoms
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293 | PickedAtomNrs.clear();
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294 | do {
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295 | index = (rand() % PointsLeft);
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296 | current = PickedAtomNrs.find(index); // not present?
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297 | if (current == PickedAtomNrs.end()) {
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298 | //Log() << Verbose(2) << "Picking atom nr. " << index << "." << endl;
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299 | PickedAtomNrs.insert(index);
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300 | }
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301 | } while (PickedAtomNrs.size() < PointsToPick);
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302 |
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303 | index = 0; // now go through all and pick those whose from PickedAtomsNr
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304 | PointsPicked=0;
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305 | current = PickedAtomNrs.begin();
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306 | for (LC->n[0] = Nlower[0]; LC->n[0] <= Nupper[0]; LC->n[0]++)
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307 | for (LC->n[1] = Nlower[1]; LC->n[1] <= Nupper[1]; LC->n[1]++)
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308 | for (LC->n[2] = Nlower[2]; LC->n[2] <= Nupper[2]; LC->n[2]++) {
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309 | const LinkedCell::LinkedNodes *List = LC->GetCurrentCell();
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310 | // Log() << Verbose(2) << "Current cell is " << LC->n[0] << ", " << LC->n[1] << ", " << LC->n[2] << " with No. " << LC->index << " containing " << List->size() << " points." << endl;
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311 | if (List != NULL) {
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312 | // if (List->begin() != List->end())
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313 | // Log() << Verbose(2) << "Going through candidates ... " << endl;
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314 | // else
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315 | // Log() << Verbose(2) << "Cell is empty ... " << endl;
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316 | for (LinkedCell::LinkedNodes::const_iterator Runner = List->begin(); Runner != List->end(); Runner++) {
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317 | if ((current != PickedAtomNrs.end()) && (*current == index)) {
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318 | Candidate = (*Runner);
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319 | DoLog(2) && (Log() << Verbose(2) << "Current picked node is " << (*Runner)->getName() << " with index " << index << "." << endl);
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320 | x[PointsPicked++] = Candidate->getPosition(); // we have one more atom picked
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321 | current++; // next pre-picked atom
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322 | }
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323 | index++; // next atom nr.
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324 | }
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325 | // } else {
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326 | // Log() << Verbose(2) << "List for this index not allocated!" << endl;
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327 | }
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328 | }
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329 | DoLog(2) && (Log() << Verbose(2) << "The following points were picked: " << endl);
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330 | for (size_t i=0;i<PointsPicked;i++)
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331 | DoLog(2) && (Log() << Verbose(2) << x[i] << endl);
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332 | if (PointsPicked == PointsToPick) // break out of loop if we have all
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333 | break;
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334 | } while(1);
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335 |
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336 | DoLog(2) && (Log() << Verbose(2) << "End of PickRandomPointSet" << endl);
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337 | };
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338 |
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339 | /** Picks a number of random points from a set of boundary points as a fitting set.
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340 | * \param *out output stream for debugging
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341 | * \param *T Tesselation containing boundary points
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342 | * \param *&x random point set on return (not allocated!)
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343 | * \param PointsToPick number of points in set to pick
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344 | */
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345 | void PickRandomPointSet(class Tesselation *T, Vector *&x, size_t PointsToPick)
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346 | {
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347 | size_t PointsLeft = (size_t) T->PointsOnBoundaryCount;
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348 | size_t PointsPicked = 0;
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349 | double value, threshold;
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350 | PointMap *List = &T->PointsOnBoundary;
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351 | DoLog(2) && (Log() << Verbose(2) << "Begin of PickRandomPointSet" << endl);
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352 |
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353 | // allocate array
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354 | if (x == NULL) {
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355 | x = new Vector[PointsToPick];
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356 | } else {
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357 | DoeLog(2) && (eLog()<< Verbose(2) << "Given pointer to vector array seems already allocated." << endl);
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358 | }
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359 |
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360 | if (List != NULL)
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361 | for (PointMap::iterator Runner = List->begin(); Runner != List->end(); Runner++) {
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362 | threshold = 1. - (double)(PointsToPick - PointsPicked)/(double)PointsLeft;
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363 | value = (double)rand()/(double)RAND_MAX;
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364 | //Log() << Verbose(3) << "Current node is " << *Runner->second->node << " with " << value << " ... " << threshold << ": ";
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365 | if (value > threshold) {
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366 | x[PointsPicked] = (Runner->second->node->getPosition());
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367 | PointsPicked++;
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368 | //Log() << Verbose(0) << "IN." << endl;
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369 | } else {
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370 | //Log() << Verbose(0) << "OUT." << endl;
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371 | }
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372 | PointsLeft--;
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373 | }
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374 | DoLog(2) && (Log() << Verbose(2) << "The following points were picked: " << endl);
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375 | for (size_t i=0;i<PointsPicked;i++)
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376 | DoLog(3) && (Log() << Verbose(3) << x[i] << endl);
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377 |
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378 | DoLog(2) && (Log() << Verbose(2) << "End of PickRandomPointSet" << endl);
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379 | };
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380 |
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381 | /** Finds best fitting ellipsoid parameter set in least square sense for a given point set.
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382 | * \param *out output stream for debugging
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383 | * \param *T Tesselation containing boundary points
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384 | * \param *LCList linked cell list of all atoms
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385 | * \param N number of unique points in ellipsoid fit, must be greater equal 6
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386 | * \param number of fits (i.e. parameter sets in output file)
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387 | * \param *filename name for output file
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388 | */
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389 | void FindDistributionOfEllipsoids(class Tesselation *T, class LinkedCell *LCList, int N, int number, const char *filename)
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390 | {
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391 | ofstream output;
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392 | Vector *x = NULL;
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393 | Vector Center;
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394 | Vector EllipsoidCenter;
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395 | double EllipsoidLength[3];
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396 | double EllipsoidAngle[3];
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397 | double distance, MaxDistance, MinDistance;
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398 | DoLog(0) && (Log() << Verbose(0) << "Begin of FindDistributionOfEllipsoids" << endl);
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399 |
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400 | // construct center of gravity of boundary point set for initial ellipsoid center
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401 | Center.Zero();
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402 | for (PointMap::iterator Runner = T->PointsOnBoundary.begin(); Runner != T->PointsOnBoundary.end(); Runner++)
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403 | Center += (Runner->second->node->getPosition());
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404 | Center.Scale(1./T->PointsOnBoundaryCount);
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405 | DoLog(1) && (Log() << Verbose(1) << "Center is at " << Center << "." << endl);
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406 |
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407 | // Output header
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408 | output.open(filename, ios::trunc);
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409 | output << "# Nr.\tCenterX\tCenterY\tCenterZ\ta\tb\tc\tpsi\ttheta\tphi" << endl;
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410 |
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411 | // loop over desired number of parameter sets
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412 | for (;number >0;number--) {
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413 | DoLog(1) && (Log() << Verbose(1) << "Determining data set " << number << " ... " << endl);
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414 | // pick the point set
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415 | x = NULL;
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416 | //PickRandomPointSet(T, LCList, x, N);
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417 | PickRandomNeighbouredPointSet(T, LCList, x, N);
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418 |
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419 | // calculate some sensible starting values for parameter fit
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420 | MaxDistance = 0.;
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421 | MinDistance = x[0].ScalarProduct(x[0]);
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422 | for (int i=0;i<N;i++) {
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423 | distance = x[i].ScalarProduct(x[i]);
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424 | if (distance > MaxDistance)
|
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425 | MaxDistance = distance;
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426 | if (distance < MinDistance)
|
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427 | MinDistance = distance;
|
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428 | }
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429 | //Log() << Verbose(2) << "MinDistance " << MinDistance << ", MaxDistance " << MaxDistance << "." << endl;
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430 | EllipsoidCenter = Center; // use Center of Gravity as initial center of ellipsoid
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431 | for (int i=0;i<3;i++)
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432 | EllipsoidAngle[i] = 0.;
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433 | EllipsoidLength[0] = sqrt(MaxDistance);
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434 | EllipsoidLength[1] = sqrt((MaxDistance+MinDistance)/2.);
|
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435 | EllipsoidLength[2] = sqrt(MinDistance);
|
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436 |
|
---|
437 | // fit the parameters
|
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438 | if (FitPointSetToEllipsoid(x, N, &EllipsoidCenter, &EllipsoidLength[0], &EllipsoidAngle[0])) {
|
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439 | DoLog(1) && (Log() << Verbose(1) << "Picking succeeded!" << endl);
|
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440 | // output obtained parameter set
|
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441 | output << number << "\t";
|
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442 | for (int i=0;i<3;i++)
|
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443 | output << setprecision(9) << EllipsoidCenter[i] << "\t";
|
---|
444 | for (int i=0;i<3;i++)
|
---|
445 | output << setprecision(9) << EllipsoidLength[i] << "\t";
|
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446 | for (int i=0;i<3;i++)
|
---|
447 | output << setprecision(9) << EllipsoidAngle[i] << "\t";
|
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448 | output << endl;
|
---|
449 | } else { // increase N to pick one more
|
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450 | DoLog(1) && (Log() << Verbose(1) << "Picking failed!" << endl);
|
---|
451 | number++;
|
---|
452 | }
|
---|
453 | delete[](x); // free allocated memory for point set
|
---|
454 | }
|
---|
455 | // close output and finish
|
---|
456 | output.close();
|
---|
457 |
|
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458 | DoLog(0) && (Log() << Verbose(0) << "End of FindDistributionOfEllipsoids" << endl);
|
---|
459 | };
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