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annotate include/interpolator.hpp @ 6:188facdd5a60

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Still buggy. Need a better way to precompute RBFs.
author Jordi Guitérrez Hermoso <jordigh@gmail.com>
date Sun, 29 Jun 2008 05:00:15 -0500
parents 9d4fda54a41d
children d0076d9b2ef1
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1 #ifndef __INTERPOLATOR_H__
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2 #define __INTERPOLATOR_H__
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3
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4 #include <vector>
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5 #include <map>
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6 #include <boost/shared_ptr.hpp>
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7 #include "bvp.hpp"
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8 #include "linalg.hpp"
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9 #include "func.hpp"
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10 #include "diff_op.hpp"
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11
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12 namespace bvp{
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13 using std::map;
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14 using boost::shared_ptr;
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15
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16 template<typename RBF>
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17 class interpolator : public realfunc{
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18 public:
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19
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20 /** @name Constructors
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21 *
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22 * Constructors that take interpolation data perform the
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23 * interpolation as part of the initialisation, which includes
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24 * factoring a matrix
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25 */
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26 //@{
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27 ///Does not initialise the interpolator.
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28 interpolator();
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29
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30 ///Interpolate given a BVP
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31 interpolator(shared_ptr<linear_BVP2> bvp);
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32
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33 ///Interpolate given some data points and the value at those points
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34 interpolator(const map<point, double>& Xi);
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35
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36 /** \short Interpolate given a domain, data points and the value
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37 * at those points
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38 *
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39 * Must provide domain information. The values of Xi must match
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40 * points on the given domain Omega.
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41 */
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42 interpolator(shared_ptr<domain> Omega, const map<point, double>& Xi);
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43 //@}
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44
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45 /** @name Interpolation
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46 *
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47 * Interpolate again either given new data or a different BVP.
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48 */
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49 //@{
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50 void interpolate(const map<point, double>& Xi);
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51 void interpolate(shared_ptr<linear_BVP2> bvp);
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52 //@}
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53
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54 /** @name Evaluations and derivatives
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55 */
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56 //@{
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57 ///Evaluation
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58 double operator()(const point& p) const;
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59 ///Evaluation
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60 double at(const point& p) const;
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61
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62 /// First derivative
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63 double d(const point& p, size_t k) const;
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64 /// Second derivatives
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65 double d2(const point &p, size_t k1, size_t k2) const;
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66 //@}
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67
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68 /** @name Partial redefinitions
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69 *
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70 * These functions allow for partial redefinition of the BVP as
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71 * equired for the additive Schwartz domain decomposition method,
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72 * a nd for other methods. They do not factor a matrix again.
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73 */
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74 //@{
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75 void set_f(const realfunc &f);
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76 void set_g(const realfunc &g);
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77 void set_f(const map<point, double>& f);
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78 void set_g(const map<point, double>& g);
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79 //@}
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80
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81 /** @name Linear arithmetic operators
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82 *
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83 * These functions return a new interpolator. They are pointwise
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84 * linear operations.
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85 */
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86 //@{
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87 /// Needs two operators on the same domain.
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88 interpolator<RBF> operator+(const interpolator<RBF>& u) const;
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89 /// Needs two operators on the same domain.
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90 interpolator<RBF> operator-(const interpolator<RBF>& u) const;
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91 /// Returns a scaled interpolator.
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92 interpolator<RBF> operator*(double a) const;
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93 /// Returns a scaled interpolator.
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94 interpolator<RBF> operator/(double a) const;
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95 //@}
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96
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97 //debug
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98 mutable map<std::vector<size_t>, matrix> precomp_rbfs;
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99 private:
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100 //Once the matrix is defined, this function inverts it.
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101 void computecoeffs();
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102
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103 //Perform the actual interpolation.
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104 void init(shared_ptr<linear_BVP2> bvp);
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105
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106 shared_ptr<linear_BVP2> thebvp;
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107
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108 //Number of interior points.
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109 size_t n;
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110 //Number of boundary points.
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111 size_t m;
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112
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113 //The matrix to invert.
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114 matrix M;
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115
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116 //Is the interpolator ready for use?
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117 bool initted;
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118 void not_initted(int line, string file) const; //Exception thrower
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119
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120 //Coefficients of the RBFs
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121 linalg::vector coeffs;
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122 //The RBFS
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123 std::vector<RBF> rbfs;
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124 //Their hash
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125 size_t rbfs_hash;
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126
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127 size_t hash_value(const std::vector<RBF>& rbfs_in);
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128
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129 /** \short Precomputed RBFs
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130 *
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131 * For all points on the domain, this stores all the RBFs
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132 * evaluated at those points, as well as the derivatives on where
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133 * the RBFs have been evaluated. This is to speed up successive
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134 * evaluations of the interpolator when the interpolator's domain
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135 * doesn't change.
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136 *
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137 * The keys in this vector are vectors that represent the
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138 * multindex for the derivative, where missing trailing entries in
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139 * the vector represents zeros. Thus, an empty vector represents
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140 * evaluation instead of derivatives.
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141 */
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142
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143
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144 /// Precomputed values using precomp_rbfs
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145 mutable map<std::vector<size_t>, map<point, double> > precomp_values;
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146 map<point, double> precompute_values(const matrix& phis) const;
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147 };
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148
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149 //For comfortable syntax
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150 template <typename RBF>
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151 interpolator<RBF> operator*(double a, const interpolator<RBF>& u)
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152 {
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153 return u*a;
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154 }
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155 }
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156
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157 #endif