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annotate src/include/interpolator.hpp @ 29:24f3c4ed5c84

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Halfway to replacing all namespaces with the kwantxi namespace
author Jordi Gutiérrez Hermoso <jordigh@gmail.com>
date Wed, 03 Feb 2010 18:18:38 -0600
parents 0af772242000
children d22bce6382d7
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1 /*!\file interpolator.hpp
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2 *
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3 * \brief An interpolator \f$ \displaystyle u(x) = \sum_{\xi \in \Xi}
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4 * \lambda_\xi \varphi_\xi(x) \f$, templated by RBFs, and its helper
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5 * classes are declared here.
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6 *
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7 * \file interpolator.cpp
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8 * \brief Implementations and instantiations of the functions and
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9 * classes declared in interpolator.hpp
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10 */
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11 #ifndef __INTERPOLATOR_HPP__
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12 #define __INTERPOLATOR_HPP__
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13
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14 #include <vector>
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15 #include <map>
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16 #include <boost/shared_ptr.hpp>
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17 #include <iostream>
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18 #include "bvp.hpp"
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19 #include "linalg.hpp"
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20 #include "func.hpp"
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21 #include "diff_op.hpp"
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22 #include "interp_values.hpp"
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24 namespace kwantxi{
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25 using std::map;
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26 using boost::shared_ptr;
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28 //FIXME: Break this up into an ansatz class and an interpolator
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29 //class.
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30 /*! \brief An interpolator \f$ \displaystyle u(x) = \sum_{\xi \in
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31 * \Xi} \lambda_\xi \varphi_\xi(x) \f$, where the \f$ \varphi_\xi
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32 * \f$ are RBFs.
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33 *
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34 * An interpolator \f$ \displaystyle u(x) = \sum_{\xi \in \Xi}
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35 * \lambda_\xi \varphi_\xi(x) \f$, where the \f$\varphi_\xi\f$ are
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36 * RBFs centred at \f$\xi\f$, and \f$\Xi\f$ is a set of points on
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37 * the interior and boundary of some domain \f$\Omega\f$.
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38 *
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39 * The interpolator can be used in various ways, initialised by
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40 * either a BVP::linear_bvp2 or by interpolation data
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41 * (i.e. std::map< linalg::point, double>). Once an interpolator is
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42 * initialised, it becomes a bona fide bvp::realfunc, so that its
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43 * evaluations and derivatives become available. For certain
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44 * problems, it is convenient to be able to evaluate the
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45 * interpolator or its derivatives at all points of the domain. It
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46 * is also useful to be able to interpolate again on the same domain
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47 * or with a slightly modified BVP. Interfaces to both of these
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48 * functions are provided.
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49 */
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50 template<typename RBF>
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51 class interpolator : public realfunc{
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52 public:
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53
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54 /** @name Constructors
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55 *
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56 * Constructors that take interpolation data perform the
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57 * interpolation as part of the initialisation, which includes
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58 * factoring a matrix
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59 */
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60 //@{
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61 ///Does not initialise the interpolator.
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62 interpolator();
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63
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64 ///Interpolate given a BVP
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65 interpolator(shared_ptr<linear_BVP2> bvp);
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66
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67 ///Interpolate given some data points and the value at those points
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68 interpolator(const map<point, double>& Xi);
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69
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70 /** \short Interpolate given a domain, data points and the value
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71 * at those points
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72 *
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73 * Must provide domain information. The values of Xi must match
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74 * points on the given domain Omega. The reason why the domain
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75 * might be relevant is in case it is important to specify which
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76 * points are on the interior and which are on the boundary, so
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77 * that it's possible to interpolate again by changing the values
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78 * on either the interior or the boundary.
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79 */
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80 interpolator(shared_ptr<domain> Omega, const map<point, double>& Xi);
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81 //@}
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82
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83 /** @name Interpolation
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84 *
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85 * Interpolate again either given new data or a different BVP.
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86 */
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87 //@{
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88 void interpolate(const map<point, double>& Xi);
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89 void interpolate(shared_ptr<linear_BVP2> bvp);
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90
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91 /** \short Interpolate given values on the domain
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92 *
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93 * The given values must match the values returned by other
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94 * interpolators on compatible domains.
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95 */
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96 void interpolate(const interp_values& values);
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97 //@}
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98
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99 /** @name Pointwise evaluation and derivatives
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100 */
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101 //@{
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102 ///Point evaluation
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103 double operator()(const point& p) const;
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104 ///Point evaluation
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105 double at(const point& p) const;
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106 /// Pointwise first derivative
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107 double d(const point& p, size_t k) const;
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108 /// Pointwise second derivatives
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109 double d2(const point &p, size_t k1, size_t k2) const;
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110 //@}
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111
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112 /** @name Full domain evaluation and derivatives
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113 */
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114 //@{
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115 ///Full domain evaluation
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116 interp_values operator()() const;
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117 ///Full domain evaluation
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118 interp_values at() const;
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119 /// Full domain first derivative
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120 interp_values d(size_t k) const;
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121 /// Full domain second derivatives
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122 interp_values d2(size_t k1, size_t k2) const;
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123 //@}
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124
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125 /** @name Precomputation of RBFs
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126 *
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127 * The following functions will precompute upon request all the
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128 * interpolator's RBFs at all points of the domain. This may speed
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129 * up some computations at the expense of increasing memory
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130 * usage.
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131 */
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132 //@{
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133 ///Precompute all the function evaluation of the RBFs.
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134 void precompute_ev();
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135 ///Precompute all relevant first derivatives.
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136 void precompute_d1() ;
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137 ///Precompute all relevant second derivatives.
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138 void precompute_d2();
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139 //@}
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140
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141 /** @name Partial redefinitions
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142 *
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143 * These functions allow for partial redefinition of the BVP as
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144 * equired for the additive Schwartz domain decomposition method,
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145 * and for other methods. They do not factor a matrix again.
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146 */
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147 //@{
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148 void set_f(const intr_values &f);
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149 void set_g(const bdry_values &g);
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150 void set_f(const realfunc &f);
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151 void set_g(const realfunc &g);
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152 void set_f(const map<point, double>& f);
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153 void set_g(const map<point, double>& g);
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154 //@}
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155
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156 /** @name Reinterpolate again
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157 *
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158 * As above group of functions, but for purely interpolating
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159 * interpolators
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160 */
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161 //@{
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162 void set_bdry_values(const bdry_values& b_new);
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163 //@}
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164
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165 /** @name Linear arithmetic operators
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166 *
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167 * These functions return a new interpolator. They are pointwise
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168 * linear operations and work by manipulating interpolator
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169 * coefficients.
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170 */
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171 //@{
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172 /// Needs two operators on the same domain.
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173 interpolator<RBF> operator+(const interpolator<RBF>& u) const;
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174 /// Needs two operators on the same domain.
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175 interpolator<RBF> operator-(const interpolator<RBF>& u) const;
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176 /// Returns a scaled interpolator.
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177 interpolator<RBF> operator*(double a) const;
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178 /// Returns a scaled interpolator.
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179 interpolator<RBF> operator/(double a) const;
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180 //@}
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181
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182 /** \brief Provide a unit normals object associated to the
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183 * interpolator.
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184 */
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185 normals get_normals() const;
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186
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187 /** \brief This will put into an ostream a kwantxi::matrix where
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188 * the first \f$n-1\f$ columns will be all the points where the
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189 * interpolator is defined and the \f$n^{th}\f$ column is the
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190 * values that the interpolator takes on that point.
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191 */
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192 void into_os(std::ostream& os) const;
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193
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194 private:
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195 ///Once the matrix is defined, this function inverts it.
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196 void computecoeffs(bool rhs_defined = false);
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197
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198 ///Perform the actual interpolation.
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199 void init(shared_ptr<linear_BVP2> bvp);
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200
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201 ///If the coefficients change, need to recompute precomputed values
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202 void recompute_values_vec();
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203
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204 ///BVP associated to this interpolator
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205 shared_ptr<linear_BVP2> thebvp;
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206
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207 ///Number of interior points.
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208 size_t n;
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209 ///Number of boundary points.
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210 size_t m;
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211
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212 ///The matrix to invert.
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213 matrix M;
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214
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215 ///Is the interpolator ready for use?
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216 bool initted;
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217
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218
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219 /** @name Exception builders
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220 */
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221 //@{
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222 kwantxi::badArgument not_initted(int line, string file) const;
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223 kwantxi::badArgument not_precomputed(int line, string file) const;
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224 //@}
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225
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226 ///Coefficients of the RBFs
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227 kwantxi::vector coeffs;
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228 ///The RBFS
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229 std::vector<RBF> rbfs;
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230 ///Their hash
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231 size_t rbfs_hash;
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232
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233 ///An RBF hasher
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234 size_t hash_value(const std::vector<RBF>& rbfs_in);
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235
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236 ///The normals at the domain's boundary
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237 normals nrmls;
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238
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239 /** \short Precomputed RBFs
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240 *
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241 * For all points on the domain, this stores all the RBFs
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242 * evaluated at those points, as well as the derivatives on where
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243 * the RBFs have been evaluated. This is to speed up successive
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244 * evaluations of the interpolator when the interpolator's domain
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245 * doesn't change.
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246 *
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247 * The keys in this map are vectors that represent the multindex
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248 * for the derivative, where missing trailing entries in the
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249 * vector represents zeros. Thus, an empty vector represents
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250 * evaluation instead of derivatives.
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251 */
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252 mutable map<std::vector<size_t>, matrix> precomp_rbfs;
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253
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254 /** @name Evaluation flags
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255 *Have the RBFs or their derivatives been precomputed?
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256 */
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257 //@{
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258 bool ev_precomp;
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259 bool d1_precomp;
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260 bool d2_precomp;
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261 //@}
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262
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263 /// Precomputed values using precomp_rbfs
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264 mutable map<std::vector<size_t>, map<point, double> >
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265 precomp_values;
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266 /// Same, but storing the vectors.
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267 mutable map<std::vector<size_t>, kwantxi::vector >
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268 precomp_values_vec;
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269 /// Convert vector of values to a map
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270 map<point, double> valsvec2map(const kwantxi::vector& values) const;
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271 };
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272
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273
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274 /// For comfortable syntax
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275 template <typename RBF>
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276 interpolator<RBF> operator*(double a, const interpolator<RBF>& u)
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277 {
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278 return u*a;
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279 }
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280
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281 /// Stream insertion
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282 template <typename RBF>
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283 std::ostream& operator<< (std::ostream& os, const interpolator<RBF>& u)
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284 {
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285 u.into_os(os);
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286 return os;
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287 }
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288
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289
0
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290 }
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291
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292 #endif