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Update the doxygen documentation
author Jordi Gutiérrez Hermoso <jordigh@gmail.com>
date Sat, 29 May 2010 20:01:40 -0500
parents 11395e64852f
children
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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 #pragma once
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12
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13 #include <vector>
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14 #include <map>
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15 #include <boost/shared_ptr.hpp>
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16 #include <iostream>
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17 #include "bvp.hpp"
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18 #include "linalg.hpp"
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19 #include "func.hpp"
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20 #include "diff_op.hpp"
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21 #include "interp_values.hpp"
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23 namespace kwantix{
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24 using std::map;
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25 using boost::shared_ptr;
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27 /** \defgroup Interpolator */
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28 /// \{
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29 class vtkplot;
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31 //FIXME: Break this up into an ansatz class and an interpolator
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32 //class.
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33 /*! \brief An interpolator \f$ \displaystyle u(x) = \sum_{\xi \in
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34 * \Xi} \lambda_\xi \varphi_\xi(x) \f$, where the \f$ \varphi_\xi
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35 * \f$ are RBFs.
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36 *
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37 * An interpolator \f$ \displaystyle u(x) = \sum_{\xi \in \Xi}
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38 * \lambda_\xi \varphi_\xi(x) \f$, where the \f$\varphi_\xi\f$ are
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39 * RBFs centred at \f$\xi\f$, and \f$\Xi\f$ is a set of points on
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40 * the interior and boundary of some domain \f$\Omega\f$.
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41 *
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42 * The interpolator can be used in various ways, initialised by
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43 * either a BVP::linear_bvp2 or by interpolation data
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44 * (i.e. std::map< kwantix::point, double>). Once an interpolator is
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45 * initialised, it becomes a bona fide kwantix::realfunc, so that its
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46 * evaluations and derivatives become available. For certain
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47 * problems, it is convenient to be able to evaluate the
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48 * interpolator or its derivatives at all points of the domain. It
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49 * is also useful to be able to interpolate again on the same domain
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50 * or with a slightly modified BVP. Interfaces to both of these
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51 * functions are provided.
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52 */
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53 template<typename RBF>
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54 class interpolator : public realfunc{
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55 public:
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56
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57 /** @name Constructors
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58 *
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59 * Constructors that take interpolation data perform the
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60 * interpolation as part of the initialisation, which includes
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61 * factoring a matrix
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62 */
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63 //@{
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64 ///Does not initialise the interpolator.
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65 interpolator();
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66
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67 ///Interpolate given a BVP
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68 interpolator(shared_ptr<linear_BVP2> bvp);
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70 ///Interpolate given some data points and the value at those points
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71 interpolator(const map<point, double>& Xi);
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73 /** \short Interpolate given a domain, data points and the value
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74 * at those points
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75 *
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76 * Must provide domain information. The values of Xi must match
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77 * points on the given domain Omega. The reason why the domain
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78 * might be relevant is in case it is important to specify which
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79 * points are on the interior and which are on the boundary, so
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80 * that it's possible to interpolate again by changing the values
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81 * on either the interior or the boundary.
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82 */
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83 interpolator(shared_ptr<domain> Omega, const map<point, double>& Xi);
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84 //@}
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85
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86 /** @name Interpolation
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87 *
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88 * Interpolate again either given new data or a different BVP.
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89 */
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90 //@{
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91 void interpolate(const map<point, double>& Xi);
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92 void interpolate(shared_ptr<linear_BVP2> bvp);
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93
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94 /** \short Interpolate given values on the domain
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95 *
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96 * The given values must match the values returned by other
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97 * interpolators on compatible domains.
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98 */
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99 void interpolate(const interp_values& values);
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100 //@}
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101
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102 /** @name Pointwise evaluation and derivatives
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103 */
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104 //@{
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105 ///Point evaluation
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106 double operator()(const point& p) const;
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107 ///Point evaluation
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108 double at(const point& p) const;
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109 /// Pointwise first derivative
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110 double d(const point& p, size_t k) const;
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111 /// Pointwise second derivatives
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112 double d2(const point &p, size_t k1, size_t k2) const;
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113 //@}
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114
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115 /** @name Full domain evaluation and derivatives
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116 */
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117 //@{
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118 ///Full domain evaluation
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119 interp_values operator()() const;
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120 ///Full domain evaluation
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121 interp_values at() const;
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122 /// Full domain first derivative
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123 interp_values d(size_t k) const;
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124 /// Full domain second derivatives
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125 interp_values d2(size_t k1, size_t k2) const;
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126 //@}
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127
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128 /** @name Precomputation of RBFs
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129 *
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130 * The following functions will precompute upon request all the
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131 * interpolator's RBFs at all points of the domain. This may speed
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132 * up some computations at the expense of increasing memory
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133 * usage.
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134 */
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135 //@{
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136 ///Precompute all the function evaluation of the RBFs.
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137 void precompute_ev();
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138 ///Precompute all relevant first derivatives.
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139 void precompute_d1() ;
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140 ///Precompute all relevant second derivatives.
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141 void precompute_d2();
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142 //@}
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143
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144 /** @name Partial redefinitions
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145 *
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146 * These functions allow for partial redefinition of the BVP as
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147 * equired for the additive Schwartz domain decomposition method,
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148 * and for other methods. They do not factor a matrix again.
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149 */
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150 //@{
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151 void set_f(const intr_values &f);
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152 void set_g(const bdry_values &g);
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153 void set_f(const realfunc &f);
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154 void set_g(const realfunc &g);
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155 void set_f(const map<point, double>& f);
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156 void set_g(const map<point, double>& g);
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157 //@}
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158
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159 /** @name Reinterpolate again
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160 *
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161 * As above group of functions, but for purely interpolating
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162 * interpolators
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163 */
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164 //@{
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165 void set_bdry_values(const bdry_values& b_new);
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166 //@}
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167
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168 /** @name Linear arithmetic operators
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169 *
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170 * These functions return a new interpolator. They are pointwise
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171 * linear operations and work by manipulating interpolator
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172 * coefficients.
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173 */
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174 //@{
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175 /// Needs two operators on the same domain.
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176 interpolator<RBF> operator+(const interpolator<RBF>& u) const;
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177 /// Needs two operators on the same domain.
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178 interpolator<RBF> operator-(const interpolator<RBF>& u) const;
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179 /// Returns a scaled interpolator.
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180 interpolator<RBF> operator*(double a) const;
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181 /// Returns a scaled interpolator.
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182 interpolator<RBF> operator/(double a) const;
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183 //@}
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184
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185 /** \brief Provide a unit normals object associated to the
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186 * interpolator.
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187 */
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188 normals get_normals() const;
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189
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190 /** \brief This will put into an ostream a kwantix::matrix where
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191 * the first \f$n-1\f$ columns will be all the points where the
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192 * interpolator is defined and the \f$n^{th}\f$ column is the
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193 * values that the interpolator takes on that point.
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194 */
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195 void into_os(std::ostream& os) const;
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196
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197 ///Needed in order to plot the data
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198 friend class vtkplot;
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199
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200 private:
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201 ///Once the matrix is defined, this function inverts it.
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202 void computecoeffs(bool rhs_defined = false);
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203
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204 ///Perform the actual interpolation.
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205 void init(shared_ptr<linear_BVP2> bvp);
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206
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207 ///If the coefficients change, need to recompute precomputed values
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208 void recompute_values_vec();
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209
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210 ///BVP associated to this interpolator
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211 shared_ptr<linear_BVP2> thebvp;
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212
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213 ///Number of interior points.
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214 size_t n;
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215 ///Number of boundary points.
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216 size_t m;
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217
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218 ///The matrix to invert.
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219 shared_ptr<matrix> M;
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220
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221 ///Is the interpolator ready for use?
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222 bool initted;
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223
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224
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225 /** @name Exception builders
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226 */
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227 //@{
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228 kwantix::badArgument not_initted(int line, string file) const;
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229 kwantix::badArgument not_precomputed(int line, string file) const;
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230 //@}
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231
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232 ///Coefficients of the RBFs
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233 kwantix::vector coeffs;
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234 ///The RBFS
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235 std::vector<RBF> rbfs;
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236 ///Their hash
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237 size_t rbfs_hash;
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238
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239 ///An RBF hasher
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240 size_t hash_value(const std::vector<RBF>& rbfs_in);
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241
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242 ///The normals at the domain's boundary
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243 normals nrmls;
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244
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245 /** \short Precomputed RBFs
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246 *
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247 * For all points on the domain, this stores all the RBFs
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248 * evaluated at those points, as well as the derivatives on where
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249 * the RBFs have been evaluated. This is to speed up successive
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250 * evaluations of the interpolator when the interpolator's domain
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251 * doesn't change.
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252 *
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253 * The keys in this map are vectors that represent the multindex
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254 * for the derivative, where missing trailing entries in the
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255 * vector represents zeros. Thus, an empty vector represents
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256 * evaluation instead of derivatives.
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257 */
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258 mutable map<std::vector<size_t>,
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259 shared_ptr<matrix> > precomp_rbfs;
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260
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261 /** @name Evaluation flags
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262 *Have the RBFs or their derivatives been precomputed?
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263 */
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264 //@{
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265 bool ev_precomp;
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266 bool d1_precomp;
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267 bool d2_precomp;
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268 //@}
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269
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270 /// Precomputed values using precomp_rbfs
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271 mutable map<std::vector<size_t>, map<point, double> >
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272 precomp_values;
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273 /// Same, but storing the vectors.
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274 mutable map<std::vector<size_t>, kwantix::vector >
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275 precomp_values_vec;
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276 /// Convert vector of values to a map
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277 map<point, double> valsvec2map(const kwantix::vector& values) const;
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278 };
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279 /// \}
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280
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281
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282 /// For comfortable syntax
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283 template <typename RBF>
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284 interpolator<RBF> operator*(double a, const interpolator<RBF>& u)
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285 {
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286 return u*a;
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287 }
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288
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289 /// Stream insertion
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290 template <typename RBF>
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291 std::ostream& operator<< (std::ostream& os, const interpolator<RBF>& u)
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292 {
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293 u.into_os(os);
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294 return os;
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295 }
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296
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297 }//namespace kwantix
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298