1 | // |
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2 | // C++ Implementation: CubicSplineInterpolator1D |
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3 | // |
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4 | // Description: |
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5 | // |
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6 | // |
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7 | // Author: Takeshi Nakazato <takeshi.nakazato@nao.ac.jp>, (C) 2012 |
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8 | // |
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9 | // Copyright: See COPYING file that comes with this distribution |
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10 | // |
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11 | // |
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12 | #include <assert.h> |
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13 | |
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14 | #include <iostream> |
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15 | using namespace std; |
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16 | |
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17 | #include "CubicSplineInterpolator1D.h" |
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18 | |
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19 | namespace asap { |
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20 | |
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21 | CubicSplineInterpolator1D::CubicSplineInterpolator1D() |
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22 | : Interpolator1D(), |
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23 | y2_(0), |
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24 | ny2_(0), |
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25 | reusable_(false) |
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26 | {} |
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27 | |
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28 | CubicSplineInterpolator1D::~CubicSplineInterpolator1D() |
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29 | { |
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30 | if (y2_) |
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31 | delete[] y2_; |
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32 | } |
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33 | |
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34 | void CubicSplineInterpolator1D::setData(double *x, float *y, unsigned int n) |
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35 | { |
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36 | Interpolator1D::setData(x, y, n); |
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37 | reusable_ = false; |
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38 | } |
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39 | |
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40 | void CubicSplineInterpolator1D::setY(float *y, unsigned int n) |
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41 | { |
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42 | Interpolator1D::setY(y, n); |
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43 | reusable_ = false; |
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44 | } |
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45 | |
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46 | float CubicSplineInterpolator1D::interpolate(double x) |
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47 | { |
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48 | assert(isready()); |
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49 | if (n_ == 1) |
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50 | return y_[0]; |
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51 | |
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52 | unsigned int i = locator_->locate(x); |
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53 | |
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54 | // do not perform extrapolation |
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55 | if (i == 0) { |
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56 | return y_[i]; |
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57 | } |
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58 | else if (i == n_) { |
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59 | return y_[i-1]; |
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60 | } |
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61 | |
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62 | // determine second derivative of each point |
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63 | if (!reusable_) { |
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64 | evaly2(); |
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65 | reusable_ = true; |
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66 | } |
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67 | |
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68 | // cubic spline interpolation |
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69 | float y = dospline(x, i); |
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70 | return y; |
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71 | } |
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72 | |
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73 | void CubicSplineInterpolator1D::evaly2() |
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74 | { |
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75 | if (n_ > ny2_) { |
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76 | if (y2_) |
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77 | delete[] y2_; |
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78 | y2_ = new float[n_]; |
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79 | ny2_ = n_; |
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80 | } |
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81 | |
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82 | float *u = new float[ny2_-1]; |
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83 | |
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84 | // Natural cubic spline. |
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85 | y2_[0] = 0.0; |
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86 | y2_[ny2_-1] = 0.0; |
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87 | u[0] = 0.0; |
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88 | |
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89 | // Solve tridiagonal system. |
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90 | // Here, tridiagonal matrix is decomposed to triangular matrix |
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91 | // u stores upper triangular components while y2_ stores |
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92 | // right-hand side vector. |
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93 | double a1 = x_[1] - x_[0]; |
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94 | double a2, bi; |
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95 | for (unsigned int i = 1; i < ny2_ - 1; i++) { |
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96 | a2 = x_[i+1] - x_[i]; |
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97 | bi = 1.0 / (x_[i+1] - x_[i-1]); |
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98 | y2_[i] = 3.0 * bi * ((y_[i+1] - y_[i]) / a2 - (y_[i] - y_[i-1]) / a1 |
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99 | - y2_[i-1] * 0.5 * a1); |
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100 | a1 = 1.0 / (1.0 - u[i-1] * 0.5 * a1 * bi); |
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101 | y2_[i] *= a1; |
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102 | u[i] = 0.5 * a2 * bi * a1; |
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103 | a1 = a2; |
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104 | } |
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105 | |
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106 | // Then, solve the system by backsubstitution and store solution |
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107 | // vector to y2_. |
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108 | for (int k = ny2_ - 2; k >= 0; k--) |
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109 | y2_[k] -= u[k] * y2_[k+1]; |
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110 | |
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111 | delete[] u; |
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112 | } |
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113 | |
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114 | float CubicSplineInterpolator1D::dospline(double x, unsigned int i) |
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115 | { |
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116 | unsigned int j = i - 1; |
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117 | double h = x_[i] - x_[j]; |
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118 | double a = (x_[i] - x) / h; |
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119 | double b = (x - x_[j]) / h; |
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120 | float y = a * y_[j] + b * y_[i] + |
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121 | ((a * a * a - a) * y2_[j] + (b * b * b - b) * y2_[i]) * (h * h) / 6.0; |
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122 | return y; |
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123 | } |
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124 | |
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125 | } |
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