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 <casa/Exceptions/Error.h> |
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15 | #include <casa/Utilities/Assert.h> |
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16 | |
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17 | #include <iostream> |
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18 | using namespace std; |
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19 | |
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20 | #include "CubicSplineInterpolator1D.h" |
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21 | |
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22 | namespace asap { |
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23 | |
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24 | template <class T, class U> |
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25 | CubicSplineInterpolator1D<T, U>::CubicSplineInterpolator1D() |
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26 | : Interpolator1D<T, U>(), |
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27 | y2_(0), |
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28 | ny2_(0), |
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29 | reusable_(false) |
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30 | {} |
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31 | |
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32 | template <class T, class U> |
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33 | CubicSplineInterpolator1D<T, U>::~CubicSplineInterpolator1D() |
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34 | { |
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35 | if (y2_) |
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36 | delete[] y2_; |
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37 | } |
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38 | |
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39 | template <class T, class U> |
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40 | void CubicSplineInterpolator1D<T, U>::setData(T *x, U *y, unsigned int n) |
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41 | { |
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42 | Interpolator1D<T, U>::setData(x, y, n); |
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43 | reusable_ = false; |
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44 | } |
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45 | |
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46 | template <class T, class U> |
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47 | void CubicSplineInterpolator1D<T, U>::setX(T *x, unsigned int n) |
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48 | { |
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49 | Interpolator1D<T, U>::setX(x, n); |
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50 | reusable_ = false; |
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51 | } |
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52 | |
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53 | template <class T, class U> |
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54 | void CubicSplineInterpolator1D<T, U>::setY(U *y, unsigned int n) |
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55 | { |
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56 | Interpolator1D<T, U>::setY(y, n); |
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57 | reusable_ = false; |
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58 | } |
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59 | |
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60 | template <class T, class U> |
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61 | U CubicSplineInterpolator1D<T, U>::interpolate(T x) |
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62 | { |
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63 | //assert(this->isready()); |
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64 | assert_<casa::AipsError>(this->isready(), "object is not ready to process."); |
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65 | if (this->n_ == 1) |
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66 | return this->y_[0]; |
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67 | |
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68 | unsigned int i = this->locator_->locate(x); |
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69 | |
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70 | // do not perform extrapolation |
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71 | if (i == 0) { |
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72 | return this->y_[i]; |
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73 | } |
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74 | else if (i == this->n_) { |
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75 | return this->y_[i-1]; |
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76 | } |
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77 | |
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78 | // determine second derivative of each point |
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79 | if (!reusable_) { |
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80 | evaly2(); |
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81 | reusable_ = true; |
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82 | } |
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83 | |
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84 | // cubic spline interpolation |
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85 | float y = dospline(x, i); |
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86 | return y; |
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87 | } |
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88 | |
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89 | template <class T, class U> |
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90 | void CubicSplineInterpolator1D<T, U>::evaly2() |
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91 | { |
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92 | if (this->n_ > ny2_) { |
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93 | if (y2_) |
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94 | delete[] y2_; |
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95 | y2_ = new U[this->n_]; |
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96 | ny2_ = this->n_; |
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97 | } |
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98 | |
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99 | U *u = new U[ny2_-1]; |
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100 | unsigned int *idx = new unsigned int[this->n_]; |
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101 | |
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102 | // Natural cubic spline. |
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103 | y2_[0] = 0.0; |
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104 | y2_[ny2_-1] = 0.0; |
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105 | u[0] = 0.0; |
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106 | |
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107 | if (this->x_[0] < this->x_[this->n_-1]) { |
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108 | // ascending |
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109 | for (unsigned int i = 0; i < this->n_; ++i) |
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110 | idx[i] = i; |
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111 | } |
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112 | else { |
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113 | // descending |
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114 | for (unsigned int i = 0; i < this->n_; ++i) |
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115 | idx[i] = this->n_ - 1 - i; |
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116 | } |
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117 | |
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118 | |
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119 | // Solve tridiagonal system. |
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120 | // Here, tridiagonal matrix is decomposed to upper triangular |
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121 | // matrix. u stores upper triangular components while y2_ stores |
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122 | // right-hand side vector. The diagonal elements are normalized |
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123 | // to 1. |
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124 | T a1 = this->x_[idx[1]] - this->x_[idx[0]]; |
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125 | T a2, bi; |
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126 | for (unsigned int i = 1; i < ny2_ - 1; i++) { |
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127 | a2 = this->x_[idx[i+1]] - this->x_[idx[i]]; |
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128 | bi = 1.0 / (this->x_[idx[i+1]] - this->x_[idx[i-1]]); |
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129 | y2_[i] = 3.0 * bi * ((this->y_[idx[i+1]] - this->y_[idx[i]]) / a2 |
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130 | - (this->y_[idx[i]] - this->y_[idx[i-1]]) / a1 |
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131 | - y2_[i-1] * 0.5 * a1); |
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132 | a1 = 1.0 / (1.0 - u[i-1] * 0.5 * a1 * bi); |
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133 | y2_[i] *= a1; |
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134 | u[i] = 0.5 * a2 * bi * a1; |
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135 | a1 = a2; |
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136 | } |
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137 | |
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138 | // Then, solve the system by backsubstitution and store solution |
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139 | // vector to y2_. |
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140 | for (int k = ny2_ - 2; k >= 1; k--) |
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141 | y2_[k] -= u[k] * y2_[k+1]; |
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142 | |
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143 | delete[] idx; |
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144 | delete[] u; |
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145 | } |
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146 | |
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147 | template <class T, class U> |
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148 | U CubicSplineInterpolator1D<T, U>::dospline(T x, unsigned int i) |
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149 | { |
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150 | unsigned int index_lower; |
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151 | unsigned int index_higher; |
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152 | unsigned int index_lower_correct; |
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153 | unsigned int index_higher_correct; |
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154 | if (this->x_[0] < this->x_[this->n_-1]) { |
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155 | index_lower = i - 1; |
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156 | index_higher = i; |
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157 | index_lower_correct = index_lower; |
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158 | index_higher_correct = index_higher; |
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159 | } |
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160 | else { |
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161 | index_lower = i; |
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162 | index_higher = i - 1; |
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163 | index_lower_correct = this->n_ - 1 - index_lower; |
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164 | index_higher_correct = this->n_ - 1 - index_higher; |
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165 | } |
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166 | T dx = this->x_[index_higher] - this->x_[index_lower]; |
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167 | T a = (this->x_[index_higher] - x) / dx; |
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168 | T b = (x - this->x_[index_lower]) / dx; |
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169 | U y = a * this->y_[index_lower] + b * this->y_[index_higher] + |
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170 | ((a * a * a - a) * y2_[index_lower_correct] + (b * b * b - b) * y2_[index_higher_correct]) * (dx * dx) / 6.0; |
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171 | return y; |
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172 | } |
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173 | |
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174 | } |
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