1 | // |
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2 | // C++ Implementation: PolynomialInterpolator1D |
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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 | #include <math.h> |
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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 <casa/Exceptions/Error.h> |
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18 | #include <casa/Utilities/Assert.h> |
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19 | |
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20 | #include "PolynomialInterpolator1D.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 | PolynomialInterpolator1D<T, U>::PolynomialInterpolator1D() |
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26 | : Interpolator1D<T, U>() |
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27 | {} |
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28 | |
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29 | template <class T, class U> |
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30 | PolynomialInterpolator1D<T, U>::~PolynomialInterpolator1D() |
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31 | {} |
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32 | |
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33 | template <class T, class U> |
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34 | U PolynomialInterpolator1D<T, U>::interpolate(T x) |
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35 | { |
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36 | //casa::AlwaysAssert((this->isready()),(casa::AipsError)); |
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37 | casa::assert_<casa::AipsError>(this->isready(), "object is not ready to process."); |
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38 | if (this->n_ == 1) |
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39 | return this->y_[0]; |
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40 | |
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41 | unsigned int i = this->locator_->locate(x); |
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42 | |
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43 | // do not perform extrapolation |
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44 | if (i == 0) { |
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45 | return this->y_[i]; |
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46 | } |
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47 | else if (i == this->n_) { |
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48 | return this->y_[i-1]; |
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49 | } |
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50 | |
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51 | // polynomial interpolation |
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52 | U y; |
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53 | if (this->order_ >= this->n_ - 1) { |
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54 | // use full region |
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55 | y = dopoly(x, 0, this->n_); |
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56 | } |
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57 | else { |
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58 | // use sub-region |
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59 | int j = i - 1 - this->order_ / 2; |
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60 | unsigned int m = this->n_ - 1 - this->order_; |
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61 | unsigned int k = (unsigned int)((j > 0) ? j : 0); |
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62 | k = ((k > m) ? m : k); |
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63 | y = dopoly(x, k, this->order_ + 1); |
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64 | } |
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65 | |
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66 | return y; |
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67 | } |
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68 | |
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69 | template <class T, class U> |
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70 | U PolynomialInterpolator1D<T, U>::dopoly(T x, unsigned int left, |
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71 | unsigned int n) |
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72 | { |
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73 | T *xa = &this->x_[left]; |
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74 | U *ya = &this->y_[left]; |
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75 | |
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76 | // storage for C and D in Neville's algorithm |
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77 | U *c = new U[n]; |
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78 | U *d = new U[n]; |
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79 | for (unsigned int i = 0; i < n; i++) { |
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80 | c[i] = ya[i]; |
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81 | d[i] = ya[i]; |
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82 | } |
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83 | |
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84 | // Neville's algorithm |
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85 | U y = c[0]; |
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86 | for (unsigned int m = 1; m < n; m++) { |
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87 | // Evaluate Cm1, Cm2, Cm3, ... Cm[n-m] and Dm1, Dm2, Dm3, ... Dm[n-m]. |
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88 | // Those are stored to c[0], c[1], ..., c[n-m-1] and d[0], d[1], ..., |
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89 | // d[n-m-1]. |
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90 | for (unsigned int i = 0; i < n - m; i++) { |
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91 | U cd = c[i+1] - d[i]; |
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92 | T dx = xa[i] - xa[i+m]; |
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93 | try { |
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94 | cd /= (U)dx; |
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95 | } |
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96 | catch (...) { |
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97 | delete[] c; |
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98 | delete[] d; |
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99 | throw casa::AipsError("x_ has duplicate elements"); |
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100 | } |
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101 | c[i] = (xa[i] - x) * cd; |
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102 | d[i] = (xa[i+m] - x) * cd; |
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103 | } |
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104 | |
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105 | // In each step, c[0] holds Cm1 which is a correction between |
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106 | // P12...m and P12...[m+1]. Thus, the following repeated update |
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107 | // corresponds to the route P1 -> P12 -> P123 ->...-> P123...n. |
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108 | y += c[0]; |
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109 | } |
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110 | |
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111 | delete[] c; |
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112 | delete[] d; |
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113 | |
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114 | return y; |
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115 | } |
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116 | } |
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