[2733] | 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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[2756] | 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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[2733] | 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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[2736] | 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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[2733] | 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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[2756] | 63 | //assert(this->isready()); |
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| 64 | assert_<casa::AipsError>(this->isready(), "object is not ready to process."); |
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[2733] | 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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[2849] | 100 | unsigned int *idx = new unsigned int[this->n_]; |
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[2733] | 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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[2849] | 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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[2733] | 119 | // Solve tridiagonal system. |
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[2736] | 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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[2849] | 124 | T a1 = this->x_[idx[1]] - this->x_[idx[0]]; |
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[2733] | 125 | T a2, bi; |
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| 126 | for (unsigned int i = 1; i < ny2_ - 1; i++) { |
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[2849] | 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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[2733] | 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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[2850] | 140 | for (int k = ny2_ - 2; k >= 1; k--) |
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[2733] | 141 | y2_[k] -= u[k] * y2_[k+1]; |
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[2849] | 142 | |
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| 143 | delete[] idx; |
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[2733] | 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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[2849] | 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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[2733] | 171 | return y; |
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| 172 | } |
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| 173 | |
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| 174 | } |
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