[2733] | 1 | // |
---|
| 2 | // C++ Implementation: CubicSplineInterpolator1D |
---|
| 3 | // |
---|
| 4 | // Description: |
---|
| 5 | // |
---|
| 6 | // |
---|
| 7 | // Author: Takeshi Nakazato <takeshi.nakazato@nao.ac.jp>, (C) 2012 |
---|
| 8 | // |
---|
| 9 | // Copyright: See COPYING file that comes with this distribution |
---|
| 10 | // |
---|
| 11 | // |
---|
| 12 | #include <assert.h> |
---|
| 13 | |
---|
| 14 | #include <iostream> |
---|
| 15 | using namespace std; |
---|
| 16 | |
---|
| 17 | #include "CubicSplineInterpolator1D.h" |
---|
| 18 | |
---|
| 19 | namespace asap { |
---|
| 20 | |
---|
| 21 | template <class T, class U> |
---|
| 22 | CubicSplineInterpolator1D<T, U>::CubicSplineInterpolator1D() |
---|
| 23 | : Interpolator1D<T, U>(), |
---|
| 24 | y2_(0), |
---|
| 25 | ny2_(0), |
---|
| 26 | reusable_(false) |
---|
| 27 | {} |
---|
| 28 | |
---|
| 29 | template <class T, class U> |
---|
| 30 | CubicSplineInterpolator1D<T, U>::~CubicSplineInterpolator1D() |
---|
| 31 | { |
---|
| 32 | if (y2_) |
---|
| 33 | delete[] y2_; |
---|
| 34 | } |
---|
| 35 | |
---|
| 36 | template <class T, class U> |
---|
| 37 | void CubicSplineInterpolator1D<T, U>::setData(T *x, U *y, unsigned int n) |
---|
| 38 | { |
---|
| 39 | Interpolator1D<T, U>::setData(x, y, n); |
---|
| 40 | reusable_ = false; |
---|
| 41 | } |
---|
| 42 | |
---|
| 43 | template <class T, class U> |
---|
[2736] | 44 | void CubicSplineInterpolator1D<T, U>::setX(T *x, unsigned int n) |
---|
| 45 | { |
---|
| 46 | Interpolator1D<T, U>::setX(x, n); |
---|
| 47 | reusable_ = false; |
---|
| 48 | } |
---|
| 49 | |
---|
| 50 | template <class T, class U> |
---|
[2733] | 51 | void CubicSplineInterpolator1D<T, U>::setY(U *y, unsigned int n) |
---|
| 52 | { |
---|
| 53 | Interpolator1D<T, U>::setY(y, n); |
---|
| 54 | reusable_ = false; |
---|
| 55 | } |
---|
| 56 | |
---|
| 57 | template <class T, class U> |
---|
| 58 | U CubicSplineInterpolator1D<T, U>::interpolate(T x) |
---|
| 59 | { |
---|
| 60 | assert(this->isready()); |
---|
| 61 | if (this->n_ == 1) |
---|
| 62 | return this->y_[0]; |
---|
| 63 | |
---|
| 64 | unsigned int i = this->locator_->locate(x); |
---|
| 65 | |
---|
| 66 | // do not perform extrapolation |
---|
| 67 | if (i == 0) { |
---|
| 68 | return this->y_[i]; |
---|
| 69 | } |
---|
| 70 | else if (i == this->n_) { |
---|
| 71 | return this->y_[i-1]; |
---|
| 72 | } |
---|
| 73 | |
---|
| 74 | // determine second derivative of each point |
---|
| 75 | if (!reusable_) { |
---|
| 76 | evaly2(); |
---|
| 77 | reusable_ = true; |
---|
| 78 | } |
---|
| 79 | |
---|
| 80 | // cubic spline interpolation |
---|
| 81 | float y = dospline(x, i); |
---|
| 82 | return y; |
---|
| 83 | } |
---|
| 84 | |
---|
| 85 | template <class T, class U> |
---|
| 86 | void CubicSplineInterpolator1D<T, U>::evaly2() |
---|
| 87 | { |
---|
| 88 | if (this->n_ > ny2_) { |
---|
| 89 | if (y2_) |
---|
| 90 | delete[] y2_; |
---|
| 91 | y2_ = new U[this->n_]; |
---|
| 92 | ny2_ = this->n_; |
---|
| 93 | } |
---|
| 94 | |
---|
| 95 | U *u = new U[ny2_-1]; |
---|
| 96 | |
---|
| 97 | // Natural cubic spline. |
---|
| 98 | y2_[0] = 0.0; |
---|
| 99 | y2_[ny2_-1] = 0.0; |
---|
| 100 | u[0] = 0.0; |
---|
| 101 | |
---|
| 102 | // Solve tridiagonal system. |
---|
[2736] | 103 | // Here, tridiagonal matrix is decomposed to upper triangular |
---|
| 104 | // matrix. u stores upper triangular components while y2_ stores |
---|
| 105 | // right-hand side vector. The diagonal elements are normalized |
---|
| 106 | // to 1. |
---|
[2733] | 107 | T a1 = this->x_[1] - this->x_[0]; |
---|
| 108 | T a2, bi; |
---|
| 109 | for (unsigned int i = 1; i < ny2_ - 1; i++) { |
---|
| 110 | a2 = this->x_[i+1] - this->x_[i]; |
---|
| 111 | bi = 1.0 / (this->x_[i+1] - this->x_[i-1]); |
---|
| 112 | y2_[i] = 3.0 * bi * ((this->y_[i+1] - this->y_[i]) / a2 |
---|
| 113 | - (this->y_[i] - this->y_[i-1]) / a1 |
---|
| 114 | - y2_[i-1] * 0.5 * a1); |
---|
| 115 | a1 = 1.0 / (1.0 - u[i-1] * 0.5 * a1 * bi); |
---|
| 116 | y2_[i] *= a1; |
---|
| 117 | u[i] = 0.5 * a2 * bi * a1; |
---|
| 118 | a1 = a2; |
---|
| 119 | } |
---|
| 120 | |
---|
| 121 | // Then, solve the system by backsubstitution and store solution |
---|
| 122 | // vector to y2_. |
---|
| 123 | for (int k = ny2_ - 2; k >= 0; k--) |
---|
| 124 | y2_[k] -= u[k] * y2_[k+1]; |
---|
| 125 | |
---|
| 126 | delete[] u; |
---|
| 127 | } |
---|
| 128 | |
---|
| 129 | template <class T, class U> |
---|
| 130 | U CubicSplineInterpolator1D<T, U>::dospline(T x, unsigned int i) |
---|
| 131 | { |
---|
| 132 | unsigned int j = i - 1; |
---|
| 133 | T h = this->x_[i] - this->x_[j]; |
---|
| 134 | T a = (this->x_[i] - x) / h; |
---|
| 135 | T b = (x - this->x_[j]) / h; |
---|
| 136 | U y = a * this->y_[j] + b * this->y_[i] + |
---|
| 137 | ((a * a * a - a) * y2_[j] + (b * b * b - b) * y2_[i]) * (h * h) / 6.0; |
---|
| 138 | return y; |
---|
| 139 | } |
---|
| 140 | |
---|
| 141 | } |
---|