53 lines
1.5 KiB
C
53 lines
1.5 KiB
C
static double domega(const double* const xn, const unsigned int n, const unsigned int k, const double x);
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/**
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* @brief 拉格朗日插值算法。
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* 算法说明：https://blacktea.vip.cpolar.top/OrgLion-Writes/NotePublic/src/branch/master/Algorithm/DSP/拉格朗日插值.md
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*
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* @param xn 输入：已知采样点的 x 坐标。
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* @param yn 输入：已知采样点的 y 坐标。
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* @param n 输入：采样点数。
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* @param x 输入：插值点 x 坐标。
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* @return double 输出：插值点的 y 坐标值。
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*/
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double Lagrange(const double* const xn, const double* const yn, const unsigned int n, const double x) {
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unsigned int i;
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double l = 0.0;
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for (i=0; i<n; i++)
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l += yn[i]*domega(xn, n, i, x);
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return l;
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}
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static double domega(const double* const xn, const unsigned int n, const unsigned int k, const double x) {
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unsigned int i;
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double omega=1.0;
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double omega_deri = 1.0;
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for (i=0; i<n; i++) {
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if (i==k)
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continue;
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omega *= (x-xn[i]);
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omega_deri *= (xn[k] - xn[i]);
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}
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return omega/omega_deri;
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}
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/** Demo */
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static double Xn[] = {0, 0.3000, 0.6000, 0.9000, 1.2000, 1.5000, 1.8000, 2.1000, 2.4000, 2.7000, 3.0000};
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static double Yn[] = {2.0000, 2.3780, 3.9440, 7.3460, 13.2320, 22.2500, 35.0480, 52.2740, 74.5760, 102.6020, 137.0000};
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/**
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* @brief 拉格朗日插值示例。
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*
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* @return int
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*/
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int main(void) {
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double out = 0.0;
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out = Lagrange(Xn, Yn, 11, 1.5);
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return 0;
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}
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