Created
November 1, 2016 06:34
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不等距拉格朗日插值公式
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| /** | |
| 不等距拉格朗日插值公式 | |
| */ | |
| func CalcByLagrange(x []float64, y []float64, t float64) float64 { | |
| // 初值 | |
| result := 0.0 | |
| // 特例处理 | |
| if len(x) <= 1 { | |
| return result | |
| } | |
| if len(x) == 2 { | |
| result = (y[0] * (t - x[1]) - y[1] * (t - x[0])) / (x[0] - x[1]) | |
| return result | |
| } | |
| // 一般情景处理 | |
| i := 0 | |
| for pos, xv := range x { | |
| if xv < t && pos < len(x) { | |
| i = pos + 1 | |
| } | |
| } | |
| // 为在可允许误差范围内简化运算，只运算插值点左右附近三个点 | |
| k := i - 4 | |
| if k < 0 { | |
| k = 0 | |
| } | |
| m := i + 3 | |
| if m > len(x) - 1 { | |
| m = len(x) - 1 | |
| } | |
| for i = k; i <= m; i++ { | |
| s := 1.0 | |
| for j := k; j <= m; j++ { | |
| if j != i { | |
| // 拉格朗日插值公式 | |
| s = s * (t - x[j]) / (x[i] - x[j]); | |
| } | |
| } | |
| result += s * y[i] | |
| } | |
| return result | |
| } |
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