121 lines
2.3 KiB
Go
121 lines
2.3 KiB
Go
package utils
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import (
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"fmt"
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"sort"
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"github.com/nuknal/goNum"
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)
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type LagrangeInterpolator struct {
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coeffs []float64
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n int
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}
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func (li *LagrangeInterpolator) Fit(x []float64, y []float64) error {
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li.n = len(x) - 1
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if li.n < 0 || len(y) != li.n+1 {
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return fmt.Errorf("invalid input data")
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}
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if li.n > 9 {
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li.n = 9 // 限制最大阶数为9
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}
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n := li.n + 1
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// 初始化系数数组
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li.coeffs = make([]float64, n)
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for i := range li.coeffs {
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li.coeffs[i] = 0
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}
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// 计算拉格朗日插值多项式的系数
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for i := 0; i < n; i++ {
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li_coeff := make([]float64, n)
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li_coeff[0] = 1
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for j := 0; j < n; j++ {
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if i != j {
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for k := n - 1; k >= 0; k-- {
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li_coeff[k] *= -x[j]
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if k > 0 {
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li_coeff[k] += li_coeff[k-1]
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}
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}
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for k := 0; k < n; k++ {
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li_coeff[k] /= (x[i] - x[j])
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}
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}
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}
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for k := 0; k < n; k++ {
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li.coeffs[k] += y[i] * li_coeff[k]
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}
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}
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return nil
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}
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func (li LagrangeInterpolator) Predict(x float64) float64 {
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n := len(li.coeffs)
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y := 0.0
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for i := 0; i < n; i++ {
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term := li.coeffs[i]
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for j := 0; j < i; j++ {
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term *= x
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}
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y += term
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}
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return y
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}
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func (li LagrangeInterpolator) N() int {
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return li.n
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}
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// InterpLagrange 利用拉格朗日插值法计算函数值
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// 尽量9阶采用内插值
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const STEP_N = 7
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func InterpLagrange(x []float64, y []float64, xq float64) float64 {
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if len(x) != len(y) {
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return 0.0
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}
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// 限制阶数为9
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var data []float64
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start, end := FindClosestSubset(x, xq, STEP_N)
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for i := start; i <= end; i++ {
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data = append(data, x[i])
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data = append(data, y[i])
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}
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A := goNum.NewMatrix(len(data)/2, 2, data)
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yq, _ := goNum.InterpLagrange(A, xq)
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return yq
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}
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// FindClosestSubset 找到包含xq的最近的n个元素的子数组
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func FindClosestSubset(x []float64, xq float64, n int) (int, int) {
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if len(x) <= n {
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return 0, len(x) - 1 // 如果元素数量少于等于n，直接返回整个数组
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}
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// 找到xq在数组中的插入点
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idx := sort.Search(len(x), func(i int) bool { return x[i] >= xq })
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// 计算子数组的起始和结束位置
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start := idx - n/2 // 尽量让xq在中间，4是因为9个元素的中间位置是4
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end := idx + n/2
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// 调整边界
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if start < 0 {
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start = 0
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end = n
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} else if end >= n {
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end = n - 1
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start = end - n + 1
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}
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return start, end
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}
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