package utils

import (
	"fmt"
	"sort"

	"github.com/chfenger/goNum"
)

type LagrangeInterpolator struct {
	coeffs []float64
	n      int
}

func (li *LagrangeInterpolator) Fit(x []float64, y []float64) error {
	li.n = len(x) - 1
	if li.n < 0 || len(y) != li.n+1 {
		return fmt.Errorf("invalid input data")
	}

	if li.n > 9 {
		li.n = 9 // 限制最大阶数为9
	}

	n := li.n + 1

	// 初始化系数数组
	li.coeffs = make([]float64, n)
	for i := range li.coeffs {
		li.coeffs[i] = 0
	}

	// 计算拉格朗日插值多项式的系数
	for i := 0; i < n; i++ {
		li_coeff := make([]float64, n)
		li_coeff[0] = 1
		for j := 0; j < n; j++ {
			if i != j {
				for k := n - 1; k >= 0; k-- {
					li_coeff[k] *= -x[j]
					if k > 0 {
						li_coeff[k] += li_coeff[k-1]
					}
				}
				for k := 0; k < n; k++ {
					li_coeff[k] /= (x[i] - x[j])
				}
			}
		}
		for k := 0; k < n; k++ {
			li.coeffs[k] += y[i] * li_coeff[k]
		}
	}

	return nil
}

func (li LagrangeInterpolator) Predict(x float64) float64 {
	n := len(li.coeffs)
	y := 0.0
	for i := 0; i < n; i++ {
		term := li.coeffs[i]
		for j := 0; j < i; j++ {
			term *= x
		}
		y += term
	}
	return y
}

func (li LagrangeInterpolator) N() int {
	return li.n
}

// InterpLagrange 利用拉格朗日插值法计算函数值
// 尽量9阶采用内插值
const STEP_N = 7

func InterpLagrange(x []float64, y []float64, xq float64) float64 {
	if len(x) != len(y) {
		return 0.0
	}

	// 限制阶数为9
	var data []float64
	start, end := FindClosestSubset(x, xq, STEP_N)
	for i := start; i <= end; i++ {
		data = append(data, x[i])
		data = append(data, y[i])
	}

	A := goNum.NewMatrix(len(data)/2, 2, data)
	yq, _ := goNum.InterpLagrange(A, xq)
	return yq
}

// FindClosestSubset 找到包含xq的最近的n个元素的子数组
func FindClosestSubset(x []float64, xq float64, n int) (int, int) {
	if len(x) <= n {
		return 0, len(x) - 1 // 如果元素数量少于等于n，直接返回整个数组
	}

	// 找到xq在数组中的插入点
	idx := sort.Search(len(x), func(i int) bool { return x[i] >= xq })

	// 计算子数组的起始和结束位置
	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
	end := idx + n/2

	// 调整边界
	if start < 0 {
		start = 0
		end = n
	} else if end >= n {
		end = n - 1
		start = end - n + 1
	}

	return start, end
}