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datalist_linear_interpolation.go
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/
datalist_linear_interpolation.go
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package insyra
import "math"
// LinearInterpolation performs linear interpolation for the given x value using the DataList.
func (dl *DataList) LinearInterpolation(x float64) float64 {
if dl.Len() < 2 {
LogWarning("DataList.LinearInterpolation(): Not enough data points.")
return math.NaN()
}
for i := 0; i < dl.Len()-1; i++ {
x0 := float64(i)
x1 := float64(i + 1)
y0 := dl.Data()[i].(float64)
y1 := dl.Data()[i+1].(float64)
if x >= x0 && x <= x1 {
return y0 + (y1-y0)*(x-x0)/(x1-x0)
}
}
LogWarning("DataList.LinearInterpolation(): X value out of bounds.")
return math.NaN()
}
// QuadraticInterpolation performs quadratic interpolation for the given x value using the DataList.
func (dl *DataList) QuadraticInterpolation(x float64) float64 {
if dl.Len() < 3 {
LogWarning("DataList.QuadraticInterpolation(): Not enough data points.")
return math.NaN()
}
for i := 0; i < dl.Len()-2; i++ {
x0 := float64(i)
x1 := float64(i + 1)
x2 := float64(i + 2)
y0 := dl.Data()[i].(float64)
y1 := dl.Data()[i+1].(float64)
y2 := dl.Data()[i+2].(float64)
if x >= x0 && x <= x2 {
l0 := (x - x1) * (x - x2) / ((x0 - x1) * (x0 - x2))
l1 := (x - x0) * (x - x2) / ((x1 - x0) * (x1 - x2))
l2 := (x - x0) * (x - x1) / ((x2 - x0) * (x2 - x1))
return y0*l0 + y1*l1 + y2*l2
}
}
LogWarning("DataList.QuadraticInterpolation(): X value out of bounds.")
return math.NaN()
}
// LagrangeInterpolation performs Lagrange interpolation for the given x value using the DataList.
func (dl *DataList) LagrangeInterpolation(x float64) float64 {
n := dl.Len()
if n < 2 {
LogWarning("DataList.LagrangeInterpolation(): Not enough data points.")
return math.NaN()
}
result := 0.0
for i := 0; i < n; i++ {
term := dl.Data()[i].(float64)
for j := 0; j < n; j++ {
if i != j {
term *= (x - float64(j)) / (float64(i) - float64(j))
}
}
result += term
}
return result
}
// NearestNeighborInterpolation performs nearest-neighbor interpolation for the given x value using the DataList.
func (dl *DataList) NearestNeighborInterpolation(x float64) float64 {
closestIndex := 0
minDiff := math.Abs(x - 0) // 初始化差異
for i := 1; i < dl.Len(); i++ {
diff := math.Abs(x - float64(i))
if diff < minDiff {
closestIndex = i
minDiff = diff
}
}
if closestIndex < 0 || closestIndex >= dl.Len() {
LogWarning("DataList.NearestNeighborInterpolation(): X value out of bounds.")
return math.NaN()
}
return dl.Data()[closestIndex].(float64)
}
// NewtonInterpolation performs Newton's interpolation for the given x value using the DataList.
func (dl *DataList) NewtonInterpolation(x float64) float64 {
n := dl.Len()
if n < 2 {
LogWarning("DataList.NewtonInterpolation(): Not enough data points.")
return math.NaN()
}
// 計算差分
dividedDiff := make([]float64, n)
copy(dividedDiff, dl.ToF64Slice())
for i := 1; i < n; i++ {
for j := n - 1; j >= i; j-- {
dividedDiff[j] = (dividedDiff[j] - dividedDiff[j-1]) / (float64(j) - float64(j-i))
}
}
// 使用差分進行插值
result := dividedDiff[n-1]
for i := n - 2; i >= 0; i-- {
result = result*(x-float64(i)) + dividedDiff[i]
}
return result
}
// HermiteInterpolation performs Hermite interpolation for the given x value using the DataList.
func (dl *DataList) HermiteInterpolation(x float64, derivatives []float64) float64 {
n := dl.Len()
if n != len(derivatives) {
LogWarning("DataList.HermiteInterpolation(): Data and derivatives length mismatch.")
return math.NaN()
}
if n < 2 {
LogWarning("DataList.HermiteInterpolation(): Not enough data points.")
return math.NaN()
}
result := 0.0
for i := 0; i < n; i++ {
h := 1.0
for j := 0; j < n; j++ {
if i != j {
h *= (x - float64(j)) / (float64(i) - float64(j))
}
}
result += dl.Data()[i].(float64)*h + derivatives[i]*h*(x-float64(i))
}
return result
}