C# 線性插值的實(shí)現(xiàn)示例
更新時(shí)間：2024年03月01日 16:01:31 作者：ou.cs
線性插值是針對(duì)一維數(shù)據(jù)的插值方法,本文主要介紹了C# 線性插值的實(shí)現(xiàn)示例,具有一定的參考價(jià)值,感興趣的可以了解一下
線性插值是一種常用的插值算法，適用于許多實(shí)際場(chǎng)景。
傳感器數(shù)據(jù)處理：在傳感器數(shù)據(jù)處理中，可能會(huì)出現(xiàn)數(shù)據(jù)點(diǎn)不連續(xù)或不均勻的情況。使用線性插值可以根據(jù)已知的數(shù)據(jù)點(diǎn)來(lái)估算在兩個(gè)數(shù)據(jù)點(diǎn)之間的數(shù)值，從而填補(bǔ)數(shù)據(jù)中的缺失或不連續(xù)之處。
圖像處理：在圖像處理中，可能需要調(diào)整圖像的大小或分辨率。線性插值可以用來(lái)估算新像素點(diǎn)的數(shù)值，從而實(shí)現(xiàn)圖像的縮放或放大。
信號(hào)處理：在數(shù)字信號(hào)處理中，線性插值可以用來(lái)估算信號(hào)在離散時(shí)間點(diǎn)之間的數(shù)值，從而平滑信號(hào)或填充信號(hào)中的缺失值。
數(shù)值模擬：在線性數(shù)值模擬中，線性插值可以用來(lái)逼近復(fù)雜函數(shù)的數(shù)值輸出，從而簡(jiǎn)化數(shù)學(xué)模型的計(jì)算過(guò)程。
運(yùn)動(dòng)學(xué)模型：在線性運(yùn)動(dòng)學(xué)模型中，可能需要根據(jù)已知的位置數(shù)據(jù)來(lái)估算物體在不同時(shí)間點(diǎn)的軌跡或位置信息，線性插值可以幫助實(shí)現(xiàn)這一目標(biāo)。
案例有一組數(shù)據(jù)，電壓，溫度會(huì)隨著改變，電壓和溫度都是浮點(diǎn)型數(shù)據(jù)，快速獲取（-40~120）整形溫度對(duì)應(yīng)的電壓。
using System;
class Program
{
static void Main()
{
// 假設(shè)已知的電壓-溫度數(shù)據(jù)點(diǎn)
double[] temperatures = { -40, 0, 25, 50, 100 };
double[] voltages = { 1.0, 2.5, 3.0, 3.5, 4.0 };
// 需要獲取的整數(shù)溫度值
int targetTemperature = 75;
// 尋找相鄰的溫度數(shù)據(jù)點(diǎn)
int lowerIndex = Array.BinarySearch(temperatures, targetTemperature);
if (lowerIndex < 0)
{
lowerIndex = ~lowerIndex - 1;
}
int upperIndex = lowerIndex + 1;
// 線性插值計(jì)算電壓值
double lowerTemperature = temperatures[lowerIndex];
double upperTemperature = temperatures[upperIndex];
double lowerVoltage = voltages[lowerIndex];
double upperVoltage = voltages[upperIndex];
double interpolatedVoltage = lowerVoltage + (upperVoltage - lowerVoltage) * (targetTemperature - lowerTemperature) / (upperTemperature - lowerTemperature);
Console.WriteLine($"在溫度 {targetTemperature} 度時(shí)對(duì)應(yīng)的電壓值為: {interpolatedVoltage}");
}
}1、分段線性插值
/// <summary>
/// 分段線性插值，將一組數(shù)插值為所需點(diǎn)數(shù)
/// </summary>
/// <param name="dataIn">待插值的數(shù)據(jù)數(shù)組</param>
/// <param name="n">插值點(diǎn)數(shù)</param>
/// <returns>插值后的數(shù)據(jù)數(shù)組</returns>
public static float[] Interpolation(float[] dataIn, int n)
{
float[] dataOut = new float[n];
int lenIn = dataIn.Length;
float[] a = new float[lenIn];
float[] divIn = new float[lenIn];
float[] divOut = new float[n];
divIn[0] = 0;
for (int i = 1; i < lenIn; i++)
{
divIn[i] = divIn[i - 1] + 1;
}
divOut[0] = 0;
for (int i = 1; i < n; i++)
{
divOut[i] = divOut[i - 1] + lenIn / (float)n;
}
int k = 0;
for (int i = k; i < n; i++)
{
for (int j = 0; j < lenIn - 1; j++)
{
if (divOut[i] >= divIn[j] && divOut[i] < divIn[j + 1])
{
dataOut[i] = (dataIn[j + 1] - dataIn[j]) * (divOut[i] - divIn[j]) / (divIn[j + 1] - divIn[j]) + dataIn[j];
k = i;
}
}
}
return dataOut;
}2、三次樣條插值
/// <summary>
/// 三次樣條插值
/// </summary>
/// <param name="points">排序好的x、y點(diǎn)集合</param>
/// <param name="xs">輸入x軸數(shù)據(jù)，插值計(jì)算出對(duì)應(yīng)的y軸點(diǎn)</param>
/// <param name="chf">寫(xiě)1</param>
/// <returns>返回計(jì)算好的Y軸數(shù)值</returns>
public static double[] SplineInsertPoint(PointClass[] points, double[] xs, int chf)
{
int plength = points.Length;
double[] h = new double[plength];
double[] f = new double[plength];
double[] l = new double[plength];
double[] v = new double[plength];
double[] g = new double[plength];
for (int i = 0; i < plength - 1; i++)
{
h[i] = points[i + 1].x - points[i].x;
f[i] = (points[i + 1].y - points[i].y) / h[i];
}
for (int i = 1; i < plength - 1; i++)
{
l[i] = h[i] / (h[i - 1] + h[i]);
v[i] = h[i - 1] / (h[i - 1] + h[i]);
g[i] = 3 * (l[i] * f[i - 1] + v[i] * f[i]);
}
double[] b = new double[plength];
double[] tem = new double[plength];
double[] m = new double[plength];
double f0 = (points[0].y - points[1].y) / (points[0].x - points[1].x);
double fn = (points[plength - 1].y - points[plength - 2].y) / (points[plength - 1].x - points[plength - 2].x);
b[1] = v[1] / 2;
for (int i = 2; i < plength - 2; i++)
{
// Console.Write(" " + i);
b[i] = v[i] / (2 - b[i - 1] * l[i]);
}
tem[1] = g[1] / 2;
for (int i = 2; i < plength - 1; i++)
{
//Console.Write(" " + i);
tem[i] = (g[i] - l[i] * tem[i - 1]) / (2 - l[i] * b[i - 1]);
}
m[plength - 2] = tem[plength - 2];
for (int i = plength - 3; i > 0; i--)
{
//Console.Write(" " + i);
m[i] = tem[i] - b[i] * m[i + 1];
}
m[0] = 3 * f[0] / 2.0;
m[plength - 1] = fn;
int xlength = xs.Length;
double[] insertRes = new double[xlength];
for (int i = 0; i < xlength; i++)
{
int j = 0;
for (j = 0; j < plength; j++)
{
if (xs[i] < points[j].x)
break;
}
j = j - 1;
Console.WriteLine(j);
if (j == -1 || j == points.Length - 1)
{
if (j == -1)
throw new Exception("插值下邊界超出");
if (j == points.Length - 1 && xs[i] == points[j].x)
insertRes[i] = points[j].y;
else
throw new Exception("插值下邊界超出");
}
else
{
double p1;
p1 = (xs[i] - points[j + 1].x) / (points[j].x - points[j + 1].x);
p1 = p1 * p1;
double p2; p2 = (xs[i] - points[j].x) / (points[j + 1].x - points[j].x);
p2 = p2 * p2;
double p3; p3 = p1 * (1 + 2 * (xs[i] - points[j].x) / (points[j + 1].x - points[j].x)) * points[j].y + p2 * (1 + 2 * (xs[i] - points[j + 1].x) / (points[j].x - points[j + 1].x)) * points[j + 1].y;
double p4; p4 = p1 * (xs[i] - points[j].x) * m[j] + p2 * (xs[i] - points[j + 1].x) * m[j + 1];
// Console.WriteLine(m[j] + " " + m[j + 1] + " " + j);
p4 = p4 + p3;
insertRes[i] = p4;
//Console.WriteLine("f(" + xs[i] + ")= " + p4);
}
}
//Console.ReadLine();
return insertRes;
}排序計(jì)算
public class PointClass
{
public double x = 0;
public double y = 0;
public PointClass()
{
x = 0; y = 0;
}
//-------寫(xiě)一個(gè)排序函數(shù)，使得輸入的點(diǎn)按順序排列，是因?yàn)椴逯邓惴ǖ囊笫?，x軸遞增有序的---------
public static PointClass[] DeSortX(PointClass[] points)
{
int length = points.Length;
double temx, temy;
for (int i = 0; i < length - 1; i++)
{
for (int j = 0; j < length - i - 1; j++)
if (points[j].x > points[j + 1].x)
{
temx = points[j + 1].x;
points[j + 1].x = points[j].x;
points[j].x = temx;
temy = points[j + 1].y;
points[j + 1].y = points[j].y;
points[j].y = temy;
}
}
return points;
}
}3、拉格朗日插值
（1）一元全區(qū)間不等距插值
/// <summary>
/// 一元全區(qū)間不等距插值
/// 拉格朗日插值算法
/// </summary>
/// <param name="x">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的值x(i)，要求x(0)<x(1)<...<x(n-1)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Lagrange(double[] x, double[] y, double t)
{
// x,y點(diǎn)數(shù)
int n = x.Length;
double z = 0.0;
// 特例處理
if (n < 1)
{
return (z);
}
else if (n == 1)
{
z = y[0];
return (z);
}
else if (n == 2)
{
z = (y[0] * (t - x[1]) - y[1] * (t - x[0])) / (x[0] - x[1]);
return (z);
}
// 開(kāi)始插值
int ik = 0;
while ((x[ik] < t) && (ik < n))
{
ik = ik + 1;
}
int k = ik - 4;
if (k < 0)
{
k = 0;
}
int m = ik + 3;
if (m > n - 1)
{
m = n - 1;
}
for (int i = k; i <= m; i++)
{
double s = 1.0;
for (int 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]);
}
}
z = z + s * y[i];
}
return (z);
} /// <summary>
/// 一元全區(qū)間不等距插值
/// </summary>
/// <param name="points">點(diǎn)集（含XY坐標(biāo)）</param>
/// <param name="t"></param>
/// <returns></returns>
public static double Lagrange(PointF[] points, double t)
{
double[] x = new double[points.Length];
double[] y = new double[points.Length];
for (int i = 0; i < points.Length; i++)
{
x[i] = points[i].X;
y[i] = points[i].Y;
}
return Lagrange(x, y, t);
} /// <summary>
/// 一元全區(qū)間不等距插值
/// </summary>
/// <param name="points">二元組類型的點(diǎn)集（含XY坐標(biāo)）</param>
/// <param name="t"></param>
/// <returns></returns>
public static double Lagrange(List<Tuple<double, double>> points, double t)
{
double[] x = new double[points.Count];
double[] y = new double[points.Count];
for (int i = 0; i < points.Count; i++)
{
x[i] = points[i].Item1;
y[i] = points[i].Item2;
}
return Lagrange(x, y, t);
} /// <summary>
/// 一元全區(qū)間不等距插值，獲得插值后的曲線（折線擬合）數(shù)據(jù)
/// </summary>
/// <param name="points">點(diǎn)集（含XY坐標(biāo)）</param>
/// <param name="segment_count">每數(shù)據(jù)段的分割數(shù)</param>
/// <returns></returns>
public static PointF[] Lagrange_Curve(PointF[] points, int segment_count = 10)
{
int n = points.Length;
PointF[] segments = new PointF[n * segment_count + 1];
for (int i = 0; i < points.Length - 1; i++)
{
double dt = (points[i + 1].X - points[i].X) / segment_count;
double t = points[i].X;
for (int j = 0; j <= segment_count; j++, t += dt)
{
PointF p = new PointF(0.0F, 0.0F);
p.X = (float)t;
if (j == 0) p.Y = points[i].Y;
else if (j == segment_count) p.Y = points[i + 1].Y;
else p.Y = (float)(Lagrange(points, t));
segments[i] = p;
}
}
return segments;
} /// <summary>
/// 一元全區(qū)間等距插值
/// (使用非等距插值的方法)
/// </summary>
/// <param name="x0">存放等距n個(gè)結(jié)點(diǎn)中第一個(gè)結(jié)點(diǎn)的值</param>
/// <param name="step">等距結(jié)點(diǎn)的步長(zhǎng)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Lagrange(double x0, double step, double[] y, double t)
{
double[] x = new double[y.Length];
for (int i = 0; i < y.Length; i++, x0 += step)
{
x[i] = x0;
}
return Lagrange(x, y, t);
}（2）一元全區(qū)間等距插值
/// <summary>
/// 一元全區(qū)間等距插值
/// </summary>
/// <param name="x0">存放等距n個(gè)結(jié)點(diǎn)中第一個(gè)結(jié)點(diǎn)的值</param>
/// <param name="step">等距結(jié)點(diǎn)的步長(zhǎng)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Lagrange_Equidistant(double x0, double step, double[] y, double t)
{
int n = y.Length;
double z = 0.0;
// 特例處理
if (n < 1)
{
return (z);
}
else if (n == 1)
{
z = y[0];
return (z);
}
else if (n == 2)
{
z = (y[1] * (t - x0) - y[0] * (t - x0 - step)) / step;
return (z);
}
// 開(kāi)始插值
int ik = 0;
if (t > x0)
{
double p = (t - x0) / step;
ik = (int)p;
double q = (float)ik;
if (p > q)
{
ik = ik + 1;
}
}
else
{
ik = 0;
}
int k = ik - 4;
if (k < 0)
{
k = 0;
}
int m = ik + 3;
if (m > n - 1)
{
m = n - 1;
}
for (int i = k; i <= m; i++)
{
double s = 1.0;
double xi = x0 + i * step;
for (int j = k; j <= m; j++)
{
if (j != i)
{
double xj = x0 + j * step;
// 拉格朗日插值公式
s = s * (t - xj) / (xi - xj);
}
}
z = z + s * y[i];
}
return (z);
}4、埃爾米特插值
（1）埃爾米特不等距插值
/// <summary>
/// 埃爾米特不等距插值
/// </summary>
/// <param name="x">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的值x(i)，要求x(0)<x(1)<...<x(n-1)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="dy">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)導(dǎo)數(shù)值y'(i)，y'(i) = f'(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Hermite(double[] x, double[] y, double[] dy, double t)
{
int n = x.Length;
double z = 0.0;
// 循環(huán)插值
for (int i = 1; i <= n; i++)
{
double s = 1.0;
for (int j = 1; j <= n; j++)
{
if (j != i)
{
s = s * (t - x[j - 1]) / (x[i - 1] - x[j - 1]);
}
}
s = s * s;
double p = 0.0;
for (int j = 1; j <= n; j++)
{
if (j != i)
{
p = p + 1.0 / (x[i - 1] - x[j - 1]);
}
}
double q = y[i - 1] + (t - x[i - 1]) * (dy[i - 1] - 2.0 * y[i - 1] * p);
z = z + q * s;
}
return (z);
} /// <summary>
/// 埃爾米特等距插值
/// (使用非等距插值的方法)
/// </summary>
/// <param name="x0">存放等距n個(gè)結(jié)點(diǎn)中第一個(gè)結(jié)點(diǎn)的值</param>
/// <param name="step">等距結(jié)點(diǎn)的步長(zhǎng)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="dy">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)導(dǎo)數(shù)值y'(i)，y'(i) = f'(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Hermite(double x0, double step, double[] y, double[] dy, double t)
{
double[] x = new double[y.Length];
for (int i = 0; i < y.Length; i++, x0 += step)
{
x[i] = x0;
}
return Hermite(x, y, dy, t);
}（2）埃爾米特等距插值
/// <summary>
/// 埃爾米特等距插值
/// </summary>
/// <param name="x0">等距n個(gè)結(jié)點(diǎn)中第一個(gè)結(jié)點(diǎn)的值</param>
/// <param name="step">等距結(jié)點(diǎn)的步長(zhǎng)</param>
/// <param name="y">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)值y(i)，y(i) = f(x(i)), i=0,1,...,n-1</param>
/// <param name="dy">一維數(shù)組，長(zhǎng)度為n，存放給定的n個(gè)結(jié)點(diǎn)的函數(shù)導(dǎo)數(shù)值y'(i)，y'(i) = f'(x(i)), i=0,1,...,n-1</param>
/// <param name="t">存放指定的插值點(diǎn)的x值</param>
/// <returns>指定的查指點(diǎn)t的函數(shù)近似值y=f(t)</returns>
public static double Hermite(double x0, double step, double[] y, double[] dy, double t)
{
int n = y.Length;
double z = 0.0;
// 循環(huán)插值
for (int i = 1; i <= n; i++)
{
double s = 1.0;
double q = x0 + (i - 1) * step;
double p;
for (int j = 1; j <= n; j++)
{
p = x0 + (j - 1) * step;
if (j != i)
{
s = s * (t - p) / (q - p);
}
}
s = s * s;
p = 0.0;
for (int j = 1; j <= n; j++)
{
if (j != i)
{
p = p + 1.0 / (q - (x0 + (j - 1) * step));
}
}
q = y[i - 1] + (t - q) * (dy[i - 1] - 2.0 * y[i - 1] * p);
z = z + q * s;
}
return (z);
}到此這篇關(guān)于C# 線性插值的實(shí)現(xiàn)示例的文章就介紹到這了,更多相關(guān)C# 線性插值內(nèi)容請(qǐng)搜索腳本之家以前的文章或繼續(xù)瀏覽下面的相關(guān)文章希望大家以后多多支持腳本之家！
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