用ps做网站页面,网站如何配置域名,响应式网站用什么语言,wap手机网站开发埃尔米特插值 原理 #pragma once
#include vector
#include functional
/*埃尔米特插值*/
struct InterpolationPoint {double x; // 插值点的横坐标double y; // 插值点的纵坐标double derivative; // 插值点的导数值// 默认构造函数InterpolationPoint() : x…埃尔米特插值 原理 #pragma once
#include vector
#include functional
/*埃尔米特插值*/
struct InterpolationPoint {double x; // 插值点的横坐标double y; // 插值点的纵坐标double derivative; // 插值点的导数值// 默认构造函数InterpolationPoint() : x(0.0), y(0.0), derivative(0.0) {}// 带参数的构造函数InterpolationPoint(double x_val, double y_val, double derivative_val) : x(x_val), y(y_val), derivative(derivative_val) {}// 拷贝构造函数InterpolationPoint(const InterpolationPoint other) : x(other.x), y(other.y), derivative(other.derivative) {}// 移动构造函数InterpolationPoint(InterpolationPoint other) noexcept : x(other.x), y(other.y), derivative(other.derivative) {other.x 0.0;other.y 0.0;other.derivative 0.0;}// Copy assignment operatorInterpolationPoint operator(const InterpolationPoint other) {if (this ! other) {x other.x;y other.y;derivative other.derivative;}return *this;}// 设置插值点的值void set(double x_val, double y_val, double derivative_val) {x x_val;y y_val;derivative derivative_val;}// 获取插值点的横坐标double get_x() const {return x;}// 获取插值点的纵坐标double get_y() const {return y;}// 获取插值点的导数值double get_derivative() const {return derivative;}
};class HermiteInterpolator {
public:HermiteInterpolator(const std::vectorInterpolationPoint points);HermiteInterpolator(int width, std::vectorint adjPoints);void setPoints(const std::vectorInterpolationPoint points);double interpolate(double x) ;private:// 返回连接两点的线段函数std::functiondouble(double) getLineFunction( InterpolationPoint p1, InterpolationPoint p2);private:std::vectorInterpolationPoint points_;
};
#include pch.h
#include HermiteInterpolator.h
#include fstream
HermiteInterpolator::HermiteInterpolator(const std::vectorInterpolationPoint points) : points_(points)
{
}
HermiteInterpolator::HermiteInterpolator(int width, std::vectorint adjPoints)
{float step width / adjPoints.size();for (int i 0; i adjPoints.size(); i){InterpolationPoint point(step*i, adjPoints[i] , 0);points_.push_back(point);}
}
void HermiteInterpolator::setPoints(const std::vectorInterpolationPoint points)
{points_ points;
}// 返回连接两点的线段函数
std::functiondouble(double) HermiteInterpolator::getLineFunction( InterpolationPoint p1, InterpolationPoint p2) {// 计算线段的斜率和截距double slope (p2.y - p1.y) / (p2.x - p1.x);double intercept p1.y - slope * p1.x;// 返回线段的lambda表达式return [slope, intercept](double x) {return slope * x intercept;};
}
// 计算三次分段Hermite插值函数的值
double HermiteInterpolator::interpolate(double x) {int y 0;int n points_.size();if (n 3){// 获取线段函数std::functiondouble(double) lineFunction getLineFunction(points_[0], points_[1]);y lineFunction(x);}else{for (int i 0; i n - 1; i) {if (x points_[i].x x points_[i 1].x) {double h points_[i 1].x - points_[i].x;double t (x - points_[i].x) / h;// (x-x_k)/(x_{k1} - x_k)double tk (x - points_[i 1].x) / (-h); // (x - x_{ k 1 }) / (x_k - x_{ k 1 }) double y0 (1 2 * t) * tk * tk;double y1 (1 2 * tk) * t * t;double y2 (x - points_[i].x) * tk * tk;double y3 (x - points_[i 1].x) * t * t;y points_[i].y * y0 points_[i 1].y * y1 points_[i].derivative * y2 points_[i 1].derivative * y3;}}}//ofstream f;//f.open(D:\\work\\documentation\\HermiteInterpolator.txt, ios::app);//f x, y endl;//f.close();return y; // 如果找不到对应的插值段返回默认值
}为了可视化效果可以把结果写到HermiteInterpolator.txt 画图python代码
import matplotlib.pyplot as plt# 打开文本文件进行读取
with open(D:\\work\\documentation\\HermiteInterpolator.txt) as f:data f.readlines()# 定义两个列表分别存储横坐标和纵坐标的数据
x []
y [] # 遍历每一行
for i, line in enumerate(data):# 去除换行符if line:user_pwd_list line.strip().split(,)# 横坐标是行号x.append(float(user_pwd_list[0]))# 纵坐标是数值数据y.append(float(user_pwd_list[1]))# 创建散点图
plt.scatter(x, y)# 添加标题和轴标签
plt.title(Scatter Plot)
plt.xlabel(Line)
plt.ylabel(Value)# 显示并保存图像
#plt.savefig(plot.png)
plt.show()
