数值分析试验四 runge_kutta 龙格库塔c++代码

结果调用了一个外接图形库，以函数图形展示：

主cpp：

// wangdiedang is a good guy! =v=
#include<iostream>
#include<vector>
#include<cmath>
#include<iomanip>
#include<fstream>
#include "graph2d.h"
using namespace std;double z(double x,double y) {return (pow(x, 2) + 4 * x - y - 1) / 2;
}void R_K(double x,double y,double ul,double h) {vector<pair<double, double>> re;double k1, k2, k3, k4;re.push_back(make_pair(0, 0));while (x * h < ul) {k1 = z(x * h, y);k2 = z(x * h + h/2, y + h / 2 * k1);k3 = z(x * h + h/2, y + h / 2 * k2);k4 = z(x * h + h, y + h * k3);y += h / 6 * (k1 + 2 * k2 + 2 * k3 + k4);re.push_back(make_pair((++x) * h, y));}//for (int i = 0; i < re.size(); i++) {// if (i % 5 == 0) cout << endl;// cout << setiosflags(ios::fixed) << setprecision(9) << re[i].second << "  ";//}vector<double> x1, y1;for (int i = 0; i < re.size(); i++) {x1.push_back(re[i].first);y1.push_back(re[i].second);}graph2d g2d(700, 590, { 0,-0.06 }, { 0.5,0.04 });g2d.xlabel("x轴");g2d.ylabel("y 轴");g2d.title("结果");g2d.plot(x1, y1, BLACK);g2d.waitKey();
}int main() {double x, y, h, ul; // xy初始值和步长和阈值cin >> x >> y >> h >> ul;R_K(x, y, ul, h);return 0;
}

外接图库cpp：

#include "graph2d.h"
graph2d::graph2d()
{width = 700;height = 590;initgraph(int(width), int(height), SHOWCONSOLE);setGrid({ 0,0 }, { 10,10 });setlen();initAxis();
}
graph2d::graph2d(double _width, double _height)
{width = _width;height = _height;initgraph(int(width), int(height), SHOWCONSOLE);setGrid({ 0,0 }, { 10,10 });setlen();initAxis();
}
graph2d::graph2d(double _width, double _height, Point _pointlb, Point _pointrt)
{width = _width;height = _height;initgraph(int(width), int(height), SHOWCONSOLE);setGrid(_pointlb, _pointrt);setlen();initAxis();
}
graph2d::~graph2d()
{closegraph();
}
wchar_t* graph2d::ctow(const char* str)
{int length = strlen(str) + 1;wchar_t* t = (wchar_t*)malloc(sizeof(wchar_t) * length);memset(t, 0, length * sizeof(wchar_t));MultiByteToWideChar(CP_ACP, 0, str, strlen(str), t, length);return t;
}
void graph2d::setlen(int _len)
{x_len = max(int(1 + log10(max(pointlb.x, pointrt.x))), _len);y_len = max(int(1 + log10(max(pointlb.y, pointrt.y))), _len);
}
std::string graph2d::dtos(double _num, char _axis)
{int _len = 3;std::string _str = "";    // 储存结果int _lg = 0;            // 10^__lgif (_axis == 'x' || _axis == 'X')_len = x_len;if (_axis == 'y' || _axis == 'Y')_len = y_len;if (int(_num * pow(10.0, _len - 1)) == 0) {for (int i = 0; i < _len - 1; i++) {_str += '0';}return "0." + _str;}if (_num < 0) { _num = -_num; _str += '-'; }else { _str += ' '; }while (int(_num) > 1) { _num /= 10; _lg++; }while (int(_num) < 1 && _lg > 0) { _num *= 10; _lg--; }for (int i = 0; i < _len; i++) {_str += ('0' + int(_num) % 10);if (i == _lg && i + 1 != _len) {_str += '.';}_num *= 10;}return _str;
}
void graph2d::waitKey(int _delay)
{_getch();
}
void graph2d::setGrid(Point _pointlb, Point _pointrt)
{pointlb = { min(_pointlb.x,_pointrt.x), min(_pointlb.y,_pointrt.y) };pointrt = { max(_pointlb.x,_pointrt.x), max(_pointlb.y,_pointrt.y) };
}
void graph2d::drawGrid()
{setlinecolor(0xE0E0E0);setlinestyle(PS_SOLID, 1);for (int i = 1; i < 10; i++) {line(numConversion(0.078 * width * i + 0.12 * width, 'x'), numConversion(0.1 * height, 'y'), numConversion(0.078 * width * i + 0.12 * width, 'x'), numConversion(0.88 * height, 'y'));line(numConversion(0.12 * width, 'x'), numConversion(0.078 * height * i + 0.1 * height, 'y'), numConversion(0.9 * width, 'x'), numConversion(0.078 * height * i + 0.1 * height, 'y'));}
}
void graph2d::drawAxisX()
{std::string _str = "     ";for (int i = 0; i <= 10; i++) {_str += dtos((pointrt.x - pointlb.x) / 10 * i + pointlb.x, 'x') + "  ";}RECT r = { numConversion(0,'x'), numConversion(0.04 * height,'y'), numConversion(width,'x'), numConversion(0.11 * height,'y') };settextcolor(BLACK);settextstyle(int((24 - 2 * x_len) * (width / 700) * 0.9), 0, _T("宋体"));drawtext(ctow(_str.c_str()), &r, DT_CENTER | DT_VCENTER | DT_SINGLELINE);
}
void graph2d::drawAxisY()
{std::string _str = "\n\n\n\n\n";for (int i = 10; i >= 0; i--) {_str += dtos((pointrt.y - pointlb.y) / 10 * i + pointlb.y, 'y') + "\n\n\n";}RECT r = { numConversion(0,'x'), numConversion(height,'y'), numConversion(0.11 * width,'x'), numConversion(0,'y') };settextcolor(BLACK);settextstyle(int(15 * height / 590), 0, _T("宋体"));drawtext(ctow(_str.c_str()), &r, DT_NOCLIP | DT_RIGHT);
}
bool graph2d::isBorder(Point _point)
{return (pointlb.x <= _point.x && _point.x <= pointrt.x && pointlb.y <= _point.y && _point.y <= pointrt.y);
}
int graph2d::numConversion(double _num, char _axis)
{if (_axis == 'x' || _axis == 'X') {return int(_num);}if (_axis == 'y' || _axis == 'Y') {return int(height - _num);}return 0;
}
Point graph2d::fucCSDataToAbsCSData(Point _point)
{return { ((_point.x - pointlb.x) / (pointrt.x - pointlb.x) * 0.78 * width + 0.12 * width),((_point.y - pointlb.y) / (pointrt.y - pointlb.y) * 0.78 * height + 0.1 * height) };
}
Point graph2d::absCSDataToFucCSData(Point _point)
{return { ((_point.x - 0.12 * width) * (pointrt.x - pointlb.x) / 0.78 / width + pointlb.x),((_point.y - 0.1 * height) * (pointrt.y - pointlb.y) / 0.78 / height + pointlb.y) };
}
void graph2d::showError(std::string _err)
{std::cout << "Maybe a " << _err << " is not in the coordinates" << std::endl;
}
void graph2d::setBackgroundColor(COLORREF _color)
{setbkcolor(_color);cleardevice();
}
void graph2d::setAxisColor()
{drawRectangle({ 0.12 * width ,0.1 * height }, { 0.9 * width ,0.88 * height }, BLACK, WHITE);
}
void graph2d::drawRectangle(Point _pointlb, Point _pointrt, COLORREF _colorl, COLORREF _colorf, int _style)
{setlinecolor(_colorl);setfillcolor(_colorf);setfillstyle(_style);fillrectangle(numConversion(_pointlb.x, 'x'), numConversion(_pointrt.y, 'y'), numConversion(_pointrt.x, 'x'), numConversion(_pointlb.y, 'y'));
}
void graph2d::initAxis()
{setBackgroundColor();setAxisColor();drawGrid();drawAxisX();drawAxisY();
}
void graph2d::plot(Point _point, COLORREF _color, int _size, int _type)
{if (isBorder(_point)) {setlinecolor(_color);setfillcolor(_color);setfillstyle(_type);fillcircle(numConversion(fucCSDataToAbsCSData(_point).x, 'x'), numConversion(fucCSDataToAbsCSData(_point).y, 'y'), _size);}else {showError("point");}
}
void graph2d::plot(std::vector<Point> _point, COLORREF _color, int _thickness, int _type)
{setlinecolor(_color);setlinestyle(_type, _thickness);for (int i = 1; i < _point.size(); i++) {if (isBorder(_point[i - 1]) && isBorder(_point[i])) {line(numConversion(fucCSDataToAbsCSData(_point[i - 1]).x, 'x'), numConversion(fucCSDataToAbsCSData(_point[i - 1]).y, 'y'), numConversion(fucCSDataToAbsCSData(_point[i]).x, 'x'), numConversion(fucCSDataToAbsCSData(_point[i]).y, 'y'));}else {showError("line");}}
}
void graph2d::plot(std::vector<double> x, std::vector<double> y, COLORREF _color, int _thickness, int _type)
{std::vector<Point> _point;for (int i = 0; i < x.size(); i++) {_point.push_back({ x[i], y[i] });}plot(_point, _color, _thickness, _type);
}
void graph2d::title(std::string _str)
{RECT r = { numConversion(0,'x'), numConversion(0.88 * height,'y'), numConversion(width,'x'), numConversion(height,'y') };settextcolor(BLACK);settextstyle(int(20 * height / 590), 0, _T("宋体"));drawtext(ctow(_str.c_str()), &r, DT_CENTER | DT_VCENTER | DT_SINGLELINE);
}
void graph2d::xlabel(std::string _str)
{RECT r = { numConversion(0,'x'), numConversion(0,'y'), numConversion(width,'x'), numConversion(0.05 * height,'y') };settextcolor(BLACK);settextstyle(int(20 * height / 590), 0, _T("宋体"));drawtext(ctow(_str.c_str()), &r, DT_CENTER | DT_VCENTER | DT_SINGLELINE);
}
void graph2d::ylabel(std::string _str)
{RECT r = { numConversion(0.01 * width,'x'), numConversion(0.6 * height,'y'), numConversion(0.05 * width,'x'), numConversion(0,'y') };settextcolor(BLACK);settextstyle(int(20 * width / 700), 0, _T("宋体"));drawtext(ctow(_str.c_str()), &r, DT_NOCLIP | DT_LEFT | DT_WORDBREAK);
}
void graph2d::text(std::string _str)
{//TODO
}
void graph2d::legend(std::string _str, COLORREF _color, int _num)
{//TODO
}
void graph2d::mouseClick()
{//TODO
}

外接头文件.h

#pragma once
#pragma once
#include <iostream>
#include <graphics.h>
#include <conio.h>
#include <vector>
#include <math.h>
#define f(_lambda) ([](double x) {return (_lambda); })
typedef struct mypoint {double x;double y;
}Point;
class graph2d
{
private:double height;                                          // 画板高度double width;                                            // 画板宽度Point pointlb;                                           // 坐标轴左下角的点Point pointrt;                                           // 坐标轴右上角的点int x_len;                                               // x轴字的宽度int y_len;                                             // y轴字的宽度
public:/*********************************** 初始化、坐标转换、绘制坐标等等**********************************/graph2d();                                                // 初始化为默认值graph2d(double _width, double _height);                   // 初始化画板宽高graph2d(double _width, double _height, Point _pointlb, Point _pointrt);       // 初始化画板宽高及网格~graph2d();                                                // 析构函数void waitKey(int _delay = 0);                           // 等待关闭
private:/***********************************    坐标转换、绘制坐标等等**********************************/wchar_t* ctow(const char* str);                           // char* to wchar_t*void setlen(int _len = 3);                             // 设置坐标文本长度std::string dtos(double _num, char _axis);               // string to doublevoid setGrid(Point _pointlb, Point _pointrt);            // 设置网格void drawGrid();                                     // 绘制网格void drawAxisX();                                        // 绘制X轴void drawAxisY();                                        // 绘制Y轴bool isBorder(Point _point);                         // 是否在边界内int numConversion(double _num, char _axis);                // 将y轴颠倒Point fucCSDataToAbsCSData(Point _point);               // 方程的点转换到画板的点Point absCSDataToFucCSData(Point _point);             // 画板的点转换到方程的点void showError(std::string _err);                     // 显示错误void drawRectangle(Point _pointlb, Point _pointrt, COLORREF _colorl, COLORREF _colorf, int _style = BS_SOLID);  //画正方形void setBackgroundColor(COLORREF _color = 0xEAEAEA); // 设置画板背景颜色void setAxisColor();                                 // 设置坐标系背景颜色void initAxis();                                        // 初始化坐标轴内的信息void mouseClick();                                     // 鼠标点击来获取该点函数坐标
public:/*********************************** 绘制坐标方程函数**********************************/void plot(Point _point, COLORREF _color = RED, int _size = 3, int _type = BS_SOLID);      // 绘制点void plot(std::vector<Point> _point, COLORREF _color = BLACK, int _thickness = 3, int _type = PS_SOLID);     // 绘制一连串的线void plot(std::vector<double> x, std::vector<double> y, COLORREF _color = BLACK, int _thickness = 3, int _type = PS_SOLID);        // 绘制f(x)方程void title(std::string _str);                            // 标题void xlabel(std::string _str);                         // x轴文本注释void ylabel(std::string _str);                         // y轴文本注释,可以用空格换行void text(std::string _str);                           // 在坐标中添加注释void legend(std::string _str, COLORREF _color, int _num);// 标签
};

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