powell法c/c++程序

以下代码的vs2019工程文件打包点此下载去掉运行部分的注释即可

/*powell.cpp*/
#include "stdafx.h"
#include <stdio.h>
#include <math.h>
#include "Powell.h"
#include <iostream>
#define m 10              /*数组长度m  >=  维数n    */float powell::powell_f(float x[])
{float result;//result = (x[0] - 2)*(x[0] - 2) + (x[1] - 3)*(x[1] - 3) + (x[2] - 4)*(x[2] - 4);result = x[0] * x[0] + 2 * x[1] * x[1] - 2 * x[0] * x[1] - 4 * x[0];return result;
}/*多维进退法子程序*/
void powell::mjtf(int n, float x0[], float h, float s[], float a[], float b[])
{int i;float x1[m], x2[m], x3[m], powell_f1, powell_f2, powell_f3;for (i = 0; i<n; i++)         /*计算初始两试点*/{x1[i] = x0[i];x2[i] = x0[i] + h*s[i];}powell_f1 = powell_f(x1);powell_f2 = powell_f(x2);if (powell_f2 >= powell_f1)               /*判断搜索方向*/{                       /*搜索方向为反向，转身*/h = (-1)*h;for (i = 0; i<n; i++)x3[i] = x1[i];powell_f3 = powell_f1;for (i = 0; i<n; i++)x1[i] = x2[i];powell_f1 = powell_f2;for (i = 0; i<n; i++)x2[i] = x3[i];powell_f2 = powell_f3;}                       /*搜索方向为正向*/for (i = 0; i<n; i++)         /*计算第三试点*/x3[i] = x2[i] + h*s[i];powell_f3 = powell_f(x3);while (powell_f3<powell_f2)             /*判断是否未完成搜索*/{                       /*未完成，继续搜索*/h = 2 * h;for (i = 0; i<n; i++)x1[i] = x2[i];powell_f1 = powell_f2;for (i = 0; i<n; i++)x2[i] = x3[i];powell_f2 = powell_f3;for (i = 0; i<n; i++)x3[i] = x2[i] + h*s[i];powell_f3 = powell_f(x3);}                       /*已完成*/for (i = 0; i<n; i++)         /*输出初始搜索区间*/{if (x1[i]<x3[i]){a[i] = x1[i];b[i] = x3[i];}else{a[i] = x3[i];b[i] = x1[i];}}
}/*多维黄金分割法子程序*/
void powell::mhjfgf(int n, float a[], float b[], float flag, float x[])
{int i;float x1[m], x2[m], powell_f1, powell_f2, sum;for (i = 0; i<n; i++)              /*计算初始两试点*/x1[i] = b[i] - (float)0.618*(b[i] - a[i]);powell_f1 = powell_f(x1);for (i = 0; i<n; i++)x2[i] = a[i] + (float)0.618*(b[i] - a[i]);powell_f2 = powell_f(x2);do{if (powell_f1 <= powell_f2)                  /*判断消去区间*/{                          /*消去右*/for (i = 0; i<n; i++)b[i] = x2[i];for (i = 0; i<n; i++)x2[i] = x1[i];powell_f2 = powell_f1;for (i = 0; i<n; i++)x1[i] = b[i] - (float)0.618*(b[i] - a[i]);powell_f1 = powell_f(x1);}else{                          /*消去左*/for (i = 0; i<n; i++)a[i] = x1[i];for (i = 0; i<n; i++)x1[i] = x2[i];powell_f1 = powell_f2;for (i = 0; i<n; i++)x2[i] = a[i] + (float)0.618*(b[i] - a[i]);powell_f2 = powell_f(x2);}sum = 0;for (i = 0; i<n; i++)sum += (b[i] - a[i])*(b[i] - a[i]);} while (sqrt(sum)>flag*0.1);for (i = 0; i<n; i++)x[i] = (float)0.5*(b[i] + a[i]);
}/*鲍威尔法子程序*/
void powell::mbwef(int n, float x0[], float h, float flag, float a[], float b[], float x[])
{int i, j, k, r;float x1[m], x11[m], x2[m], powell_f0, powell_f1, powell_f2, fn[m], s[m][m], sum;for (i = 0; i<n; i++)//构造一个单位对角矩阵sfor (k = 0; k<n; k++)if (i == k)s[i][k] = 1;elses[i][k] = 0;k = 0;while (1){for (i = 0; i<n; i++){x1[i] = x0[i];x11[i] = x1[i];}for (i = 0; i<n; i++){mjtf(n, x1, h, s[i], a, b);mhjfgf(n, a, b, flag, x1);fn[i] = powell_f(x11) - powell_f(x1);}for (i = 0; i<n; i++)x2[i] = 2 * x1[i] - x0[i];for (i = 1; i<n; i++)if (fn[0]<fn[i]){fn[0] = fn[i];r = i;}elser = 0;powell_f0 = powell_f(x0);powell_f1 = powell_f(x1);powell_f2 = powell_f(x2);if (powell_f2 >= powell_f0 || (powell_f0 - 2 * powell_f1 + powell_f2)*(powell_f0 - powell_f1 - fn[0])*(powell_f0 - powell_f1 - fn[0]) >= 0.5*fn[0] * (powell_f0 - powell_f2)*(powell_f0 - powell_f2)){sum = 0;for (i = 0; i<n; i++)sum += (x1[i] - x0[i])*(x1[i] - x0[i]);if (powell_f1 <= powell_f2)for (i = 0; i<n; i++)x0[i] = x1[i];elsefor (i = 0; i<n; i++)x0[i] = x2[i];}else{for (i = r; i<n - 1; i++)for (j = 0; j<n; j++)s[i][j] = s[i + 1][j];for (i = 0; i<n; i++)s[n - 1][i] = x1[i] - x0[i];mjtf(n, x1, h, s[n - 1], a, b);mhjfgf(n, a, b, flag, x1);sum = 0;for (i = 0; i<n; i++)sum += (x1[i] - x0[i])*(x1[i] - x0[i]);for (i = 0; i<n; i++)x0[i] = x1[i];}if (sqrt(sum) <= flag)break;elsek += 1;}for (i = 0; i<n; i++)x[i] = x1[i];
}/*鲍威尔法主程序*/int main(void)
{int i, n = 2;float h, flag, x0[m], a[m], b[m], x[m];printf("\n<鲍威尔法>\n");/*printf("请输入维数:\n");scanf_s("%d", &n);*/printf("请输入初始点:");for (i = 0; i<n; i++){printf("\nx0[%d]=", i);scanf_s("%f", &x0[i]);}printf("\n请输入初始步长:\n");scanf_s("%f", &h);printf("\n请输入精度:\n");scanf_s("%f", &flag);powell one;one.mbwef(n, x0, h, flag, a, b, x);printf("\n极小点坐标为:\n");for (i = 0; i<n; i++)printf("x[%d]=%f\n", i, x[i]);printf("\n极小值为:\n%f\n", one.powell_f(x));while (1){;}}

#ifndef _powell_h_
#define _powell_h_class powell
{public:float powell_f(float x[]);void mjtf(int n, float x0[], float h, float s[], float a[], float b[]);void mhjfgf(int n, float a[], float b[], float flag, float x[]);void mbwef(int n, float x0[], float h, float flag, float a[], float b[], float x[]);
private:};#endif // !
#pragma once

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