Numerical Recipes in C
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一书及所附程序，有完整程序。不过我封装了它的C++版本，可以对但参数或多参数求极值，完整的头文件为：
#ifndef __OPTIMIZATION_H__
#define __OPTIMIZATION_H__
//////////////////////////////////////////////////////////////////////////
// class TOptimization
//
// $ 求函数一个或多个参数的最小值
//
// 该类默认对一个参数优化，一般只要输入优化参数数目
// 优化目标函数就可以使用。
//
// ...主要代码来自：
// Numerical Recipes in C++
// The Art of Scientific Computing
// Second Edition
// William H. Press Saul A. Teukolsky
// William T. Vetterling Brian P. Flannery
//
// 中译本：
// C++ 数值算法(第二版) 胡健伟 赵志勇 薛运华 等译
// 电子工业出版社 北京 (2005)
//
// Author: Jian Feng
// Email: fengj@tom.com
// Dec. 9, 2006
//
//////////////////////////////////////////////////////////////////////////
//
// 输入函数：
//
// @MaxIterationStep: 最大迭代次数， 默认 1000
// @ParameterNumbers: 优化参数数目， 默认 1
// @InitMatrix: 初始化矩阵参数(N*N)， 默认
// @Tolerance: 容许公差， 默认 1E-7
//
// 执行函数：
//
// @ExecutePowell: 利用powell方法进行多参数优化
// @ExecuteBrent: 利用brent方法进行单参数优化
//
// 输出函数：
//
// @OptimizatedParameters: 优化结果数据
// @ObjectiveFunctionValue: 目标函数在优化值处的值
//
// 使用示例：
//
// 1. 单参数
// double objfun(double a){
// double sum = 0;
// for(int i = 0; i DataPoints; ++i)
// sum += SQR(Exps[i] - Theo(a));
// }
// double value
// TOptimization opt;
// if(opt.ExecuteBrent(objfun, -10, -1)) opt.OptimizatedParameters(value);
//
// 2. 多参数
// double objfun(double *a){
// double sum = 0;
// for(int i = 0; i DataPoints; ++i)
// sum += SQR(Exps[i] - Theo(a));
// }
// double value[3]
// TOptimization opt(3);
// double ival[3] = ;
// if(opt.ExecutePowell(objfun, ival)) opt.OptimizatedParameters(value);
//
namespace{
static int ncom; //公用变量
static double *pcom_p; //公用变量
static double *xicom_p; //公用变量
static double (*nrfunc)(double*); //公用函数指针
}
class TOptimization
{
private:
typedef double (*Reff)(double *);
typedef double (*Ptrf)(double );
public:
TOptimization(int n = 1);
~TOptimization()
//主要方法
void ParameterNumbers(int n)
//利用powell方法对一个或多个参数优化
bool ExecutePowell(Reff obj, double *a = 0);
//利用brent方法对一个参数优化，需给出参数所在的区间
bool ExecuteBrent(Ptrf obj, double vFrom = 0, double vTo = 1);
void OptimizatedParameters(double *a)
void OptimizatedParameters(double a)
//void OptimizatedParameters(double *a){
// if(method) for(int i=0; inum; ++i) a[i]=coef[i];
// else *a = vmin;
//}
//其它方法
void InitMatrix(double **m)
{
for(int i=0; inum; ++i)
for(int j = 0; jnum; ++j)
matx[i][j]=m[i][j];
setm = true;
}
void MaxIterationStep(int s)
void Tolerance(double eps)
double ObjectiveFunctionValue()const
private:
double brent(double ax, double bx, double cx, Ptrf f, double tol, double xmin, int flag);
void mnbrak(double ax, double bx, double cx, double fa, double fb, double fc, Ptrf func);
void linmin(double *p, double *xi, double fret, Reff func);
bool powell(double *p, double **xi, double ftol, int iter, double fret, Reff func);
void shft2(double a, double b, const double c)
void shft3(double a, double b, double c, const double d)
double SQR(double x)
void SWAP(double a, double b)
double SIGN(const double a, const double b)
double MAX(const double a, const double b)
void AllocateMemory();
void FreeMemory();
static double f1dim(double x)
{
int j;
double *xt = new double [ncom];
//Vec_Dp pcom=*pcom_p,xicom=*xicom_p;
double *pcom = pcom_p, *xicom = xicom_p;
for (j=0;jncom;j++)
xt[j]=pcom[j]+x*xicom[j];
//delete []xt;
double val = nrfunc(xt);
delete []xt;
return val;
}
bool setm; //是否设置优化方向初始矩阵
int num; //优化参数
int ITMAX; //最大迭代数
int iter; //实际迭代步数
int method; //优化方法 0: 1-D brent, 2: M-D Powell
double vmin; //一维优化参数
double ftol; //容许差
double fret; //目标函数值
double *coef; //多维优化参数值
double **matx; //多维优化参数方向的初始值
};
//////////////////////////////////////////////////////////////////////////
inline TOptimization::TOptimization(int n )
{
num = n;
ftol = 1e-7;
ITMAX = 1000;
iter = 0;
fret = 0.;
vmin = 0.;
method = 0;
setm = false;
AllocateMemory();
}
inline void TOptimization::AllocateMemory()
{
pcom_p = new double [num];
xicom_p = new double [num];
coef = new double [num];
matx = new double *[num];
for(int i = 0; i num; ++i)
{
coef[i] = 0.;
matx[i] = new double [num];
for(int j = 0; j num; ++j)
matx[i][j]=(i == j ? 1.0 : 0.0);
}
}
inline void TOptimization::FreeMemory()
{
for(int i = 0; i num; ++i)
{
delete []matx[i];
}
delete []matx;
delete []pcom_p;
delete []xicom_p;
delete []coef;
}
inline bool TOptimization::ExecutePowell(Reff obj, double *a)
{
method = 1;
if(a)
for(int i = 0; i num; ++i) coef[i] = a[i];
return powell(coef, matx, ftol, iter, fret, obj);
}
inline bool TOptimization::ExecuteBrent(Ptrf obj, double vFrom, double vTo)
{
method = 0;
int flag;
double cx, fa, fb, fc;
mnbrak(vFrom,vTo,cx,fa,fb,fc,obj);
fret = brent(vFrom,vTo,cx,obj, ftol,vmin, flag);
return flag ? true : false;
}
inline void TOptimization::mnbrak(double ax, double bx, double cx, double fa,
double fb, double fc, Ptrf func)
{
const double GOLD=1.618034,GLIMIT=100.0,TINY=1.0e-20;
double ulim,u,r,q,fu;
fa=func(ax);
fb=func(bx);
if (fb fa) {
SWAP(ax,bx);
SWAP(fb,fa);
}
cx=bx+GOLD*(bx-ax);
fc=func(cx);
while (fb fc) {
r=(bx-ax)*(fb-fc);
q=(bx-cx)*(fb-fa);
u=bx-((bx-cx)*q-(bx-ax)*r)/
(2.0*SIGN(MAX(fabs(q-r),TINY),q-r));
ulim=bx+GLIMIT*(cx-bx);
if ((bx-u)*(u-cx) 0.0) {
fu=func(u);
if (fu fc) {
ax=bx;
bx=u;
fa=fb;
fb=fu;
return;
} else if (fu fb) {
cx=u;
fc=fu;
return;
}
u=cx+GOLD*(cx-bx);
fu=func(u);
} else if ((cx-u)*(u-ulim) 0.0) {
fu=func(u);
if (fu fc) {
shft3(bx,cx,u,cx+GOLD*(cx-bx));
shft3(fb,fc,fu,func(u));
}
} else if ((u-ulim)*(ulim-cx) = 0.0) {
u=ulim;
fu=func(u);
} else {
u=cx+GOLD*(cx-bx);
fu=func(u);
}
shft3(ax,bx,cx,u);
shft3(fa,fb,fc,fu);
}
}
inline double TOptimization::brent(double ax, double bx, double cx,
Ptrf f, double tol, double xmin, int flag)
{
flag = 1;
const double CGOLD=0.3819660;
const double ZEPS=1.0e-20;
int iter;
double a,b,d=0.0,etemp,fu,fv,fw,fx;
double p,q,r,tol1,tol2,u,v,w,x,xm;
double e=0.0;
a=(ax cx ? ax : cx);
b=(ax cx ? ax : cx);
x=w=v=bx;
fw=fv=fx=f(x);
for (iter=0;iterITMAX;iter++) {
xm=0.5*(a+b);
tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
if (fabs(x-xm) = (tol2-0.5*(b-a))) {
xmin=x;
return fx;
}
if (fabs(e) tol1) {
r=(x-w)*(fx-fv);
q=(x-v)*(fx-fw);
p=(x-v)*q-(x-w)*r;
q=2.0*(q-r);
if (q 0.0) p = -p;
q=fabs(q);
etemp=e;
e=d;
if (fabs(p) = fabs(0.5*q*etemp) || p = q*(a-x) || p = q*(b-x))
d=CGOLD*(e=(x = xm ? a-x : b-x));
else {
d=p/q;
u=x+d;
if (u-a tol2 || b-u tol2)
d=SIGN(tol1,xm-x);
}
} else {
d=CGOLD*(e=(x = xm ? a-x : b-x));
}
u=(fabs(d) = tol1 ? x+d : x+SIGN(tol1,d));
fu=f(u);
if (fu = fx) {
if (u = x) a=x; else b=x;
shft3(v,w,x,u);
shft3(fv,fw,fx,fu);
} else {
if (u x) a=u; else b=u;
if (fu = fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else if (fu = fv || v == x || v == w) {
v=u;
fv=fu;
}
}
}
flag = 0;
xmin=x;
return fx;
}
inline void TOptimization::linmin(double *p, double *xi, double fret, Reff func)
{
int j, flag;
const double TOL=1.0e-8;
double xx,xmin,fx,fb,fa,bx,ax;
int n=num;
ncom=n;
//pcom_p=new Vec_Dp(n);
//xicom_p=new Vec_Dp(n);
nrfunc=func;
//Vec_Dp pcom=*pcom_p,xicom=*xicom_p;
double *pcom = pcom_p, *xicom = xicom_p;
for (j=0;jn;j++) {
pcom[j]=p[j];
xicom[j]=xi[j];
}
ax=0.0;
xx=1.0;
mnbrak(ax,xx,bx,fa,fx,fb,f1dim);
fret=brent(ax,xx,bx,f1dim,TOL,xmin, flag);
for (j=0;jn;j++) {
xi[j] *= xmin;
p[j] += xi[j];
}
//delete xicom_p;
//delete pcom_p;
}
inline bool TOptimization::powell(double *p, double **xi, double ftol, int iter,
double fret, Reff func)
{
const int ITMAX=500;
const double TINY=1.0e-20;
int i,j,ibig;
double del,fp,fptt,t;
int n=num;
//Vec_Dp pt(n),ptt(n),xit(n);
double *pt, *ptt, *xit;
for(i = 0; i n; ++i)
{
pt = new double [n];
ptt = new double [n];
xit = new double [n];
}
fret=func(p);
for (j=0;jn;j++) pt[j]=p[j];
for (iter=0;;++iter) {
fp=fret;
ibig=0;
del=0.0;
for (i=0;in;i++) {
for (j=0;jn;j++) xit[j]=xi[j][i];
fptt=fret;
linmin(p,xit,fret,func);
if (fptt-fret del) {
del=fptt-fret;
ibig=i+1;
}
}
if (2.0*(fp-fret) = ftol*(fabs(fp)+fabs(fret))+TINY) {
delete []pt;
delete []ptt;
delete []xit;
return true;
}
if (iter == ITMAX)
{
delete []pt;
delete []ptt;
delete []xit;
return false;
//cerr"powell exceeding maximum iterations.";
}
for (j=0;jn;j++) {
ptt[j]=2.0*p[j]-pt[j];
xit[j]=p[j]-pt[j];
pt[j]=p[j];
}
fptt=func(ptt);
if (fptt fp) {
t=2.0*(fp-2.0*fret+fptt)*SQR(fp-fret-del)-del*SQR(fp-fptt);
if (t 0.0) {
linmin(p,xit,fret,func);
for (j=0;jn;j++) {
xi[j][ibig-1]=xi[j][n-1];
xi[j][n-1]=xit[j];
}
}
}
}
}
#endif
#includestdio.h
void main()
{
int x,y,z,c,o,p,q,max;float m,n;
x=0;y=0;z=0;
max=0;
for(x=0;x201;x++)
{
for(y=0;y251;y++)///////////这儿写错了for(y=0;x251;y++)
{
for(z=0;z101;z++)
{
m=x+1.5*y+4*z;
n=2*x+1.2*y+z;
if(m=2000n=1000)
c=10*x+12*y+14*z;
if(maxc)
{
max=c;o=x;p=y;q=z;
}
}
}
}
printf("max=%d,x=%d,y=%d,z=%d",c,o,p,q);
}
#include stdio.h
void main ()
{
int num,i;
float x,y,l,m,n,p,a,b;
i=1;
l=0.0;
m=0.0;
n=0.0;
p=0.0;
printf ("请输入你想计算的x，y的个数：");
scanf("%d",num);
if (num=1)
{
while (i=num);
{
printf("请输入x的值");
scanf ("%lf",x);
printf("请输入y的值");
scanf ("%lf",y);
l+=x;
m+=y;
n+=x*y;
p+=x*x;
i++;
}
a=(num*n-l*m)/(num*p-l*l);
b=(p*m-n*l)/(num*p-l*l);
printf("最小二乘法所算得的斜率和截距分别为%f和%f\n",a,b);
}
else printf("mun"输入有误！);
}
一个非常简单的遗传算法源代码，是由Denis Cormier (North Carolina State University)开发的，Sita S.Raghavan (University of North Carolina at Charlotte)修正。代码保证尽可能少，实际上也不必查错。对一特定的应用修正此代码，用户只需改变常数的定义并且定义“评价函数”即可。注意代码的设计是求最大值，其中的目标函数只能取正值；且函数值和个体的适应值之间没有区别。该系统使用比率选择、精华模型、单点杂交和均匀变异。如果用Gaussian变异替换均匀变异，可能得到更好的效果。代码没有任何图形，甚至也没有屏幕输出，主要是保证在平台之间的高可移植性。读者可以从,目录 coe/evol中的文件prog.c中获得。要求输入的文件应该命名为‘gadata.txt’；系统产生的输出文件为‘galog.txt’。输入的文件由几行组成：数目对应于变量数。且每一行提供次序——对应于变量的上下界。如第一行为第一个变量提供上下界，第二行为第二个变量提供上下界，等等。
/**************************************************************************/
/* This is a simple genetic algorithm implementation where the */
/* evaluation function takes positive values only and the */
/* fitness of an individual is the same as the value of the */
/* objective function */
/**************************************************************************/
#include stdio.h
#include stdlib.h
#include math.h
/* Change any of these parameters to match your needs */
#define POPSIZE 50 /* population size */
#define MAXGENS 1000 /* max. number of generations */
#define NVARS 3 /* no. of problem variables */
#define PXOVER 0.8 /* probability of crossover */
#define PMUTATION 0.15 /* probability of mutation */
#define TRUE 1
#define FALSE 0
int generation; /* current generation no. */
int cur_best; /* best individual */
FILE *galog; /* an output file */
struct genotype /* genotype (GT), a member of the population */
{
double gene[NVARS]; /* a string of variables */
double fitness; /* GT's fitness */
double upper[NVARS]; /* GT's variables upper bound */
double lower[NVARS]; /* GT's variables lower bound */
double rfitness; /* relative fitness */
double cfitness; /* cumulative fitness */
};
struct genotype population[POPSIZE+1]; /* population */
struct genotype newpopulation[POPSIZE+1]; /* new population; */
/* replaces the */
/* old generation */
/* Declaration of procedures used by this genetic algorithm */
void initialize(void);
double randval(double, double);
void evaluate(void);
void keep_the_best(void);
void elitist(void);
void select(void);
void crossover(void);
void Xover(int,int);
void swap(double *, double *);
void mutate(void);
void report(void);
/***************************************************************/
/* Initialization function: Initializes the values of genes */
/* within the variables bounds. It also initializes (to zero) */
/* all fitness values for each member of the population. It */
/* reads upper and lower bounds of each variable from the */
/* input file `gadata.txt'. It randomly generates values */
/* between these bounds for each gene of each genotype in the */
/* population. The format of the input file `gadata.txt' is */
/* var1_lower_bound var1_upper bound */
/* var2_lower_bound var2_upper bound ... */
/***************************************************************/
void initialize(void)
{
FILE *infile;
int i, j;
double lbound, ubound;
if ((infile = fopen("gadata.txt","r"))==NULL)
{
fprintf(galog,"\nCannot open input file!\n");
exit(1);
}
/* initialize variables within the bounds */
for (i = 0; i NVARS; i++)
{
fscanf(infile, "%lf",lbound);
fscanf(infile, "%lf",ubound);
for (j = 0; j POPSIZE; j++)
{
population[j].fitness = 0;
population[j].rfitness = 0;
population[j].cfitness = 0;
population[j].lower[i] = lbound;
population[j].upper[i]= ubound;
population[j].gene[i] = randval(population[j].lower[i],
population[j].upper[i]);
}
}
fclose(infile);
}
/***********************************************************/
/* Random value generator: Generates a value within bounds */
/***********************************************************/
double randval(double low, double high)
{
double val;
val = ((double)(rand()%1000)/1000.0)*(high - low) + low;
return(val);
}
/*************************************************************/
/* Evaluation function: This takes a user defined function. */
/* Each time this is changed, the code has to be recompiled. */
/* The current function is: x[1]^2-x[1]*x[2]+x[3] */
/*************************************************************/
void evaluate(void)
{
int mem;
int i;
double x[NVARS+1];
for (mem = 0; mem POPSIZE; mem++)
{
for (i = 0; i NVARS; i++)
x[i+1] = population[mem].gene[i];
population[mem].fitness = (x[1]*x[1]) - (x[1]*x[2]) + x[3];
}
}
/***************************************************************/
/* Keep_the_best function: This function keeps track of the */
/* best member of the population. Note that the last entry in */
/* the array Population holds a copy of the best individual */
/***************************************************************/
void keep_the_best()
{
int mem;
int i;
cur_best = 0; /* stores the index of the best individual */
for (mem = 0; mem POPSIZE; mem++)
{
if (population[mem].fitness population[POPSIZE].fitness)
{
cur_best = mem;
population[POPSIZE].fitness = population[mem].fitness;
}
}
/* once the best member in the population is found, copy the genes */
for (i = 0; i NVARS; i++)
population[POPSIZE].gene[i] = population[cur_best].gene[i];
}
/****************************************************************/
/* Elitist function: The best member of the previous generation */
/* is stored as the last in the array. If the best member of */
/* the current generation is worse then the best member of the */
/* previous generation, the latter one would replace the worst */
/* member of the current population */
/****************************************************************/
void elitist()
{
int i;
double best, worst; /* best and worst fitness values */
int best_mem, worst_mem; /* indexes of the best and worst member */
best = population[0].fitness;
worst = population[0].fitness;
for (i = 0; i POPSIZE - 1; ++i)
{
if(population[i].fitness population[i+1].fitness)
{
if (population[i].fitness = best)
{
best = population[i].fitness;
best_mem = i;
}
if (population[i+1].fitness = worst)
{
worst = population[i+1].fitness;
worst_mem = i + 1;
}
}
else
{
if (population[i].fitness = worst)
{
worst = population[i].fitness;
worst_mem = i;
}
if (population[i+1].fitness = best)
{
best = population[i+1].fitness;
best_mem = i + 1;
}
}
}
/* if best individual from the new population is better than */
/* the best individual from the previous population, then */
/* copy the best from the new population; else replace the */
/* worst individual from the current population with the */
/* best one from the previous generation */
if (best = population[POPSIZE].fitness)
{
for (i = 0; i NVARS; i++)
population[POPSIZE].gene[i] = population[best_mem].gene[i];
population[POPSIZE].fitness = population[best_mem].fitness;
}
else
{
for (i = 0; i NVARS; i++)
population[worst_mem].gene[i] = population[POPSIZE].gene[i];
population[worst_mem].fitness = population[POPSIZE].fitness;
}
}
/**************************************************************/
/* Selection function: Standard proportional selection for */
/* maximization problems incorporating elitist model - makes */
/* sure that the best member survives */
/**************************************************************/
void select(void)
{
int mem, i, j, k;
double sum = 0;
double p;
/* find total fitness of the population */
for (mem = 0; mem POPSIZE; mem++)
{
sum += population[mem].fitness;
}
/* calculate relative fitness */
for (mem = 0; mem POPSIZE; mem++)
{
population[mem].rfitness = population[mem].fitness/sum;
}
population[0].cfitness = population[0].rfitness;
/* calculate cumulative fitness */
for (mem = 1; mem POPSIZE; mem++)
{
population[mem].cfitness = population[mem-1].cfitness +
population[mem].rfitness;
}
/* finally select survivors using cumulative fitness. */
for (i = 0; i POPSIZE; i++)
{
p = rand()%1000/1000.0;
if (p population[0].cfitness)
newpopulation[i] = population[0];
else
{
for (j = 0; j POPSIZE;j++)
if (p = population[j].cfitness
ppopulation[j+1].cfitness)
newpopulation[i] = population[j+1];
}
}
/* once a new population is created, copy it back */
for (i = 0; i POPSIZE; i++)
population[i] = newpopulation[i];
}
/***************************************************************/
/* Crossover selection: selects two parents that take part in */
/* the crossover. Implements a single point crossover */
/***************************************************************/
void crossover(void)
{
int i, mem, one;
int first = 0; /* count of the number of members chosen */
double x;
for (mem = 0; mem POPSIZE; ++mem)
{
x = rand()%1000/1000.0;
if (x PXOVER)
{
++first;
if (first % 2 == 0)
Xover(one, mem);
else
one = mem;
}
}
}
/**************************************************************/
/* Crossover: performs crossover of the two selected parents. */
/**************************************************************/
void Xover(int one, int two)
{
int i;
int point; /* crossover point */
/* select crossover point */
if(NVARS 1)
{
if(NVARS == 2)
point = 1;
else
point = (rand() % (NVARS - 1)) + 1;
for (i = 0; i point; i++)
swap(population[one].gene[i], population[two].gene[i]);
}
}
/*************************************************************/
/* Swap: A swap procedure that helps in swapping 2 variables */
/*************************************************************/
void swap(double *x, double *y)
{
double temp;
temp = *x;
*x = *y;
*y = temp;
}
/**************************************************************/
/* Mutation: Random uniform mutation. A variable selected for */
/* mutation is replaced by a random value between lower and */
/* upper bounds of this variable */
/**************************************************************/
void mutate(void)
{
int i, j;
double lbound, hbound;
double x;
for (i = 0; i POPSIZE; i++)
for (j = 0; j NVARS; j++)
{
x = rand()%1000/1000.0;
if (x PMUTATION)
{
/* find the bounds on the variable to be mutated */
lbound = population[i].lower[j];
hbound = population[i].upper[j];
population[i].gene[j] = randval(lbound, hbound);
}
}
}
/***************************************************************/
/* Report function: Reports progress of the simulation. Data */
/* dumped into the output file are separated by commas */
/***************************************************************/
。。。。。
代码太多 你到下面呢个网站看看吧
void main(void)
{
int i;
if ((galog = fopen("galog.txt","w"))==NULL)
{
exit(1);
}
generation = 0;
fprintf(galog, "\n generation best average standard \n");
fprintf(galog, " number value fitness deviation \n");
initialize();
evaluate();
keep_the_best();
while(generationMAXGENS)
{
generation++;
select();
crossover();
mutate();
report();
evaluate();
elitist();
}
fprintf(galog,"\n\n Simulation completed\n");
fprintf(galog,"\n Best member: \n");
for (i = 0; i NVARS; i++)
{
fprintf (galog,"\n var(%d) = %3.3f",i,population[POPSIZE].gene[i]);
}
fprintf(galog,"\n\n Best fitness = %3.3f",population[POPSIZE].fitness);
fclose(galog);
printf("Success\n");
}
我也在学这个课，老兄。我编的这个用于解决二次的问题。输入目标函数系数和初始区间及熟练精度。 黄金分割法：
# include stdio.h
# include math.h
float d,e,f;
void main ()
{printf("请输入目标函数的二次项，一次项，常数项，中间用空格分开\n");
scanf("%f %f %f",d,e,f);
float fox (float x);
float a0,b0,z,a,b,x1,x2,f1,f2,xx;
char k,m;
int n;
printf("请输入初始区间a0,b0,收敛精度z，中间用空格分开\n");
scanf("%f %f %f",a,b,z);
a=a0;
b=b0;
x1=a+0.382*(b-a);
f1=fox(x1);
x2=a+0.618*(b-a);
f2=fox(x2);
if(f1f2) {n=0;
b=x2;
x2=x1;
f2=f1;
}
else {n=1;
a=x1;
x1=x2;
f1=f2;
}
while(fabs((b-a))z)
{if(n==0) {x1=a+0.382*(b-a);
f1=fox(x1);
}
else {x2=a+0.618*(b-a);
f2=fox(x2);
}
}
if(f1f2) {n=0;
b=x2;
x2=x1;
f2=f1;
}
else {n=1;
a=x1;
x1=x2;
f1=f2;
}
xx=(a+b)/2;
printf("极小点和极小值xx=%f,ff=%f\n",xx,fox(xx));
k=getchar();
m=getchar();
}
float fox(float x)
{float r;
r=d*x*x+e*x+f;
return(r);
}
