共轭梯度法求三元函数极小值.doc

#include#includeclass Vectorpublic:Vector()x1=0;x2=0;x3=0;Vector(double xx1,double xx2,double xx3)x1=xx1;x2=xx2;x3=xx3; friend Vector operator + (Vector v1,Vector v2); friend Vector operator - (Vector & v1,Vector & v2); friend Vector operator - (Vector & v1);friend double operator * (Vector & v1,Vector & v2);friend Vector operator * (double c,Vector & v);friend Vector operator * (Vector & v,double c);Vector()void display();/private:double x1,x2,x3;Vector operator + (Vector v1,Vector v2)return Vector(v1.x1+v2.x1,v1.x2+v2.x2,v1.x3+v2.x3);Vector operator - (Vector & v1,Vector & v2)return Vector(v1.x1-v2.x1,v1.x2-v2.x2,v1.x3-v2.x3); Vector operator - (Vector & v1)return Vector(-v1.x1,-v1.x2,-v1.x3);double operator * (Vector & v1,Vector & v2)return (v1.x1*v2.x1+v1.x2*v2.x2+v1.x3*v2.x3);Vector operator * (double c,Vector & v)return Vector(c*v.x1,c*v.x2,c*v.x3);Vector operator * (Vector & v,double c)return Vector(c*v.x1,c*v.x2,c*v.x3);void Vector:display() cout(x1,x2,x3)endl;double ValueFunction(Vector &p)/求某点处函数值的函数，返回值为一个double型数return p.x1*p.x1-2*p.x1*p.x2+2*p.x2*p.x2+p.x3*p.x3-p.x2*p.x3+2*p.x1+3*p.x2-p.x3;Vector GradFuction(Vector &p)/求梯度的函数，返回值为一个向量return Vector(2*(p.x1-p.x2)+2,-2*p.x1+4*p.x2-p.x3+3,2*p.x3-p.x2-1);double GetModulus(Vector &p)return sqrt(p.x1*p.x1+p.x2*p.x2+p.x3*p.x3);/*double GetFValue(double la) /求函数值f(xk+lamda*sk)return ValueFunction(xk+la*sk);*/void main()int n=3;/本题为三维问题double ValueFunction(Vector &p);Vector GradFuction(Vector &p);Vector startpoint(0,0,0);Vector x10000=startpoint,g10000,s10000;double lamda10000,lamdak;int k;cout选取初始点为：x0= ;x0.display();double precision=0.000001;step2:g0=GradFuction(x0);s0=-g0;k=0;step3: double GetFValue(double la); double f1,f0,la1,la0=1,h=10,e=0.0000001; step12: la1=la0+h;f1=ValueFunction(xk+la1*sk);f0=ValueFunction(xk+la0*sk);if(f1f0)/coutf1f0endl;la0=la1;h=h*2;goto step12;else /coutf0endl;if(fabs(h)e)lamdak=la0;/cout|h|为：fabs(h)endl;/coute为：eendl;/cout达到结束条件：|h|e，计算结束。endl;goto step15;else/couteendl;h=-h/4;goto step12;step15: cout极小值点为：lamdak=lamdakendl;/cout极值为：f(x)min=GetFValue(xx)endl;xk+1=xk+lamdak*sk; cout带入lamdak求得xk+1点为t; xk+1.display(); gk+1=GradFuction(xk+1);coutxk+1点的梯度为t;gk+1.display(); /step3结束step4: if (GetModulus(gk+1)precision) goto step6 ;else goto step5;step5: if (kn-1) sk+1=-gk+1+(pow(GetModulus(gk+1),2)/pow(GetModulus(gk),2)*sk; k+; goto step3; if (k=n-1) x0=xn; goto step2; step6: cout程序结束，求得极小点为：t;xk+1.display(); cout迭代次数为：tk+1endl;/*/-以下是测试部分Vector v1(1,2,0),v2(1,2,3),v3(3,1,2),v4,v5,v6,v7(0,3,4);double n;Vector v_arry133=v1,v2,v3;/int ia=;int l=45;v3=v1+v2;v_arry0=v3;/v3=GradFuction(v1);n=ValueFunction(v1);GradFuction(v1).display();v_arry0.display();v4=-v