机械优化设计外推法,黄金分割法,二次插值法
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if(f(x1)>f(x2)) *a=x1; else *b=x2; *n=*n+1; s=hj(a,b,e,n); } return s; } void main() { double s,a,b,e,m; int n=0; printf("输入 a，b 值和精度 e 值\n"); scanf("%lf %lf %lf",&a,&b,&e); s=hj(&a,&b,e,&n); m=(a+b)/2; printf("a=%lf,b=%lf,s=%lf,m=%lf,n=%d\n",a,b,s,m,n); }
二次插值 #include<stdio.h> #include<math.h> int main(void) { double a1,a2,a3,ap,y1,y2,y3,yp,c1,c2,m; double j[3]; int i,h=1;
void finding(double a[3]); finding(j);
y1=t; } a=a1; b=a3; a1=b-l*(b-a); a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); if(b<1e-3) {
return ; }
机械优化设计课程作业
外推法 #include <stdio.h> #include <math.h> #define R 0.01 double fun(double t) {
double m; m=t*t-10*t+36; return m; } void main() { double h0=R,y1,y2,y3,t1,t2,t3,h; t1=0;h=h0;t2=h; y1=fun(t1);y2=fun(t2); if(y2>y1) {
黄金分割法 #include<stdio.h> #include<math.h> #define f(x) x*x*x*x-5*x*x*x+4*x*x-6*x+60
double hj(double *a,double *b,double e,int *n) {
double x1,x2,s; if(fabs((*b-*a)/(*b))<=e) s=f((*b+*a)/2); else { x1=*b-0.618*(*b-*a); x2=*a+0.618*(*b-*a);
break; h=2*h; a[0]=a[1];y[0]=y[1]; a[1]=a[2];y[1]=y[2];} } return; }
#include <stdio.h> #include <math.h> #include <conio.h>
float fun1(float x,float a,float b) {float y; y=x+a*b; return y; } float fun2(float x,float y) {float z; z=4*(x-5)*(x-5)+(y-6)*(y-6); return z; }
y1=y2; a2=a3; y2=y3; a3=a2+h; x[i][1]=fun1(x[i-1][1],d[i][1],a3); x[i][2]=fun1(x[i-1][2],d[i][2],a3); y3=fun2(x[i][1],x[i][2]); } while(y3<y2);
for(;a1>a3;) {t=a3; a3=a1; a1=t; t=y1; y3=y1;
int main() {
float d[100][3],x[100][3],xx[3],ax[100][3]; float a1,a2,a3,h,t,y1,y2,y3,e,a,b,l,fi; int i,k; printf("enter the initiate coordinate\n"); scanf("%f%f",&x[0][1],&x[0][2]); e=0.000001; l=0.618; x[2][1]=x[0][1]; x[2][2]=x[0][2]; k=0; k--; do {x[0][1]=x[2][1]; x[0][2]=x[2][2]; k++;
h=-h; t3=t1; y3=y1; t1=t2; y1=y2; t2=t3; y2=y3; } t3=t2+h; y3=fun(t3); while(y3<y2) { h*=2.0; t1=t2; y1=y2; t2=t3; y2=y3; t3=t2+h; y3=fun(t3); } printf("fun(%f)=%f,fun(%f)=%f,fun(%f)= %f\n",t1,y1,t2,y2,t3,y3); }
h=-h; a[2]=a[0];y[2]=y[0]; do{ a[0]=a[1];a[1]=a[2]; y[0]=y[1];y[1]=y[2]; a[2]=a[1]+h;y[2]=f(a[2]); h=2*h; }while(y[2]<y[1]); } else{ for(i=1;i>=1;i++){ a[2]=a[1]+h;y[2]=f(a[2]); if(y[2]>=y[1])
a1=a2; y1=y2;
a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); } else {b=a2; a2=a1; y2=y1; a1=b-l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); } } } ax[k][i]=0.5*(a+b); x[i][1]=fun1(x[i-1][1],d[i][1],ax[k][i]); x[i][2]=fun1(x[i-1][2],d[i][2],ax[k][i]);
for(;fabs(b-a)>e;) {
if(y1>=y2) {a=a1; a1=a2; y1=y2; a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); } else {b=a2; a2=a1; y2=y1; a1=b-l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); } } } else { for(;fabs((b-a)/b)>=e||fabs((y2-y1)/y2)>=e;) { if(y1>=y2) {a=a1;
for(i=1;i<=2;i++) { if(i==1) {d[i][1]=1;
d[i][2]=0; }
else {d[i][1]=0;
Biblioteka Baidu
d[i][2]=1; }
h=0.1; a1=0; a2=h; x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]);
a1=j[0]; a2=j[1]; a3=j[2]; m=0.001; double f(double x);
y1=f(a1); y2=f(a2); y3=f(a3); for(i=1;1>=1;i++) { c1=(y3-y1)/(a3-a1); c2=((y2-y1)/(a2-a1)-c1)/(a2-a3); ap=0.5*(a1+a3-c1/c2); yp=f(ap); if(fabs((y2-yp)/y2)<m)
x=a2;y=y2;} else{ x=ap;y=yp;} printf("a*=%f\n",x); printf("y*=%f\n",y); return 0; }
double f(double x) { double y; y=(x+1)*(x-2)*(x-2); return y; } void finding(double a[3]) { int h,i; double y[3]; a[0]=0; h=1; a[1]=h; y[0]=f(a[0]);y[1]=f(a[1]); if(y[1]>y[0]) {
} } while(sqrt(pow((x[2][1]-x[0][1]),2)+ pow((x[2][2]-x[0][2]),2))>=1e-6); xx[1]=x[2][1]; xx[2]=x[2][2]; fi=fun2(xx[1],xx[2]); printf("the best answer is : \nx1*= %f\nx2*=%f\nf*=%f\n",xx[1],xx[2],fi);
break; else if((ap-a2)*h>0) { if(y2>=yp){
a1=a2;y1=y2; a2=ap;y2=yp;} else{ a3=ap;y3=yp;} } else if(y2>=yp){ a3=a2;y3=y2; a2=ap;y2=yp;} else{a1=ap;y1=yp;} } double x,y; if(y2<=yp){
if(y2>y1) {h=-h; a3=a1; y3=y1; a1=a2; a2=a3; y1=y2; y2=y3; } a3=a2+h; x[i][1]=fun1(x[i-1][1],d[i][1],a3); x[i][2]=fun1(x[i-1][2],d[i][2],a3); y3=fun2(x[i][1],x[i][2]); do {a1=a2;
二次插值 #include<stdio.h> #include<math.h> int main(void) { double a1,a2,a3,ap,y1,y2,y3,yp,c1,c2,m; double j[3]; int i,h=1;
void finding(double a[3]); finding(j);
y1=t; } a=a1; b=a3; a1=b-l*(b-a); a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); if(b<1e-3) {
return ; }
机械优化设计课程作业
外推法 #include <stdio.h> #include <math.h> #define R 0.01 double fun(double t) {
double m; m=t*t-10*t+36; return m; } void main() { double h0=R,y1,y2,y3,t1,t2,t3,h; t1=0;h=h0;t2=h; y1=fun(t1);y2=fun(t2); if(y2>y1) {
黄金分割法 #include<stdio.h> #include<math.h> #define f(x) x*x*x*x-5*x*x*x+4*x*x-6*x+60
double hj(double *a,double *b,double e,int *n) {
double x1,x2,s; if(fabs((*b-*a)/(*b))<=e) s=f((*b+*a)/2); else { x1=*b-0.618*(*b-*a); x2=*a+0.618*(*b-*a);
break; h=2*h; a[0]=a[1];y[0]=y[1]; a[1]=a[2];y[1]=y[2];} } return; }
#include <stdio.h> #include <math.h> #include <conio.h>
float fun1(float x,float a,float b) {float y; y=x+a*b; return y; } float fun2(float x,float y) {float z; z=4*(x-5)*(x-5)+(y-6)*(y-6); return z; }
y1=y2; a2=a3; y2=y3; a3=a2+h; x[i][1]=fun1(x[i-1][1],d[i][1],a3); x[i][2]=fun1(x[i-1][2],d[i][2],a3); y3=fun2(x[i][1],x[i][2]); } while(y3<y2);
for(;a1>a3;) {t=a3; a3=a1; a1=t; t=y1; y3=y1;
int main() {
float d[100][3],x[100][3],xx[3],ax[100][3]; float a1,a2,a3,h,t,y1,y2,y3,e,a,b,l,fi; int i,k; printf("enter the initiate coordinate\n"); scanf("%f%f",&x[0][1],&x[0][2]); e=0.000001; l=0.618; x[2][1]=x[0][1]; x[2][2]=x[0][2]; k=0; k--; do {x[0][1]=x[2][1]; x[0][2]=x[2][2]; k++;
h=-h; t3=t1; y3=y1; t1=t2; y1=y2; t2=t3; y2=y3; } t3=t2+h; y3=fun(t3); while(y3<y2) { h*=2.0; t1=t2; y1=y2; t2=t3; y2=y3; t3=t2+h; y3=fun(t3); } printf("fun(%f)=%f,fun(%f)=%f,fun(%f)= %f\n",t1,y1,t2,y2,t3,y3); }
h=-h; a[2]=a[0];y[2]=y[0]; do{ a[0]=a[1];a[1]=a[2]; y[0]=y[1];y[1]=y[2]; a[2]=a[1]+h;y[2]=f(a[2]); h=2*h; }while(y[2]<y[1]); } else{ for(i=1;i>=1;i++){ a[2]=a[1]+h;y[2]=f(a[2]); if(y[2]>=y[1])
a1=a2; y1=y2;
a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); } else {b=a2; a2=a1; y2=y1; a1=b-l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); } } } ax[k][i]=0.5*(a+b); x[i][1]=fun1(x[i-1][1],d[i][1],ax[k][i]); x[i][2]=fun1(x[i-1][2],d[i][2],ax[k][i]);
for(;fabs(b-a)>e;) {
if(y1>=y2) {a=a1; a1=a2; y1=y2; a2=a+l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]); } else {b=a2; a2=a1; y2=y1; a1=b-l*(b-a); x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); } } } else { for(;fabs((b-a)/b)>=e||fabs((y2-y1)/y2)>=e;) { if(y1>=y2) {a=a1;
for(i=1;i<=2;i++) { if(i==1) {d[i][1]=1;
d[i][2]=0; }
else {d[i][1]=0;
Biblioteka Baidu
d[i][2]=1; }
h=0.1; a1=0; a2=h; x[i][1]=fun1(x[i-1][1],d[i][1],a1); x[i][2]=fun1(x[i-1][2],d[i][2],a1); y1=fun2(x[i][1],x[i][2]); x[i][1]=fun1(x[i-1][1],d[i][1],a2); x[i][2]=fun1(x[i-1][2],d[i][2],a2); y2=fun2(x[i][1],x[i][2]);
a1=j[0]; a2=j[1]; a3=j[2]; m=0.001; double f(double x);
y1=f(a1); y2=f(a2); y3=f(a3); for(i=1;1>=1;i++) { c1=(y3-y1)/(a3-a1); c2=((y2-y1)/(a2-a1)-c1)/(a2-a3); ap=0.5*(a1+a3-c1/c2); yp=f(ap); if(fabs((y2-yp)/y2)<m)
x=a2;y=y2;} else{ x=ap;y=yp;} printf("a*=%f\n",x); printf("y*=%f\n",y); return 0; }
double f(double x) { double y; y=(x+1)*(x-2)*(x-2); return y; } void finding(double a[3]) { int h,i; double y[3]; a[0]=0; h=1; a[1]=h; y[0]=f(a[0]);y[1]=f(a[1]); if(y[1]>y[0]) {
} } while(sqrt(pow((x[2][1]-x[0][1]),2)+ pow((x[2][2]-x[0][2]),2))>=1e-6); xx[1]=x[2][1]; xx[2]=x[2][2]; fi=fun2(xx[1],xx[2]); printf("the best answer is : \nx1*= %f\nx2*=%f\nf*=%f\n",xx[1],xx[2],fi);
break; else if((ap-a2)*h>0) { if(y2>=yp){
a1=a2;y1=y2; a2=ap;y2=yp;} else{ a3=ap;y3=yp;} } else if(y2>=yp){ a3=a2;y3=y2; a2=ap;y2=yp;} else{a1=ap;y1=yp;} } double x,y; if(y2<=yp){
if(y2>y1) {h=-h; a3=a1; y3=y1; a1=a2; a2=a3; y1=y2; y2=y3; } a3=a2+h; x[i][1]=fun1(x[i-1][1],d[i][1],a3); x[i][2]=fun1(x[i-1][2],d[i][2],a3); y3=fun2(x[i][1],x[i][2]); do {a1=a2;