Mavzu: Jarayon matematik modelini tuzishda eng kichik kvadratlar usulidan foydalanish

Mavzu: Kvadratik, teskari proporsional bog’lanish modellari.

Fan: Algoritmlarni loyihalash

10- laboratoriya mashg’uloti

Teskari proporsional bog’lanish
Masalan (xi ;yi) (i=1,2,…, n) nuqtalar biror to’g’ri chiziq atrofida guruhlashgan bo’lsin. U holda bog’lanishni y=10^(a+b*lgx) ko’rinishda izlaymiz.
Demak, a , b noma’lum parametrlarini aniqlash maqsadida.
a=

i	1	2	3	4	5	6
x	0,43	0,48	0,55	0,62	0,70	0,72
y	1,63597	1,73234	1,87686	2,03345	2,22846	2,35973

1-misol. Ushbu
x ning qiymati 0,45 bo’lganda y funksiya nimani qabul qilishini hisoblovchi dastur tuzing.

#include

• #include
• #include
• using namespace std;
• int main(){
• int n,i;
• cin>>n;
• float x[20],y[20],a,b1,b0,s5=0,
• s6=0, s7=0, s2=0,s3=0,s4=0;
• for(i=1;i<=n;i++){
• cin>>x[i]>>y[i];
• }
• for(i=1;i<=n;i++){
• s2+=x[i];
• s3+=log10(x[i]);
• s4+=log10(y[i]);
• s5+=log10(x[i])*log10(y[i]);
• s6+=log10(x[i]*x[i]);
• s7+= log10(x[i])* log10(x[i]);
• }
• b1=(n*s5-s4*s3)*1.0/(s7-pow(s3,2));
• b0=(s4-b1*s3)*1.0/(n);
• cout<<"so`ralayotgan nuqtani kiriting x=";cin>>a;
• cout<<"so`ralayotgan nuqtada funksiya y="<
  
• }

x	3	4	6	7	9	11	13	15	16	19
y	4	7	11	16	18	22	24	27	30	33

Misol:

№	x	y	xy	x2
1	3	4	12	9
2	4	7	28	16
3	6	11	66	36
4	7	16	112	49
5	9	18	162	81
6	11	22	242	121
7	13	24	312	169
8	15	27	405	225
9	16	30	480	256
10	19	33	627	361
Σ	103	192	2446	1323

Yechish:
x va y ning ko'paytmasi, yig'indisi qiymatlarini hisoblash jadvalda keltirilgan.

#include #include using namespace std; int main(){ int n,i; cin>>n; float x[20],y[20],a,b1,b0,s1=0,s2=0,s3=0,s4=0; for(i=1;i<=n;i++){ cin>>x[i]>>y[i]; } for(i=1;i<=n;i++){ s1+=pow(x[i],2); s2+=y[i]; s3+=x[i]; s4+=y[i]*x[i]; } b0=(s1*s2-s3*s4)*1.0/(n*s1-pow(s3,2)); b1=(n*s4-s2*s3)*1.0/(n*s1-pow(s3,2)); cout<<"so`ralayotgan nuqtani kiriting x=";cin>>a; cout<<"so`ralayotgan nuqtada funksiya y="<