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| #include <vcl.h>
#pragma hdrstop
#include "Unit1.h"
//---------------------------------------------------------------------------
#pragma package(smart_init)
#pragma resource "*.dfm"
TForm1 *Form1;
//---------------------------------------------------------------------------
const double dx=0.25;
__fastcall TForm1::TForm1(TComponent* Owner)
: TForm(Owner)
{
Form1->Button1->Caption="Внести точку на график";
Form1->Button2->Caption="Лагранж";
Form1->Button3->Caption="Ньютон";
Form1->Button4->Caption="МНК 1 степени";
Form1->Button5->Caption="МНК 2 степени";
Form1->Button6->Caption="МНК 3 степени";
Form1->Button7->Caption="Построить многочлен по коэффициентам";
Form1->Button8->Caption="Очистить всё, кроме исходного графика";
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Button1Click(TObject *Sender)
{
if(Edit1->Text == "")
{
ShowMessage("Вы не ввели значение X !");
return ;
}
if(Edit2->Text == "")
{
ShowMessage("Вы не ввели значение Y !");
return ;
}
double y;
double x;
x = Edit1->Text.ToDouble();
X.push_back(x);
y = Edit2->Text.ToDouble();
Y.push_back(y);
Кривая->AddXY(x,y);
Точки->AddXY(x,y);
Edit1->Text = "";
Edit2->Text = "";
}
double l(int index, vector<double> x, double x_current )
{
double l=1;
for (int i=0;i<x.size();i++)
{
if (i!=index)
{
l*=(x_current-x[i])/(x[index]-x[i]);
}
}
return l;
}
double interpolateLagrange(double x_current) {
size_t N = Form1->get_size();
vector<double> X = Form1->get_vectorX();
vector<double> Y = Form1->get_vectorY();
double res = 0;
for (int i = 0; i < X.size(); i++)
{
res+=Y[i]*l(i,X,x_current);
}
return res;
}
void __fastcall TForm1::Button2Click(TObject *Sender)
{
vector<double>x_lagr;
vector<double>y_lagr;
double x1= *min_element(begin(X),end(X));
double x2= *max_element(begin(X),end(X));
for (double x_current = x1;x_current<=x2;x_current+=dx)
{
x_lagr.push_back(x_current);
y_lagr.push_back(interpolateLagrange(x_current));
}
for(size_t i=0;i<x_lagr.size(); ++i){
Лагранж->AddXY(x_lagr[i],y_lagr[i]);
}
}
int fact(int a)
{
if (a==1) return 1;
return fact(a-1)*a;
}
double u_cal1 (double u, int n) {
double temp = u;
for (int i = 1; i < n; i++) temp *= (u - i);
return temp;
}
double u_cal2 (double u, int n) {
double temp = u;
for (int i = 1; i < n; i++) temp *= (u + i);
return temp;
}
double dy(vector<double> x, vector<double> y)
{
if(y.size()>2)
{
vector<double>x_left =x;
vector<double>y_left =y;
x_left.erase(x_left.begin());
y_left.erase(y_left.begin());
vector<double>x_right =x;
vector<double>y_right =y;
x_right.erase(x_right.end()-1);
y_right.erase(y_right.end()-1);
return (dy(x_left,y_left)-dy(x_right,y_right))/(x[x.size()-1]-x[0]);
}
else if(y.size()==2)
{
return (y[1]-y[0])/(x[1]-x[0]);
}
return 0;
}
double interpolateNewton(double x_current) {
size_t N = Form1->get_size();
vector<double> X = Form1->get_vectorX();
vector<double> Y = Form1->get_vectorY();
double res = Y[0];
double tmp;
for (int i=1; i<Y.size();i++)
{
vector <double> x_list = vector<double>(X.begin(),X.begin()+i+1);
vector <double> y_list = vector<double>(Y.begin(),Y.begin()+i+1);
tmp=1;
for(int j=0;j<i;j++)
tmp*=x_current-X[j];
res+=dy(x_list,y_list)*tmp;
}
return res;
}
void __fastcall TForm1::Button3Click(TObject *Sender)
{
size_t N= X.size();
vector <double> x_newt;
vector <double> y_newt;
double x1= *min_element(begin(X),end(X));
double x2= *max_element(begin(X),end(X));
for (double x_current = x1;x_current<=x2;x_current+=dx)
{
x_newt.push_back(x_current);
y_newt.push_back(interpolateNewton(x_current));
}
for(size_t i=0;i<x_newt.size(); ++i){
Ньютон->AddXY(x_newt[i],y_newt[i]);
}
}
vector <double> interpolateLeastSquare(int K)
{
size_t N = Form1->get_size();
vector<double> X = Form1->get_vectorX();
vector<double> Y = Form1->get_vectorY();
vector<vector<double>> sums;
sums.assign(K+1, vector<double>(K+1));
vector<double> a(K+1,0);
vector<double> b(K+1,0);
for(int i=0; i<K+1; i++)
{
for(int j=0; j<K+1; j++)
{
sums[i][j] = 0;
for(int k=0; k<N; k++)
{
sums[i][j] += pow(X[k], i+j);
}
}
}
for(int i=0; i<K+1; i++)
{
for(int k=0; k<N; k++)
{
b[i] += pow(X[k], i) * Y[k];
}
}
double temp=0;
for(int i=0; i<K+1; i++) //приведение к диагональному виду
{
if(sums[i][i]==0)
{
for(int j=0; j<K+1; j++)
{
if(j==i) continue;
if(sums[j][i] !=0 && sums[i][j]!=0)
{
for(int k=0; k<K+1; k++){
temp = sums[j][k];
sums[j][k] = sums[i][k];
sums[i][k] = temp;
}
temp = b[j];
b[j] = b[i];
b[i] = temp;
break;
}
}
}
}
for(int k=0; k<K+1; k++) //расчет решения
{
for(int i=k+1; i<K+1; i++)
{
if(sums[k][k]==0)
{
printf("\nРешения не существует\n");
exit(1);
}
double M = sums[i][k] / sums[k][k];
for(int j=k; j<K+1; j++)
{
sums[i][j] -= M * sums[k][j];
}
b[i] -= M*b[k];
}
}
for(int i=(K+1)-1; i>=0; i--)
{
float s = 0;
for(int j = i; j<K+1; j++)
{
s = s + sums[i][j]*a[j];
}
a[i] = (b[i] - s) / sums[i][i]; }
return a;
}
void __fastcall TForm1::Button4Click(TObject *Sender)
{
vector <double> x_squ1;
vector <double> y_squ1;
vector<double> a;
double x1= *min_element(begin(X),end(X));
double x2= *max_element(begin(X),end(X));
int K=1;
a=interpolateLeastSquare(K);
for (double x_current = x1;x_current<=x2;x_current+=dx)
{
double sum=0;
for(int i=0;i<K+1;i++)
{
sum+=a[i]*pow(x_current,i);
}
x_squ1.push_back(x_current);
y_squ1.push_back(sum);
}
for(size_t i=0;i<x_squ1.size(); ++i){
МНК_1->AddXY(x_squ1[i],y_squ1[i]);
}
}
void __fastcall TForm1::Button5Click(TObject *Sender)
{
vector <double> x_squ2;
vector <double> y_squ2;
vector<double> a;
double x1= *min_element(begin(X),end(X));
double x2= *max_element(begin(X),end(X));
int K=2;
a=interpolateLeastSquare(K);
for (double x_current = x1;x_current<=x2;x_current+=dx)
{
double sum=0;
for(int i=0;i<K+1;i++)
{
sum+=a[i]*pow(x_current,i);
}
x_squ2.push_back(x_current);
y_squ2.push_back(sum);
}
for(size_t i=0;i<x_squ2.size(); ++i){
МНК_2->AddXY(x_squ2[i],y_squ2[i]);
}
}
//---------------------------------------------------------------------------
void __fastcall TForm1::Button6Click(TObject *Sender)
{
vector <double> x_squ3;
vector <double> y_squ3;
vector<double> a;
double x1= *min_element(begin(X),end(X));
double x2= *max_element(begin(X),end(X));
int K=3;
a=interpolateLeastSquare(K);
for (double x_current = x1;x_current<=x2;x_current+=dx)
{
double sum=0;
for(int i=0;i<K+1;i++)
{
sum+=a[i]*pow(x_current,i);
}
x_squ3.push_back(x_current);
y_squ3.push_back(sum);
}
for(size_t i=0;i<x_squ3.size(); ++i){
МНК_3->AddXY(x_squ3[i],y_squ3[i]);
}
}
double Func(double a, double b, double c, double d, double e, double x){
return a*pow(x,4)+ b*pow(x,3)+ c*pow(x,2)+ d*x + e;
}
void __fastcall TForm1::Button7Click(TObject *Sender)
{
double x2= *max_element(begin(X),end(X));
double h = 0.05;
double ak,bk,ck,dk,ek;
ak = a->Text.ToDouble();
bk = b->Text.ToDouble();
ck = c->Text.ToDouble();
dk = d->Text.ToDouble();
ek = e->Text.ToDouble();
for (double x1 = *min_element(begin(X),end(X)); x1 < x2; x1+=h) {
double y = Func(ak,bk,ck,dk,ek,x1);
Функция -> AddXY(x1,y);
}
a->Text = "";
b->Text = "";
c->Text = "";
d->Text = "";
e->Text = "";
}
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
void __fastcall TForm1::Button8Click(TObject *Sender)
{
Лагранж->Clear();
Ньютон->Clear();
МНК_1->Clear();
МНК_2->Clear();
МНК_3->Clear();
Функция->Clear();
}
//--------------------------------------------------------------------------- |
(
