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StrongerProgrammer7StrongerProgrammer7
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Newton's interpolation polynomial
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‎InterpolationNewton/InterpolationNewton.cpp‎

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#include <iostream>
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#include <iomanip>
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#include <vector>
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#include <fstream>
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#include <cmath>
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#define PI 3.14159265358979323846
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using namespace std;
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void read_dataFile(vector <double>& , vector<double>& );
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void Newton(vector <double> , vector <double>);
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void Input_Decidee();
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double function(double);
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void printVector(vector<vector<double>>, int );
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int main()
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{
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setlocale(LC_ALL, "russian");
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cout << " \t\t\tИнтерполяционный полином Ньютона\n";
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for (int i = 0; i < 80; i++)
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cout << "-";
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vector <double>x, y;
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cout << "\n 1. Считать данные с файла.\n"
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" 2. Ввести данные в ручную.\n";
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int chose = 0;
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cin >> chose;
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switch (chose)
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{
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case 1:
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cout << " В файле должно быть следующие расположение: X Y[X]\n";
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read_dataFile(x, y);
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Newton(x, y);
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break;
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case 2:
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Input_Decidee();
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break;
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default:
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break;
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}
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}
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void read_dataFile(vector <double>& x, vector<double>& y)
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{
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ifstream file("data.txt");
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if (!file.is_open())
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{
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cout << "Файла не существует.";
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return;
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}
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double temp = 0;
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while (!file.eof())
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{
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file >> temp;
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x.push_back(temp);
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file >> temp;
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y.push_back(temp);
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}
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file.close();
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}
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void Newton(vector <double> x, vector <double>y)
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{
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vector<vector<double>> dy; // аналог двумерный динамический массив
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double h=0; //шаг
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h = (x[1] - x[0]);
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for (unsigned i = 0; i < x.size(); ++i)
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cout << "x[" << i << "] = " << x[i] << "\t" << "y[" << x[i] << "] = " << y[i] << endl;
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int maxIndex = x.size() - 1;
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dy.resize(maxIndex);
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for (int i = 0; i < maxIndex; i++)
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{
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dy[i].resize(maxIndex);
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for (int j = 0; j < maxIndex; j++)
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dy[i][j] = 0;
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}
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//Первые конечные разности
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for (int i = 0; i < maxIndex; i++)
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dy[i][0] = y[i + 1] - y[i];
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//Вторые
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for (int j = 1; j < maxIndex; j++)
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{
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for (int i = 0; i < maxIndex - j; i++) // потому что идем лестницей
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dy[i][j] = dy[i + 1][j - 1] - dy[i][j - 1];
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}
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cout << endl;
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printVector(dy,maxIndex);
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double x0 = PI / 9;
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cout << " \n Ввести свое значения x или задать приближенное?(0/1): ";
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bool flag = false; cin >> flag;
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if (flag == false)
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{
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cin >> x0;
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}
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double mult = 1;
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double sum = y[0];
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double q = (x0 - x[0]) / h;
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int factorial = 1;
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for (int i = 0; i < maxIndex; i++)
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{
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mult *= (q - i);
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factorial *= i + 1;
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sum += mult * dy[0][i] / (factorial);
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}
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cout << "\n Первая формула Ньютона: " << setprecision(5) << sum << endl;
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q = (x0 - x[maxIndex]) / h;
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sum = y[maxIndex];
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mult = 1;
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factorial = 1;
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for (int i = 0; i < maxIndex; i++)
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{
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mult *= (q + i);
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factorial *= i+1;
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sum += mult * dy[maxIndex - i - 1][i] / (factorial); // по мнимой диагонали
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}
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cout << "\n Вторая формула Ньютона: " << setprecision(5) << sum << endl;
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}
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void Input_Decidee()
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{
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vector<double> x, y;
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cout << " Укажите количество точек: ";
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int n; cin >> n;
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for (int i = 0; i < n; i++)
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{
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double temp = 0;
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cin >> temp;
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x.push_back(temp);
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y.push_back(function(temp));
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}
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system("cls");
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cout << endl;
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Newton(x, y);
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}
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double function(double x)
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{
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return cos(x)* sqrt(x);//sin(x)* x;
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}
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void printVector(vector<vector<double>> V,int maxIndex)
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{
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for (int i = 0; i < maxIndex; i++)
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{
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for (int j = 0; j < maxIndex; j++)
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cout << V[i][j] << setprecision(4) << " ";
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cout << endl;
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}
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}

‎InterpolationNewton/InterpolationNewton.sln‎

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Microsoft Visual Studio Solution File, Format Version 12.00
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# Visual Studio Version 16
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VisualStudioVersion = 16.0.28803.202
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MinimumVisualStudioVersion = 10.0.40219.1
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "InterpolationNewton", "InterpolationNewton.vcxproj", "{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}"
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EndProject
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Global
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GlobalSection(SolutionConfigurationPlatforms) = preSolution
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Debug|x64 = Debug|x64
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Debug|x86 = Debug|x86
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Release|x64 = Release|x64
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Release|x86 = Release|x86
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EndGlobalSection
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GlobalSection(ProjectConfigurationPlatforms) = postSolution
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Debug|x64.ActiveCfg = Debug|x64
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Debug|x64.Build.0 = Debug|x64
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Debug|x86.ActiveCfg = Debug|Win32
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Debug|x86.Build.0 = Debug|Win32
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Release|x64.ActiveCfg = Release|x64
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Release|x64.Build.0 = Release|x64
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Release|x86.ActiveCfg = Release|Win32
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{50AA8E0E-E077-436D-9253-C8E13BFD6DC3}.Release|x86.Build.0 = Release|Win32
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EndGlobalSection
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GlobalSection(SolutionProperties) = preSolution
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HideSolutionNode = FALSE
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EndGlobalSection
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GlobalSection(ExtensibilityGlobals) = postSolution
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SolutionGuid = {5662B9C4-5D59-4958-94C6-787F78CB952B}
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EndGlobalSection
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EndGlobal

‎InterpolationNewton/InterpolationNewton.vcxproj‎

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‎InterpolationNewton/InterpolationNewton.vcxproj.filters‎

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‎InterpolationNewton/InterpolationNewton.vcxproj.user‎

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‎InterpolationNewton/data.txt‎

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0 0
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2 -0.6
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4 -1.2
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6 2.4
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8 -0.3
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10 -2.9

‎InterpolationNewton/data1.txt‎

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0 0
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0.5235987 0.5
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1.0471975 0.8660254
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1.5707963 1
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2.0943951 0.8660254

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