internal override bool Check(LinearSystem system)
{
bool check = true;
List <List <double> > A = new List <List <double> >();
List <double> B = new List <double>();
PreCalculations(system, out A, out B);
int rangA = 0, rangB = 0;
for (int i = 0; i < B.Count; i++)
{
if (A[i][i] != 0.0)
{
rangA++;
}
if (B[i] != 0.0)
{
rangB++;
}
}
if (rangA != rangB)
{
check = false;
}
return(check);
}
internal override List <double> FinalCalculations(LinearSystem system)
{
if (Check(system) == true)
{
List <double> x = new List <double>();
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
x.Add(0.0);
}
List <List <double> > A = new List <List <double> >();
List <double> B = new List <double>();
PreCalculations(system, out A, out B);
for (int k = system.NumberOfUnknowns - 1; k >= 0; k--)
{
x[k] = B[k];
for (int i = 0; i < k; i++)
{
B[i] = B[i] - A[i][k] * x[k];
}
}
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
Console.WriteLine($"x{i + 1} = {x[i]}; ");
}
return(x);
}
else
{
Console.WriteLine("System has endless number of solutions or none, please enter another system");
return(null);
}
}
internal override void PreCalculations(LinearSystem system, out List <List <double> > A, out List <double> B)
{
A = new List <List <double> >(system.Coefficients.Count);
for (int i = 0; i < system.Coefficients.Count; i++)
{
List <double> row = new List <double>(system.Coefficients[i]);
A.Add(row);
}
B = new List <double>(system.ConstantTerms);
int k = 0;
double Amax;
while (k < system.NumberOfEquations)
{
Amax = A[k][k];
int p = k;
for (int i = k + 1; i < system.NumberOfEquations; i++)
{
if (Math.Abs(A[i][k]) > Amax)
{
Amax = Math.Abs(A[i][k]);
p = i;
}
}
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
double tempA = A[k][i];
A[k][i] = A[p][i];
A[p][i] = tempA;
}
double temp = B[k];
B[k] = B[p];
B[p] = temp;
temp = A[k][k];
for (int i = 0; i < system.NumberOfEquations; i++)
{
A[k][i] = A[k][i] / temp;
}
B[k] = B[k] / temp;
Console.WriteLine("Converted matrixes on current step: ");
ShowMatrixes(A, B, system.NumberOfEquations, system.NumberOfUnknowns);
Console.WriteLine("");
for (int i = k + 1; i < system.NumberOfEquations; i++)
{
double M = A[i][k];
for (int j = k; j < system.NumberOfEquations; j++)
{
A[i][j] = A[i][j] - M * A[k][j];
}
B[i] = B[i] - M * B[k];
}
Console.WriteLine("Converted matrixes on current step: ");
ShowMatrixes(A, B, system.NumberOfEquations, system.NumberOfUnknowns);
Console.WriteLine("");
k++;
}
} //method that convertes matrixes to triagonal form
//class to output linear system to the screen
public static void Show(LinearSystem system)
{
for (int i = 0; i < system.NumberOfEquations; i++)
{
Console.Write($"{system.Coefficients[i][0]} * x1 ");
for (int j = 1; j < system.NumberOfUnknowns; j++)
{
Console.Write($"+ {system.Coefficients[i][j]} * x{j + 1} ");
}
Console.WriteLine($"= {system.ConstantTerms[i]}");
}
}
internal void OutputResultsToFile(TextWriter w, LinearSystem system, List <double> results, List <double> r) //method to output final results to a file
{
w.WriteLine("System: ");
LinearSystemOperator.FileOutput(system, w);
w.WriteLine("Results: ");
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
w.WriteLine($"x{i + 1} = {results[i]}; ");
}
w.WriteLine("Error: ");
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
w.WriteLine($"Error for x{i + 1} = {r[i]}");
}
}
protected internal List <double> R(LinearSystem system, List <double> results) //method to calculate error //b-A*x
{
List <double> r = new List <double>();
List <double> xA = new List <double>();
Console.WriteLine(" ");
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
xA.Add(0.0);
r.Add(0.0);
for (int j = 0; j < system.NumberOfUnknowns; j++)
{
xA[i] += system.Coefficients[i][j] * results[j];
}
r[i] = system.ConstantTerms[i] - xA[i];
Console.WriteLine($"Error for x{i + 1} = {r[i]}");
}
return(r);
}
public static void FileOutput(LinearSystem system, TextWriter w)
{
try
{
for (int i = 0; i < system.NumberOfEquations; i++)
{
w.Write($"{system.Coefficients[i][0]} * x1 ");
for (int j = 1; j < system.NumberOfUnknowns; j++)
{
w.Write($"+ {system.Coefficients[i][j]} * x{j + 1} ");
}
w.WriteLine($"= {system.ConstantTerms[i]}");
}
}
catch (Exception ex)
{
Console.WriteLine($"{ ex.GetType()} says { ex.Message}");
Console.ReadLine();
}
}
internal override List <double> FinalCalculations(LinearSystem system)
{
if (Check(system) == true)
{
List <double> x = new List <double>();
var A = new List <List <double> >(system.Coefficients.Count);
for (int i = 0; i < system.Coefficients.Count; i++)
{
List <double> row = new List <double>(system.Coefficients[i]);
A.Add(row);
}
var B = new List <double>(system.ConstantTerms);
Console.WriteLine("Coefficients matrix (A):");
ShowMatrixes(A, system.NumberOfUnknowns);
double determinant = Det(A);
Console.WriteLine($"Determinant = {determinant}");
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
List <List <double> > newA = ReplacingColumn(A, B, i);
Console.WriteLine("Converted matrix on current step: ");
ShowMatrixes(newA, system.NumberOfUnknowns);
Console.WriteLine($"Determinant = {Det(newA)}");
x.Add(Det(newA) / determinant);
}
for (int i = 0; i < system.NumberOfUnknowns; i++)
{
Console.WriteLine($"x{i + 1} = {x[i]}; ");
}
return(x);
}
else
{
Console.WriteLine("You can't use this method");
return(null);
}
}
public static LinearSystem Read() //class to input linear system from a file
{
try
{
int n = 0;
int m = 0;
List <List <double> > A = new List <List <double> >();
List <double> B = new List <double>();
Console.WriteLine("Please, enter number of unknowns in your linear system:");
if (Int32.TryParse(Console.ReadLine(), out n))
{
Console.WriteLine("Please, enter number of equations in your linear system:");
if (Int32.TryParse(Console.ReadLine(), out m))
{
Console.WriteLine("Please, start entering coefficients, after you see '=' enter constant term:");
for (int i = 0; i < n; i++)
{
double temp = 0.0;
int consolePosition = 0;
var row = new List <double>();
if (Double.TryParse(Console.ReadLine(), out temp))
{
row.Add(temp);
Console.CursorTop--;
consolePosition += (temp.ToString()).Length;
Console.CursorLeft = consolePosition;
Console.Write($" * x1 + ");
}
else
{
throw new ArgumentException();
}
for (int j = 1; j < m; j++)
{
if (Double.TryParse(Console.ReadLine(), out temp))
{
row.Add(temp);
Console.CursorTop--;
consolePosition += (temp.ToString()).Length + 8;
Console.CursorLeft = consolePosition;
if (j + 1 == m)
{
Console.Write($" * x{j + 1} = ");
}
else
{
Console.Write($" * x{j + 1} + ");
}
}
else
{
throw new ArgumentException();
}
}
if (Double.TryParse(Console.ReadLine(), out temp))
{
B.Add(temp);
}
else
{
throw new ArgumentException();
}
A.Add(row);
}
}
else
{
throw new ArgumentException();
}
}
else
{
throw new ArgumentException();
}
LinearSystem system = new LinearSystem(m, n, A, B);
return(system);
}
catch (ArgumentException)
{
Console.WriteLine("You entered inappropriate value, please follow the instructions!");
LinearSystem system = Read();
return(system);
}
catch (Exception ex)
{
Console.WriteLine($"{ ex.GetType()} says { ex.Message}");
Console.ReadLine();
LinearSystem system = Read();
return(system);
}
}
internal override void PreCalculations(LinearSystem system, out List <List <double> > A, out List <double> B)
{
A = new List <List <double> >(system.Coefficients.Count);
for (int i = 0; i < system.Coefficients.Count; i++)
{
List <double> row = new List <double>(system.Coefficients[i]);
A.Add(row);
}
B = new List <double>(system.ConstantTerms);
double Amax;
int k = 0;
int p;
while (k < system.NumberOfEquations)
{
Amax = Math.Abs(A[k][k]);
p = k;
for (int i = k + 1; i < system.NumberOfEquations; i++)
{
if (Math.Abs(A[i][k]) > Amax)
{
Amax = Math.Abs(A[i][k]);
p = i;
}
}
for (int j = 0; j < system.NumberOfUnknowns; j++)
{
double tempA = A[k][j];
A[k][j] = A[p][j];
A[p][j] = tempA;
}
double tempB = B[k];
B[k] = B[p];
B[p] = tempB;
Console.WriteLine("Converted matrixes on current step: ");
ShowMatrixes(A, B, system.NumberOfEquations, system.NumberOfUnknowns);
Console.WriteLine("");
for (int i = k; i < system.NumberOfEquations; i++)
{
double temp = A[i][k];
if (Math.Abs(temp) == 0.0)
{
continue;
}
for (int j = 0; j < system.NumberOfUnknowns; j++)
{
A[i][j] = A[i][j] / temp;
}
B[i] = B[i] / temp;
if (i == k)
{
continue;
}
for (int j = 0; j < system.NumberOfUnknowns; j++)
{
A[i][j] = A[i][j] - A[k][j];
}
B[i] = B[i] - B[k];
}
Console.WriteLine("Converted matrixes on current step: ");
ShowMatrixes(A, B, system.NumberOfEquations, system.NumberOfUnknowns);
Console.WriteLine("");
k++;
}
}
internal abstract void PreCalculations(LinearSystem system, out List <List <double> > A, out List <double> B);
abstract internal List <double> FinalCalculations(LinearSystem system); //method that does final calculations to find unknowns abstract internal bool Check(LinearSystem system);
abstract internal List <double> FinalCalculations(LinearSystem system); //method that does final calculations to find unknowns
internal override bool Check(LinearSystem system) => (system.NumberOfEquations == system.NumberOfUnknowns && Det(system.Coefficients) != 0);
public static void RunMenu()
{
uint key;
try
{
Console.WriteLine("Hello! This program is designed as a calculator for linear system. This program uses direct methods such as Gauss and Cramer's method." +
"To start using this program you have to enter linear system of equations. Please follow instractions!");
LinearSystem system = LinearSystemOperator.Read();
do
{
Console.WriteLine("Press 1 to show linear system.");
Console.WriteLine("Press 2 to find results using Gauss Method with main element");
Console.WriteLine("Press 3 to find results using Gauss Method with unit diagonal");
Console.WriteLine("Press 4 to find results using Cramer's Method");
Console.WriteLine("Press 5 to enter new linear system");
Console.WriteLine("Press 0 to exit program");
Console.WriteLine("Enter key: ");
key = Convert.ToUInt32(Console.ReadLine());
switch (key)
{
case 1:
{
LinearSystemOperator.Show(system);
break;
}
case 2:
{
LinearSystemOperator.Show(system);
MainElementGaussMethod gaussMethod = new MainElementGaussMethod();
List <double> results = gaussMethod.FinalCalculations(system);
if (results != null)
{
List <double> error = gaussMethod.R(system, results);
Console.WriteLine("Please, enter 1 if you want to save results to file, press enter to go back to menu: ");
if (Int32.TryParse(Console.ReadLine(), out int saveKey) && saveKey == 1)
{
Console.WriteLine("Please, enter name of file: ");
string fileName = Console.ReadLine();
using (StreamWriter w = new StreamWriter(fileName))
{
gaussMethod.OutputResultsToFile(w, system, results, error);
}
}
}
break;
}
case 3:
{
LinearSystemOperator.Show(system);
var gaussMethod = new UnitDiagonalGaussMethod();
List <double> results = gaussMethod.FinalCalculations(system);
if (results != null)
{
List <double> error = gaussMethod.R(system, results);
Console.WriteLine("Please, enter 1 if you want to save results to file, press enter to go back to menu: ");
if (Int32.TryParse(Console.ReadLine(), out int saveKey) && saveKey == 1)
{
Console.WriteLine("Please, enter name of file: ");
string fileName = Console.ReadLine();
using (StreamWriter w = new StreamWriter(fileName))
{
gaussMethod.OutputResultsToFile(w, system, results, error);
}
}
}
break;
}
case 4:
{
LinearSystemOperator.Show(system);
var method = new CramersMethod();
List <double> results = method.FinalCalculations(system);
if (results != null)
{
List <double> error = method.R(system, results);
Console.WriteLine("Please, enter 1 if you want to save results to file, press enter to go back to menu: ");
if (Int32.TryParse(Console.ReadLine(), out int saveKey) && saveKey == 1)
{
Console.WriteLine("Please, enter name of file: ");
string fileName = Console.ReadLine();
using (StreamWriter w = new StreamWriter(fileName))
{
method.OutputResultsToFile(w, system, results, error);
}
}
}
break;
}
case 5:
{
system = LinearSystemOperator.Read();
break;
}
case 0:
break;
}
} while (key != 0);
}
catch (ArgumentException)
{
Console.WriteLine("You entered inappropriate value, the program will restart now, please follow instructions.");
Menu.RunMenu();
}
catch (Exception ex)
{
Console.WriteLine("An error occured during while program was running, please follow instructions");
Console.WriteLine($"{ ex.GetType()} says { ex.Message}");
Menu.RunMenu();
}
}
