/// <summary>
/// Method is used to get a minor of the matrix.
/// </summary>
/// <param name="matrix">initial matrix.</param>
/// <param name="rowIndex">Row index to exclude.</param>
/// <param name="columnIndex">Column index to exclude</param>
/// <returns></returns>
public static MatrixT <T> GetMinor(MatrixT <T> matrix, int rowIndex, int columnIndex)
{
MatrixT <T> result = new MatrixT <T>(matrix.Rows - 1, matrix.Columns - 1);
int ki = 0;
for (int i = 0; i < matrix.Rows; i++)
{
if (i != rowIndex)
{
for (int j = 0, kj = 0; j < matrix.Columns; j++)
{
if (j != columnIndex)
{
result[ki, kj] = matrix[i, j];
kj++;
}
}
ki++;
}
}
return(result);
}
private void SortRows(MatrixT <double> matrix, ref double[] rightPart, int sortIndex)
{
double maxElement = matrix[sortIndex, sortIndex];
int maxElementIndex = sortIndex;
for (int i = sortIndex + 1; i < this.Matrix.Rows; i++)
{
if (matrix[i, sortIndex] > maxElement)
{
maxElement = matrix[i, sortIndex];
maxElementIndex = i;
}
}
if (maxElement > sortIndex)
{
double temp;
temp = rightPart[maxElementIndex];
rightPart[maxElementIndex] = rightPart[sortIndex];
rightPart[sortIndex] = temp;
for (int i = 0; i < this.Matrix.Columns; i++)
{
temp = matrix[maxElementIndex, i];
matrix[maxElementIndex, i] = matrix[sortIndex, i];
matrix[sortIndex, i] = temp;
}
}
}
/// <summary>
/// Summarizing operator overloading.
/// </summary>
/// <param name="A">Left operand.</param>
/// <param name="B">Right operand.</param>
/// <returns>The result of summarizing operator.</returns>
public static MatrixT <T> operator +(MatrixT <T> A, MatrixT <T> B)
{
if (Paral)
{
MatrixT <T> ans = new MatrixT <T>(new T[A.Elements.GetLength(0), A.Elements.GetLength(1)]);
Parallel.For(0, A.Elements.GetLength(0), (i) =>
{
for (int j = 0; j < A.Elements.GetLength(1); j++)
{
ans.Elements[i, j] = (dynamic)(A.Elements[i, j]) + (dynamic)(B.Elements[i, j]);
}
});
return(ans);
}
else
{
MatrixT <T> ans = new MatrixT <T>(new T[A.Elements.GetLength(0), A.Elements.GetLength(1)]);
for (int i = 0; i < A.Elements.GetLength(0); i++)
{
for (int j = 0; j < A.Elements.GetLength(1); j++)
{
ans.Elements[i, j] = (dynamic)(A.Elements[i, j]) + (dynamic)(B.Elements[i, j]);
}
}
return(ans);
}
}
/// <summary>
/// Method is used to get a determinant of the required matrix.
/// </summary>
/// <param name="matrix">Initial matrix to get determinant.</param>
/// <returns>Matrix determinant.</returns>
public static double GetMatrixDeterminant(MatrixT <T> matrix)
{
if (matrix.Elements.Length == 1)
{
return((dynamic)matrix[0, 0]);
}
if (matrix.Elements.Length == 4)
{
return((dynamic)matrix[0, 0] * (dynamic)matrix[1, 1] - (dynamic)matrix[0, 1] * (dynamic)matrix[1, 0]);
}
double sign = 1;
double result = 0;
for (int i = 0; i < matrix.Elements.GetLength(1); i++)
{
T[,] minor = MatrixT <T> .GetMinor(matrix.Elements, i);
result += sign * (dynamic)matrix[0, i] * GetMatrixDeterminant(new MatrixT <T>(minor));
sign = -sign;
}
return(result);
}
private LAEAnswer CalculateKramerMethodAsync(out List <LAEVariable> lAEVariables)
{
bool systemCompatible = this.CheckLinearAlgebraicEquationSystemCompatibility();
if (!systemCompatible)
{
lAEVariables = null;
return(LAEAnswer.NoSolutions);
}
double matrixDeterminant = MatrixT <double> .GetMatrixDeterminant(this.Matrix);
ConcurrentBag <LAEVariable> result = new ConcurrentBag <LAEVariable>();
Parallel.For(0, this.Matrix.Columns, (i) =>
{
MatrixT <double> currentMatrix = MatrixT <double> .SubstituteMatrixColumn(this.Matrix, i, this.RightPartEquations);
double currentDeterminant = MatrixT <double> .GetMatrixDeterminant(currentMatrix);
result.Add(new LAEVariable(this.Variables[i].Name, currentDeterminant / matrixDeterminant));
});
lAEVariables = result.Cast <LAEVariable>().ToList();
return(LAEAnswer.OneSolution);
}
/// <summary>
/// Method is used to get matrix rang.
/// </summary>
/// <param name="matrix">Initial matrix to get its rang.</param>
/// <returns>Matrix rang.</returns>
public static int GetRang(MatrixT <T> matrix)
{
int rank = 0;
int q = 1;
while (q <= MatrixT <int> .GetMinValue(matrix.Elements.GetLength(0), matrix.Elements.GetLength(1)))
{
MatrixT <T> matbv = new MatrixT <T>(q, q);
for (int i = 0; i < (matrix.Elements.GetLength(0) - (q - 1)); i++)
{
for (int j = 0; j < (matrix.Elements.GetLength(1) - (q - 1)); j++)
{
for (int k = 0; k < q; k++)
{
for (int c = 0; c < q; c++)
{
matbv[k, c] = matrix[i + k, j + c];
}
}
if (MatrixT <T> .GetMatrixDeterminant(matbv) != 0)
{
rank = q;
}
}
}
q++;
}
return(rank);
}
private LAEAnswer CalculateKramerMethod(out List <LAEVariable> lAEVariables)
{
bool systemCompatible = this.CheckLinearAlgebraicEquationSystemCompatibility();
if (!systemCompatible)
{
lAEVariables = null;
return(LAEAnswer.NoSolutions);
}
double matrixDeterminant = MatrixT <double> .GetMatrixDeterminant(this.Matrix);
List <LAEVariable> result = new List <LAEVariable>();
for (int i = 0; i < this.Matrix.Columns; i++)
{
MatrixT <double> currentMatrix = MatrixT <double> .SubstituteMatrixColumn(this.Matrix, i, this.RightPartEquations);
double currentDeterminant = MatrixT <double> .GetMatrixDeterminant(currentMatrix);
result.Add(new LAEVariable(this.Variables[i].Name, currentDeterminant / matrixDeterminant));
}
lAEVariables = result;
return(LAEAnswer.OneSolution);
}
/// <summary>
/// Method is used to transpone the required matrix.
/// </summary>
/// <param name="matrix">Initial matrix.</param>
/// <returns>Transponed matrix of the initial one.</returns>
public static MatrixT <T> TransponeMatrix(MatrixT <T> matrix)
{
MatrixT <T> result = new MatrixT <T>(matrix.Columns, matrix.Rows);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
result[j, i] = matrix[i, j];
}
}
return(result);
}
/// <summary>
/// Method is used to check the compatibility of linear algebraic equation system.
/// </summary>
/// <returns>The flag which represents if this system is compatibile</returns>
public bool CheckLinearAlgebraicEquationSystemCompatibility()
{
int matrixRank = MatrixT <double> .GetRang(this.Matrix);
MatrixT <double> extendedMatrix = MatrixT <double> .ExtendMatrix(this.Matrix, this.RightPartEquations.ToArray());
int extendedMatrixRank = MatrixT <double> .GetRang(extendedMatrix);
if (matrixRank == extendedMatrixRank)
{
return(true);
}
return(false);
}
public static void CopyMatrixItems(MatrixT <T> sourceMatrix, MatrixT <T> destinationMatrix)
{
if (sourceMatrix.Columns != destinationMatrix.Columns ||
sourceMatrix.Rows != destinationMatrix.Rows)
{
throw new ArgumentException("Matrixes don't have the same amount of rows and columns!");
}
for (int i = 0; i < sourceMatrix.Rows; i++)
{
for (int j = 0; j < sourceMatrix.Columns; j++)
{
destinationMatrix[i, j] = sourceMatrix[i, j];
}
}
}
/// <summary>
/// Method is used to add one column to a matrix.
/// </summary>
/// <param name="matrix">Initial matrix.</param>
/// <param name="extension">Extra column which will be added.</param>
/// <returns>The extended matrix.</returns>
public static MatrixT <T> ExtendMatrix(MatrixT <T> matrix, T[] extension)
{
MatrixT <T> result = new MatrixT <T>(matrix.Rows, matrix.Columns + 1);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
result[i, j] = matrix[i, j];
}
result[i, result.Columns - 1] = extension[i];
}
return(result);
}
/// <summary>
/// Method is used to set a basis for a scpecified matrix.
/// </summary>
/// <param name="matrix">The matrix to set a basis there.</param>
public static void SetBaseMatrix(MatrixT <T> matrix)
{
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
if (i == j)
{
matrix[i, j] = (dynamic)1;
}
else
{
matrix[i, j] = (dynamic)0;
}
}
}
}
private LAEAnswer CalculateMatrixMethod(out List <LAEVariable> lAEVariables)
{
bool systemCompatible = this.CheckLinearAlgebraicEquationSystemCompatibility();
if (!systemCompatible)
{
lAEVariables = null;
return(LAEAnswer.NoSolutions);
}
MatrixT <double> inversedMatrix = MatrixT <double> .GetInverseMatrix(this.Matrix);
MatrixT <double> resultMatrix = inversedMatrix * new MatrixT <double>(this.RightPartEquations.ToArray());
lAEVariables = LAEVariable.FillLAEVariablesWithMatrix(resultMatrix, this.Variables);
return(LAEAnswer.OneSolution);
}
internal static List <LAEVariable> FillLAEVariablesWithMatrix <T>(MatrixT <T> matrix, List <Variable> lAEVariables)
{
if (matrix != null && matrix.Columns == 1 && matrix.Rows == lAEVariables.Count)
{
List <LAEVariable> result = new List <LAEVariable>();
for (int i = 0; i < lAEVariables.Count; i++)
{
result.Add(new LAEVariable(lAEVariables[i].Name, (dynamic)matrix[i, 0]));
}
return(result);
}
else
{
throw new ArgumentException("Inapropriate matrix to fill the list of variables!");
}
}
/// <summary>
/// Method is used to substitute matrix column with other values.
/// </summary>
/// <param name="matrix">Initial matrix for substitution.</param>
/// <param name="columnIndex">Index of a column which will be substituted.</param>
/// <param name="newColumn">New values of the column.</param>
/// <returns></returns>
public static MatrixT <T> SubstituteMatrixColumn(MatrixT <T> matrix, int columnIndex, List <T> newColumn)
{
if (newColumn.Count != matrix.Rows)
{
throw new ArgumentException($"Amount of matrix rows: {matrix.Rows} and amount of matrix columns: {newColumn.Count}");
}
MatrixT <T> result = new MatrixT <T>(matrix.Rows, matrix.Columns);
MatrixT <T> .CopyMatrixItems(matrix, result);
for (int i = 0; i < result.Rows; i++)
{
result[i, columnIndex] = newColumn[i];
}
return(result);
}
public static void PrintMatrix(MatrixT <T> matrix, StreamWriter streamWriter = null)
{
if (streamWriter == null)
{
streamWriter = new StreamWriter(Console.OpenStandardOutput());
streamWriter.AutoFlush = true;
Console.SetOut(streamWriter);
}
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
streamWriter.Write($"{matrix[i, j]} ");
}
streamWriter.WriteLine();
}
}
/// <summary>
/// Multiplication by a number overloading.
/// </summary>
/// <param name="a">Number to multiply a matrix.</param>
/// <param name="B">Matrix which will be multiplied.</param>
/// <returns>The result of multiplication by a number.</returns>
public static MatrixT <T> operator *(dynamic a, MatrixT <T> B)
{
Type type = a.GetType();
bool isNumber = (type.IsPrimitive && type != typeof(bool) && type != typeof(char));
if (isNumber)
{
MatrixT <T> result = new MatrixT <T>(B.Rows, B.Columns);
for (int i = 0; i < B.Rows; i++)
{
for (int j = 0; j < B.Columns; j++)
{
result[i, j] = B[i, j] * a;
}
}
return(result);
}
throw new ArgumentException($"Cannot multiply the matrix by a number {a}.");
}
/// <summary>
/// Method describes two matrixes equation process.
/// </summary>
/// <param name="obj">Matrix to compare.</param>
/// <returns>Flag if two matrixes are equal.</returns>
public override bool Equals(object obj)
{
MatrixT <T> inputMatrix = (MatrixT <T>)obj;
if (this.Columns != inputMatrix.Columns || this.Rows != inputMatrix.Rows)
{
return(false);
}
for (int i = 0; i < this.Rows; i++)
{
for (int j = 0; j < this.Columns; j++)
{
if ((dynamic)this.Elements[i, j] != (dynamic)inputMatrix[i, j])
{
return(false);
}
}
}
return(true);
}
/// <summary>
/// Method is used to take inversed matrix.
/// </summary>
/// <param name="matrix">Initial matrix.</param>
/// <returns>Inversed matrix.</returns>
public static MatrixT <T> GetInverseMatrix(MatrixT <T> matrix)
{
double determinant = MatrixT <T> .GetMatrixDeterminant(matrix);
if (determinant != 0)
{
MatrixT <T> reversedMatrix = new MatrixT <T>(matrix.Rows, matrix.Columns);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
MatrixT <T> tempMatrix = MatrixT <T> .GetMinor(matrix, i, j);
reversedMatrix[i, j] = (dynamic)Math.Pow(-1.0, i + j + 2) * (dynamic)MatrixT <T> .GetMatrixDeterminant(tempMatrix) / (dynamic)determinant;
}
}
return(MatrixT <T> .TransponeMatrix(reversedMatrix));
}
return(null);
}
/// <summary>
/// Multiplication operator overloading.
/// </summary>
/// <param name="A">Left operand.</param>
/// <param name="B">Right operand.</param>
/// <returns>The result of multiplication operand.</returns>
public static MatrixT <T> operator *(MatrixT <T> A, MatrixT <T> B)
{
if (Paral)
{
MatrixT <T> ans = new MatrixT <T>(new T[A.Elements.GetLength(0), B.Elements.GetLength(1)]);
Parallel.For(0, A.Elements.GetLength(0), (i) =>
{
for (int j = 0; j < B.Elements.GetLength(1); j++)
{
ans.Elements[i, j] = (dynamic)0;
for (int k = 0; k < A.Elements.GetLength(1); k++)
{
ans.Elements[i, j] += (dynamic)A.Elements[i, k] * (dynamic)B.Elements[k, j];
}
}
});
return(ans);
}
else
{
MatrixT <T> ans = new MatrixT <T>(new T[A.Elements.GetLength(0), B.Elements.GetLength(1)]);
for (int i = 0; i < A.Elements.GetLength(0); i++)
{
for (int j = 0; j < B.Elements.GetLength(1); j++)
{
ans.Elements[i, j] = (dynamic)0;
for (int k = 0; k < A.Elements.GetLength(1); k++)
{
ans.Elements[i, j] += (dynamic)A.Elements[i, k] * (dynamic)B.Elements[k, j];
}
}
}
return(ans);
}
}
/// <summary>
/// Method is used to set matrix of linear alebraic equation system.
/// </summary>
/// <param name="leftEquationsParts">parts of the left equations system.</param>
/// <param name="variables">LAE system variables.</param>
/// <param name="constants">LAE system constants.</param>
/// <returns>matrix of the relevant linear alebraic equation system.</returns>
private static MatrixT <double> SetMatrix(List <Expression> leftEquationsParts, List <Variable> variables, List <Variable> constants)
{
MatrixT <double> result = new MatrixT <double>(leftEquationsParts.Count, variables.Count);
for (int i = 0; i < leftEquationsParts.Count; i++)
{
for (int j = 0; j < variables.Count; j++)
{
List <Variable> currentVariables = variables;
LinearAlgebraicEquationSystem.SetVariablesWithValues(currentVariables, 0);
currentVariables[j].Value = 1.0;
if (constants != null && constants.Count > 0)
{
currentVariables.AddRange(constants);
}
result[i, j] = leftEquationsParts[i].GetResultValue(currentVariables);
}
}
return(result);
}
private LAEAnswer CalculateGaussMethod(out List <LAEVariable> results)
{
results = null;
MatrixT <double> currentMatrix = new MatrixT <double>(this.Matrix.Rows, this.Matrix.Columns);
MatrixT <double> .CopyMatrixItems(this.Matrix, currentMatrix);
double[] rightPart = new double[this.RightPartEquations.Count];
for (int i = 0; i < this.RightPartEquations.Count; i++)
{
rightPart[i] = this.RightPartEquations[i];
}
double[] answer = new double[this.Variables.Count];
if (currentMatrix.Rows != currentMatrix.Columns)
{
results = null;
return(LAEAnswer.NoSolutions);
}
for (int i = 0; i < currentMatrix.Rows - 1; i++)
{
SortRows(currentMatrix, ref rightPart, i);
for (int j = i + 1; j < currentMatrix.Rows; j++)
{
if (currentMatrix[i, i] != 0)
{
double multElement = currentMatrix[j, i] / currentMatrix[i, i];
for (int k = i; k < currentMatrix.Columns; k++)
{
currentMatrix[j, k] -= currentMatrix[i, k] * multElement;
}
rightPart[j] -= rightPart[i] * multElement;
}
}
}
for (int i = currentMatrix.Rows - 1; i >= 0; i--)
{
answer[i] = rightPart[i];
for (int j = currentMatrix.Rows - 1; j > i; j--)
{
answer[i] -= currentMatrix[i, j] * answer[j];
}
if (currentMatrix[i, i] == 0)
{
if (rightPart[i] == 0)
{
return(LAEAnswer.ManySolutions);
}
else
{
return(LAEAnswer.NoSolutions);
}
}
answer[i] /= currentMatrix[i, i];
}
results = new List <LAEVariable>();
for (int i = 0; i < this.Variables.Count; i++)
{
results.Add(new LAEVariable(this.Variables[i].Name, answer[i]));
}
return(LAEAnswer.OneSolution);
}
/// <summary>
/// Method is used to take inversed matrix.
/// </summary>
/// <param name="matrix">Initial matrix.</param>
/// <returns>Inversed matrix.</returns>
public static MatrixT <T> GetInverseMatrix3(MatrixT <T> matrix)
{
if (matrix.Columns == matrix.Rows)
{
if (MatrixT <T> .GetMatrixDeterminant(matrix) != 0.0)
{
MatrixT <T> matrixCopy = new MatrixT <T>(matrix.Rows, matrix.Columns);
for (int i = 0; i < matrix.Rows; i++)
{
for (int j = 0; j < matrix.Columns; j++)
{
matrixCopy[i, j] = matrix[i, j];
}
}
MatrixT <T> reverseMatrix = new MatrixT <T>(matrix.Rows, matrix.Columns);
MatrixT <T> .SetBaseMatrix(reverseMatrix);
for (int k = 0; k < matrix.Rows; k++)
{
T div = matrixCopy[k, k];
for (int m = 0; m < matrix.Columns; m++)
{
matrixCopy[k, m] /= (dynamic)div;
reverseMatrix[k, m] /= (dynamic)div;
}
for (int i = k + 1; i < matrix.Rows; i++)
{
T multi = matrixCopy[i, k];
for (int j = 0; j < matrix.Columns; j++)
{
matrixCopy[i, j] -= (dynamic)multi * (dynamic)matrixCopy[k, j];
reverseMatrix[i, j] -= (dynamic)multi * (dynamic)reverseMatrix[i, j];
}
}
}
for (int kk = matrix.Rows - 1; kk > 0; kk--)
{
matrixCopy[kk, matrix.Columns - 1] /= (dynamic)matrixCopy[kk, kk];
reverseMatrix[kk, matrix.Columns - 1] /= (dynamic)matrixCopy[kk, kk];
for (int i = kk - 1; i + 1 > 0; i--)
{
T multi2 = matrixCopy[i, kk];
for (int j = 0; j < matrix.Columns; j++)
{
matrixCopy[i, j] -= (dynamic)multi2 * (dynamic)matrixCopy[kk, j];
reverseMatrix[i, j] -= (dynamic)multi2 * (dynamic)reverseMatrix[kk, j];
}
}
}
return(MatrixT <T> .TransponeMatrix(reverseMatrix));
}
}
return(null);
}