private static MatrixNxN <T> CreateMatrixForCramersRule(MatrixNxN <T> matrixFrom, int skipColumn, List <T> equationRightSideResults)
{
var matrix = new MatrixNxN <T>(matrixFrom);
matrix.SetColumn(skipColumn, equationRightSideResults);
return(matrix);
}
/// <summary>
/// Create inverse of matrix.
/// </summary>
/// <returns>Matrix inverse</returns>
public MatrixNxN <T> Inverse()
{
var cofactorMatrix = new MatrixNxN <T>(Rows);
for (int row = 0; row < Rows; row++)
{
for (int column = 0; column < Columns; column++)
{
var submatrix = CreateSubmatrix(this, row, column);
cofactorMatrix[row, column] = (dynamic)submatrix.Determinant() * (int)Math.Pow(-1, row + column);
}
}
return(new MatrixNxN <T>(cofactorMatrix.Transpose() * ((dynamic)1.0 / Determinant())));
}
private static MatrixNxN <T> CreateSubmatrix(MatrixNxN <T> matrix, int skipRow, int skipColumn)
{
var submatrix = new MatrixNxN <T>(matrix.Rows - 1);
var column = 0;
for (int k = 0; k < matrix.Columns; k++)
{
if (k != skipColumn)
{
var columnValues = matrix.GetColumn(k).ToList();
columnValues.RemoveAt(skipRow);
submatrix.SetColumn(column, columnValues);
column++;
}
}
return(submatrix);
}
private static T DeterminantLaPlace(MatrixNxN <T> matrix)
{
if (matrix.Rows == 1) // matrix.Columns == 1
{
return(matrix[0, 0]);
}
if (matrix.Rows == 2) // matrix.Columns == 2
{
var ac = (dynamic)matrix[0, 0] * matrix[1, 1];
var bd = (dynamic)matrix[0, 1] * matrix[1, 0];
return(ac - bd);
}
dynamic determinant = 0;
for (int i = 0; i < matrix.Columns; i++)
{
var submatrix = CreateSubmatrix(matrix, 0, i);
determinant += (int)Math.Pow(-1, i) * (dynamic)matrix[0, i] * submatrix.Determinant();
}
return(determinant);
}
