/// <summary>
/// Gets determinant matrix by Kramer algorithm.
/// </summary>
/// <param name="matrix">matrix.</param>
/// <param name="arr">array.</param>
/// <typeparam name="T">unmanaged type.</typeparam>
/// <returns>Gets array x.</returns>
/// <exception cref="MatrixDotNetException">
/// array length not equal matrix rows.
/// </exception>
public static Vectorization.Vector <T> KramerSolve <T>(this Matrix <T> matrix, Vectorization.Vector <T> arr) where T : unmanaged
{
if (matrix.Rows != arr.Length)
{
throw new SizeNotEqualException(ExceptionArgument.RowSizeOfMatrixIsNotEqualSizeOfVector);
}
var det = matrix.GetDeterminant();
var vr = new Vectorization.Vector <T>(matrix.Columns);
if (!(matrix.Clone() is Matrix <T> temp))
{
throw new NullReferenceException();
}
for (int i = 0; i < matrix.Columns; i++)
{
for (int j = 0; j < matrix.Rows; j++)
{
temp[j, i] = arr[j];
}
vr[i] = MathUnsafe <T> .Div(temp.GetDeterminant(), det);
}
return(vr);
}
public static Matrix <T> ProcessGrammShmidtByRows <T>(this Matrix <T> matrix) where T : unmanaged
{
if (!MathGeneric.IsFloatingPoint <T>())
{
throw new NotSupportedTypeException(ExceptionArgument.NotSupportedTypeFloatType);
}
if (!matrix.IsSquare)
{
throw new MatrixDotNetException("matrix is not square");
}
int m = matrix.Rows;
Matrix <T> b = new Matrix <T>(m, matrix.Columns)
{
[0] = matrix[0]
};
for (int i = 1; i < m; i++)
{
Vectorization.Vector <T> ai = matrix[i];
Vectorization.Vector <T> sum = new T[m];
for (int j = 0; j < i; j++)
{
Vectorization.Vector <T> bi = b[j];
T scalarProduct = ai * bi;
T biMul = bi * bi;
T ci = MathGeneric <T> .Divide(scalarProduct, biMul);
sum += ci * bi;
}
var res = ai - sum;
b[i] = res.Array;
}
return(b);
}
