/// <summary>
/// The full gauss with swapping rows and columns of equation.
/// </summary>
/// <param name="matrix">
/// The matrix.
/// </param>
/// <param name="vector">
/// The vector.
/// </param>
/// <typeparam name="T">
/// </typeparam>
/// <returns>
/// The <see cref="MyMatrix{T}"/>.
/// </returns>
public static MyMatrix <T> FullGauss <T>(MyMatrix <T> matrix, MyMatrix <T> vector)
where T : Value <T>, new()
{
var m = new MyMatrix <T>(matrix);
var v = new MyMatrix <T>(vector);
int[] columnsLocations = Enumerable.Range(0, vector.Height).ToArray();
for (int i = 0; i < vector.Height; i++)
{
#if DEBUG
Console.WriteLine($"Full GAUSS: ROW:{i}/{vector.Height}");
#endif
int rowToSwap = i;
int columnToSwap = i;
// Select best column and row to swap.
for (int j = i + 1; j < vector.Height; j++)
{
for (int k = i; k < matrix.Width; k++)
{
if (m[j, k].Absolute() > m[rowToSwap, columnToSwap].Absolute())
{
rowToSwap = j;
columnToSwap = k;
}
}
}
if (rowToSwap != i || columnToSwap != i)
{
// Swap information about columns for future reading result.
columnsLocations.Swap(columnToSwap, i);
// Swap rows and columns
m.SwapRows(rowToSwap, i);
m.SwapColumns(columnToSwap, i);
v.SwapRows(rowToSwap, i);
}
CreateStep(m, v, i);
}
// Retrieve result and sort it according to the columns locations
var result = RetrieveResult(m, v);
var originalResult = new MyMatrix <T>(result);
for (int j = 0; j < v.Height; j++)
{
originalResult[columnsLocations[j], 0] = result[j, 0];
}
return(originalResult);
}
/// <summary>
/// For given row create step with zeros on left.
/// </summary>
/// <param name="matrix">
/// The matrix.
/// </param>
/// <param name="vector">
/// The vector.
/// </param>
/// <param name="row">
/// The row.
/// </param>
/// <typeparam name="T">
/// </typeparam>
private static void CreateStep <T>(MyMatrix <T> matrix, MyMatrix <T> vector, int row)
where T : Value <T>, new()
{
for (var i = row + 1; i < vector.Height; i++)
{
var multiplier = matrix[i, row] / matrix[row, row];
vector[i, 0] = vector[i, 0] - (multiplier * vector[row, 0]);
for (var j = row; j < vector.Height; j++)
{
matrix[i, j] = matrix[i, j] - (multiplier * matrix[row, j]);
}
}
}
/// <summary>
/// The simple gauss solving algorithm.
/// </summary>
/// <param name="matrix">
/// The matrix.
/// </param>
/// <param name="vector">
/// The vector.
/// </param>
/// <typeparam name="T">
/// </typeparam>
/// <returns>
/// The <see cref="MyMatrix{T}"/>.
/// </returns>
public static MyMatrix <T> Gauss <T>(MyMatrix <T> matrix, MyMatrix <T> vector)
where T : Value <T>, new()
{
// Create deep copies of received matrices
var m = new MyMatrix <T>(matrix);
var v = new MyMatrix <T>(vector);
for (var row = 0; row < v.Height; row++)
{
#if DEBUG
Console.WriteLine($"GAUSS: ROW:{row}/{v.Height}");
#endif
CreateStep(m, v, row);
}
return(RetrieveResult(m, v));
}
/// <summary>
/// The retrieve result from stepped matrix.
/// </summary>
/// <param name="matrix">
/// The matrix.
/// </param>
/// <param name="vector">
/// The vector.
/// </param>
/// <typeparam name="T">
/// </typeparam>
/// <returns>
/// The <see cref="MyMatrix{T}"/>.
/// </returns>
private static MyMatrix <T> RetrieveResult <T>(MyMatrix <T> matrix, MyMatrix <T> vector)
where T : Value <T>, new()
{
var resultVector = new MyMatrix <T>(1, vector.Height);
for (var i = vector.Height - 1; i >= 0; i--)
{
Value <T> sum = new T();
for (var j = i + 1; j < vector.Height; j++)
{
sum += matrix[i, j] * resultVector[j, 0];
}
resultVector[i, 0] = (vector[i, 0] - sum) / matrix[i, i];
}
return(resultVector);
}
