public static Matrix CalculatGivensRotation(Complex a, Complex b)
{
Complex c, s, r;
r = ComplexMath.Sqrt(a.Conjugate() * a + b.Conjugate() * b);
if (b == 0) {
c = 1;
s = 0;
} else if (a == 0) {
c = 0;
s = ComplexMath.Sign(b.Conjugate());
} else {
c = a.Abs() / r;
s = ComplexMath.Sign(a) * b.Conjugate() / r;
}
Matrix givensRot = new Matrix(2);
givensRot[0, 0] = c;
givensRot[0, 1] = s;
givensRot[1, 0] = -s.Conjugate();
givensRot[1, 1] = c;
return givensRot;
}
/// <summary>
/// RowEchelon
/// </summary>
/// <returns> </returns>
public Matrix RowEchelon()
{
var echelon = Elements;
var rows = (int) Rows;
var cols = (int) Cols;
var row = 0;
var col = 0;
for (; row < rows; )
{
var maxPivot = new Complex(0); //echelon[row, col]
//First Leftmost Max Column
var pivotRow = row;
for (var i = row; i < rows; ++i)
{
var pivot = echelon[i, col];
if (!(pivot.Abs() > maxPivot.Abs())) continue;
pivotRow = i;
maxPivot = pivot;
}
if (maxPivot == 0)
{
++col;
if (col == cols) break;
continue;
}
//Interchange rows
if (row != pivotRow)
{
var tmpRow = new Complex[cols];
for (var j = 0; j < cols; ++j) tmpRow[j] = echelon[row, j];
for (var j = 0; j < cols; ++j) echelon[row, j] = echelon[pivotRow, j];
for (var j = 0; j < cols; ++j) echelon[pivotRow, j] = tmpRow[j];
}
//Leading 1
for (var j = col; j < cols; ++j) echelon[row, j] /= maxPivot;
//Leading 0
for (var i = row + 1; i < rows; ++i)
{
var multiple = echelon[i, col];
for (var j = col; j < cols; ++j) echelon[i, j] -= multiple * echelon[row, j];
}
++row;
++col;
}
return new Matrix(echelon);
}
/// <summary>
/// Reduce RowEchelon
/// </summary>
/// <returns> </returns>
public Matrix ReduceRowEchelon()
{
var rechelon = RowEchelon().Elements;
var rows = (int) Rows;
var cols = (int) Cols;
for (var row = rows - 1; row >= 0; --row)
{
var col = 0;
var nonzero = new Complex(0);
//First Leftmost Nonzero Column (Leading 1)
for (; col < cols; ++col)
{
nonzero = rechelon[row, col];
if (Math.Abs(nonzero.Abs() - 0) > EPSILON) break;
}
if (nonzero == 0) continue;
//Trailing 0
for (var i = row - 1; i >= 0; --i)
{
var multiple = rechelon[i, col];
for (uint j = 0; j < cols; ++j) rechelon[i, j] -= multiple * rechelon[row, j];
}
}
return new Matrix(rechelon);
}