/// <summary>
/// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an unitary matrix
/// using the modified Gram-Schmidt method.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
public UserGramSchmidt(Matrix <Complex32> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount < matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixDimensions);
}
MatrixQ = matrix.Clone();
MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
for (var k = 0; k < MatrixQ.ColumnCount; k++)
{
var norm = MatrixQ.Column(k).Norm(2).Real;
if (norm == 0.0f)
{
throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
}
MatrixR.At(k, k, norm);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
MatrixQ.At(i, k, MatrixQ.At(i, k) / norm);
}
for (var j = k + 1; j < MatrixQ.ColumnCount; j++)
{
var dot = Complex32.Zero;
for (int i = 0; i < MatrixQ.RowCount; i++)
{
dot += MatrixQ.Column(k)[i].Conjugate() * MatrixQ.Column(j)[i];
}
MatrixR.At(k, j, dot);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot);
MatrixQ.At(i, j, value);
}
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="UserGramSchmidt"/> class. This object creates an orthogonal matrix
/// using the modified Gram-Schmidt method.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
/// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
public UserGramSchmidt(Matrix <float> matrix)
{
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount < matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixDimensions);
}
MatrixQ = matrix.Clone();
MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount);
for (var k = 0; k < MatrixQ.ColumnCount; k++)
{
var norm = MatrixQ.Column(k).Norm(2);
if (norm == 0.0)
{
throw new ArgumentException(Resources.ArgumentMatrixNotRankDeficient);
}
MatrixR.At(k, k, norm);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
MatrixQ.At(i, k, MatrixQ.At(i, k) / norm);
}
for (var j = k + 1; j < MatrixQ.ColumnCount; j++)
{
var dot = MatrixQ.Column(k).DotProduct(MatrixQ.Column(j));
MatrixR.At(k, j, dot);
for (var i = 0; i < MatrixQ.RowCount; i++)
{
var value = MatrixQ.At(i, j) - (MatrixQ.At(i, k) * dot);
MatrixQ.At(i, j, value);
}
}
}
}
