/// <summary>
/// Explicitly creates the matrix Q1, which consists of the first n columns of the orthogonal matrix Q that resulted
/// from the factorization: A = Q * R = [Q1, Q2] * [R1; 0] (Matlab notation) = Q1 * R1,
/// where A is m-by-n, Q is m-by-m, R is m-by-n, Q1 is m-by-n and R1 is (n-by-n).
/// This method is safe to use as the factorization data are copied (if necessary). However, it is inefficient if the
/// generated matrix is only used once.
/// </summary>
public Matrix GetEconomyFactorQ()
{
if (NumRows < NumColumns)
{
throw new NotImplementedException("For now, the number of rows must be >= the number of columns");
}
int m = NumRows;
int n = NumColumns;
int k = NumColumns;
int ldA = m;
var matrixQ = new double[NumRows * NumColumns];
Array.Copy(reflectorsAndR, matrixQ, matrixQ.Length);
// Call Lapack
int numRowsQ = NumRows;
int numColsQ = NumColumns;
int numReflectors = NumColumns;
int leadingDimQ = numRowsQ;
LapackLeastSquares.Dorgqr(numRowsQ, numColsQ, numReflectors, matrixQ, 0, leadingDimQ, reflectorScalars, 0);
return(Matrix.CreateFromArray(matrixQ, NumRows, NumColumns, false));
}
/// <summary>
/// Explicitly creates the orthogonal matrix Q that resulted from the factorization: A = Q * R, where A is m-by-n,
/// Q is m-by-m and R is m-by-n.
/// This method is safe to use as the factorization data are copied (if necessary). However, it is inefficient if the
/// generated matrix is only used once.
/// </summary>
public Matrix GetFactorQ()
{
if (NumRows < NumColumns)
{
throw new NotImplementedException("For now, the number of rows must be >= the number of columns");
}
// We need a larger buffer for Q (m-by-m) > reflectorsAndR (m-by-p)
double[] matrixQ = ArrayColMajor.ResizeCols(NumRows, NumColumns, NumRows, reflectorsAndR);
// Call Lapack
int numRowsQ = NumRows;
int numColsQ = numRowsQ;
int numReflectors = NumColumns;
int leadingDimQ = numRowsQ;
LapackLeastSquares.Dorgqr(numRowsQ, numColsQ, numReflectors, matrixQ, 0, leadingDimQ, reflectorScalars, 0);
return(Matrix.CreateFromArray(matrixQ, NumRows, NumRows, false));
}