Function rgsl::linear_algebra::QRPT_decomp

pub fn QRPT_decomp(
    a: &mut MatrixF64,
    tau: &mut VectorF64,
    p: &mut Permutation,
    signum: &mut i32,
    norm: &mut VectorF64
) -> Value

This function factorizes the M-by-N matrix A into the QRP^T decomposition A = Q R P^T. On output the diagonal and upper triangular part of the input matrix contain the matrix R. The permutation matrix P is stored in the permutation p. The sign of the permutation is given by signum. It has the value (-1)^n, where n is the number of interchanges in the permutation. The vector tau and the columns of the lower triangular part of the matrix A contain the Householder coefficients and vectors which encode the orthogonal matrix Q. The vector tau must be of length k=\min(M,N). The matrix Q is related to these components by, Q = Q_k … Q_2 Q_1 where Q_i = I - \tau_i v_i v_i^T and v_i is the Householder vector v_i = (0,…,1,A(i+1,i),A(i+2,i),…,A(m,i)). This is the same storage scheme as used by LAPACK. The vector norm is a workspace of length N used for column pivoting.

The algorithm used to perform the decomposition is Householder QR with column pivoting (Golub & Van Loan, Matrix Computations, Algorithm 5.4.1).