.Modelica.Math.Matrices.LAPACK.dgeqp3

Information

Lapack documentation
    Purpose
    =======

    DGEQP3 computes a QR factorization with column pivoting of a
    matrix A:  A*P = Q*R  using Level 3 BLAS.

    Arguments
    =========

    M       (input) INTEGER
            The number of rows of the matrix A. M >= 0.

    N       (input) INTEGER
            The number of columns of the matrix A.  N >= 0.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the M-by-N matrix A.
            On exit, the upper triangle of the array contains the
            min(M,N)-by-N upper trapezoidal matrix R; the elements below
            the diagonal, together with the array TAU, represent the
            orthogonal matrix Q as a product of min(M,N) elementary
            reflectors.

    LDA     (input) INTEGER
            The leading dimension of the array A. LDA >= max(1,M).

    JPVT    (input/output) INTEGER array, dimension (N)
            On entry, if JPVT(J).ne.0, the J-th column of A is permuted
            to the front of A*P (a leading column); if JPVT(J)=0,
            the J-th column of A is a free column.
            On exit, if JPVT(J)=K, then the J-th column of A*P was the
            the K-th column of A.

    TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
            The scalar factors of the elementary reflectors.

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
            On exit, if INFO=0, WORK(1) returns the optimal LWORK.

    LWORK   (input) INTEGER
            The dimension of the array WORK. LWORK >= 3*N+1.
            For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
            is the optimal blocksize.

            If LWORK = -1, then a workspace query is assumed; the routine
            only calculates the optimal size of the WORK array, returns
            this value as the first entry of the WORK array, and no error
            message related to LWORK is issued by XERBLA.

    INFO    (output) INTEGER
            = 0: successful exit.
            < 0: if INFO = -i, the i-th argument had an illegal value.

    Further Details
    ===============

    The matrix Q is represented as a product of elementary reflectors

       Q = H(1) H(2) . . . H(k), where k = min(m,n).

    Each H(i) has the form

       H(i) = I - tau * v * v'

    where tau is a real/complex scalar, and v is a real/complex vector
    with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
    A(i+1:m,i), and tau in TAU(i).

    Based on contributions by
      G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
      X. Sun, Computer Science Dept., Duke University, USA

Interface

pure function dgeqp3
  extends Modelica.Icons.Function;
  input Real A[:, :] "Square or rectangular matrix";
  input Integer lwork = max(1, 3*size(A, 2) + 1) "Length of work array";
  output Real QR[size(A, 1), size(A, 2)] = A "QR factorization in packed format";
  output Real tau[min(size(A, 1), size(A, 2))] "The scalar factors of the elementary reflectors of Q";
  output Integer p[size(A, 2)] = zeros(size(A, 2)) "Pivot vector";
  output Integer info;
end dgeqp3;