Generate a Real orthogonal matrix Q which is defined as the product of elementary reflectors as returned from dgeqrf

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This information is part of the Modelica Standard Library maintained by the Modelica Association.

Lapack documentation

    DORGQR generates an M-by-N real matrix Q with orthonormal columns,
    which is defined as the first N columns of a product of K elementary
    reflectors of order M

          Q  =  H(1) H(2) . . . H(k)

    as returned by DGEQRF.


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

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

    K       (input) INTEGER
            The number of elementary reflectors whose product defines the
            matrix Q. N >= K >= 0.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the i-th column must contain the vector which
            defines the elementary reflector H(i), for i = 1,2,...,k, as
            returned by DGEQRF in the first k columns of its array
            argument A.
            On exit, the M-by-N matrix Q.

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

    TAU     (input) DOUBLE PRECISION array, dimension (K)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEQRF.

    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 >= max(1,N).
            For optimum performance LWORK >= N*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 has an illegal value


(Q, info) = dorgqr(QR, tau)

Inputs (2)


Type: Real[:,:]

Description: QR from dgeqrf


Type: Real[min(size(QR, 1), size(QR, 2))]

Description: The scalar factors of the elementary reflectors of Q

Outputs (2)


Default Value: QR

Type: Real[size(QR, 1),size(QR, 2)]

Description: Orthogonal matrix Q


Type: Integer