dorghr

Generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD

Information

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

Lapack documentation
    Purpose
    =======

    DORGHR generates a real orthogonal matrix Q which is defined as the
    product of IHI-ILO elementary reflectors of order N, as returned by
    DGEHRD:

    Q = H(ilo) H(ilo+1) . . . H(ihi-1).

    Arguments
    =========

    N       (input) INTEGER
            The order of the matrix Q. N >= 0.

    ILO     (input) INTEGER
    IHI     (input) INTEGER
            ILO and IHI must have the same values as in the previous call
            of DGEHRD. Q is equal to the unit matrix except in the
            submatrix Q(ilo+1:ihi,ilo+1:ihi).
            1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

    A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
            On entry, the vectors which define the elementary reflectors,
            as returned by DGEHRD.
            On exit, the N-by-N orthogonal matrix Q.

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

    TAU     (input) DOUBLE PRECISION array, dimension (N-1)
            TAU(i) must contain the scalar factor of the elementary
            reflector H(i), as returned by DGEHRD.

    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 >= IHI-ILO.
            For optimum performance LWORK >= (IHI-ILO)*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

Syntax

(Aout, info) = dorghr(A, ilo, ihi, tau)

Inputs (4)

A

Type: Real[:,size(A, 1)]

Description: Square matrix with the elementary reflectors

ilo

Default Value: 1

Type: Integer

Description: Lowest index where the original matrix is not in upper triangular form - ilo must have the same value as in the previous call of DGEHRD

ihi

Default Value: size(A, 1)

Type: Integer

Description: Highest index where the original matrix is not in upper triangular form - ihi must have the same value as in the previous call of DGEHRD

tau

Type: Real[max(0, size(A, 1) - 1)]

Description: Scalar factors of the elementary reflectors

Outputs (2)

Aout

Default Value: A

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

Description: Orthogonal matrix as a result of elementary reflectors

info

Type: Integer