ungl2(3)

NAME
ungl2 - {un,or}gl2: generate explicit Q, level 2, step in unglq

SYNOPSIS

  Functions

subroutine cungl2 (m, n, k, a, lda, tau, work, info)
CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
subroutine dorgl2 (m, n, k, a, lda, tau, work, info)
DORGL2
subroutine sorgl2 (m, n, k, a, lda, tau, work, info)
SORGL2
subroutine zungl2 (m, n, k, a, lda, tau, work, info)
ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Detailed Description

Function Documentation

  subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

    !>
    !> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
    !> which is defined as the first m rows of a product of k elementary
    !> reflectors of order n
    !>
    !>       Q  =  H(k)**H . . . H(2)**H H(1)**H
    !>
    !> as returned by CGELQF.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix Q. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix Q. N >= M.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines the
    !>          matrix Q. M >= K >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the i-th row must contain the vector which defines
    !>          the elementary reflector H(i), for i = 1,2,...,k, as returned
    !>          by CGELQF in the first k rows of its array argument A.
    !>          On exit, the m by n matrix Q.
    !>

    LDA

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

    TAU

    !>          TAU is COMPLEX array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by CGELQF.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument has an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORGL2

Purpose:

    !>
    !> DORGL2 generates an m by n real matrix Q with orthonormal rows,
    !> which is defined as the first m rows of a product of k elementary
    !> reflectors of order n
    !>
    !>       Q  =  H(k) . . . H(2) H(1)
    !>
    !> as returned by DGELQF.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix Q. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix Q. N >= M.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines the
    !>          matrix Q. M >= K >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the i-th row must contain the vector which defines
    !>          the elementary reflector H(i), for i = 1,2,...,k, as returned
    !>          by DGELQF in the first k rows of its array argument A.
    !>          On exit, the m-by-n matrix Q.
    !>

    LDA

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

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by DGELQF.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument has an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORGL2

Purpose:

    !>
    !> SORGL2 generates an m by n real matrix Q with orthonormal rows,
    !> which is defined as the first m rows of a product of k elementary
    !> reflectors of order n
    !>
    !>       Q  =  H(k) . . . H(2) H(1)
    !>
    !> as returned by SGELQF.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix Q. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix Q. N >= M.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines the
    !>          matrix Q. M >= K >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the i-th row must contain the vector which defines
    !>          the elementary reflector H(i), for i = 1,2,...,k, as returned
    !>          by SGELQF in the first k rows of its array argument A.
    !>          On exit, the m-by-n matrix Q.
    !>

    LDA

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

    TAU

    !>          TAU is REAL array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by SGELQF.
    !>

    WORK

    !>          WORK is REAL array, dimension (M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument has an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

    !>
    !> ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
    !> which is defined as the first m rows of a product of k elementary
    !> reflectors of order n
    !>
    !>       Q  =  H(k)**H . . . H(2)**H H(1)**H
    !>
    !> as returned by ZGELQF.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix Q. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix Q. N >= M.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines the
    !>          matrix Q. M >= K >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the i-th row must contain the vector which defines
    !>          the elementary reflector H(i), for i = 1,2,...,k, as returned
    !>          by ZGELQF in the first k rows of its array argument A.
    !>          On exit, the m by n matrix Q.
    !>

    LDA

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

    TAU

    !>          TAU is COMPLEX*16 array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by ZGELQF.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (M)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument has an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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