unglq(3)

NAME
unglq - {un,or}glq: generate explicit Q from gelqf

SYNOPSIS

  Functions

subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info)
CUNGLQ
subroutine dorglq (m, n, k, a, lda, tau, work, lwork, info)
DORGLQ
subroutine sorglq (m, n, k, a, lda, tau, work, lwork, info)
SORGLQ
subroutine zunglq (m, n, k, a, lda, tau, work, lwork, info)
ZUNGLQ

Detailed Description

Function Documentation

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

CUNGLQ

Purpose:

    !>
    !> CUNGLQ 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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= max(1,M).
    !>          For optimum performance LWORK >= M*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

    !>          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 dorglq (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGLQ

Purpose:

    !>
    !> DORGLQ 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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= max(1,M).
    !>          For optimum performance LWORK >= M*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

    !>          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 sorglq (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGLQ

Purpose:

    !>
    !> SORGLQ 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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= max(1,M).
    !>          For optimum performance LWORK >= M*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

    !>          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 zunglq (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGLQ

Purpose:

    !>
    !> ZUNGLQ 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 (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= max(1,M).
    !>          For optimum performance LWORK >= M*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

    !>          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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