ungqr(3)

NAME
ungqr - {un,or}gqr: generate explicit Q from geqrf

SYNOPSIS

  Functions

subroutine cungqr (m, n, k, a, lda, tau, work, lwork, info)
CUNGQR
subroutine dorgqr (m, n, k, a, lda, tau, work, lwork, info)
DORGQR
subroutine sorgqr (m, n, k, a, lda, tau, work, lwork, info)
SORGQR
subroutine zungqr (m, n, k, a, lda, tau, work, lwork, info)
ZUNGQR

Detailed Description

Function Documentation

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

CUNGQR

Purpose:

    !>
    !> CUNGQR generates an M-by-N complex 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 CGEQRF.
    !>

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. M >= N >= 0.
    !>

    K

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

    A

    !>          A is COMPLEX 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 CGEQRF in the first k columns 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 CGEQRF.
    !>

    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,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

    !>          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 dorgqr (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)

DORGQR

Purpose:

    !>
    !> 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.
    !>

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. M >= N >= 0.
    !>

    K

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

    A

    !>          A is 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

    !>          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 DGEQRF.
    !>

    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,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

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

SORGQR

Purpose:

    !>
    !> SORGQR 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 SGEQRF.
    !>

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. M >= N >= 0.
    !>

    K

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

    A

    !>          A is REAL 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 SGEQRF in the first k columns 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 SGEQRF.
    !>

    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,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

    !>          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 zungqr (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)

ZUNGQR

Purpose:

    !>
    !> ZUNGQR generates an M-by-N complex 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 ZGEQRF.
    !>

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. M >= N >= 0.
    !>

    K

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

    A

    !>          A is COMPLEX*16 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 ZGEQRF in the first k columns 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 ZGEQRF.
    !>

    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,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

    !>          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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