gemlq(3)

NAME
gemlq - gemlq: multiply by Q from gelq

SYNOPSIS

  Functions

subroutine cgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
CGEMLQ
subroutine dgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
DGEMLQ
subroutine sgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
SGEMLQ
subroutine zgemlq (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info)
ZGEMLQ

Detailed Description

Function Documentation

  subroutine cgemlq (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CGEMLQ

Purpose:

    !>
    !>     CGEMLQ overwrites the general real M-by-N matrix C with
    !>
    !>                      SIDE = 'L'     SIDE = 'R'
    !>      TRANS = 'N':      Q * C          C * Q
    !>      TRANS = 'C':      Q**H * C       C * Q**H
    !>      where Q is a complex unitary matrix defined as the product
    !>      of blocked elementary reflectors computed by short wide
    !>      LQ factorization (CGELQ)
    !>
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left;
    !>          = 'R': apply Q or Q**H from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Conjugate transpose, apply Q**H.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          Part of the data structure to represent Q as returned by CGELQ.
    !>

    LDA

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

    T

    !>          T is COMPLEX array, dimension (MAX(5,TSIZE)).
    !>          Part of the data structure to represent Q as returned by CGELQ.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          The dimension of the array T. TSIZE >= 5.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          (workspace) COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1, then a workspace query is assumed. The routine
    !>          only calculates the size of the WORK array, returns this
    !>          value as WORK(1), and no error message related to WORK
    !>          is issued by XERBLA.
    !>

    INFO

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details

    !>
    !> These details are particular for this LAPACK implementation. Users should not
    !> take them for granted. These details may change in the future, and are not likely
    !> true for another LAPACK implementation. These details are relevant if one wants
    !> to try to understand the code. They are not part of the interface.
    !>
    !> In this version,
    !>
    !>          T(2): row block size (MB)
    !>          T(3): column block size (NB)
    !>          T(6:TSIZE): data structure needed for Q, computed by
    !>                           CLASWQR or CGELQT
    !>
    !>  Depending on the matrix dimensions M and N, and row and column
    !>  block sizes MB and NB returned by ILAENV, CGELQ will use either
    !>  CLASWLQ (if the matrix is wide-and-short) or CGELQT to compute
    !>  the LQ factorization.
    !>  This version of CGEMLQ will use either CLAMSWLQ or CGEMLQT to
    !>  multiply matrix Q by another matrix.
    !>  Further Details in CLAMSWLQ or CGEMLQT.
    !>

  subroutine dgemlq (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DGEMLQ

Purpose:

    !>
    !>     DGEMLQ overwrites the general real M-by-N matrix C with
    !>
    !>                    SIDE = 'L'     SIDE = 'R'
    !>    TRANS = 'N':      Q * C          C * Q
    !>    TRANS = 'T':      Q**T * C       C * Q**T
    !>    where Q is a real orthogonal matrix defined as the product
    !>    of blocked elementary reflectors computed by short wide LQ
    !>    factorization (DGELQ)
    !>
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left;
    !>          = 'R': apply Q or Q**T from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'T':  Transpose, apply Q**T.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          Part of the data structure to represent Q as returned by DGELQ.
    !>

    LDA

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

    T

    !>          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)).
    !>          Part of the data structure to represent Q as returned by DGELQ.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          The dimension of the array T. TSIZE >= 5.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1, then a workspace query is assumed. The routine
    !>          only calculates the size of the WORK array, returns this
    !>          value as WORK(1), and no error message related to WORK
    !>          is issued by XERBLA.
    !>

    INFO

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details

    !>
    !> These details are particular for this LAPACK implementation. Users should not
    !> take them for granted. These details may change in the future, and are not likely
    !> true for another LAPACK implementation. These details are relevant if one wants
    !> to try to understand the code. They are not part of the interface.
    !>
    !> In this version,
    !>
    !>          T(2): row block size (MB)
    !>          T(3): column block size (NB)
    !>          T(6:TSIZE): data structure needed for Q, computed by
    !>                           DLASWLQ or DGELQT
    !>
    !>  Depending on the matrix dimensions M and N, and row and column
    !>  block sizes MB and NB returned by ILAENV, DGELQ will use either
    !>  DLASWLQ (if the matrix is wide-and-short) or DGELQT to compute
    !>  the LQ factorization.
    !>  This version of DGEMLQ will use either DLAMSWLQ or DGEMLQT to
    !>  multiply matrix Q by another matrix.
    !>  Further Details in DLAMSWLQ or DGEMLQT.
    !>

  subroutine sgemlq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SGEMLQ

Purpose:

    !>
    !>     SGEMLQ overwrites the general real M-by-N matrix C with
    !>
    !>                    SIDE = 'L'     SIDE = 'R'
    !>    TRANS = 'N':      Q * C          C * Q
    !>    TRANS = 'T':      Q**T * C       C * Q**T
    !>    where Q is a real orthogonal matrix defined as the product
    !>    of blocked elementary reflectors computed by short wide LQ
    !>    factorization (SGELQ)
    !>
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left;
    !>          = 'R': apply Q or Q**T from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'T':  Transpose, apply Q**T.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is REAL array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          Part of the data structure to represent Q as returned by SGELQ.
    !>

    LDA

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

    T

    !>          T is REAL array, dimension (MAX(5,TSIZE)).
    !>          Part of the data structure to represent Q as returned by SGELQ.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          The dimension of the array T. TSIZE >= 5.
    !>

    C

    !>          C is REAL array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1, then a workspace query is assumed. The routine
    !>          only calculates the size of the WORK array, returns this
    !>          value as WORK(1), and no error message related to WORK
    !>          is issued by XERBLA.
    !>

    INFO

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details

    !>
    !> These details are particular for this LAPACK implementation. Users should not
    !> take them for granted. These details may change in the future, and are not likely
    !> true for another LAPACK implementation. These details are relevant if one wants
    !> to try to understand the code. They are not part of the interface.
    !>
    !> In this version,
    !>
    !>          T(2): row block size (MB)
    !>          T(3): column block size (NB)
    !>          T(6:TSIZE): data structure needed for Q, computed by
    !>                           SLASWLQ or SGELQT
    !>
    !>  Depending on the matrix dimensions M and N, and row and column
    !>  block sizes MB and NB returned by ILAENV, SGELQ will use either
    !>  SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
    !>  the LQ factorization.
    !>  This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
    !>  multiply matrix Q by another matrix.
    !>  Further Details in SLAMSWLQ or SGEMLQT.
    !>

  subroutine zgemlq (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZGEMLQ

Purpose:

    !>
    !>     ZGEMLQ overwrites the general real M-by-N matrix C with
    !>
    !>                      SIDE = 'L'     SIDE = 'R'
    !>      TRANS = 'N':      Q * C          C * Q
    !>      TRANS = 'C':      Q**H * C       C * Q**H
    !>      where Q is a complex unitary matrix defined as the product
    !>      of blocked elementary reflectors computed by short wide
    !>      LQ factorization (ZGELQ)
    !>
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left;
    !>          = 'R': apply Q or Q**H from the Right.
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N':  No transpose, apply Q;
    !>          = 'C':  Conjugate transpose, apply Q**H.
    !>

    M

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

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix C. N >= 0.
    !>

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>
    !>

    A

    !>          A is COMPLEX*16 array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          Part of the data structure to represent Q as returned by ZGELQ.
    !>

    LDA

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

    T

    !>          T is COMPLEX*16 array, dimension (MAX(5,TSIZE)).
    !>          Part of the data structure to represent Q as returned by ZGELQ.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          The dimension of the array T. TSIZE >= 5.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC,N)
    !>          On entry, the M-by-N matrix C.
    !>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1, then a workspace query is assumed. The routine
    !>          only calculates the size of the WORK array, returns this
    !>          value as WORK(1), and no error message related to WORK
    !>          is issued by XERBLA.
    !>

    INFO

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details

    !>
    !> These details are particular for this LAPACK implementation. Users should not
    !> take them for granted. These details may change in the future, and are not likely
    !> true for another LAPACK implementation. These details are relevant if one wants
    !> to try to understand the code. They are not part of the interface.
    !>
    !> In this version,
    !>
    !>          T(2): row block size (MB)
    !>          T(3): column block size (NB)
    !>          T(6:TSIZE): data structure needed for Q, computed by
    !>                           ZLASWLQ or ZGELQT
    !>
    !>  Depending on the matrix dimensions M and N, and row and column
    !>  block sizes MB and NB returned by ILAENV, ZGELQ will use either
    !>  ZLASWLQ (if the matrix is wide-and-short) or ZGELQT to compute
    !>  the LQ factorization.
    !>  This version of ZGEMLQ will use either ZLAMSWLQ or ZGEMLQT to
    !>  multiply matrix Q by another matrix.
    !>  Further Details in ZLAMSWLQ or ZGEMLQT.
    !>

Author

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