gelq(3)

NAME
gelq - gelq: LQ factor, flexible

SYNOPSIS

  Functions

subroutine cgelq (m, n, a, lda, t, tsize, work, lwork, info)
CGELQ
subroutine dgelq (m, n, a, lda, t, tsize, work, lwork, info)
DGELQ
subroutine sgelq (m, n, a, lda, t, tsize, work, lwork, info)
SGELQ
subroutine zgelq (m, n, a, lda, t, tsize, work, lwork, info)
ZGELQ

Detailed Description

Function Documentation

  subroutine cgelq (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) t, integer tsize, complex, dimension( * ) work, integer lwork, integer info)

CGELQ

Purpose:

    !>
    !> CGELQ computes an LQ factorization of a complex M-by-N matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a N-by-N orthogonal matrix;
    !>    L is a lower-triangular M-by-M matrix;
    !>    0 is a M-by-(N-M) zero matrix, if M < N.
    !>
    !>

Parameters
    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 A.  N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and below the diagonal of the array
    !>          contain the M-by-min(M,N) lower trapezoidal matrix L
    !>          (L is lower triangular if M <= N);
    !>          the elements above the diagonal are used to store part of the
    !>          data structure to represent Q.
    !>

    LDA

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

    T

    !>          T is COMPLEX array, dimension (MAX(5,TSIZE))
    !>          On exit, if INFO = 0, T(1) returns optimal (or either minimal
    !>          or optimal, if query is assumed) TSIZE. See TSIZE for details.
    !>          Remaining T contains part of the data structure used to represent Q.
    !>          If one wants to apply or construct Q, then one needs to keep T
    !>          (in addition to A) and pass it to further subroutines.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          If TSIZE >= 5, the dimension of the array T.
    !>          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If TSIZE = -1, the routine calculates optimal size of T for the
    !>          optimum performance and returns this value in T(1).
    !>          If TSIZE = -2, the routine calculates minimal size of T and
    !>          returns this value in T(1).
    !>

    WORK

    !>          (workspace) COMPLEX array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
    !>          or optimal, if query was assumed) LWORK.
    !>          See LWORK for details.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If LWORK = -1, the routine calculates optimal size of WORK for the
    !>          optimal performance and returns this value in WORK(1).
    !>          If LWORK = -2, the routine calculates minimal size of WORK and
    !>          returns this value in WORK(1).
    !>

    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

    !>
    !> The goal of the interface is to give maximum freedom to the developers for
    !> creating any LQ factorization algorithm they wish. The triangular
    !> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
    !> and the array T can be used to store any relevant information for applying or
    !> constructing the Q factor. The WORK array can safely be discarded after exit.
    !>
    !> Caution: One should not expect the sizes of T and WORK to be the same from one
    !> LAPACK implementation to the other, or even from one execution to the other.
    !> A workspace query (for T and WORK) is needed at each execution. However,
    !> for a given execution, the size of T and WORK are fixed and will not change
    !> from one query to the next.
    !>
    !>

Further Details particular to this LAPACK implementation:

    !>
    !> 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
    !>                           CLASWLQ 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 short-and-wide) or CGELQT to compute
    !>  the LQ factorization.
    !>

  subroutine dgelq (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) t, integer tsize, double precision, dimension( * ) work, integer lwork, integer info)

DGELQ

Purpose:

    !>
    !> DGELQ computes an LQ factorization of a real M-by-N matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a N-by-N orthogonal matrix;
    !>    L is a lower-triangular M-by-M matrix;
    !>    0 is a M-by-(N-M) zero matrix, if M < N.
    !>
    !>

Parameters
    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 A.  N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and below the diagonal of the array
    !>          contain the M-by-min(M,N) lower trapezoidal matrix L
    !>          (L is lower triangular if M <= N);
    !>          the elements above the diagonal are used to store part of the
    !>          data structure to represent Q.
    !>

    LDA

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

    T

    !>          T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
    !>          On exit, if INFO = 0, T(1) returns optimal (or either minimal
    !>          or optimal, if query is assumed) TSIZE. See TSIZE for details.
    !>          Remaining T contains part of the data structure used to represent Q.
    !>          If one wants to apply or construct Q, then one needs to keep T
    !>          (in addition to A) and pass it to further subroutines.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          If TSIZE >= 5, the dimension of the array T.
    !>          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If TSIZE = -1, the routine calculates optimal size of T for the
    !>          optimum performance and returns this value in T(1).
    !>          If TSIZE = -2, the routine calculates minimal size of T and
    !>          returns this value in T(1).
    !>

    WORK

    !>          (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
    !>          or optimal, if query was assumed) LWORK.
    !>          See LWORK for details.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If LWORK = -1, the routine calculates optimal size of WORK for the
    !>          optimal performance and returns this value in WORK(1).
    !>          If LWORK = -2, the routine calculates minimal size of WORK and
    !>          returns this value in WORK(1).
    !>

    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

    !>
    !> The goal of the interface is to give maximum freedom to the developers for
    !> creating any LQ factorization algorithm they wish. The triangular
    !> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
    !> and the array T can be used to store any relevant information for applying or
    !> constructing the Q factor. The WORK array can safely be discarded after exit.
    !>
    !> Caution: One should not expect the sizes of T and WORK to be the same from one
    !> LAPACK implementation to the other, or even from one execution to the other.
    !> A workspace query (for T and WORK) is needed at each execution. However,
    !> for a given execution, the size of T and WORK are fixed and will not change
    !> from one query to the next.
    !>
    !>

Further Details particular to this LAPACK implementation:

    !>
    !> 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 short-and-wide) or DGELQT to compute
    !>  the LQ factorization.
    !>

  subroutine sgelq (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) t, integer tsize, real, dimension( * ) work, integer lwork, integer info)

SGELQ

Purpose:

    !>
    !> SGELQ computes an LQ factorization of a real M-by-N matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a N-by-N orthogonal matrix;
    !>    L is a lower-triangular M-by-M matrix;
    !>    0 is a M-by-(N-M) zero matrix, if M < N.
    !>
    !>

Parameters
    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 A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and below the diagonal of the array
    !>          contain the M-by-min(M,N) lower trapezoidal matrix L
    !>          (L is lower triangular if M <= N);
    !>          the elements above the diagonal are used to store part of the
    !>          data structure to represent Q.
    !>

    LDA

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

    T

    !>          T is REAL array, dimension (MAX(5,TSIZE))
    !>          On exit, if INFO = 0, T(1) returns optimal (or either minimal
    !>          or optimal, if query is assumed) TSIZE. See TSIZE for details.
    !>          Remaining T contains part of the data structure used to represent Q.
    !>          If one wants to apply or construct Q, then one needs to keep T
    !>          (in addition to A) and pass it to further subroutines.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          If TSIZE >= 5, the dimension of the array T.
    !>          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If TSIZE = -1, the routine calculates optimal size of T for the
    !>          optimum performance and returns this value in T(1).
    !>          If TSIZE = -2, the routine calculates minimal size of T and
    !>          returns this value in T(1).
    !>

    WORK

    !>          (workspace) REAL array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
    !>          or optimal, if query was assumed) LWORK.
    !>          See LWORK for details.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If LWORK = -1, the routine calculates optimal size of WORK for the
    !>          optimal performance and returns this value in WORK(1).
    !>          If LWORK = -2, the routine calculates minimal size of WORK and
    !>          returns this value in WORK(1).
    !>

    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

    !>
    !> The goal of the interface is to give maximum freedom to the developers for
    !> creating any LQ factorization algorithm they wish. The triangular
    !> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
    !> and the array T can be used to store any relevant information for applying or
    !> constructing the Q factor. The WORK array can safely be discarded after exit.
    !>
    !> Caution: One should not expect the sizes of T and WORK to be the same from one
    !> LAPACK implementation to the other, or even from one execution to the other.
    !> A workspace query (for T and WORK) is needed at each execution. However,
    !> for a given execution, the size of T and WORK are fixed and will not change
    !> from one query to the next.
    !>
    !>

Further Details particular to this LAPACK implementation:

    !>
    !> 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 short-and-wide) or SGELQT to compute
    !>  the LQ factorization.
    !>

  subroutine zgelq (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) t, integer tsize, complex*16, dimension( * ) work, integer lwork, integer info)

ZGELQ

Purpose:

    !>
    !> ZGELQ computes an LQ factorization of a complex M-by-N matrix A:
    !>
    !>    A = ( L 0 ) *  Q
    !>
    !> where:
    !>
    !>    Q is a N-by-N orthogonal matrix;
    !>    L is a lower-triangular M-by-M matrix;
    !>    0 is a M-by-(N-M) zero matrix, if M < N.
    !>
    !>

Parameters
    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 A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and below the diagonal of the array
    !>          contain the M-by-min(M,N) lower trapezoidal matrix L
    !>          (L is lower triangular if M <= N);
    !>          the elements above the diagonal are used to store part of the
    !>          data structure to represent Q.
    !>

    LDA

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

    T

    !>          T is COMPLEX*16 array, dimension (MAX(5,TSIZE))
    !>          On exit, if INFO = 0, T(1) returns optimal (or either minimal
    !>          or optimal, if query is assumed) TSIZE. See TSIZE for details.
    !>          Remaining T contains part of the data structure used to represent Q.
    !>          If one wants to apply or construct Q, then one needs to keep T
    !>          (in addition to A) and pass it to further subroutines.
    !>

    TSIZE

    !>          TSIZE is INTEGER
    !>          If TSIZE >= 5, the dimension of the array T.
    !>          If TSIZE = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If TSIZE = -1, the routine calculates optimal size of T for the
    !>          optimum performance and returns this value in T(1).
    !>          If TSIZE = -2, the routine calculates minimal size of T and
    !>          returns this value in T(1).
    !>

    WORK

    !>          (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
    !>          or optimal, if query was assumed) LWORK.
    !>          See LWORK for details.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= 1.
    !>          If LWORK = -1 or -2, then a workspace query is assumed. The routine
    !>          only calculates the sizes of the T and WORK arrays, returns these
    !>          values as the first entries of the T and WORK arrays, and no error
    !>          message related to T or WORK is issued by XERBLA.
    !>          If LWORK = -1, the routine calculates optimal size of WORK for the
    !>          optimal performance and returns this value in WORK(1).
    !>          If LWORK = -2, the routine calculates minimal size of WORK and
    !>          returns this value in WORK(1).
    !>

    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

    !>
    !> The goal of the interface is to give maximum freedom to the developers for
    !> creating any LQ factorization algorithm they wish. The triangular
    !> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
    !> and the array T can be used to store any relevant information for applying or
    !> constructing the Q factor. The WORK array can safely be discarded after exit.
    !>
    !> Caution: One should not expect the sizes of T and WORK to be the same from one
    !> LAPACK implementation to the other, or even from one execution to the other.
    !> A workspace query (for T and WORK) is needed at each execution. However,
    !> for a given execution, the size of T and WORK are fixed and will not change
    !> from one query to the next.
    !>
    !>

Further Details particular to this LAPACK implementation:

    !>
    !> 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 short-and-wide) or ZGELQT to compute
    !>  the LQ factorization.
    !>

Author

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