Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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.
                     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.
                     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.
                     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.
                     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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