SGELQ computes a LQ factorization of an M-by-N matrix A.

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

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