GELQ - 5.2 English - 68552

Computes LQ factorization of a real matrix.

Purpose:

 GELQ 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 an lower-triangular M-by-M matrix;
 0 is a M-by-(N-M) zero matrix, if M < N.

Parameters:

• M – [in]

  M is INTEGER

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

• N – [in]

  N is INTEGER

  The number of columns of the matrix A. N >= 0.

• A – [inout]

  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 - computes row and column scaling to reduce condition number of matrix

• LDA – [in]

  LDA is INTEGER

  The leading dimension of the array A. LDA >= fla_max(1,M).

• T – [out]

  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 – [in]

  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 – [out]

  (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 – [in]

  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 – [out]

  INFO is INTEGER

  = 0: successful exit

  < 0: if INFO = -i, the i-th argument had an illegal value