SGEQRF(3)      LAPACK routine of NEC Numeric Library Collection      SGEQRF(3)



NAME
       SGEQRF

SYNOPSIS
       SUBROUTINE SGEQRF (M, N, A, LDA, TAU, WORK, LWORK, INFO)



PURPOSE
            SGEQRF computes a QR factorization of a real M-by-N matrix A:
            A = Q * R.




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           A         (input/output)
                     A is REAL array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit, the elements on and above the diagonal of the array
                     contain the min(M,N)-by-N upper trapezoidal matrix R (R is
                     upper triangular if m >= n); the elements below the diagonal,
                     with the array TAU, represent the orthogonal matrix Q as a
                     product of min(m,n) elementary reflectors (see Further
                     Details).

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

           TAU       (output)
                     TAU is REAL array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK      (output)
                     WORK is REAL array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.  LWORK >= max(1,N).
                     For optimum performance LWORK >= N*NB, where NB is
                     the optimal blocksize.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

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






FURTHER DETAILS
             The matrix Q is represented as a product of elementary reflectors

                Q = H(1) H(2) . . . H(k), where k = min(m,n).

             Each H(i) has the form

                H(i) = I - tau * v * v**T

             where tau is a real scalar, and v is a real vector with
             v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
             and tau in TAU(i).



LAPACK routine                  31 October 2017                      SGEQRF(3)