SGEQR2(3)      LAPACK routine of NEC Numeric Library Collection      SGEQR2(3)



NAME
       SGEQR2

SYNOPSIS
       SUBROUTINE SGEQR2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            SGEQR2 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 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 (N)

           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                      SGEQR2(3)