SRC/sgerq2.f(3)            Library Functions Manual            SRC/sgerq2.f(3)

NAME
       SRC/sgerq2.f

SYNOPSIS
   Functions/Subroutines
       subroutine sgerq2 (m, n, a, lda, tau, work, info)
           SGERQ2 computes the RQ factorization of a general rectangular
           matrix using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine sgerq2 (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer info)
       SGERQ2 computes the RQ factorization of a general rectangular matrix
       using an unblocked algorithm.

       Purpose:


           !>
           !> SGERQ2 computes an RQ factorization of a real m by n matrix A:
           !> A = R * Q.
           !>

       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, if m <= n, the upper triangle of the subarray
           !>          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
           !>          if m >= n, the elements on and above the (m-n)-th subdiagonal
           !>          contain the m by n upper trapezoidal matrix R; the remaining
           !>          elements, with the array TAU, represent the orthogonal matrix
           !>          Q as a product of elementary reflectors (see Further
           !>          Details).
           !>

           LDA

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

           TAU

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

           WORK

           !>          WORK is REAL array, dimension (M)
           !>

           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 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
           !>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
           !>

       Definition at line 122 of file sgerq2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/sgerq2.f(3)