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

NAME
       SRC/dgerqf.f

SYNOPSIS
   Functions/Subroutines
       subroutine dgerqf (m, n, a, lda, tau, work, lwork, info)
           DGERQF

Function/Subroutine Documentation
   subroutine dgerqf (integer m, integer n, double precision, dimension( lda,
       * ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer lwork, integer info)
       DGERQF

       Purpose:


           !>
           !> DGERQF 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 DOUBLE PRECISION 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 min(m,n) elementary
           !>          reflectors (see Further Details).
           !>

           LDA

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

           TAU

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

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
           !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
           !>

           LWORK

           !>          LWORK is INTEGER
           !>          The dimension of the array WORK.
           !>          LWORK >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
           !>          For optimum performance LWORK >= M*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

           !>          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 138 of file dgerqf.f.

Author
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LAPACK                          Version 3.12.0                 SRC/dgerqf.f(3)