SRC/dgeqr2p.f(3)           Library Functions Manual           SRC/dgeqr2p.f(3)

NAME
       SRC/dgeqr2p.f

SYNOPSIS
   Functions/Subroutines
       subroutine dgeqr2p (m, n, a, lda, tau, work, info)
           DGEQR2P computes the QR factorization of a general rectangular
           matrix with non-negative diagonal elements using an unblocked
           algorithm.

Function/Subroutine Documentation
   subroutine dgeqr2p (integer m, integer n, double precision, dimension( lda,
       * ) a, integer lda, double precision, dimension( * ) tau, double
       precision, dimension( * ) work, integer info)
       DGEQR2P computes the QR factorization of a general rectangular matrix
       with non-negative diagonal elements using an unblocked algorithm.

       Purpose:


           !>
           !> DGEQR2P computes a QR factorization of a real m-by-n matrix A:
           !>
           !>    A = Q * ( R ),
           !>            ( 0 )
           !>
           !> where:
           !>
           !>    Q is a m-by-m orthogonal matrix;
           !>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
           !>    entries;
           !>    0 is a (m-n)-by-n zero matrix, if m > n.
           !>
           !>

       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, 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 diagonal entries of R are
           !>          nonnegative; the elements below the diagonal,
           !>          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 DOUBLE PRECISION array, dimension (min(M,N))
           !>          The scalar factors of the elementary reflectors (see Further
           !>          Details).
           !>

           WORK

           !>          WORK is DOUBLE PRECISION array, dimension (N)
           !>

           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(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).
           !>
           !> See Lapack Working Note 203 for details
           !>

       Definition at line 133 of file dgeqr2p.f.

Author
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LAPACK                          Version 3.12.0                SRC/dgeqr2p.f(3)