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

NAME
       SRC/stzrzf.f

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

Function/Subroutine Documentation
   subroutine stzrzf (integer m, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( * ) tau, real, dimension( * ) work,
       integer lwork, integer info)
       STZRZF

       Purpose:


           !>
           !> STZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
           !> to upper triangular form by means of orthogonal transformations.
           !>
           !> The upper trapezoidal matrix A is factored as
           !>
           !>    A = ( R  0 ) * Z,
           !>
           !> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
           !> triangular matrix.
           !>

       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 >= M.
           !>

           A

           !>          A is REAL array, dimension (LDA,N)
           !>          On entry, the leading M-by-N upper trapezoidal part of the
           !>          array A must contain the matrix to be factorized.
           !>          On exit, the leading M-by-M upper triangular part of A
           !>          contains the upper triangular matrix R, and elements M+1 to
           !>          N of the first M rows of A, with the array TAU, represent the
           !>          orthogonal matrix Z as a product of M elementary reflectors.
           !>

           LDA

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

           TAU

           !>          TAU is REAL array, dimension (M)
           !>          The scalar factors of the elementary reflectors.
           !>

           WORK

           !>          WORK is REAL 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 >= max(1,M).
           !>          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.

       Contributors:
           A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:


           !>
           !>  The N-by-N matrix Z can be computed by
           !>
           !>     Z =  Z(1)*Z(2)* ... *Z(M)
           !>
           !>  where each N-by-N Z(k) is given by
           !>
           !>     Z(k) = I - tau(k)*v(k)*v(k)**T
           !>
           !>  with v(k) is the kth row vector of the M-by-N matrix
           !>
           !>     V = ( I   A(:,M+1:N) )
           !>
           !>  I is the M-by-M identity matrix, A(:,M+1:N)
           !>  is the output stored in A on exit from STZRZF,
           !>  and tau(k) is the kth element of the array TAU.
           !>
           !>

       Definition at line 150 of file stzrzf.f.

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