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.

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

  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.