NAME

       dtzrzf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
           DTZRZF

Function/Subroutine Documentation

   subroutine dtzrzf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
       double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK,
       integerINFO)
       DTZRZF

       Purpose:

            DTZRZF 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M)
                     The scalar factors of the elementary reflectors.

           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 >= 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.

       Date:
           April 2012

       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 DTZRZF,
             and tau(k) is the kth element of the array TAU.

       Definition at line 152 of file dtzrzf.f.

Author

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