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      SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
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*
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*  -- LAPACK routine (version 3.2.2) --
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*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
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*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*     June 2010
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*
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*     .. Scalar Arguments ..
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      INTEGER            L, LDA, M, N
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*     ..
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*     .. Array Arguments ..
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      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
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*  [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z, by means
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*  of orthogonal transformations.  Z is an (M+L)-by-(M+L) orthogonal
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*  matrix and, R and A1 are M-by-M upper triangular matrices.
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*
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*  Arguments
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*  =========
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*
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*  M       (input) INTEGER
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*          The number of rows of the matrix A.  M >= 0.
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*
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*  N       (input) INTEGER
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*          The number of columns of the matrix A.  N >= 0.
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*
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*  L       (input) INTEGER
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*          The number of columns of the matrix A containing the
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*          meaningful part of the Householder vectors. N-M >= L >= 0.
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*
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*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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*          On entry, the leading M-by-N upper trapezoidal part of the
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*          array A must contain the matrix to be factorized.
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*          On exit, the leading M-by-M upper triangular part of A
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*          contains the upper triangular matrix R, and elements N-L+1 to
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*          N of the first M rows of A, with the array TAU, represent the
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*          orthogonal matrix Z as a product of M elementary reflectors.
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*
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*  LDA     (input) INTEGER
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*          The leading dimension of the array A.  LDA >= max(1,M).
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*
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*  TAU     (output) DOUBLE PRECISION array, dimension (M)
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*          The scalar factors of the elementary reflectors.
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*
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*  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
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*
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*  Further Details
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*  ===============
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*
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*  Based on contributions by
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*    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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*
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*  The factorization is obtained by Householder's method.  The kth
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*  transformation matrix, Z( k ), which is used to introduce zeros into
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*  the ( m - k + 1 )th row of A, is given in the form
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*
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*     Z( k ) = ( I     0   ),
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*              ( 0  T( k ) )
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*
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*  where
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*
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*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
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*                                                 (   0    )
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*                                                 ( z( k ) )
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*
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*  tau is a scalar and z( k ) is an l element vector. tau and z( k )
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*  are chosen to annihilate the elements of the kth row of A2.
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*
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*  The scalar tau is returned in the kth element of TAU and the vector
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*  u( k ) in the kth row of A2, such that the elements of z( k ) are
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*  in  a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
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*  the upper triangular part of A1.
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*
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*  Z is given by
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*
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*     Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
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*
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*  =====================================================================
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*
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*     .. Parameters ..
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      DOUBLE PRECISION   ZERO
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      PARAMETER          ( ZERO = 0.0D+0 )
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*     ..
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*     .. Local Scalars ..
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      INTEGER            I
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*     ..
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*     .. External Subroutines ..
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      EXTERNAL           DLARFG, DLARZ
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input arguments
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*
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*     Quick return if possible
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*
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      IF( M.EQ.0 ) THEN
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         RETURN
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      ELSE IF( M.EQ.N ) THEN
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         DO 10 I = 1, N
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            TAU( I ) = ZERO
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   10    CONTINUE
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         RETURN
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      END IF
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*
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      DO 20 I = M, 1, -1
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*
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*        Generate elementary reflector H(i) to annihilate
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*        [ A(i,i) A(i,n-l+1:n) ]
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*
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         CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) )
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*
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*        Apply H(i) to A(1:i-1,i:n) from the right
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*
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         CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
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     $               TAU( I ), A( 1, I ), LDA, WORK )
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*
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   20 CONTINUE
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*
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      RETURN
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*
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*     End of DLATRZ
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*
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      END