numeric-linalg

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*> \brief \b ZGTT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
*                          LDWORK, RWORK, RESID )
*
*       .. Scalar Arguments ..
*       INTEGER            LDWORK, N
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   RWORK( * )
*       COMPLEX*16         D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
*      $                   DU2( * ), DUF( * ), WORK( LDWORK, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGTT01 reconstructs a tridiagonal matrix A from its LU factorization
*> and computes the residual
*>    norm(L*U - A) / ( norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*>          DL is COMPLEX*16 array, dimension (N-1)
*>          The (n-1) sub-diagonal elements of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is COMPLEX*16 array, dimension (N)
*>          The diagonal elements of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*>          DU is COMPLEX*16 array, dimension (N-1)
*>          The (n-1) super-diagonal elements of A.
*> \endverbatim
*>
*> \param[in] DLF
*> \verbatim
*>          DLF is COMPLEX*16 array, dimension (N-1)
*>          The (n-1) multipliers that define the matrix L from the
*>          LU factorization of A.
*> \endverbatim
*>
*> \param[in] DF
*> \verbatim
*>          DF is COMPLEX*16 array, dimension (N)
*>          The n diagonal elements of the upper triangular matrix U from
*>          the LU factorization of A.
*> \endverbatim
*>
*> \param[in] DUF
*> \verbatim
*>          DUF is COMPLEX*16 array, dimension (N-1)
*>          The (n-1) elements of the first super-diagonal of U.
*> \endverbatim
*>
*> \param[in] DU2
*> \verbatim
*>          DU2 is COMPLEX*16 array, dimension (N-2)
*>          The (n-2) elements of the second super-diagonal of U.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices; for 1 <= i <= n, row i of the matrix was
*>          interchanged with row IPIV(i).  IPIV(i) will always be either
*>          i or i+1; IPIV(i) = i indicates a row interchange was not
*>          required.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (LDWORK,N)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*>          LDWORK is INTEGER
*>          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          The scaled residual:  norm(L*U - A) / (norm(A) * EPS)
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE ZGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
     $                   LDWORK, RWORK, RESID )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            LDWORK, N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
     $                   DU2( * ), DUF( * ), WORK( LDWORK, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IP, J, LASTJ
      DOUBLE PRECISION   ANORM, EPS
      COMPLEX*16         LI
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, ZLANGT, ZLANHS
      EXTERNAL           DLAMCH, ZLANGT, ZLANHS
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MIN
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZAXPY, ZSWAP
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( N.LE.0 ) THEN
         RESID = ZERO
         RETURN
      END IF
*
      EPS = DLAMCH( 'Epsilon' )
*
*     Copy the matrix U to WORK.
*
      DO 20 J = 1, N
         DO 10 I = 1, N
            WORK( I, J ) = ZERO
   10    CONTINUE
   20 CONTINUE
      DO 30 I = 1, N
         IF( I.EQ.1 ) THEN
            WORK( I, I ) = DF( I )
            IF( N.GE.2 )
     $         WORK( I, I+1 ) = DUF( I )
            IF( N.GE.3 )
     $         WORK( I, I+2 ) = DU2( I )
         ELSE IF( I.EQ.N ) THEN
            WORK( I, I ) = DF( I )
         ELSE
            WORK( I, I ) = DF( I )
            WORK( I, I+1 ) = DUF( I )
            IF( I.LT.N-1 )
     $         WORK( I, I+2 ) = DU2( I )
         END IF
   30 CONTINUE
*
*     Multiply on the left by L.
*
      LASTJ = N
      DO 40 I = N - 1, 1, -1
         LI = DLF( I )
         CALL ZAXPY( LASTJ-I+1, LI, WORK( I, I ), LDWORK,
     $               WORK( I+1, I ), LDWORK )
         IP = IPIV( I )
         IF( IP.EQ.I ) THEN
            LASTJ = MIN( I+2, N )
         ELSE
            CALL ZSWAP( LASTJ-I+1, WORK( I, I ), LDWORK, WORK( I+1, I ),
     $                  LDWORK )
         END IF
   40 CONTINUE
*
*     Subtract the matrix A.
*
      WORK( 1, 1 ) = WORK( 1, 1 ) - D( 1 )
      IF( N.GT.1 ) THEN
         WORK( 1, 2 ) = WORK( 1, 2 ) - DU( 1 )
         WORK( N, N-1 ) = WORK( N, N-1 ) - DL( N-1 )
         WORK( N, N ) = WORK( N, N ) - D( N )
         DO 50 I = 2, N - 1
            WORK( I, I-1 ) = WORK( I, I-1 ) - DL( I-1 )
            WORK( I, I ) = WORK( I, I ) - D( I )
            WORK( I, I+1 ) = WORK( I, I+1 ) - DU( I )
   50    CONTINUE
      END IF
*
*     Compute the 1-norm of the tridiagonal matrix A.
*
      ANORM = ZLANGT( '1', N, DL, D, DU )
*
*     Compute the 1-norm of WORK, which is only guaranteed to be
*     upper Hessenberg.
*
      RESID = ZLANHS( '1', N, WORK, LDWORK, RWORK )
*
*     Compute norm(L*U - A) / (norm(A) * EPS)
*
      IF( ANORM.LE.ZERO ) THEN
         IF( RESID.NE.ZERO )
     $      RESID = ONE / EPS
      ELSE
         RESID = ( RESID / ANORM ) / EPS
      END IF
*
      RETURN
*
*     End of ZGTT01
*
      END