zgtt01.f

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      SUBROUTINE ZGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
     $                   LDWORK, RWORK, RESID )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. 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, * )
*     ..
*
*  Purpose
*  =======
*
*  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.
*
*  Arguments
*  =========
*
*  N       (input) INTEGTER
*          The order of the matrix A.  N >= 0.
*
*  DL      (input) COMPLEX*16 array, dimension (N-1)
*          The (n-1) sub-diagonal elements of A.
*
*  D       (input) COMPLEX*16 array, dimension (N)
*          The diagonal elements of A.
*
*  DU      (input) COMPLEX*16 array, dimension (N-1)
*          The (n-1) super-diagonal elements of A.
*
*  DLF     (input) COMPLEX*16 array, dimension (N-1)
*          The (n-1) multipliers that define the matrix L from the
*          LU factorization of A.
*
*  DF      (input) COMPLEX*16 array, dimension (N)
*          The n diagonal elements of the upper triangular matrix U from
*          the LU factorization of A.
*
*  DUF     (input) COMPLEX*16 array, dimension (N-1)
*          The (n-1) elements of the first super-diagonal of U.
*
*  DU2     (input) COMPLEX*16 array, dimension (N-2)
*          The (n-2) elements of the second super-diagonal of U.
*
*  IPIV    (input) 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.
*
*  WORK    (workspace) COMPLEX*16 array, dimension (LDWORK,N)
*
*  LDWORK  (input) INTEGER
*          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*
*  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
*
*  RESID   (output) DOUBLE PRECISION
*          The scaled residual:  norm(L*U - A) / (norm(A) * EPS)
*
*  =====================================================================
*
*     .. 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