cgtt01.f

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      SUBROUTINE cgtt01( 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
      REAL               resid
*     ..
*     .. Array Arguments ..
      INTEGER            ipiv( * )
      REAL               rwork( * )
      COMPLEX            d( * ), df( * ), dl( * ), dlf( * ), du( * ),
     $                   du2( * ), duf( * ), work( ldwork, * )
*     ..
*
*  Purpose
*  =======
*
*  CGTT01 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 array, dimension (N-1)
*          The (n-1) sub-diagonal elements of A.
*
*  D       (input) COMPLEX array, dimension (N)
*          The diagonal elements of A.
*
*  DU      (input) COMPLEX array, dimension (N-1)
*          The (n-1) super-diagonal elements of A.
*
*  DLF     (input) COMPLEX array, dimension (N-1)
*          The (n-1) multipliers that define the matrix L from the
*          LU factorization of A.
*
*  DF      (input) COMPLEX array, dimension (N)
*          The n diagonal elements of the upper triangular matrix U from
*          the LU factorization of A.
*
*  DUF     (input) COMPLEX array, dimension (N-1)
*          The (n-1) elements of the first super-diagonal of U.
*
*  DU2     (input) COMPLEX 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 array, dimension (LDWORK,N)
*
*  LDWORK  (input) INTEGER
*          The leading dimension of the array WORK.  LDWORK >= max(1,N).
*
*  RWORK   (workspace) REAL array, dimension (N)
*
*  RESID   (output) REAL
*          The scaled residual:  norm(L*U - A) / (norm(A) * EPS)
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               one, zero
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            i, ip, j, lastj
      REAL               anorm, eps
      COMPLEX            li
*     ..
*     .. External Functions ..
      REAL               clangt, clanhs, slamch
      EXTERNAL           clangt, clanhs, slamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          min
*     ..
*     .. External Subroutines ..
      EXTERNAL           caxpy, cswap
*     ..
*     .. Executable Statements ..
*
*     Quick return if possible
*
      IF( n.LE.0 ) THEN
         resid = zero
         return
      END IF
*
      eps = slamch( '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 caxpy( 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 cswap( 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 = clangt( '1', n, dl, d, du )
*
*     Compute the 1-norm of WORK, which is only guaranteed to be
*     upper Hessenberg.
*
      resid = clanhs( '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 CGTT01
*
      END