dgtt01()

subroutine dgtt01	(	integer	N,
		double precision, dimension( * )	DL,
		double precision, dimension( * )	D,
		double precision, dimension( * )	DU,
		double precision, dimension( * )	DLF,
		double precision, dimension( * )	DF,
		double precision, dimension( * )	DUF,
		double precision, dimension( * )	DU2,
		integer, dimension( * )	IPIV,
		double precision, dimension( ldwork, * )	WORK,
		integer	LDWORK,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

DGTT01

Purpose:

 DGTT01 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.

Parameters

[in]	N	N is INTEGTER The order of the matrix A. N >= 0.
[in]	DL	DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) sub-diagonal elements of A.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.
[in]	DU	DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) super-diagonal elements of A.
[in]	DLF	DLF is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.
[in]	DF	DF is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	DUF	DUF is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.
[in]	DU2	DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.
[in]	IPIV	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.
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
[in]	LDWORK	LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).
[out]	RWORK	RWORK is DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION The scaled residual: norm(L*U - A) / (norm(A) * EPS)

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 136 of file dgtt01.f.

*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            LDWORK, N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
     $                   DU2( * ), DUF( * ), RWORK( * ),
     $                   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, LI
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANGT, DLANHS
      EXTERNAL           dlamch, dlangt, dlanhs
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          min
*     ..
*     .. External Subroutines ..
      EXTERNAL           daxpy, dswap
*     ..
*     .. 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 daxpy( 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 dswap( 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 = dlangt( '1', n, dl, d, du )
*
*     Compute the 1-norm of WORK, which is only guaranteed to be
*     upper Hessenberg.
*
      resid = dlanhs( '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 DGTT01
*

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