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      DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )

*

*  -- LAPACK auxiliary routine (version 3.2) --

*  -- LAPACK is a software package provided by Univ. of Tennessee,    --

*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--

*     November 2006

*

*     .. Scalar Arguments ..

      CHARACTER          NORM

      INTEGER            N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   D( * ), E( * )

*     ..

*

*  Purpose

*  =======

*

*  DLANST  returns the value of the one norm,  or the Frobenius norm, or

*  the  infinity norm,  or the  element of  largest absolute value  of a

*  real symmetric tridiagonal matrix A.

*

*  Description

*  ===========

*

*  DLANST returns the value

*

*     DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'

*              (

*              ( norm1(A),         NORM = '1', 'O' or 'o'

*              (

*              ( normI(A),         NORM = 'I' or 'i'

*              (

*              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

*

*  where  norm1  denotes the  one norm of a matrix (maximum column sum),

*  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and

*  normF  denotes the  Frobenius norm of a matrix (square root of sum of

*  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.

*

*  Arguments

*  =========

*

*  NORM    (input) CHARACTER*1

*          Specifies the value to be returned in DLANST as described

*          above.

*

*  N       (input) INTEGER

*          The order of the matrix A.  N >= 0.  When N = 0, DLANST is

*          set to zero.

*

*  D       (input) DOUBLE PRECISION array, dimension (N)

*          The diagonal elements of A.

*

*  E       (input) DOUBLE PRECISION array, dimension (N-1)

*          The (n-1) sub-diagonal or super-diagonal elements of A.

*

*  =====================================================================

*

*     .. Parameters ..

      DOUBLE PRECISION   ONE, ZERO

      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )

*     ..

*     .. Local Scalars ..

      INTEGER            I

      DOUBLE PRECISION   ANORM, SCALE, SUM

*     ..

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     ..

*     .. External Subroutines ..

      EXTERNAL           DLASSQ

*     ..

*     .. Intrinsic Functions ..

      INTRINSIC          ABS, MAX, SQRT

*     ..

*     .. Executable Statements ..

*

      IF( N.LE.0 ) THEN

         ANORM = ZERO

      ELSE IF( LSAME( NORM, 'M' ) ) THEN

*

*        Find max(abs(A(i,j))).

*

         ANORM = ABS( D( N ) )

         DO 10 I = 1, N - 1

            ANORM = MAX( ANORM, ABS( D( I ) ) )

            ANORM = MAX( ANORM, ABS( E( I ) ) )

   10    CONTINUE

      ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.

     $         LSAME( NORM, 'I' ) ) THEN

*

*        Find norm1(A).

*

         IF( N.EQ.1 ) THEN

            ANORM = ABS( D( 1 ) )

         ELSE

            ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),

     $              ABS( E( N-1 ) )+ABS( D( N ) ) )

            DO 20 I = 2, N - 1

               ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+

     $                 ABS( E( I-1 ) ) )

   20       CONTINUE

         END IF

      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN

*

*        Find normF(A).

*

         SCALE = ZERO

         SUM = ONE

         IF( N.GT.1 ) THEN

            CALL DLASSQ( N-1, E, 1, SCALE, SUM )

            SUM = 2*SUM

         END IF

         CALL DLASSQ( N, D, 1, SCALE, SUM )

         ANORM = SCALE*SQRT( SUM )

      END IF

*

      DLANST = ANORM

      RETURN

*

*     End of DLANST

*

      END