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    1:       DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
    2: *
    3: *  -- LAPACK auxiliary routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          NORM
   10:       INTEGER            N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   D( * ), E( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DLANST  returns the value of the one norm,  or the Frobenius norm, or
   20: *  the  infinity norm,  or the  element of  largest absolute value  of a
   21: *  real symmetric tridiagonal matrix A.
   22: *
   23: *  Description
   24: *  ===========
   25: *
   26: *  DLANST returns the value
   27: *
   28: *     DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm'
   29: *              (
   30: *              ( norm1(A),         NORM = '1', 'O' or 'o'
   31: *              (
   32: *              ( normI(A),         NORM = 'I' or 'i'
   33: *              (
   34: *              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
   35: *
   36: *  where  norm1  denotes the  one norm of a matrix (maximum column sum),
   37: *  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
   38: *  normF  denotes the  Frobenius norm of a matrix (square root of sum of
   39: *  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
   40: *
   41: *  Arguments
   42: *  =========
   43: *
   44: *  NORM    (input) CHARACTER*1
   45: *          Specifies the value to be returned in DLANST as described
   46: *          above.
   47: *
   48: *  N       (input) INTEGER
   49: *          The order of the matrix A.  N >= 0.  When N = 0, DLANST is
   50: *          set to zero.
   51: *
   52: *  D       (input) DOUBLE PRECISION array, dimension (N)
   53: *          The diagonal elements of A.
   54: *
   55: *  E       (input) DOUBLE PRECISION array, dimension (N-1)
   56: *          The (n-1) sub-diagonal or super-diagonal elements of A.
   57: *
   58: *  =====================================================================
   59: *
   60: *     .. Parameters ..
   61:       DOUBLE PRECISION   ONE, ZERO
   62:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   63: *     ..
   64: *     .. Local Scalars ..
   65:       INTEGER            I
   66:       DOUBLE PRECISION   ANORM, SCALE, SUM
   67: *     ..
   68: *     .. External Functions ..
   69:       LOGICAL            LSAME
   70:       EXTERNAL           LSAME
   71: *     ..
   72: *     .. External Subroutines ..
   73:       EXTERNAL           DLASSQ
   74: *     ..
   75: *     .. Intrinsic Functions ..
   76:       INTRINSIC          ABS, MAX, SQRT
   77: *     ..
   78: *     .. Executable Statements ..
   79: *
   80:       IF( N.LE.0 ) THEN
   81:          ANORM = ZERO
   82:       ELSE IF( LSAME( NORM, 'M' ) ) THEN
   83: *
   84: *        Find max(abs(A(i,j))).
   85: *
   86:          ANORM = ABS( D( N ) )
   87:          DO 10 I = 1, N - 1
   88:             ANORM = MAX( ANORM, ABS( D( I ) ) )
   89:             ANORM = MAX( ANORM, ABS( E( I ) ) )
   90:    10    CONTINUE
   91:       ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
   92:      $         LSAME( NORM, 'I' ) ) THEN
   93: *
   94: *        Find norm1(A).
   95: *
   96:          IF( N.EQ.1 ) THEN
   97:             ANORM = ABS( D( 1 ) )
   98:          ELSE
   99:             ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
  100:      $              ABS( E( N-1 ) )+ABS( D( N ) ) )
  101:             DO 20 I = 2, N - 1
  102:                ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
  103:      $                 ABS( E( I-1 ) ) )
  104:    20       CONTINUE
  105:          END IF
  106:       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
  107: *
  108: *        Find normF(A).
  109: *
  110:          SCALE = ZERO
  111:          SUM = ONE
  112:          IF( N.GT.1 ) THEN
  113:             CALL DLASSQ( N-1, E, 1, SCALE, SUM )
  114:             SUM = 2*SUM
  115:          END IF
  116:          CALL DLASSQ( N, D, 1, SCALE, SUM )
  117:          ANORM = SCALE*SQRT( SUM )
  118:       END IF
  119: *
  120:       DLANST = ANORM
  121:       RETURN
  122: *
  123: *     End of DLANST
  124: *
  125:       END