dlanst.f

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*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
* 
*       .. Scalar Arguments ..
*       CHARACTER          NORM
*       INTEGER            N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   D( * ), E( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
*> \return DLANST
*> \verbatim
*>
*>    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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies the value to be returned in DLANST as described
*>          above.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.  When N = 0, DLANST is
*>          set to zero.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*>          D is DOUBLE PRECISION array, dimension (N)
*>          The diagonal elements of A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*>          E is DOUBLE PRECISION array, dimension (N-1)
*>          The (n-1) sub-diagonal or super-diagonal elements of A.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*  =====================================================================
      DOUBLE PRECISION FUNCTION dlanst( NORM, N, D, E )
*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * ), E( * )
*     ..
*
*  =====================================================================
*
*     .. 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, DISNAN
      EXTERNAL           lsame, disnan
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlassq
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, 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
            sum = abs( d( i ) )
            IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
            sum = abs( e( i ) )
            IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
   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 = abs( d( 1 ) )+abs( e( 1 ) )
            sum = abs( e( n-1 ) )+abs( d( n ) )
            IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
            DO 20 i = 2, n - 1
               sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
               IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
   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