#include "ESMF_LapackBlas.inc" !> \brief \b DLANST ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLANST + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanst.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanst.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanst.f"> !> [TXT]</a> !> \endhtmlonly ! ! 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 November 2011 ! !> \ingroup auxOTHERauxiliary ! ! ===================================================================== DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) ! ! -- LAPACK auxiliary routine (version 3.4.0) -- ! -- LAPACK is a software package provided by Univ. of Tennessee, -- ! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- ! November 2011 ! ! .. 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 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