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*> \brief \b DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLANGT + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangt.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangt.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangt.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU )
*
* .. Scalar Arguments ..
* CHARACTER NORM
* INTEGER N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), DL( * ), DU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLANGT 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 tridiagonal matrix A.
*> \endverbatim
*>
*> \return DLANGT
*> \verbatim
*>
*> DLANGT = ( 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 DLANGT as described
*> above.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0. When N = 0, DLANGT is
*> set to zero.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) sub-diagonal elements of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> The diagonal elements of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) 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 December 2016
*
*> \ingroup doubleOTHERauxiliary
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU )
*
* -- LAPACK auxiliary 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 ..
CHARACTER NORM
INTEGER N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), DL( * ), DU( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION ANORM, SCALE, SUM, TEMP
* ..
* .. 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
IF( ANORM.LT.ABS( DL( I ) ) .OR. DISNAN( ABS( DL( I ) ) ) )
$ ANORM = ABS(DL(I))
IF( ANORM.LT.ABS( D( I ) ) .OR. DISNAN( ABS( D( I ) ) ) )
$ ANORM = ABS(D(I))
IF( ANORM.LT.ABS( DU( I ) ) .OR. DISNAN (ABS( DU( I ) ) ) )
$ ANORM = ABS(DU(I))
10 CONTINUE
ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' ) THEN
*
* Find norm1(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = ABS( D( 1 ) )+ABS( DL( 1 ) )
TEMP = ABS( D( N ) )+ABS( DU( N-1 ) )
IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
DO 20 I = 2, N - 1
TEMP = ABS( D( I ) )+ABS( DL( I ) )+ABS( DU( I-1 ) )
IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
20 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = ABS( D( 1 ) )+ABS( DU( 1 ) )
TEMP = ABS( D( N ) )+ABS( DL( N-1 ) )
IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
DO 30 I = 2, N - 1
TEMP = ABS( D( I ) )+ABS( DU( I ) )+ABS( DL( I-1 ) )
IF( ANORM .LT. TEMP .OR. DISNAN( TEMP ) ) ANORM = TEMP
30 CONTINUE
END IF
ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
*
* Find normF(A).
*
SCALE = ZERO
SUM = ONE
CALL DLASSQ( N, D, 1, SCALE, SUM )
IF( N.GT.1 ) THEN
CALL DLASSQ( N-1, DL, 1, SCALE, SUM )
CALL DLASSQ( N-1, DU, 1, SCALE, SUM )
END IF
ANORM = SCALE*SQRT( SUM )
END IF
*
DLANGT = ANORM
RETURN
*
* End of DLANGT
*
END
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