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DOUBLE PRECISION FUNCTION DLANGT( NORM, N, DL, D, DU )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER NORM
INTEGER N
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), DL( * ), DU( * )
* ..
*
* Purpose
* =======
*
* 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.
*
* Description
* ===========
*
* DLANGT returns the value
*
* 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 matrix norm.
*
* Arguments
* =========
*
* NORM (input) CHARACTER*1
* Specifies the value to be returned in DLANGT as described
* above.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0. When N = 0, DLANGT is
* set to zero.
*
* DL (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) sub-diagonal elements of A.
*
* D (input) DOUBLE PRECISION array, dimension (N)
* The diagonal elements of A.
*
* DU (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) 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( DL( I ) ) )
ANORM = MAX( ANORM, ABS( D( I ) ) )
ANORM = MAX( 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 = MAX( ABS( D( 1 ) )+ABS( DL( 1 ) ),
$ ABS( D( N ) )+ABS( DU( N-1 ) ) )
DO 20 I = 2, N - 1
ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DL( I ) )+
$ ABS( DU( I-1 ) ) )
20 CONTINUE
END IF
ELSE IF( LSAME( NORM, 'I' ) ) THEN
*
* Find normI(A).
*
IF( N.EQ.1 ) THEN
ANORM = ABS( D( 1 ) )
ELSE
ANORM = MAX( ABS( D( 1 ) )+ABS( DU( 1 ) ),
$ ABS( D( N ) )+ABS( DL( N-1 ) ) )
DO 30 I = 2, N - 1
ANORM = MAX( ANORM, ABS( D( I ) )+ABS( DU( I ) )+
$ ABS( DL( I-1 ) ) )
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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