DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) 2,2
!
! -- LAPACK auxiliary routine (version 3.1) --
! Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
! November 2006
!
! .. Scalar Arguments ..
CHARACTER NORM
INTEGER N
! ..
! .. Array Arguments ..
DOUBLE PRECISION D( * ), E( * )
! ..
!
! Purpose
! =======
!
! 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.
!
! Description
! ===========
!
! DLANST returns the value
!
! 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.
!
! Arguments
! =========
!
! NORM (input) CHARACTER*1
! Specifies the value to be returned in DLANST as described
! above.
!
! N (input) INTEGER
! The order of the matrix A. N >= 0. When N = 0, DLANST is
! set to zero.
!
! D (input) DOUBLE PRECISION array, dimension (N)
! The diagonal elements of A.
!
! E (input) DOUBLE PRECISION array, dimension (N-1)
! The (n-1) sub-diagonal or 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( 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 FUNCTION DLANST