slangb()

real function slangb	(	character	norm,
		integer	n,
		integer	kl,
		integer	ku,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( * )	work )

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Download SLANGB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> SLANGB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
!> 

Returns

SLANGB

!>
!>    SLANGB = ( 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.
!> 

Parameters

[in]	NORM	!> NORM is CHARACTER*1 !> Specifies the value to be returned in SLANGB as described !> above. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, SLANGB is !> set to zero. !>
[in]	KL	!> KL is INTEGER !> The number of sub-diagonals of the matrix A. KL >= 0. !>
[in]	KU	!> KU is INTEGER !> The number of super-diagonals of the matrix A. KU >= 0. !>
[in]	AB	!> AB is REAL array, dimension (LDAB,N) !> The band matrix A, stored in rows 1 to KL+KU+1. The j-th !> column of A is stored in the j-th column of the array AB as !> follows: !> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)), !> where LWORK >= N when NORM = 'I'; otherwise, WORK is not !> referenced. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.