slantb()

real function slantb	(	character	norm,
		character	uplo,
		character	diag,
		integer	n,
		integer	k,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( * )	work )

SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

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Purpose:

!>
!> SLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
!> 

Returns

SLANTB

!>
!>    SLANTB = ( 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 SLANTB as described !> above. !>
[in]	UPLO	!> UPLO is CHARACTER*1 !> Specifies whether the matrix A is upper or lower triangular. !> = 'U': Upper triangular !> = 'L': Lower triangular !>
[in]	DIAG	!> DIAG is CHARACTER*1 !> Specifies whether or not the matrix A is unit triangular. !> = 'N': Non-unit triangular !> = 'U': Unit triangular !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. When N = 0, SLANTB is !> set to zero. !>
[in]	K	!> K is INTEGER !> The number of super-diagonals of the matrix A if UPLO = 'U', !> or the number of sub-diagonals of the matrix A if UPLO = 'L'. !> K >= 0. !>
[in]	AB	!> AB is REAL array, dimension (LDAB,N) !> The upper or lower triangular band matrix A, stored in the !> first k+1 rows of AB. The j-th column of A is stored !> in the j-th column of the array AB as follows: !> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). !> Note that when DIAG = 'U', the elements of the array AB !> corresponding to the diagonal elements of the matrix A are !> not referenced, but are assumed to be one. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= K+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.