dlangb()

double precision function dlangb	(	character	NORM,
		integer	N,
		integer	KL,
		integer	KU,
		double precision, dimension( ldab, * )	AB,
		integer	LDAB,
		double precision, dimension( * )	WORK
	)

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

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Purpose:

 DLANGB  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

DLANGB

    DLANGB = ( 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 DLANGB as described above.
[in]	N	N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.