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dlansb-f(3)

dlansb.f –

Synopsis

Functions/Subroutines

DOUBLE PRECISION function dlansb (NORM, UPLO, N, K, AB, LDAB, WORK)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Function/Subroutine Documentation

DOUBLE PRECISION function dlansb (characterNORM, characterUPLO, integerN, integerK, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

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

Purpose:

 DLANSB 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 symmetric band matrix A, with k super-diagonals.

Returns:

DLANSB

 DLANSB = ( 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:

NORM

 NORM is CHARACTER*1
 Specifies the value to be returned in DLANSB as described
 above.

UPLO

 UPLO is CHARACTER*1
 Specifies whether the upper or lower triangular part of the
 band matrix A is supplied.
 = 'U': Upper triangular part is supplied
 = 'L': Lower triangular part is supplied

N

 N is INTEGER
 The order of the matrix A. N >= 0. When N = 0, DLANSB is
 set to zero.

K

 K is INTEGER
 The number of super-diagonals or sub-diagonals of the
 band matrix A. K >= 0.

AB

 AB is DOUBLE PRECISION array, dimension (LDAB,N)
 The upper or lower triangle of the symmetric 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).

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= K+1.

WORK

 WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
 where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
 WORK is not referenced.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 129 of file dlansb.f.

Author

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