# zlangb.f man page

zlangb.f

## Synopsis

### Functions/Subroutines

double precision function zlangb (NORM, N, KL, KU, AB, LDAB, WORK)
ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

## Function/Subroutine Documentation

### double precision function zlangb (character NORM, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK)

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

Purpose:

ZLANGB  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:

ZLANGB

ZLANGB = ( 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 ZLANGB as described
above.

N

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

KL

KL is INTEGER
The number of sub-diagonals of the matrix A.  KL >= 0.

KU

KU is INTEGER
The number of super-diagonals of the matrix A.  KU >= 0.

AB

AB is COMPLEX*16 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).

LDAB

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

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

NAG Ltd.

Date:

December 2016

Definition at line 127 of file zlangb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlangb(3) is an alias of zlangb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK