# 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

Univ. of Colorado Denver

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