# zlangb.f man page

zlangb.f —

## Synopsis

### Functions/Subroutines

DOUBLE PRECISION functionzlangb(NORM, N, KL, KU, AB, LDAB, WORK)ZLANGBreturns 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 (characterNORM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, 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:**

September 2012

Definition at line 125 of file zlangb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlangb(3) is an alias of zlangb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK