# zlantb (3) - Linux Manuals

zlantb.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### DOUBLE PRECISION function zlantb (characterNORM, characterUPLO, characterDIAG, integerN, integerK, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

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

Purpose:

``` ZLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
```

Returns:

ZLANTB

```    ZLANTB = ( 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 ZLANTB as described
above.
```

UPLO

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

DIAG

```          DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N':  Non-unit triangular
= 'U':  Unit triangular
```

N

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

K

```          K is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals of the matrix A if UPLO = 'L'.
K >= 0.
```

AB

```          AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular 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).
Note that when DIAG = 'U', the elements of the array AB
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.
```

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'; otherwise, WORK is not
referenced.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley