# ?lantb

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.

## Syntax

val = slantb( norm, uplo, diag, n, k, ab, ldab, work )

val = dlantb( norm, uplo, diag, n, k, ab, ldab, work )

val = clantb( norm, uplo, diag, n, k, ab, ldab, work )

val = zlantb( norm, uplo, diag, n, k, ab, ldab, work )

## Include Files

• Fortran: mkl.fi
• C: mkl.h

## Description

The function ?lantb returns the value of the 1-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.

## Input Parameters

norm

CHARACTER*1. Specifies the value to be returned by the routine:

= 'M' or 'm': `val = max(abs(Aij))`, largest absolute value of the matrix A.

= '1' or 'O' or 'o': `val = norm1(A)`, 1-norm of the matrix A (maximum column sum),

= 'I' or 'i': `val = normI(A)`, infinity norm of the matrix A (maximum row sum),

= 'F', 'f', 'E' or 'e': `val = normF(A)`, Frobenius norm of the matrix A (square root of sum of squares).

uplo

CHARACTER*1.

Specifies whether the matrix A is upper or lower triangular.

= 'U': Upper triangular

= 'L': Lower triangular.

diag

CHARACTER*1.

Specifies whether or not the matrix A is unit triangular.

= 'N': Non-unit triangular

= 'U': Unit triangular.

n

INTEGER. The order of the matrix A. `n ≥ 0`. When `n = 0`, ?lantb is set to zero.

k

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

REAL for slantb

DOUBLE PRECISION for dlantb

COMPLEX for clantb

DOUBLE COMPLEX for zlantb

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

INTEGER. The leading dimension of the array ab.

`ldab ≥ k+1`.

work

REAL for slantb and clantb.

DOUBLE PRECISION for dlantb and zlantb.

Workspace array, DIMENSION `(max(1,lwork))`, where

`lwork ≥ n` when `norm = 'I'` ; otherwise, work is not referenced.

## Output Parameters

val

REAL for slantb/clantb.

DOUBLE PRECISION for dlantb/zlantb.

Value returned by the function.

For more complete information about compiler optimizations, see our Optimization Notice.