# ?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 )

## 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 vaule 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

  COMPLEX*16 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.

Parent topic: Auxiliary Routines