---
name: "dlantb"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlantb/3lapack"
---

# dlantb(3lapack)

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

## NAME

DLANTB - 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

## SYNOPSIS

- DOUBLE PRECISION

  FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )

- CHARACTER

  DIAG, NORM, UPLO

- INTEGER

  K, LDAB, N

- DOUBLE

  PRECISION AB( LDAB, \* ), WORK( \* )

## PURPOSE

DLANTB  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.

## DESCRIPTION

DLANTB returns the value\
\
    DLANTB = ( 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.

## ARGUMENTS

- NORM (input) CHARACTER\*1

  Specifies the value to be returned in DLANTB as described above.

- UPLO (input) CHARACTER\*1

  Specifies whether the matrix A is upper or lower triangular. = 'U':  Upper triangular\
   \= 'L':  Lower triangular

- DIAG (input) CHARACTER\*1

  Specifies whether or not the matrix A is unit triangular. = 'N':  Non-unit triangular\
   \= 'U':  Unit triangular

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.  When N = 0, DLANTB is set to zero.

- K (input) 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 (input) DOUBLE PRECISION 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 (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= K+1.

- WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),

  where LWORK \>= N when NORM = 'I'; otherwise, WORK is not referenced.