# zlantb (l) - Linux Manuals

## NAME

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

## SYNOPSIS

DOUBLE PRECISION
FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )

CHARACTER DIAG, NORM, UPLO

INTEGER K, LDAB, N

DOUBLE PRECISION WORK( * )

COMPLEX*16 AB( LDAB, * )

## 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.

## DESCRIPTION

ZLANTB returns the value

ZLANTB max(abs(A(i,j))), NORM aqMaq or aqmaq

(

norm1(A),         NORM aq1aq, aqOaq or aqoaq

(

normI(A),         NORM aqIaq or aqiaq

(

normF(A),         NORM aqFaq, aqfaq, aqEaq or aqeaq 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 ZLANTB as described above.
UPLO (input) CHARACTER*1
Specifies whether the matrix A is upper or lower triangular. = aqUaq: Upper triangular
= aqLaq: Lower triangular
DIAG (input) CHARACTER*1
Specifies whether or not the matrix A is unit triangular. = aqNaq: Non-unit triangular
= aqUaq: Unit triangular
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANTB is set to zero.
K (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = aqUaq, or the number of sub-diagonals of the matrix A if UPLO = aqLaq. K >= 0.
AB (input) 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 = aqUaq, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = aqLaq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that when DIAG = aqUaq, 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 = aqIaq; otherwise, WORK is not referenced.