zlantb(3)

NAME

ZLANTB - return the value of the one norm, or the Frobe

nius norm, or the infinity norm, or the element of largest abso

lute 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 ) diag

onals.

DESCRIPTION

ZLANTB returns the value

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 ma

trix (square root of sum of squares). Note that

max(abs(A(i,j))) is not a 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. = 'U': Upper triangular
= 'L': Lower triangular

DIAG (input) CHARACTER*1

Specifies whether or not the matrix A is unit tri

angular. = 'N': Non-unit triangular
= 'U': 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 = 'U', or the number of sub-diagonals of the matrix A if UP

LO = 'L'. 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 =

'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

(LWORK),

where LWORK >= N when NORM = 'I'; otherwise, WORK

is not referenced.

LAPACK version 3.0 15 June 2000

ZLANTB(3)