zlanhb.f (3) - Linux Man Pages

zlanhb.f -

SYNOPSIS

Functions/Subroutines

DOUBLE PRECISION function zlanhb (NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Function/Subroutine Documentation

DOUBLE PRECISION function zlanhb (characterNORM, characterUPLO, integerN, integerK, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )WORK)

ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Purpose:

ZLANHB  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 hermitian band matrix A,  with k super-diagonals.

Returns:

ZLANHB

ZLANHB = ( 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.

Parameters:

NORM

NORM is CHARACTER*1
Specifies the value to be returned in ZLANHB as described
above.

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular
= 'L':  Lower triangular

N

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

K

K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.

LDAB

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

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.

Author:

Univ. of Tennessee

Univ. of California Berkeley