zlansb.f man page

zlansb.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

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

Purpose:

ZLANSB  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 symmetric band matrix A,  with k super-diagonals.

Returns:

ZLANSB

   ZLANSB = ( 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 ZLANSB 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 part is supplied
= 'L':  Lower triangular part is supplied

N

N is INTEGER
The order of the matrix A.  N >= 0.  When N = 0, ZLANSB 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 symmetric 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).

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

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 130 of file zlansb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zlansb(3) is an alias of zlansb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK