# zlansb.f(3) [centos man page]

```zlansb.f(3)							      LAPACK							       zlansb.f(3)

NAME
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

NAG Ltd.

Date:
September 2012

Definition at line 130 of file zlansb.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zlansb.f(3)```

## Check Out this Related Man Page

```dlansb.f(3)							      LAPACK							       dlansb.f(3)

NAME
dlansb.f -

SYNOPSIS
Functions/Subroutines
DOUBLE PRECISION function dlansb (NORM, UPLO, N, K, AB, LDAB, WORK)
DLANSB 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 dlansb (characterNORM, characterUPLO, integerN, integerK, double precision, dimension( ldab, * )AB, integerLDAB,
double precision, dimension( * )WORK)
DLANSB 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:

DLANSB  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:
DLANSB

DLANSB = ( 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 DLANSB 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, DLANSB 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 DOUBLE PRECISION 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

NAG Ltd.

Date:
September 2012

Definition at line 129 of file dlansb.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlansb.f(3)```
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