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

```claqsb.f(3)							      LAPACK							       claqsb.f(3)

NAME
claqsb.f -

SYNOPSIS
Functions/Subroutines
subroutine claqsb (UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED)
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Function/Subroutine Documentation
subroutine claqsb (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )S, realSCOND,
realAMAX, characterEQUED)
CLAQSB scales a symmetric/Hermitian band matrix, using scaling factors computed by spbequ.

Purpose:

CLAQSB equilibrates a symmetric band matrix A using the scaling
factors in the vector S.

Parameters:
UPLO

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

N

N is INTEGER
The order of the matrix A.  N >= 0.

KD

KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array.  The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H *U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

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

S

S is REAL array, dimension (N)
The scale factors for A.

SCOND

SCOND is REAL
Ratio of the smallest S(i) to the largest S(i).

AMAX

AMAX is REAL
Absolute value of largest matrix entry.

EQUED

EQUED is CHARACTER*1
Specifies whether or not equilibration was done.
= 'N':  No equilibration.
= 'Y':  Equilibration was done, i.e., A has been replaced by
diag(S) * A * diag(S).

Internal Parameters:

THRESH is a threshold value used to decide if scaling should be done
based on the ratio of the scaling factors.  If SCOND < THRESH,
scaling is done.

LARGE and SMALL are threshold values used to decide if scaling should
be done based on the absolute size of the largest matrix element.
If AMAX > LARGE or AMAX < SMALL, scaling is done.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Definition at line 142 of file claqsb.f.

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

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

## Check Out this Related Man Page

```CLAQSB(l)								 )								 CLAQSB(l)

NAME
CLAQSB - equilibrate a symmetric band matrix A using the scaling factors in the vector S

SYNOPSIS
SUBROUTINE CLAQSB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

CHARACTER	  EQUED, UPLO

INTEGER	  KD, LDAB, N

REAL 	  AMAX, SCOND

REAL 	  S( * )

COMPLEX	  AB( LDAB, * )

PURPOSE
CLAQSB equilibrates a symmetric band matrix A using the scaling factors in the vector S.

ARGUMENTS
UPLO    (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the symmetric matrix A is stored.  = 'U':  Upper triangular
= 'L':  Lower triangular

N       (input) INTEGER
The order of the matrix A.  N >= 0.

KD      (input) INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

AB      (input/output) COMPLEX array, dimension (LDAB,N)
On  entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array.  The j-th column
of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO
= 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On  exit,  if  INFO = 0, the triangular factor U or L from the Cholesky factorization A = U'*U or A = L*L' of the band matrix A, in
the same storage format as A.

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KD+1.

S       (output) REAL array, dimension (N)
The scale factors for A.

SCOND   (input) REAL
Ratio of the smallest S(i) to the largest S(i).

AMAX    (input) REAL
Absolute value of largest matrix entry.

EQUED   (output) CHARACTER*1
Specifies whether or not equilibration was done.  = 'N':  No equilibration.
= 'Y':  Equilibration was done, i.e., A has been replaced by diag(S) * A * diag(S).

PARAMETERS
THRESH is a threshold value used to decide if scaling should be done based on the ratio of the scaling factors.	If SCOND < THRESH, scaling
is done.

LARGE and SMALL are threshold values used to decide if scaling should be done based on the absolute size of the largest matrix element.	If
AMAX > LARGE or AMAX < SMALL, scaling is done.

LAPACK version 3.0						   15 June 2000 							 CLAQSB(l)```
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