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CLAQSB(1)	    LAPACK auxiliary routine (version 3.2)	     CLAQSB(1)

NAME
       CLAQSB  - equilibrates a symmetric band matrix A using the scaling fac‐
       tors 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       (input) 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	       =  'Y':	 Equilibration	was done, i.e., A has been replaced by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	 scal‐
       ing  should  be	done  based on the absolute size of the largest matrix
       element.	 If AMAX > LARGE or AMAX < SMALL, scaling is done.

 LAPACK auxiliary routine (versioNovember 2008			     CLAQSB(1)
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