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

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

     CHARACTER EQUED, UPLO

     INTEGER KD, LDAB, N

     REAL AMAX, SCOND

     REAL S( * )

     COMPLEX AB( LDAB, * )



     #include <sunperf.h>

     void claqhb(char uplo, int n,  int  kd,  complex  *cab,  int
               ldab,  float  *s,  float  scond,  float amax, char
               *equed) ;

PURPOSE
     CLAQHB 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  sym-
               metric  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 scal-
     ing should be done based on the absolute size of the largest
     matrix element.  If AMAX > LARGE or AMAX < SMALL, scaling is
     done.

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