1CLAQHB(1)           LAPACK auxiliary routine (version 3.2)           CLAQHB(1)
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NAME

6       CLAQHB - equilibrates an Hermitian band matrix A using the scaling fac‐
7       tors in the vector S
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SYNOPSIS

10       SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
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12           CHARACTER      EQUED, UPLO
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14           INTEGER        KD, LDAB, N
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16           REAL           AMAX, SCOND
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18           REAL           S( * )
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20           COMPLEX        AB( LDAB, * )
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PURPOSE

23       CLAQHB equilibrates an Hermitian band matrix A using the  scaling  fac‐
24       tors in the vector S.
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ARGUMENTS

27       UPLO    (input) CHARACTER*1
28               Specifies  whether  the  upper  or lower triangular part of the
29               symmetric matrix A is stored.  = 'U':  Upper triangular
30               = 'L':  Lower triangular
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32       N       (input) INTEGER
33               The order of the matrix A.  N >= 0.
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35       KD      (input) INTEGER
36               The number of super-diagonals of the matrix A if UPLO = 'U', or
37               the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
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39       AB      (input/output) COMPLEX array, dimension (LDAB,N)
40               On  entry,  the  upper  or lower triangle of the symmetric band
41               matrix A, stored in the first KD+1 rows of the array.  The j-th
42               column  of  A  is  stored in the j-th column of the array AB as
43               follows: if UPLO = 'U', AB(kd+1+i-j,j) =  A(i,j)  for  max(1,j-
44               kd)<=i<=j;   if   UPLO  =  'L',  AB(1+i-j,j)     =  A(i,j)  for
45               j<=i<=min(n,j+kd).  On exit, if INFO = 0, the triangular factor
46               U  or L from the Cholesky factorization A = U'*U or A = L*L' of
47               the band matrix A, in the same storage format as A.
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49       LDAB    (input) INTEGER
50               The leading dimension of the array AB.  LDAB >= KD+1.
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52       S       (output) REAL array, dimension (N)
53               The scale factors for A.
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55       SCOND   (input) REAL
56               Ratio of the smallest S(i) to the largest S(i).
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58       AMAX    (input) REAL
59               Absolute value of largest matrix entry.
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61       EQUED   (output) CHARACTER*1
62               Specifies whether or not equilibration was done.   =  'N':   No
63               equilibration.
64               =  'Y':   Equilibration  was done, i.e., A has been replaced by
65               diag(S) * A * diag(S).
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PARAMETERS

68       THRESH is a threshold value used to decide if scaling  should  be  done
69       based  on the ratio of the scaling factors.  If SCOND < THRESH, scaling
70       is done.  LARGE and SMALL are threshold values used to decide if  scal‐
71       ing  should  be  done  based on the absolute size of the largest matrix
72       element.  If AMAX > LARGE or AMAX < SMALL, scaling is done.
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76 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       CLAQHB(1)