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

6       ZLAQHB  - equilibrates a symmetric band matrix A using the scaling fac‐
7       tors in the vector S
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SYNOPSIS

10       SUBROUTINE ZLAQHB( 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           DOUBLE         PRECISION AMAX, SCOND
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18           DOUBLE         PRECISION S( * )
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20           COMPLEX*16     AB( LDAB, * )
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PURPOSE

23       ZLAQHB equilibrates a symmetric band matrix A using the scaling factors
24       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*16 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) DOUBLE PRECISION array, dimension (N)
53               The scale factors for A.
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55       SCOND   (input) DOUBLE PRECISION
56               Ratio of the smallest S(i) to the largest S(i).
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58       AMAX    (input) DOUBLE PRECISION
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                       ZLAQHB(1)