1CLAQSB(1)           LAPACK auxiliary routine (version 3.1)           CLAQSB(1)
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NAME

6       CLAQSB  -  a  symmetric  band matrix A using the scaling factors in the
7       vector S
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SYNOPSIS

10       SUBROUTINE CLAQSB( 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       CLAQSB equilibrates a symmetric band matrix A using the scaling factors
24       in the vector S.
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ARGUMENTS

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

71       THRESH is a threshold value used to decide if scaling  should  be  done
72       based  on the ratio of the scaling factors.  If SCOND < THRESH, scaling
73       is done.
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75       LARGE and SMALL are threshold values used to decide if  scaling  should
76       be  done  based on the absolute size of the largest matrix element.  If
77       AMAX > LARGE or AMAX < SMALL, scaling is done.
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81 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLAQSB(1)
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