1ZLAQHB(1)           LAPACK auxiliary routine (version 3.1)           ZLAQHB(1)
2
3
4

NAME

6       ZLAQHB  -  a  symmetric  band matrix A using the scaling factors in the
7       vector S
8

SYNOPSIS

10       SUBROUTINE ZLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )
11
12           CHARACTER      EQUED, UPLO
13
14           INTEGER        KD, LDAB, N
15
16           DOUBLE         PRECISION AMAX, SCOND
17
18           DOUBLE         PRECISION S( * )
19
20           COMPLEX*16     AB( LDAB, * )
21

PURPOSE

23       ZLAQHB equilibrates a symmetric band matrix A using the scaling factors
24       in the vector S.
25
26

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
32
33       N       (input) INTEGER
34               The order of the matrix A.  N >= 0.
35
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.
39
40       AB      (input/output) COMPLEX*16 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).
47
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.
51
52       LDAB    (input) INTEGER
53               The leading dimension of the array AB.  LDAB >= KD+1.
54
55       S       (output) DOUBLE PRECISION array, dimension (N)
56               The scale factors for A.
57
58       SCOND   (input) DOUBLE PRECISION
59               Ratio of the smallest S(i) to the largest S(i).
60
61       AMAX    (input) DOUBLE PRECISION
62               Absolute value of largest matrix entry.
63
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).
69

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.
74
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.
78
79
80
81 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQHB(1)