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

NAME

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

SYNOPSIS

10       SUBROUTINE DLAQSB( 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 AB( LDAB, * ), S( * )
19

PURPOSE

21       DLAQSB equilibrates a symmetric band matrix A using the scaling factors
22       in the vector S.
23
24

ARGUMENTS

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65               =  'Y':   Equilibration  was done, i.e., A has been replaced by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

PARAMETERS

69       THRESH is a threshold value used to decide if scaling  should  be  done
70       based  on the ratio of the scaling factors.  If SCOND < THRESH, scaling
71       is done.
72
73       LARGE and SMALL are threshold values used to decide if  scaling  should
74       be  done  based on the absolute size of the largest matrix element.  If
75       AMAX > LARGE or AMAX < SMALL, scaling is done.
76
77
78
79 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLAQSB(1)
Impressum