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

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

10       SUBROUTINE SLAQSB( 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           AB( LDAB, * ), S( * )
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PURPOSE

21       SLAQSB equilibrates a symmetric band matrix A using the scaling factors
22       in the vector S.
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ARGUMENTS

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

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