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

6       SLAQSY - equilibrates a symmetric matrix A using the scaling factors in
7       the vector S
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SYNOPSIS

10       SUBROUTINE SLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
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12           CHARACTER      EQUED, UPLO
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14           INTEGER        LDA, N
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16           REAL           AMAX, SCOND
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18           REAL           A( LDA, * ), S( * )
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PURPOSE

21       SLAQSY equilibrates a symmetric matrix A using the scaling  factors  in
22       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       A       (input/output) REAL array, dimension (LDA,N)
34               On entry, the symmetric matrix A.  If UPLO = 'U', the leading n
35               by  n  upper triangular part of A contains the upper triangular
36               part of the matrix A, and the strictly lower triangular part of
37               A  is  not referenced.  If UPLO = 'L', the leading n by n lower
38               triangular part of A contains the lower triangular part of  the
39               matrix  A,  and  the strictly upper triangular part of A is not
40               referenced.  On exit, if EQUED = 'Y', the equilibrated  matrix:
41               diag(S) * A * diag(S).
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43       LDA     (input) INTEGER
44               The leading dimension of the array A.  LDA >= max(N,1).
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46       S       (input) REAL array, dimension (N)
47               The scale factors for A.
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49       SCOND   (input) REAL
50               Ratio of the smallest S(i) to the largest S(i).
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52       AMAX    (input) REAL
53               Absolute value of largest matrix entry.
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55       EQUED   (output) CHARACTER*1
56               Specifies  whether  or  not equilibration was done.  = 'N':  No
57               equilibration.
58               = 'Y':  Equilibration was done, i.e., A has  been  replaced  by
59               diag(S) * A * diag(S).
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PARAMETERS

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