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

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

10       SUBROUTINE ZLAQSY( 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           DOUBLE         PRECISION AMAX, SCOND
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18           DOUBLE         PRECISION S( * )
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20           COMPLEX*16     A( LDA, * )
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PURPOSE

23       ZLAQSY equilibrates a symmetric matrix A using the scaling  factors  in
24       the vector S.
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ARGUMENTS

27       UPLO    (input) CHARACTER*1
28               Specifies  whether  the  upper  or lower triangular part of the
29               symmetric matrix A is stored.  = 'U':  Upper triangular
30               = 'L':  Lower triangular
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32       N       (input) INTEGER
33               The order of the matrix A.  N >= 0.
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35       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
36               On entry, the symmetric matrix A.  If UPLO = 'U', the leading n
37               by  n  upper triangular part of A contains the upper triangular
38               part of the matrix A, and the strictly lower triangular part of
39               A  is  not referenced.  If UPLO = 'L', the leading n by n lower
40               triangular part of A contains the lower triangular part of  the
41               matrix  A,  and  the strictly upper triangular part of A is not
42               referenced.  On exit, if EQUED = 'Y', the equilibrated  matrix:
43               diag(S) * A * diag(S).
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45       LDA     (input) INTEGER
46               The leading dimension of the array A.  LDA >= max(N,1).
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48       S       (input) DOUBLE PRECISION array, dimension (N)
49               The scale factors for A.
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51       SCOND   (input) DOUBLE PRECISION
52               Ratio of the smallest S(i) to the largest S(i).
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54       AMAX    (input) DOUBLE PRECISION
55               Absolute value of largest matrix entry.
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57       EQUED   (output) CHARACTER*1
58               Specifies  whether  or  not equilibration was done.  = 'N':  No
59               equilibration.
60               = 'Y':  Equilibration was done, i.e., A has  been  replaced  by
61               diag(S) * A * diag(S).
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PARAMETERS

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