1ZLAQSY(1)           LAPACK auxiliary routine (version 3.1)           ZLAQSY(1)
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NAME

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

9       SUBROUTINE ZLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
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11           CHARACTER      EQUED, UPLO
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13           INTEGER        LDA, N
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15           DOUBLE         PRECISION AMAX, SCOND
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17           DOUBLE         PRECISION S( * )
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19           COMPLEX*16     A( LDA, * )
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PURPOSE

22       ZLAQSY  equilibrates  a symmetric matrix A using the scaling factors in
23       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.
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44               On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A *
45               diag(S).
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47       LDA     (input) INTEGER
48               The leading dimension of the array A.  LDA >= max(N,1).
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50       S       (input) DOUBLE PRECISION array, dimension (N)
51               The scale factors for A.
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53       SCOND   (input) DOUBLE PRECISION
54               Ratio of the smallest S(i) to the largest S(i).
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56       AMAX    (input) DOUBLE PRECISION
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.
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70       LARGE and SMALL are threshold values used to decide if  scaling  should
71       be  done  based on the absolute size of the largest matrix element.  If
72       AMAX > LARGE or AMAX < SMALL, scaling is done.
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76 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQSY(1)
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