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

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

9       SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
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11           CHARACTER      EQUED, UPLO
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13           INTEGER        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     AP( * )
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PURPOSE

22       ZLAQSP  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       AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
36               On  entry,  the upper or lower triangle of the symmetric matrix
37               A, packed columnwise in a linear array.  The j-th column  of  A
38               is  stored  in  the  array AP as follows: if UPLO = 'U', AP(i +
39               (j-1)*j/2) =  A(i,j)  for  1<=i<=j;  if  UPLO  =  'L',  AP(i  +
40               (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
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42               On  exit,  the  equilibrated matrix:  diag(S) * A * diag(S), in
43               the same storage format as A.
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45       S       (input) DOUBLE PRECISION array, dimension (N)
46               The scale factors for A.
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48       SCOND   (input) DOUBLE PRECISION
49               Ratio of the smallest S(i) to the largest S(i).
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51       AMAX    (input) DOUBLE PRECISION
52               Absolute value of largest matrix entry.
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54       EQUED   (output) CHARACTER*1
55               Specifies whether or not equilibration was done.   =  'N':   No
56               equilibration.
57               =  'Y':   Equilibration  was done, i.e., A has been replaced by
58               diag(S) * A * diag(S).
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PARAMETERS

61       THRESH is a threshold value used to decide if scaling  should  be  done
62       based  on the ratio of the scaling factors.  If SCOND < THRESH, scaling
63       is done.
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65       LARGE and SMALL are threshold values used to decide if  scaling  should
66       be  done  based on the absolute size of the largest matrix element.  If
67       AMAX > LARGE or AMAX < SMALL, scaling is done.
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71 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQSP(1)
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