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

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

10       SUBROUTINE ZLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )
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12           CHARACTER      EQUED, UPLO
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14           INTEGER        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     AP( * )
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PURPOSE

23       ZLAQSP 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       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.   On  exit,  the  equili‐
41               brated matrix:  diag(S) * A * diag(S), in the same storage for‐
42               mat as A.
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44       S       (input) DOUBLE PRECISION array, dimension (N)
45               The scale factors for A.
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47       SCOND   (input) DOUBLE PRECISION
48               Ratio of the smallest S(i) to the largest S(i).
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50       AMAX    (input) DOUBLE PRECISION
51               Absolute value of largest matrix entry.
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53       EQUED   (output) CHARACTER*1
54               Specifies whether or not equilibration was done.   =  'N':   No
55               equilibration.
56               =  'Y':   Equilibration  was done, i.e., A has been replaced by
57               diag(S) * A * diag(S).
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PARAMETERS

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