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

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

10       SUBROUTINE SLAQSP( 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           REAL           AMAX, SCOND
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18           REAL           AP( * ), S( * )
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PURPOSE

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54               =  'Y':   Equilibration  was done, i.e., A has been replaced by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

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