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

6       SLAQGE  - equilibrates a general M by N matrix A using the row and col‐
7       umn scaling factors in the vectors R and C
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SYNOPSIS

10       SUBROUTINE SLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED )
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12           CHARACTER      EQUED
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14           INTEGER        LDA, M, N
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16           REAL           AMAX, COLCND, ROWCND
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18           REAL           A( LDA, * ), C( * ), R( * )
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PURPOSE

21       SLAQGE equilibrates a general M by N matrix A using the row and  column
22       scaling factors in the vectors R and C.
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ARGUMENTS

25       M       (input) INTEGER
26               The number of rows of the matrix A.  M >= 0.
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28       N       (input) INTEGER
29               The number of columns of the matrix A.  N >= 0.
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31       A       (input/output) REAL array, dimension (LDA,N)
32               On  entry,  the  M  by  N  matrix A.  On exit, the equilibrated
33               matrix.  See EQUED for the form of the equilibrated matrix.
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35       LDA     (input) INTEGER
36               The leading dimension of the array A.  LDA >= max(M,1).
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38       R       (input) REAL array, dimension (M)
39               The row scale factors for A.
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41       C       (input) REAL array, dimension (N)
42               The column scale factors for A.
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44       ROWCND  (input) REAL
45               Ratio of the smallest R(i) to the largest R(i).
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47       COLCND  (input) REAL
48               Ratio of the smallest C(i) to the largest C(i).
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50       AMAX    (input) REAL
51               Absolute value of largest matrix entry.
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53       EQUED   (output) CHARACTER*1
54               Specifies the form of equilibration that was done.  = 'N':   No
55               equilibration
56               =  'R':   Row  equilibration, i.e., A has been premultiplied by
57               diag(R).  = 'C':  Column equilibration, i.e., A has been  post‐
58               multiplied  by diag(C).  = 'B':  Both row and column equilibra‐
59               tion, i.e., A has been replaced by diag(R) * A * diag(C).
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PARAMETERS

62       THRESH is a threshold value used to decide if  row  or  column  scaling
63       should be done based on the ratio of the row or column scaling factors.
64       If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
65       scaling  is  done.  LARGE and SMALL are threshold values used to decide
66       if row scaling should be done based on the absolute size of the largest
67       matrix element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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71 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLAQGE(1)