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

6       CLAQGE  - 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 CLAQGE( 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           C( * ), R( * )
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20           COMPLEX        A( LDA, * )
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PURPOSE

23       CLAQGE equilibrates a general M by N matrix A using the row and  column
24       scaling factors in the vectors R and C.
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ARGUMENTS

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

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