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

6       ZLAQGE  -  a  general  M by N matrix A using the row and column scaling
7       factors in the vectors R and C
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SYNOPSIS

10       SUBROUTINE ZLAQGE( 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           DOUBLE         PRECISION AMAX, COLCND, ROWCND
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18           DOUBLE         PRECISION C( * ), R( * )
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20           COMPLEX*16     A( LDA, * )
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PURPOSE

23       ZLAQGE 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

28       M       (input) INTEGER
29               The number of rows of the matrix A.  M >= 0.
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31       N       (input) INTEGER
32               The number of columns of the matrix A.  N >= 0.
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34       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
35               On  entry,  the  M  by  N  matrix A.  On exit, the equilibrated
36               matrix.  See EQUED for the form of the equilibrated matrix.
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38       LDA     (input) INTEGER
39               The leading dimension of the array A.  LDA >= max(M,1).
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41       R       (input) DOUBLE PRECISION array, dimension (M)
42               The row scale factors for A.
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44       C       (input) DOUBLE PRECISION array, dimension (N)
45               The column scale factors for A.
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47       ROWCND  (input) DOUBLE PRECISION
48               Ratio of the smallest R(i) to the largest R(i).
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50       COLCND  (input) DOUBLE PRECISION
51               Ratio of the smallest C(i) to the largest C(i).
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53       AMAX    (input) DOUBLE PRECISION
54               Absolute value of largest matrix entry.
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56       EQUED   (output) CHARACTER*1
57               Specifies the form of equilibration that was done.  = 'N':   No
58               equilibration
59               =  'R':   Row  equilibration, i.e., A has been premultiplied by
60               diag(R).  = 'C':  Column equilibration, i.e., A has been  post‐
61               multiplied  by diag(C).  = 'B':  Both row and column equilibra‐
62               tion, i.e., A has been replaced by diag(R) * A * diag(C).
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PARAMETERS

65       THRESH is a threshold value used to decide if  row  or  column  scaling
66       should be done based on the ratio of the row or column scaling factors.
67       If ROWCND < THRESH, row scaling is done, and if COLCND < THRESH, column
68       scaling is done.
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70       LARGE  and  SMALL  are  threshold  values used to decide if row scaling
71       should be done based on the absolute size of the  largest  matrix  ele‐
72       ment.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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76 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAQGE(1)