1CGEEQU(1)                LAPACK routine (version 3.1)                CGEEQU(1)
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NAME

6       CGEEQU  -  row  and  column  scalings intended to equilibrate an M-by-N
7       matrix A and reduce its condition number
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SYNOPSIS

10       SUBROUTINE CGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )
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12           INTEGER        INFO, LDA, M, N
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14           REAL           AMAX, COLCND, ROWCND
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16           REAL           C( * ), R( * )
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18           COMPLEX        A( LDA, * )
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PURPOSE

21       CGEEQU computes row and column scalings intended to equilibrate  an  M-
22       by-N matrix A and reduce its condition number.  R returns the row scale
23       factors and C the column scale factors,  chosen  to  try  to  make  the
24       largest  element  in  each row and column of the matrix B with elements
25       B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
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27       R(i) and C(j) are restricted to be between SMLNUM = smallest safe  num‐
28       ber  and BIGNUM = largest safe number.  Use of these scaling factors is
29       not guaranteed to reduce the condition number of A but  works  well  in
30       practice.
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ARGUMENTS

34       M       (input) INTEGER
35               The number of rows of the matrix A.  M >= 0.
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37       N       (input) INTEGER
38               The number of columns of the matrix A.  N >= 0.
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40       A       (input) COMPLEX array, dimension (LDA,N)
41               The  M-by-N  matrix  whose equilibration factors are to be com‐
42               puted.
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44       LDA     (input) INTEGER
45               The leading dimension of the array A.  LDA >= max(1,M).
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47       R       (output) REAL array, dimension (M)
48               If INFO = 0 or INFO > M, R contains the row scale  factors  for
49               A.
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51       C       (output) REAL array, dimension (N)
52               If INFO = 0,  C contains the column scale factors for A.
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54       ROWCND  (output) REAL
55               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
56               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
57               is  neither too large nor too small, it is not worth scaling by
58               R.
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60       COLCND  (output) REAL
61               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
62               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
63               C.
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65       AMAX    (output) REAL
66               Absolute value of largest matrix  element.   If  AMAX  is  very
67               close to overflow or very close to underflow, the matrix should
68               be scaled.
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70       INFO    (output) INTEGER
71               = 0:  successful exit
72               < 0:  if INFO = -i, the i-th argument had an illegal value
73               > 0:  if INFO = i,  and i is
74               <= M:  the i-th row of A is exactly zero
75               >  M:  the (i-M)-th column of A is exactly zero
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79 LAPACK routine (version 3.1)    November 2006                       CGEEQU(1)
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