1ZGEEQUB(1) LAPACK routine (version 3.2)                             ZGEEQUB(1)
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NAME

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

10       SUBROUTINE ZGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )
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12           IMPLICIT        NONE
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14           INTEGER         INFO, 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       ZGEEQUB computes row and column scalings intended to equilibrate an  M-
24       by-N matrix A and reduce its condition number.  R returns the row scale
25       factors and C the column scale factors,  chosen  to  try  to  make  the
26       largest  element  in  each row and column of the matrix B with elements
27       B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix.
28       R(i) and C(j) are restricted to be a power of the radix between  SMLNUM
29       =  smallest safe number and BIGNUM = largest safe number.  Use of these
30       scaling factors is not guaranteed to reduce the condition number  of  A
31       but works well in practice.
32       This  routine differs from ZGEEQU by restricting the scaling factors to
33       a power of the radix.  Baring over- and  underflow,  scaling  by  these
34       factors  introduces no additional rounding errors.  However, the scaled
35       entries' magnitured are no  longer  approximately  1  but  lie  between
36       sqrt(radix) and 1/sqrt(radix).
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ARGUMENTS

39       M       (input) INTEGER
40               The number of rows of the matrix A.  M >= 0.
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42       N       (input) INTEGER
43               The number of columns of the matrix A.  N >= 0.
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45       A       (input) COMPLEX*16 array, dimension (LDA,N)
46               The  M-by-N  matrix  whose equilibration factors are to be com‐
47               puted.
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49       LDA     (input) INTEGER
50               The leading dimension of the array A.  LDA >= max(1,M).
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52       R       (output) DOUBLE PRECISION array, dimension (M)
53               If INFO = 0 or INFO > M, R contains the row scale  factors  for
54               A.
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56       C       (output) DOUBLE PRECISION array, dimension (N)
57               If INFO = 0,  C contains the column scale factors for A.
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59       ROWCND  (output) DOUBLE PRECISION
60               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
61               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
62               is  neither too large nor too small, it is not worth scaling by
63               R.
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65       COLCND  (output) DOUBLE PRECISION
66               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
67               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
68               C.
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70       AMAX    (output) DOUBLE PRECISION
71               Absolute value of largest matrix  element.   If  AMAX  is  very
72               close to overflow or very close to underflow, the matrix should
73               be scaled.
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75       INFO    (output) INTEGER
76               = 0:  successful exit
77               < 0:  if INFO = -i, the i-th argument had an illegal value
78               > 0:  if INFO = i,  and i is
79               <= M:  the i-th row of A is exactly zero
80               >  M:  the (i-M)-th column of A is exactly zero
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84    LAPACK routine (version 3.2) November 2008                      ZGEEQUB(1)