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

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

10       SUBROUTINE ZGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,  AMAX,
11                          INFO )
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13           INTEGER        INFO, KL, KU, LDAB, M, N
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15           DOUBLE         PRECISION AMAX, COLCND, ROWCND
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17           DOUBLE         PRECISION C( * ), R( * )
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19           COMPLEX*16     AB( LDAB, * )
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PURPOSE

22       ZGBEQU  computes  row and column scalings intended to equilibrate an M-
23       by-N band matrix A and reduce its condition number.  R returns the  row
24       scale factors and C the column scale factors, chosen to try to make the
25       largest element in each row and column of the matrix  B  with  elements
26       B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
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

33       M       (input) INTEGER
34               The number of rows of the matrix A.  M >= 0.
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36       N       (input) INTEGER
37               The number of columns of the matrix A.  N >= 0.
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39       KL      (input) INTEGER
40               The number of subdiagonals within the band of A.  KL >= 0.
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42       KU      (input) INTEGER
43               The number of superdiagonals within the band of A.  KU >= 0.
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45       AB      (input) COMPLEX*16 array, dimension (LDAB,N)
46               The band matrix A, stored in rows 1 to KL+KU+1.  The j-th  col‐
47               umn  of  A is stored in the j-th column of the array AB as fol‐
48               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
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50       LDAB    (input) INTEGER
51               The leading dimension of the array AB.  LDAB >= KL+KU+1.
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53       R       (output) DOUBLE PRECISION array, dimension (M)
54               If INFO = 0, or INFO > M, R contains the row scale factors  for
55               A.
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57       C       (output) DOUBLE PRECISION array, dimension (N)
58               If INFO = 0, C contains the column scale factors for A.
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60       ROWCND  (output) DOUBLE PRECISION
61               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
62               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
63               is  neither too large nor too small, it is not worth scaling by
64               R.
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66       COLCND  (output) DOUBLE PRECISION
67               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
68               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
69               C.
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71       AMAX    (output) DOUBLE PRECISION
72               Absolute value of largest matrix  element.   If  AMAX  is  very
73               close to overflow or very close to underflow, the matrix should
74               be scaled.
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76       INFO    (output) INTEGER
77               = 0:  successful exit
78               < 0:  if INFO = -i, the i-th argument had an illegal value
79               > 0:  if INFO = i, and i is
80               <= M:  the i-th row of A is exactly zero
81               >  M:  the (i-M)-th column of A is exactly zero
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85 LAPACK routine (version 3.2)    November 2008                       ZGBEQU(1)