1DGBEQU(1)                LAPACK routine (version 3.2)                DGBEQU(1)
2
3
4

NAME

6       DGBEQU - computes row and column scalings intended to equilibrate an M-
7       by-N band matrix A and reduce its condition number
8

SYNOPSIS

10       SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,  AMAX,
11                          INFO )
12
13           INTEGER        INFO, KL, KU, LDAB, M, N
14
15           DOUBLE         PRECISION AMAX, COLCND, ROWCND
16
17           DOUBLE         PRECISION AB( LDAB, * ), C( * ), R( * )
18

PURPOSE

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

ARGUMENTS

31       M       (input) INTEGER
32               The number of rows of the matrix A.  M >= 0.
33
34       N       (input) INTEGER
35               The number of columns of the matrix A.  N >= 0.
36
37       KL      (input) INTEGER
38               The number of subdiagonals within the band of A.  KL >= 0.
39
40       KU      (input) INTEGER
41               The number of superdiagonals within the band of A.  KU >= 0.
42
43       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
44               The band matrix A, stored in rows 1 to KL+KU+1.  The j-th  col‐
45               umn  of  A is stored in the j-th column of the array AB as fol‐
46               lows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
47
48       LDAB    (input) INTEGER
49               The leading dimension of the array AB.  LDAB >= KL+KU+1.
50
51       R       (output) DOUBLE PRECISION array, dimension (M)
52               If INFO = 0, or INFO > M, R contains the row scale factors  for
53               A.
54
55       C       (output) DOUBLE PRECISION array, dimension (N)
56               If INFO = 0, C contains the column scale factors for A.
57
58       ROWCND  (output) DOUBLE PRECISION
59               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
60               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
61               is  neither too large nor too small, it is not worth scaling by
62               R.
63
64       COLCND  (output) DOUBLE PRECISION
65               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
66               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
67               C.
68
69       AMAX    (output) DOUBLE PRECISION
70               Absolute value of largest matrix  element.   If  AMAX  is  very
71               close to overflow or very close to underflow, the matrix should
72               be scaled.
73
74       INFO    (output) INTEGER
75               = 0:  successful exit
76               < 0:  if INFO = -i, the i-th argument had an illegal value
77               > 0:  if INFO = i, and i is
78               <= M:  the i-th row of A is exactly zero
79               >  M:  the (i-M)-th column of A is exactly zero
80
81
82
83 LAPACK routine (version 3.2)    November 2008                       DGBEQU(1)