1DGBEQU(1)                LAPACK routine (version 3.1)                DGBEQU(1)
2
3
4

NAME

6       DGBEQU - row and column scalings intended to equilibrate an M-by-N band
7       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
26       R(i)  and C(j) are restricted to be between SMLNUM = smallest safe num‐
27       ber and BIGNUM = largest safe number.  Use of these scaling factors  is
28       not  guaranteed  to  reduce the condition number of A but works well in
29       practice.
30
31

ARGUMENTS

33       M       (input) INTEGER
34               The number of rows of the matrix A.  M >= 0.
35
36       N       (input) INTEGER
37               The number of columns of the matrix A.  N >= 0.
38
39       KL      (input) INTEGER
40               The number of subdiagonals within the band of A.  KL >= 0.
41
42       KU      (input) INTEGER
43               The number of superdiagonals within the band of A.  KU >= 0.
44
45       AB      (input) DOUBLE PRECISION 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).
49
50       LDAB    (input) INTEGER
51               The leading dimension of the array AB.  LDAB >= KL+KU+1.
52
53       R       (output) DOUBLE PRECISION array, dimension (M)
54               If INFO = 0, or INFO > M, R contains the row scale factors  for
55               A.
56
57       C       (output) DOUBLE PRECISION array, dimension (N)
58               If INFO = 0, C contains the column scale factors for A.
59
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.
65
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.
70
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.
75
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
82
83
84
85 LAPACK routine (version 3.1)    November 2006                       DGBEQU(1)