1CGBEQU(1) LAPACK routine (version 3.2) CGBEQU(1)
2
6 CGBEQU - computes row and column scalings intended to equilibrate an M-
7 by-N band matrix A and reduce its condition number
8
10 SUBROUTINE CGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX,
11 INFO )
12 INTEGER INFO, KL, KU, LDAB, M, N
14 REAL AMAX, COLCND, ROWCND
16 REAL C( * ), R( * )
18 COMPLEX AB( LDAB, * )
20
22 CGBEQU 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.
31
33 M (input) INTEGER
34 The number of rows of the matrix A. M >= 0.
35 N (input) INTEGER
37 The number of columns of the matrix A. N >= 0.
38 KL (input) INTEGER
40 The number of subdiagonals within the band of A. KL >= 0.
41 KU (input) INTEGER
43 The number of superdiagonals within the band of A. KU >= 0.
44 AB (input) COMPLEX 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 LDAB (input) INTEGER
51 The leading dimension of the array AB. LDAB >= KL+KU+1.
52 R (output) REAL array, dimension (M)
54 If INFO = 0, or INFO > M, R contains the row scale factors for
55 A.
56 C (output) REAL array, dimension (N)
58 If INFO = 0, C contains the column scale factors for A.
59 ROWCND (output) REAL
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 COLCND (output) REAL
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 AMAX (output) REAL
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 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 LAPACK routine (version 3.2) November 2008 CGBEQU(1)