1SGEEQUB(1) LAPACK routine (version 3.2) SGEEQUB(1)
2
6 SGEEQUB - computes row and column scalings intended to equilibrate an
7 M-by-N matrix A and reduce its condition number
8
10 SUBROUTINE SGEEQUB( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )
11 IMPLICIT NONE
13 INTEGER INFO, LDA, M, N
15 REAL AMAX, COLCND, ROWCND
17 REAL A( LDA, * ), C( * ), R( * )
19
21 SGEEQUB computes row and column scalings intended to equilibrate an M-
22 by-N matrix A and reduce its condition number. R returns the row scale
23 factors and C the column scale factors, chosen to try to make the
24 largest element in each row and column of the matrix B with elements
25 B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most the radix.
26 R(i) and C(j) are restricted to be a power of the radix between SMLNUM
27 = smallest safe number and BIGNUM = largest safe number. Use of these
28 scaling factors is not guaranteed to reduce the condition number of A
29 but works well in practice.
30 This routine differs from SGEEQU by restricting the scaling factors to
31 a power of the radix. Baring over- and underflow, scaling by these
32 factors introduces no additional rounding errors. However, the scaled
33 entries' magnitured are no longer approximately 1 but lie between
34 sqrt(radix) and 1/sqrt(radix).
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37 M (input) INTEGER
38 The number of rows of the matrix A. M >= 0.
39 N (input) INTEGER
41 The number of columns of the matrix A. N >= 0.
42 A (input) REAL array, dimension (LDA,N)
44 The M-by-N matrix whose equilibration factors are to be com‐
45 puted.
46 LDA (input) INTEGER
48 The leading dimension of the array A. LDA >= max(1,M).
49 R (output) REAL array, dimension (M)
51 If INFO = 0 or INFO > M, R contains the row scale factors for
52 A.
53 C (output) REAL array, dimension (N)
55 If INFO = 0, C contains the column scale factors for A.
56 ROWCND (output) REAL
58 If INFO = 0 or INFO > M, ROWCND contains the ratio of the
59 smallest R(i) to the largest R(i). If ROWCND >= 0.1 and AMAX
60 is neither too large nor too small, it is not worth scaling by
61 R.
62 COLCND (output) REAL
64 If INFO = 0, COLCND contains the ratio of the smallest C(i) to
65 the largest C(i). If COLCND >= 0.1, it is not worth scaling by
66 C.
67 AMAX (output) REAL
69 Absolute value of largest matrix element. If AMAX is very
70 close to overflow or very close to underflow, the matrix should
71 be scaled.
72 INFO (output) INTEGER
74 = 0: successful exit
75 < 0: if INFO = -i, the i-th argument had an illegal value
76 > 0: if INFO = i, and i is
77 <= M: the i-th row of A is exactly zero
78 > M: the (i-M)-th column of A is exactly zero
79 LAPACK routine (version 3.2) November 2008 SGEEQUB(1)