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

NAME

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

SYNOPSIS

10       SUBROUTINE SGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )
11
12           INTEGER        INFO, LDA, M, N
13
14           REAL           AMAX, COLCND, ROWCND
15
16           REAL           A( LDA, * ), C( * ), R( * )
17

PURPOSE

19       SGEEQU computes row and column scalings intended to equilibrate  an  M-
20       by-N matrix A and reduce its condition number.  R returns the row scale
21       factors and C the column scale factors,  chosen  to  try  to  make  the
22       largest  element  in  each row and column of the matrix B with elements
23       B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
24
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
30

ARGUMENTS

32       M       (input) INTEGER
33               The number of rows of the matrix A.  M >= 0.
34
35       N       (input) INTEGER
36               The number of columns of the matrix A.  N >= 0.
37
38       A       (input) REAL array, dimension (LDA,N)
39               The  M-by-N  matrix  whose equilibration factors are to be com‐
40               puted.
41
42       LDA     (input) INTEGER
43               The leading dimension of the array A.  LDA >= max(1,M).
44
45       R       (output) REAL array, dimension (M)
46               If INFO = 0 or INFO > M, R contains the row scale  factors  for
47               A.
48
49       C       (output) REAL array, dimension (N)
50               If INFO = 0,  C contains the column scale factors for A.
51
52       ROWCND  (output) REAL
53               If  INFO  =  0  or  INFO  > M, ROWCND contains the ratio of the
54               smallest R(i) to the largest R(i).  If ROWCND >= 0.1  and  AMAX
55               is  neither too large nor too small, it is not worth scaling by
56               R.
57
58       COLCND  (output) REAL
59               If INFO = 0, COLCND contains the ratio of the smallest C(i)  to
60               the largest C(i).  If COLCND >= 0.1, it is not worth scaling by
61               C.
62
63       AMAX    (output) REAL
64               Absolute value of largest matrix  element.   If  AMAX  is  very
65               close to overflow or very close to underflow, the matrix should
66               be scaled.
67
68       INFO    (output) INTEGER
69               = 0:  successful exit
70               < 0:  if INFO = -i, the i-th argument had an illegal value
71               > 0:  if INFO = i,  and i is
72               <= M:  the i-th row of A is exactly zero
73               >  M:  the (i-M)-th column of A is exactly zero
74
75
76
77 LAPACK routine (version 3.1)    November 2006                       SGEEQU(1)
Impressum