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

NAME

6       DPOEQU  -  computes  row  and column scalings intended to equilibrate a
7       symmetric positive definite matrix A and reduce  its  condition  number
8       (with respect to the two-norm)
9

SYNOPSIS

11       SUBROUTINE DPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
12
13           INTEGER        INFO, LDA, N
14
15           DOUBLE         PRECISION AMAX, SCOND
16
17           DOUBLE         PRECISION A( LDA, * ), S( * )
18

PURPOSE

20       DPOEQU  computes row and column scalings intended to equilibrate a sym‐
21       metric positive definite matrix A and reduce its condition number (with
22       respect  to  the  two-norm).   S  contains  the  scale  factors, S(i) =
23       1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)
24       = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the
25       condition number of B within a factor N of the smallest possible condi‐
26       tion number over all possible diagonal scalings.
27

ARGUMENTS

29       N       (input) INTEGER
30               The order of the matrix A.  N >= 0.
31
32       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
33               The  N-by-N  symmetric  positive  definite matrix whose scaling
34               factors are to be computed.  Only the diagonal  elements  of  A
35               are referenced.
36
37       LDA     (input) INTEGER
38               The leading dimension of the array A.  LDA >= max(1,N).
39
40       S       (output) DOUBLE PRECISION array, dimension (N)
41               If INFO = 0, S contains the scale factors for A.
42
43       SCOND   (output) DOUBLE PRECISION
44               If  INFO  = 0, S contains the ratio of the smallest S(i) to the
45               largest S(i).  If SCOND >= 0.1 and AMAX is  neither  too  large
46               nor too small, it is not worth scaling by S.
47
48       AMAX    (output) DOUBLE PRECISION
49               Absolute  value  of  largest  matrix  element.  If AMAX is very
50               close to overflow or very close to underflow, the matrix should
51               be scaled.
52
53       INFO    (output) INTEGER
54               = 0:  successful exit
55               < 0:  if INFO = -i, the i-th argument had an illegal value
56               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
57
58
59
60 LAPACK routine (version 3.2)    November 2008                       DPOEQU(1)