1ZPOEQUB(1) LAPACK routine (version 3.2)                             ZPOEQUB(1)
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NAME

6       ZPOEQUB  -  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)
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SYNOPSIS

11       SUBROUTINE ZPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
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13           IMPLICIT        NONE
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15           INTEGER         INFO, LDA, N
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17           DOUBLE          PRECISION AMAX, SCOND
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19           COMPLEX*16      A( LDA, * )
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21           DOUBLE          PRECISION S( * )
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PURPOSE

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

33       N       (input) INTEGER
34               The order of the matrix A.  N >= 0.
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36       A       (input) COMPLEX*16 array, dimension (LDA,N)
37               The  N-by-N  symmetric  positive  definite matrix whose scaling
38               factors are to be computed.  Only the diagonal  elements  of  A
39               are referenced.
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41       LDA     (input) INTEGER
42               The leading dimension of the array A.  LDA >= max(1,N).
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44       S       (output) DOUBLE PRECISION array, dimension (N)
45               If INFO = 0, S contains the scale factors for A.
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47       SCOND   (output) DOUBLE PRECISION
48               If  INFO  = 0, S contains the ratio of the smallest S(i) to the
49               largest S(i).  If SCOND >= 0.1 and AMAX is  neither  too  large
50               nor too small, it is not worth scaling by S.
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52       AMAX    (output) DOUBLE PRECISION
53               Absolute  value  of  largest  matrix  element.  If AMAX is very
54               close to overflow or very close to underflow, the matrix should
55               be scaled.
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57       INFO    (output) INTEGER
58               = 0:  successful exit
59               < 0:  if INFO = -i, the i-th argument had an illegal value
60               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
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64    LAPACK routine (version 3.2) November 2008                      ZPOEQUB(1)