1CPOEQU(1)                LAPACK routine (version 3.1)                CPOEQU(1)
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NAME

6       CPOEQU  -  row  and column scalings intended to equilibrate a Hermitian
7       positive definite matrix  A  and  reduce  its  condition  number  (with
8       respect to the two-norm)
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SYNOPSIS

11       SUBROUTINE CPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
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13           INTEGER        INFO, LDA, N
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15           REAL           AMAX, SCOND
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17           REAL           S( * )
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19           COMPLEX        A( LDA, * )
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PURPOSE

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

32       N       (input) INTEGER
33               The order of the matrix A.  N >= 0.
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35       A       (input) COMPLEX array, dimension (LDA,N)
36               The  N-by-N  Hermitian  positive  definite matrix whose scaling
37               factors are to be computed.  Only the diagonal  elements  of  A
38               are referenced.
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40       LDA     (input) INTEGER
41               The leading dimension of the array A.  LDA >= max(1,N).
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43       S       (output) REAL array, dimension (N)
44               If INFO = 0, S contains the scale factors for A.
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46       SCOND   (output) REAL
47               If  INFO  = 0, S contains the ratio of the smallest S(i) to the
48               largest S(i).  If SCOND >= 0.1 and AMAX is  neither  too  large
49               nor too small, it is not worth scaling by S.
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51       AMAX    (output) REAL
52               Absolute  value  of  largest  matrix  element.  If AMAX is very
53               close to overflow or very close to underflow, the matrix should
54               be scaled.
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56       INFO    (output) INTEGER
57               = 0:  successful exit
58               < 0:  if INFO = -i, the i-th argument had an illegal value
59               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
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63 LAPACK routine (version 3.1)    November 2006                       CPOEQU(1)