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

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

11       SUBROUTINE SPOEQU( 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           A( LDA, * ), S( * )
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PURPOSE

20       SPOEQU  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.
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ARGUMENTS

30       N       (input) INTEGER
31               The order of the matrix A.  N >= 0.
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33       A       (input) REAL array, dimension (LDA,N)
34               The  N-by-N  symmetric  positive  definite matrix whose scaling
35               factors are to be computed.  Only the diagonal  elements  of  A
36               are referenced.
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38       LDA     (input) INTEGER
39               The leading dimension of the array A.  LDA >= max(1,N).
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41       S       (output) REAL array, dimension (N)
42               If INFO = 0, S contains the scale factors for A.
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44       SCOND   (output) REAL
45               If  INFO  = 0, S contains the ratio of the smallest S(i) to the
46               largest S(i).  If SCOND >= 0.1 and AMAX is  neither  too  large
47               nor too small, it is not worth scaling by S.
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49       AMAX    (output) REAL
50               Absolute  value  of  largest  matrix  element.  If AMAX is very
51               close to overflow or very close to underflow, the matrix should
52               be scaled.
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54       INFO    (output) INTEGER
55               = 0:  successful exit
56               < 0:  if INFO = -i, the i-th argument had an illegal value
57               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
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61 LAPACK routine (version 3.1)    November 2006                       SPOEQU(1)