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

6       SPOEQU  -  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 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

29       N       (input) INTEGER
30               The order of the matrix A.  N >= 0.
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32       A       (input) REAL 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.
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37       LDA     (input) INTEGER
38               The leading dimension of the array A.  LDA >= max(1,N).
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40       S       (output) REAL array, dimension (N)
41               If INFO = 0, S contains the scale factors for A.
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43       SCOND   (output) REAL
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.
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48       AMAX    (output) REAL
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.
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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.
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60 LAPACK routine (version 3.2)    November 2008                       SPOEQU(1)