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

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

11       SUBROUTINE DSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, 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           CHARACTER       UPLO
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21           DOUBLE          PRECISION A( LDA, * ), S( * ), WORK( * )
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PURPOSE

24       DSYEQUB computes row and column scalings intended to equilibrate a sym‐
25       metric matrix A and reduce its condition number (with  respect  to  the
26       two-norm).  S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen
27       so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has
28       ones  on the diagonal.  This choice of S puts the condition number of B
29       within a factor N of the smallest possible condition  number  over  all
30       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) DOUBLE PRECISION array, dimension (LDA,N)
37               The  N-by-N  symmetric  matrix  whose scaling factors are to be
38               computed.  Only the diagonal elements of A 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) DOUBLE PRECISION array, dimension (N)
44               If INFO = 0, S contains the scale factors for A.
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46       SCOND   (output) DOUBLE PRECISION
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) DOUBLE PRECISION
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.  INFO    (output) INTEGER = 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                      DSYEQUB(1)
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