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

6       ZSYEQUB  -  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 ZSYEQUB( 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           COMPLEX*16      A( LDA, * ), WORK( * )
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23           DOUBLE          PRECISION S( * )
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PURPOSE

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

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