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

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

11       SUBROUTINE SPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
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13           CHARACTER      UPLO
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15           INTEGER        INFO, N
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17           REAL           AMAX, SCOND
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19           REAL           AP( * ), S( * )
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PURPOSE

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

31       UPLO    (input) CHARACTER*1
32               = 'U':  Upper triangle of A is stored;
33               = 'L':  Lower triangle of A is stored.
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35       N       (input) INTEGER
36               The order of the matrix A.  N >= 0.
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38       AP      (input) REAL array, dimension (N*(N+1)/2)
39               The  upper  or lower triangle of the symmetric matrix A, packed
40               columnwise in a linear array.  The j-th column of A  is  stored
41               in  the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
42               A(i,j) for 1<=i<=j; if UPLO = 'L',  AP(i  +  (j-1)*(2n-j)/2)  =
43               A(i,j) for j<=i<=n.
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45       S       (output) REAL array, dimension (N)
46               If INFO = 0, S contains the scale factors for A.
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48       SCOND   (output) REAL
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) REAL
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.
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58       INFO    (output) INTEGER
59               = 0:  successful exit
60               < 0:  if INFO = -i, the i-th argument had an illegal value
61               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
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65 LAPACK routine (version 3.2)    November 2008                       SPPEQU(1)
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