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

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

11       SUBROUTINE ZPPEQU( 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           DOUBLE         PRECISION AMAX, SCOND
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19           DOUBLE         PRECISION S( * )
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21           COMPLEX*16     AP( * )
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PURPOSE

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

34       UPLO    (input) CHARACTER*1
35               = 'U':  Upper triangle of A is stored;
36               = 'L':  Lower triangle of A is stored.
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38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
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41       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
42               The  upper  or lower triangle of the Hermitian matrix A, packed
43               columnwise in a linear array.  The j-th column of A  is  stored
44               in  the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
45               A(i,j) for 1<=i<=j; if UPLO = 'L',  AP(i  +  (j-1)*(2n-j)/2)  =
46               A(i,j) for j<=i<=n.
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48       S       (output) DOUBLE PRECISION array, dimension (N)
49               If INFO = 0, S contains the scale factors for A.
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51       SCOND   (output) DOUBLE PRECISION
52               If  INFO  = 0, S contains the ratio of the smallest S(i) to the
53               largest S(i).  If SCOND >= 0.1 and AMAX is  neither  too  large
54               nor too small, it is not worth scaling by S.
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56       AMAX    (output) DOUBLE PRECISION
57               Absolute  value  of  largest  matrix  element.  If AMAX is very
58               close to overflow or very close to underflow, the matrix should
59               be scaled.
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61       INFO    (output) INTEGER
62               = 0:  successful exit
63               < 0:  if INFO = -i, the i-th argument had an illegal value
64               > 0:  if INFO = i, the i-th diagonal element is nonpositive.
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68 LAPACK routine (version 3.1)    November 2006                       ZPPEQU(1)
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