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

6       ZSPCON  -  estimates  the  reciprocal  of  the condition number (in the
7       1-norm) of a complex symmetric packed matrix A using the  factorization
8       A = U*D*U**T or A = L*D*L**T computed by ZSPTRF
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SYNOPSIS

11       SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
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13           CHARACTER      UPLO
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15           INTEGER        INFO, N
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17           DOUBLE         PRECISION ANORM, RCOND
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19           INTEGER        IPIV( * )
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21           COMPLEX*16     AP( * ), WORK( * )
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PURPOSE

24       ZSPCON estimates the reciprocal of the condition number (in the 1-norm)
25       of a complex symmetric packed matrix A  using  the  factorization  A  =
26       U*D*U**T  or  A = L*D*L**T computed by ZSPTRF.  An estimate is obtained
27       for norm(inv(A)), and the reciprocal of the condition  number  is  com‐
28       puted as RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

31       UPLO    (input) CHARACTER*1
32               Specifies  whether  the details of the factorization are stored
33               as an upper or lower triangular matrix.  = 'U':  Upper triangu‐
34               lar, form is A = U*D*U**T;
35               = 'L':  Lower triangular, form is A = L*D*L**T.
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37       N       (input) INTEGER
38               The order of the matrix A.  N >= 0.
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40       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
41               The  block diagonal matrix D and the multipliers used to obtain
42               the factor U or L as computed by ZSPTRF,  stored  as  a  packed
43               triangular matrix.
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45       IPIV    (input) INTEGER array, dimension (N)
46               Details  of  the  interchanges  and the block structure of D as
47               determined by ZSPTRF.
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49       ANORM   (input) DOUBLE PRECISION
50               The 1-norm of the original matrix A.
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52       RCOND   (output) DOUBLE PRECISION
53               The reciprocal of the condition number of the  matrix  A,  com‐
54               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
55               mate of the 1-norm of inv(A) computed in this routine.
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57       WORK    (workspace) COMPLEX*16 array, dimension (2*N)
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59       INFO    (output) INTEGER
60               = 0:  successful exit
61               < 0:  if INFO = -i, the i-th argument had an illegal value
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65 LAPACK routine (version 3.2)    November 2008                       ZSPCON(1)
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