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

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

11       SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK, 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( * ), IWORK( * )
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21           DOUBLE         PRECISION AP( * ), WORK( * )
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PURPOSE

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

33       UPLO    (input) CHARACTER*1
34               Specifies whether the details of the factorization  are  stored
35               as an upper or lower triangular matrix.  = 'U':  Upper triangu‐
36               lar, form is A = U*D*U**T;
37               = 'L':  Lower triangular, form is A = L*D*L**T.
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39       N       (input) INTEGER
40               The order of the matrix A.  N >= 0.
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42       AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
43               The block diagonal matrix D and the multipliers used to  obtain
44               the  factor  U  or  L as computed by DSPTRF, stored as a packed
45               triangular matrix.
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47       IPIV    (input) INTEGER array, dimension (N)
48               Details of the interchanges and the block  structure  of  D  as
49               determined by DSPTRF.
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51       ANORM   (input) DOUBLE PRECISION
52               The 1-norm of the original matrix A.
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54       RCOND   (output) DOUBLE PRECISION
55               The  reciprocal  of  the condition number of the matrix A, com‐
56               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
57               mate of the 1-norm of inv(A) computed in this routine.
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59       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
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61       IWORK    (workspace) INTEGER array, dimension (N)
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63       INFO    (output) INTEGER
64               = 0:  successful exit
65               < 0:  if INFO = -i, the i-th argument had an illegal value
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69 LAPACK routine (version 3.1)    November 2006                       DSPCON(1)
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