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# zspcon

```
NAME
ZSPCON - estimate the reciprocal of the condition number (in
the 1-norm) of a complex symmetric packed matrix A using the
factorization A = U*D*U**T or A = L*D*L**T computed by
ZSPTRF

SYNOPSIS
SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK,
INFO )

CHARACTER      UPLO

INTEGER        INFO, N

DOUBLE         PRECISION ANORM, RCOND

INTEGER        IPIV( * )

COMPLEX*16     AP( * ), WORK( * )

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

An estimate is obtained for norm(inv(A)), and the reciprocal
of the condition number is computed as RCOND = 1 / (ANORM *
norm(inv(A))).

ARGUMENTS
UPLO    (input) CHARACTER*1
Specifies whether the details of the factorization
are stored as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**T;
= 'L':  Lower triangular, form is A = L*D*L**T.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used
to obtain the factor U or L as computed by ZSPTRF,
stored as a packed triangular matrix.

IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure
of D as determined by ZSPTRF.

ANORM   (input) DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix
A, computed as RCOND = 1/(ANORM * AINVNM), where
AINVNM is an estimate of the 1-norm of inv(A) com-
puted in this routine.

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```