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# dsycon

```
NAME
DSYCON - estimate the reciprocal of the condition number (in
the 1-norm) of a real symmetric matrix A using the factori-
zation A = U*D*U**T or A = L*D*L**T computed by DSYTRF

SYNOPSIS
SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND,
WORK, IWORK, INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, N

DOUBLE         PRECISION ANORM, RCOND

INTEGER        IPIV( * ), IWORK( * )

DOUBLE         PRECISION A( LDA, * ), WORK( * )

PURPOSE
DSYCON estimates the reciprocal of the condition number (in
the 1-norm) of a real symmetric matrix A using the factori-
zation A = U*D*U**T or A = L*D*L**T computed by DSYTRF.

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.

A       (input) DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used
to obtain the factor U or L as computed by DSYTRF.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

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

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) DOUBLE PRECISION array, dimension (2*N)

IWORK    (workspace) INTEGER array, dimension (N)

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