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# dppcon

```
NAME
DPPCON - estimate the reciprocal of the condition number (in
the 1-norm) of a real symmetric positive definite packed
matrix using the Cholesky factorization A = U**T*U or A =
L*L**T computed by DPPTRF

SYNOPSIS
SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK,
INFO )

CHARACTER      UPLO

INTEGER        INFO, N

DOUBLE         PRECISION ANORM, RCOND

INTEGER        IWORK( * )

DOUBLE         PRECISION AP( * ), WORK( * )

PURPOSE
DPPCON estimates the reciprocal of the condition number (in
the 1-norm) of a real symmetric positive definite packed
matrix using the Cholesky factorization A = U**T*U or A =
L*L**T computed by DPPTRF.

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
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky fac-
torization A = U**T*U or A = L*L**T, packed column-
wise in a linear array.  The j-th column of U or L
is stored in the array AP as follows: if UPLO = 'U',
AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO =
'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

ANORM   (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the symmetric
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 (3*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
```