# dppcon (l) - Linux Manuals

## NAME

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

## 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
= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO = aqLaq, 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) computed 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