NAME¶

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

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) computed 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