NAME¶

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

SYNOPSIS¶

SUBROUTINE CSYCON(

UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO )

CHARACTER UPLO INTEGER INFO, LDA, N REAL ANORM, RCOND INTEGER IPIV( * ) COMPLEX A( LDA, * ), WORK( * )

PURPOSE¶

CSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF. 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) COMPLEX array, dimension (LDA,N)

The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF.

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 CSYTRF.

ANORM (input) REAL

The 1-norm of the original matrix A.

RCOND (output) REAL

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 array, dimension (2*N)

INFO (output) INTEGER

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