NAME

CSPCON - estimate 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 CSPTRF

SYNOPSIS

SUBROUTINE CSPCON(
UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )

CHARACTER UPLO

INTEGER INFO, N

REAL ANORM, RCOND

INTEGER IPIV( ∗ )

COMPLEX AP( ∗ ), WORK( ∗ )

PURPOSE

CSPCON 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 CSPTRF. 
 
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 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 CSPTRF, 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 CSPTRF.

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

  —  LAPACK version 2.0  —  08 October 1994