.TH CSPCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CSPCON - 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 .SH SYNOPSIS .TP 19 SUBROUTINE CSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 REAL ANORM, RCOND .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 COMPLEX AP( * ), WORK( * ) .SH 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))). .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = \(aqU\(aq: Upper triangular, form is A = U*D*U**T; .br = \(aqL\(aq: Lower triangular, form is A = L*D*L**T. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 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. .TP 8 IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSPTRF. .TP 8 ANORM (input) REAL The 1-norm of the original matrix A. .TP 8 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. .TP 8 WORK (workspace) COMPLEX array, dimension (2*N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value