.TH SPOCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME SPOCON - the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF .SH SYNOPSIS .TP 19 SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, IWORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, LDA, N .TP 19 .ti +4 REAL ANORM, RCOND .TP 19 .ti +4 INTEGER IWORK( * ) .TP 19 .ti +4 REAL A( LDA, * ), WORK( * ) .SH PURPOSE SPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF. 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 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 A (input) REAL array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 ANORM (input) REAL The 1-norm (or infinity-norm) of the symmetric 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) REAL array, dimension (3*N) .TP 8 IWORK (workspace) INTEGER array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value