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DSYCON(l)) DSYCON(l)NAMEDSYCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmet- ric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRFSYNOPSISSUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, N DOUBLE PRECISION ANORM, RCOND INTEGER IPIV( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), WORK( * )PURPOSEDSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmet- ric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is com- puted as RCOND = 1 / (ANORM * norm(inv(A))).ARGUMENTSUPLO (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) DOUBLE PRECISION array, dimension (LDA,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF. 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 DSYTRF. 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) DOUBLE PRECISION array, dimension (2*N) IWORK (workspace) INTEGER array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 DSYCON(l)

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