DSYCON_3 estimates the reciprocal of the condition number (in the


 1-norm) of a real symmetric matrix A using the factorization


 computed by DSYTRF_RK or DSYTRF_BK:


    A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),


 where U (or L) is unit upper (or lower) triangular matrix,


 U**T (or L**T) is the transpose of U (or L), P is a permutation


 matrix, P**T is the transpose of P, and D is symmetric and block


 diagonal with 1-by-1 and 2-by-2 diagonal blocks.


 An estimate is obtained for norm(inv(A)), and the reciprocal of the


 condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).


 This routine uses BLAS3 solver DSYTRS_3.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the details of the factorization are


          stored as an upper or lower triangular matrix:


          = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);


          = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)


          Diagonal of the block diagonal matrix D and factors U or L


          as computed by DSYTRF_RK and DSYTRF_BK:


            a) ONLY diagonal elements of the symmetric block diagonal


               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);


               (superdiagonal (or subdiagonal) elements of D


                should be provided on entry in array E), and


            b) If UPLO = 'U': factor U in the superdiagonal part of A.


               If UPLO = 'L': factor L in the subdiagonal part of A.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

E

          E is DOUBLE PRECISION array, dimension (N)


          On entry, contains the superdiagonal (or subdiagonal)


          elements of the symmetric block diagonal matrix D


          with 1-by-1 or 2-by-2 diagonal blocks, where


          If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;


          If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.


          NOTE: For 1-by-1 diagonal block D(k), where


          1 <= k <= N, the element E(k) is not referenced in both


          UPLO = 'U' or UPLO = 'L' cases.

IPIV

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by DSYTRF_RK or DSYTRF_BK.

ANORM

          ANORM is DOUBLE PRECISION


          The 1-norm of the original matrix A.

RCOND

          RCOND is 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

          WORK is DOUBLE PRECISION array, dimension (2*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER


          = 0:  successful exit


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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017