DSYSV(3)       LAPACK routine of NEC Numeric Library Collection       DSYSV(3)



NAME
       DSYSV

SYNOPSIS
       SUBROUTINE DSYSV (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
           INFO)



PURPOSE
            DSYSV computes the solution to a real system of linear equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            The diagonal pivoting method is used to factor A as
               A = U * D * U**T,  if UPLO = 'U', or
               A = L * D * L**T,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and D is symmetric and block diagonal with
            1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
            used to solve the system of equations A * X = B.




ARGUMENTS
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The number of linear equations, i.e., the order of the
                     matrix A.  N >= 0.

           NRHS      (input)
                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           A         (input/output)
                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, the symmetric matrix A.  If UPLO = 'U', the leading
                     N-by-N upper triangular part of A contains the upper
                     triangular part of the matrix A, and the strictly lower
                     triangular part of A is not referenced.  If UPLO = 'L', the
                     leading N-by-N lower triangular part of A contains the lower
                     triangular part of the matrix A, and the strictly upper
                     triangular part of A is not referenced.

                     On exit, if INFO = 0, the block diagonal matrix D and the
                     multipliers used to obtain the factor U or L from the
                     factorization A = U*D*U**T or A = L*D*L**T as computed by
                     DSYTRF.

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

           IPIV      (output)
                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D, as
                     determined by DSYTRF.  If IPIV(k) > 0, then rows and columns
                     k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
                     diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
                     then rows and columns k-1 and -IPIV(k) were interchanged and
                     D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
                     IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
                     -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
                     diagonal block.

           B         (input/output)
                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The length of WORK.  LWORK >= 1, and for best performance
                     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
                     DSYTRF.
                     for LWORK < N, TRS will be done with Level BLAS 2
                     for LWORK >= N, TRS will be done with Level BLAS 3

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           INFO      (output)
                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular, so the solution could not be computed.



LAPACK routine                  31 October 2017                       DSYSV(3)