Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes the solution to a real system of linear equations  A * X = B,

SYNOPSIS

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

           CHARACTER     UPLO

           INTEGER       INFO, LDA, LDB, LWORK, N, NRHS

           INTEGER       IPIV( * )

           DOUBLE        PRECISION A( LDA, * ), B( LDB, * ), WORK( * )

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

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

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

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

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

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

        LWORK   (input) 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) 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 driver routine (version 3.3.1)      April 2011                             DSYSV(3lapack)