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

NAME

       LAPACK-3 - computes the factorization of a real symmetric matrix A using the Bunch-Kaufman
       diagonal pivoting method

SYNOPSIS

       SUBROUTINE SSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

           INTEGER        IPIV( * )

           REAL           A( LDA, * ), WORK( * )

PURPOSE

       SSYTRF computes the factorization of a real symmetric matrix  A  using  the  Bunch-Kaufman
       diagonal pivoting method.  The form of the
        factorization is
           A = U*D*U**T  or  A = L*D*L**T
        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.
        This is the blocked version of the algorithm, calling Level 3 BLAS.

ARGUMENTS

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

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        A       (input/output) REAL 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, the block diagonal matrix D and the multipliers used
                to obtain the factor U or L (see below for further details).

        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.
                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.

        WORK    (workspace/output) REAL 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.  For best performance
                LWORK >= N*NB, where NB is the block size returned by ILAENV.
                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, and division by zero will occur if it
                is used to solve a system of equations.

FURTHER DETAILS

        If UPLO = 'U', then A = U*D*U**T, where
           U = P(n)*U(n)* ... *P(k)U(k)* ...,
        i.e., U is a product of terms P(k)*U(k), where k decreases from n to
        1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    v    0   )   k-s
           U(k) =  (   0    I    0   )   s
                   (   0    0    I   )   n-k
                      k-s   s   n-k
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
        If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
        and A(k,k), and v overwrites A(1:k-2,k-1:k).
        If UPLO = 'L', then A = L*D*L**T, where
           L = P(1)*L(1)* ... *P(k)*L(k)* ...,
        i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
        n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    0     0   )  k-1
           L(k) =  (   0    I     0   )  s
                   (   0    v     I   )  n-k-s+1
                      k-1   s  n-k-s+1
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
        If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
        and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

 LAPACK routine (version 3.3.1)             April 2011                            SSYTRF(3lapack)