!>
!> 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**T*D*U  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.
!> 

UPLO

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

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

A

!>          A is 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

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

IPIV

!>          IPIV is 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

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is 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

!>          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, and division by zero will occur if it
!>                is used to solve a system of equations.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

!>
!>  If UPLO = 'U', then A = U**T*D*U, 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).
!>