class TDecompBK: public TDecompBase

The Bunch-Kaufman diagonal pivoting method decomposes a real
symmetric matrix A using

A = U*D*U^T

where U is a product of permutation and unit upper triangular
matrices, U^T is the transpose of U, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.

U = P(n-1)*U(n-1)* ... *P(k)U(k)* ...,
i.e., U is a product of terms P(k)*U(k), where k decreases from n-1
  to 0 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(0: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(0:k-2,k-1:k).

fU contains on entry the symmetric matrix A of which only the upper
 triangular part is referenced . On exit fU contains the block diagonal
matrix D and the multipliers used to obtain the factor U, see above .

fIpiv if dimension n contains details of the interchanges and the
the block structure of D . If (fIPiv(k) > 0, then rows and columns k
and fIPiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPiv(k) = fIPiv(k-1) < 0, 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.