NAME

       chetf2_rook.f -

SYNOPSIS

   Functions/Subroutines
       subroutine chetf2_rook (UPLO, N, A, LDA, IPIV, INFO)
           CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using
           the bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm).

Function/Subroutine Documentation

   subroutine chetf2_rook (character UPLO, integer N, complex, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, integer INFO)
       CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the
       bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm).

       Purpose:

            CHETF2_ROOK computes the factorization of a complex Hermitian matrix A
            using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:

               A = U*D*U**H  or  A = L*D*L**H

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, U**H is the conjugate transpose of U, and D is
            Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

            This is the unblocked version of the algorithm, calling Level 2 BLAS.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     Hermitian matrix A is stored:
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           N

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

           A

                     A is COMPLEX array, dimension (LDA,N)
                     On entry, the Hermitian 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 UPLO = 'U':
                        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 IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
                        columns k and -IPIV(k) were interchanged and rows and
                        columns k-1 and -IPIV(k-1) were inerchaged,
                        D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

                     If UPLO = 'L':
                        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 IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
                        columns k and -IPIV(k) were interchanged and rows and
                        columns k+1 and -IPIV(k+1) were inerchaged,
                        D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -k, the k-th argument had an illegal value
                     > 0: if INFO = k, D(k,k) 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2013

       Further Details:

             If UPLO = 'U', then A = U*D*U**H, 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**H, 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).

       Contributors:

             November 2013,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

             September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
                             School of Mathematics,
                             University of Manchester

             01-01-96 - Based on modifications by
               J. Lewis, Boeing Computer Services Company
               A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Author

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