NAME

       zhesv_rook.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zhesv_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
           ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE
           matrices using the bounded Bunch-Kaufman ('rook') diagonal pivoting method

Function/Subroutine Documentation

   subroutine zhesv_rook (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, *
       ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer
       LDB, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)
       ZHESV_ROOK computes the solution to a system of linear equations A * X = B for HE matrices
       using the bounded Bunch-Kaufman ('rook') diagonal pivoting method

       Purpose:

            ZHESV_ROOK computes the solution to a complex system of linear equations
               A * X = B,
            where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
            matrices.

            The bounded Bunch-Kaufman ("rook") 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 Hermitian and block diagonal with
            1-by-1 and 2-by-2 diagonal blocks.

            ZHETRF_ROOK is called to compute the factorization of a complex
            Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
            pivoting method.

            The factored form of A is then used to solve the system
            of equations A * X = B by calling ZHETRS_ROOK (uses BLAS 2).

       Parameters:
           UPLO

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

           N

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

           NRHS

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

           A

                     A is COMPLEX*16 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, 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**H or A = L*D*L**H as computed by
                     ZHETRF_ROOK.

           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':
                        Only the last KB elements of IPIV are set.

                        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':
                        Only the first KB elements of IPIV are set.

                        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.

           B

                     B is COMPLEX*16 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

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

           WORK

                     WORK is COMPLEX*16 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, and for best performance
                     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
                     ZHETRF_ROOK.
                     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

                     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, so the solution could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2013

         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.fi

Author

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