NAME

       zsytrf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zsytrf (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
           ZSYTRF

Function/Subroutine Documentation

   subroutine zsytrf (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA,
       integer, dimension( * )IPIV, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
       ZSYTRF

       Purpose:

            ZSYTRF computes the factorization of a complex 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
            with 1-by-1 and 2-by-2 diagonal blocks.

            This is the blocked version of the algorithm, calling Level 3 BLAS.

       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 order of the matrix A.  N >= 0.

           A

                     A is COMPLEX*16 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 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.  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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       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).

       Definition at line 183 of file zsytrf.f.

Author

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