Provided by: liblapack-doc_3.8.0-2_all bug

NAME

       complex16SYcomputational

SYNOPSIS

   Functions
       subroutine zhetrf_aa_2stage (UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
           ZHETRF_AA_2STAGE
       subroutine zhetrs_aa_2stage (UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
           ZHETRS_AA_2STAGE
       subroutine zla_syamv (UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
           ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to
           calculate error bounds.
       double precision function zla_syrcond_c (UPLO, N, A, LDA, AF, LDAF, IPIV, C, CAPPLY, INFO,
           WORK, RWORK)
           ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for
           symmetric indefinite matrices.
       double precision function zla_syrcond_x (UPLO, N, A, LDA, AF, LDAF, IPIV, X, INFO, WORK,
           RWORK)
           ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for
           symmetric indefinite matrices.
       subroutine zla_syrfsx_extended (PREC_TYPE, UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, COLEQU,
           C, B, LDB, Y, LDY, BERR_OUT, N_NORMS, ERR_BNDS_NORM, ERR_BNDS_COMP, RES, AYB, DY,
           Y_TAIL, RCOND, ITHRESH, RTHRESH, DZ_UB, IGNORE_CWISE, INFO)
           ZLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for
           symmetric indefinite matrices by performing extra-precise iterative refinement and
           provides error bounds and backward error estimates for the solution.
       double precision function zla_syrpvgrw (UPLO, N, INFO, A, LDA, AF, LDAF, IPIV, WORK)
           ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a
           symmetric indefinite matrix.
       subroutine zlasyf (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
           ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-
           Kaufman diagonal pivoting method.
       subroutine zlasyf_aa (UPLO, J1, M, NB, A, LDA, IPIV, H, LDH, WORK)
           ZLASYF_AA
       subroutine zlasyf_rk (UPLO, N, NB, KB, A, LDA, E, IPIV, W, LDW, INFO)
           ZLASYF_RK computes a partial factorization of a complex symmetric indefinite matrix
           using bounded Bunch-Kaufman (rook) diagonal pivoting method.
       subroutine zlasyf_rook (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
           ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the
           bounded Bunch-Kaufman ('rook') diagonal pivoting method.
       subroutine zsycon (UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
           ZSYCON
       subroutine zsycon_3 (UPLO, N, A, LDA, E, IPIV, ANORM, RCOND, WORK, INFO)
           ZSYCON_3
       subroutine zsycon_rook (UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, INFO)
           ZSYCON_ROOK
       subroutine zsyconv (UPLO, WAY, N, A, LDA, IPIV, E, INFO)
           ZSYCONV
       subroutine zsyconvf (UPLO, WAY, N, A, LDA, E, IPIV, INFO)
           ZSYCONVF
       subroutine zsyconvf_rook (UPLO, WAY, N, A, LDA, E, IPIV, INFO)
           ZSYCONVF_ROOK
       subroutine zsyequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
           ZSYEQUB
       subroutine zsyrfs (UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR,
           WORK, RWORK, INFO)
           ZSYRFS
       subroutine zsyrfsx (UPLO, EQUED, N, NRHS, A, LDA, AF, LDAF, IPIV, S, B, LDB, X, LDX,
           RCOND, BERR, N_ERR_BNDS, ERR_BNDS_NORM, ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK,
           INFO)
           ZSYRFSX
       subroutine zsysv_aa_2stage (UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, WORK,
           LWORK, INFO)
            ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY
           matrices
       subroutine zsytf2 (UPLO, N, A, LDA, IPIV, INFO)
           ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
           diagonal pivoting method (unblocked algorithm).
       subroutine zsytf2_rk (UPLO, N, A, LDA, E, IPIV, INFO)
           ZSYTF2_RK computes the factorization of a complex symmetric indefinite matrix using
           the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS2 unblocked algorithm).
       subroutine zsytf2_rook (UPLO, N, A, LDA, IPIV, INFO)
           ZSYTF2_ROOK computes the factorization of a complex symmetric indefinite matrix using
           the bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm).
       subroutine zsytrf (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
           ZSYTRF
       subroutine zsytrf_aa (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
           ZSYTRF_AA
       subroutine zsytrf_aa_2stage (UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, WORK, LWORK, INFO)
           ZSYTRF_AA_2STAGE
       subroutine zsytrf_rk (UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
           ZSYTRF_RK computes the factorization of a complex symmetric indefinite matrix using
           the bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS3 blocked algorithm).
       subroutine zsytrf_rook (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
           ZSYTRF_ROOK
       subroutine zsytri (UPLO, N, A, LDA, IPIV, WORK, INFO)
           ZSYTRI
       subroutine zsytri2 (UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
           ZSYTRI2
       subroutine zsytri2x (UPLO, N, A, LDA, IPIV, WORK, NB, INFO)
           ZSYTRI2X
       subroutine zsytri_3 (UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)
           ZSYTRI_3
       subroutine zsytri_3x (UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)
           ZSYTRI_3X
       subroutine zsytri_rook (UPLO, N, A, LDA, IPIV, WORK, INFO)
           ZSYTRI_ROOK
       subroutine zsytrs (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
           ZSYTRS
       subroutine zsytrs2 (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO)
           ZSYTRS2
       subroutine zsytrs_3 (UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, INFO)
           ZSYTRS_3
       subroutine zsytrs_aa (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
           ZSYTRS_AA
       subroutine zsytrs_aa_2stage (UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, IPIV2, B, LDB, INFO)
           ZSYTRS_AA_2STAGE
       subroutine zsytrs_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
           ZSYTRS_ROOK
       subroutine ztgsyl (TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF,
           SCALE, DIF, WORK, LWORK, IWORK, INFO)
           ZTGSYL
       subroutine ztrsyl (TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C, LDC, SCALE, INFO)
           ZTRSYL

Detailed Description

       This is the group of complex16 computational functions for SY matrices

Function Documentation

   subroutine zhetrf_aa_2stage (character UPLO, integer N, complex*16, dimension( lda, * ) A,
       integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV,
       integer, dimension( * ) IPIV2, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       ZHETRF_AA_2STAGE

       Purpose:

            ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U*T*U**T  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a hermitian band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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 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, L is stored below (or above) the subdiaonal blocks,
                     when UPLO  is 'L' (or 'U').

           LDA

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

           TB

                     TB is COMPLEX array, dimension (LTB)
                     On exit, details of the LU factorization of the band matrix.

           LTB

                     The size of the array TB. LTB >= 4*N, internally
                     used to select NB such that LTB >= (3*NB+1)*N.

                     If LTB = -1, then a workspace query is assumed; the
                     routine only calculates the optimal size of LTB,
                     returns this value as the first entry of TB, and
                     no error message related to LTB is issued by XERBLA.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           IPIV2

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of T were interchanged with the
                     row and column IPIV(k).

           WORK

                     WORK is COMPLEX workspace of size LWORK

           LWORK

                     The size of WORK. LWORK >= N, internally used to select NB
                     such that LWORK >= N*NB.

                     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, band LU factorization failed on i-th column

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zhetrs_aa_2stage (character UPLO, integer N, integer NRHS, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( *
       ) IPIV, integer, dimension( * ) IPIV2, complex*16, dimension( ldb, * ) B, integer LDB,
       integer INFO)
       ZHETRS_AA_2STAGE

       Purpose:

            ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a
            hermitian matrix A using the factorization A = U*T*U**T or
            A = L*T*L**T computed by ZHETRF_AA_2STAGE.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*T*U**T;
                     = 'L':  Lower triangular, form is A = L*T*L**T.

           N

                     N is INTEGER
                     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*16array, dimension (LDA,N)
                     Details of factors computed by ZHETRF_AA_2STAGE.

           LDA

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

           TB

                     TB is COMPLEX*16array, dimension (LTB)
                     Details of factors computed by ZHETRF_AA_2STAGE.

           LTB

                     The size of the array TB. LTB >= 4*N.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges as computed by
                     ZHETRF_AA_2STAGE.

           IPIV2

                     IPIV2 is INTEGER array, dimension (N)
                     Details of the interchanges as computed by
                     ZHETRF_AA_2STAGE.

           B

                     B is COMPLEX*16array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zla_syamv (integer UPLO, integer N, double precision ALPHA, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( * ) X, integer INCX, double precision
       BETA, double precision, dimension( * ) Y, integer INCY)
       ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to
       calculate error bounds.

       Purpose:

            ZLA_SYAMV  performs the matrix-vector operation

                    y := alpha*abs(A)*abs(x) + beta*abs(y),

            where alpha and beta are scalars, x and y are vectors and A is an
            n by n symmetric matrix.

            This function is primarily used in calculating error bounds.
            To protect against underflow during evaluation, components in
            the resulting vector are perturbed away from zero by (N+1)
            times the underflow threshold.  To prevent unnecessarily large
            errors for block-structure embedded in general matrices,
            "symbolically" zero components are not perturbed.  A zero
            entry is considered "symbolic" if all multiplications involved
            in computing that entry have at least one zero multiplicand.

       Parameters:
           UPLO

                     UPLO is INTEGER
                      On entry, UPLO specifies whether the upper or lower
                      triangular part of the array A is to be referenced as
                      follows:

                         UPLO = BLAS_UPPER   Only the upper triangular part of A
                                             is to be referenced.

                         UPLO = BLAS_LOWER   Only the lower triangular part of A
                                             is to be referenced.

                      Unchanged on exit.

           N

                     N is INTEGER
                      On entry, N specifies the number of columns of the matrix A.
                      N must be at least zero.
                      Unchanged on exit.

           ALPHA

                     ALPHA is DOUBLE PRECISION .
                      On entry, ALPHA specifies the scalar alpha.
                      Unchanged on exit.

           A

                     A is COMPLEX*16 array, dimension ( LDA, n ).
                      Before entry, the leading m by n part of the array A must
                      contain the matrix of coefficients.
                      Unchanged on exit.

           LDA

                     LDA is INTEGER
                      On entry, LDA specifies the first dimension of A as declared
                      in the calling (sub) program. LDA must be at least
                      max( 1, n ).
                      Unchanged on exit.

           X

                     X is COMPLEX*16 array, dimension at least
                      ( 1 + ( n - 1 )*abs( INCX ) )
                      Before entry, the incremented array X must contain the
                      vector x.
                      Unchanged on exit.

           INCX

                     INCX is INTEGER
                      On entry, INCX specifies the increment for the elements of
                      X. INCX must not be zero.
                      Unchanged on exit.

           BETA

                     BETA is DOUBLE PRECISION .
                      On entry, BETA specifies the scalar beta. When BETA is
                      supplied as zero then Y need not be set on input.
                      Unchanged on exit.

           Y

                     Y is DOUBLE PRECISION array, dimension
                      ( 1 + ( n - 1 )*abs( INCY ) )
                      Before entry with BETA non-zero, the incremented array Y
                      must contain the vector y. On exit, Y is overwritten by the
                      updated vector y.

           INCY

                     INCY is INTEGER
                      On entry, INCY specifies the increment for the elements of
                      Y. INCY must not be zero.
                      Unchanged on exit.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

       Further Details:

             Level 2 Blas routine.

             -- Written on 22-October-1986.
                Jack Dongarra, Argonne National Lab.
                Jeremy Du Croz, Nag Central Office.
                Sven Hammarling, Nag Central Office.
                Richard Hanson, Sandia National Labs.
             -- Modified for the absolute-value product, April 2006
                Jason Riedy, UC Berkeley

   double precision function zla_syrcond_c (character UPLO, integer N, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, integer,
       dimension( * ) IPIV, double precision, dimension( * ) C, logical CAPPLY, integer INFO,
       complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK)
       ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for
       symmetric indefinite matrices.

       Purpose:

               ZLA_SYRCOND_C Computes the infinity norm condition number of
               op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.

       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.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The block diagonal matrix D and the multipliers used to
                obtain the factor U or L as computed by ZSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by ZSYTRF.

           C

                     C is DOUBLE PRECISION array, dimension (N)
                The vector C in the formula op(A) * inv(diag(C)).

           CAPPLY

                     CAPPLY is LOGICAL
                If .TRUE. then access the vector C in the formula above.

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit.
                i > 0:  The ith argument is invalid.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N).
                Workspace.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N).
                Workspace.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   double precision function zla_syrcond_x (character UPLO, integer N, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, integer,
       dimension( * ) IPIV, complex*16, dimension( * ) X, integer INFO, complex*16, dimension( *
       ) WORK, double precision, dimension( * ) RWORK)
       ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric
       indefinite matrices.

       Purpose:

               ZLA_SYRCOND_X Computes the infinity norm condition number of
               op(A) * diag(X) where X is a COMPLEX*16 vector.

       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.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The block diagonal matrix D and the multipliers used to
                obtain the factor U or L as computed by ZSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by ZSYTRF.

           X

                     X is COMPLEX*16 array, dimension (N)
                The vector X in the formula op(A) * diag(X).

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit.
                i > 0:  The ith argument is invalid.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N).
                Workspace.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N).
                Workspace.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zla_syrfsx_extended (integer PREC_TYPE, character UPLO, integer N, integer NRHS,
       complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF,
       integer LDAF, integer, dimension( * ) IPIV, logical COLEQU, double precision, dimension( *
       ) C, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldy, * ) Y,
       integer LDY, double precision, dimension( * ) BERR_OUT, integer N_NORMS, double precision,
       dimension( nrhs, * ) ERR_BNDS_NORM, double precision, dimension( nrhs, * ) ERR_BNDS_COMP,
       complex*16, dimension( * ) RES, double precision, dimension( * ) AYB, complex*16,
       dimension( * ) DY, complex*16, dimension( * ) Y_TAIL, double precision RCOND, integer
       ITHRESH, double precision RTHRESH, double precision DZ_UB, logical IGNORE_CWISE, integer
       INFO)
       ZLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for
       symmetric indefinite matrices by performing extra-precise iterative refinement and
       provides error bounds and backward error estimates for the solution.

       Purpose:

            ZLA_SYRFSX_EXTENDED improves the computed solution to a system of
            linear equations by performing extra-precise iterative refinement
            and provides error bounds and backward error estimates for the solution.
            This subroutine is called by ZSYRFSX to perform iterative refinement.
            In addition to normwise error bound, the code provides maximum
            componentwise error bound if possible. See comments for ERR_BNDS_NORM
            and ERR_BNDS_COMP for details of the error bounds. Note that this
            subroutine is only resonsible for setting the second fields of
            ERR_BNDS_NORM and ERR_BNDS_COMP.

       Parameters:
           PREC_TYPE

                     PREC_TYPE is INTEGER
                Specifies the intermediate precision to be used in refinement.
                The value is defined by ILAPREC(P) where P is a CHARACTER and
                P    = 'S':  Single
                     = 'D':  Double
                     = 'I':  Indigenous
                     = 'X', 'E':  Extra

           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.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The block diagonal matrix D and the multipliers used to
                obtain the factor U or L as computed by ZSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by ZSYTRF.

           COLEQU

                     COLEQU is LOGICAL
                If .TRUE. then column equilibration was done to A before calling
                this routine. This is needed to compute the solution and error
                bounds correctly.

           C

                     C is DOUBLE PRECISION array, dimension (N)
                The column scale factors for A. If COLEQU = .FALSE., C
                is not accessed. If C is input, each element of C should be a power
                of the radix to ensure a reliable solution and error estimates.
                Scaling by powers of the radix does not cause rounding errors unless
                the result underflows or overflows. Rounding errors during scaling
                lead to refining with a matrix that is not equivalent to the
                input matrix, producing error estimates that may not be
                reliable.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                The right-hand-side matrix B.

           LDB

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

           Y

                     Y is COMPLEX*16 array, dimension (LDY,NRHS)
                On entry, the solution matrix X, as computed by ZSYTRS.
                On exit, the improved solution matrix Y.

           LDY

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

           BERR_OUT

                     BERR_OUT is DOUBLE PRECISION array, dimension (NRHS)
                On exit, BERR_OUT(j) contains the componentwise relative backward
                error for right-hand-side j from the formula
                    max(i) ( abs(RES(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
                where abs(Z) is the componentwise absolute value of the matrix
                or vector Z. This is computed by ZLA_LIN_BERR.

           N_NORMS

                     N_NORMS is INTEGER
                Determines which error bounds to return (see ERR_BNDS_NORM
                and ERR_BNDS_COMP).
                If N_NORMS >= 1 return normwise error bounds.
                If N_NORMS >= 2 return componentwise error bounds.

           ERR_BNDS_NORM

                     ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                normwise relative error, which is defined as follows:

                Normwise relative error in the ith solution vector:
                        max_j (abs(XTRUE(j,i) - X(j,i)))
                       ------------------------------
                             max_j abs(X(j,i))

                The array is indexed by the type of error information as described
                below. There currently are up to three pieces of information
                returned.

                The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_NORM(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * slamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * slamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated normwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * slamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*A, where S scales each row by a power of the
                         radix so all absolute row sums of Z are approximately 1.

                This subroutine is only responsible for setting the second field
                above.
                See Lapack Working Note 165 for further details and extra
                cautions.

           ERR_BNDS_COMP

                     ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                componentwise relative error, which is defined as follows:

                Componentwise relative error in the ith solution vector:
                               abs(XTRUE(j,i) - X(j,i))
                        max_j ----------------------
                                    abs(X(j,i))

                The array is indexed by the right-hand side i (on which the
                componentwise relative error depends), and the type of error
                information as described below. There currently are up to three
                pieces of information returned for each right-hand side. If
                componentwise accuracy is not requested (PARAMS(3) = 0.0), then
                ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
                the first (:,N_ERR_BNDS) entries are returned.

                The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_COMP(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * slamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * slamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated componentwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * slamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*(A*diag(x)), where x is the solution for the
                         current right-hand side and S scales each row of
                         A*diag(x) by a power of the radix so all absolute row
                         sums of Z are approximately 1.

                This subroutine is only responsible for setting the second field
                above.
                See Lapack Working Note 165 for further details and extra
                cautions.

           RES

                     RES is COMPLEX*16 array, dimension (N)
                Workspace to hold the intermediate residual.

           AYB

                     AYB is DOUBLE PRECISION array, dimension (N)
                Workspace.

           DY

                     DY is COMPLEX*16 array, dimension (N)
                Workspace to hold the intermediate solution.

           Y_TAIL

                     Y_TAIL is COMPLEX*16 array, dimension (N)
                Workspace to hold the trailing bits of the intermediate solution.

           RCOND

                     RCOND is DOUBLE PRECISION
                Reciprocal scaled condition number.  This is an estimate of the
                reciprocal Skeel condition number of the matrix A after
                equilibration (if done).  If this is less than the machine
                precision (in particular, if it is zero), the matrix is singular
                to working precision.  Note that the error may still be small even
                if this number is very small and the matrix appears ill-
                conditioned.

           ITHRESH

                     ITHRESH is INTEGER
                The maximum number of residual computations allowed for
                refinement. The default is 10. For 'aggressive' set to 100 to
                permit convergence using approximate factorizations or
                factorizations other than LU. If the factorization uses a
                technique other than Gaussian elimination, the guarantees in
                ERR_BNDS_NORM and ERR_BNDS_COMP may no longer be trustworthy.

           RTHRESH

                     RTHRESH is DOUBLE PRECISION
                Determines when to stop refinement if the error estimate stops
                decreasing. Refinement will stop when the next solution no longer
                satisfies norm(dx_{i+1}) < RTHRESH * norm(dx_i) where norm(Z) is
                the infinity norm of Z. RTHRESH satisfies 0 < RTHRESH <= 1. The
                default value is 0.5. For 'aggressive' set to 0.9 to permit
                convergence on extremely ill-conditioned matrices. See LAWN 165
                for more details.

           DZ_UB

                     DZ_UB is DOUBLE PRECISION
                Determines when to start considering componentwise convergence.
                Componentwise convergence is only considered after each component
                of the solution Y is stable, which we definte as the relative
                change in each component being less than DZ_UB. The default value
                is 0.25, requiring the first bit to be stable. See LAWN 165 for
                more details.

           IGNORE_CWISE

                     IGNORE_CWISE is LOGICAL
                If .TRUE. then ignore componentwise convergence. Default value
                is .FALSE..

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit.
                  < 0:  if INFO = -i, the ith argument to ZLA_HERFSX_EXTENDED had an illegal
                        value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

   double precision function zla_syrpvgrw (character*1 UPLO, integer N, integer INFO, complex*16,
       dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF,
       integer, dimension( * ) IPIV, double precision, dimension( * ) WORK)
       ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric
       indefinite matrix.

       Purpose:

            ZLA_SYRPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The "max absolute element" norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       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.

           INFO

                     INFO is INTEGER
                The value of INFO returned from ZSYTRF, .i.e., the pivot in
                column INFO is exactly 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The block diagonal matrix D and the multipliers used to
                obtain the factor U or L as computed by ZSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by ZSYTRF.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (2*N)

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zlasyf (character UPLO, integer N, integer NB, integer KB, complex*16, dimension(
       lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldw, * ) W,
       integer LDW, integer INFO)
       ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-
       Kaufman diagonal pivoting method.

       Purpose:

            ZLASYF computes a partial factorization of a complex symmetric matrix
            A using the Bunch-Kaufman diagonal pivoting method. The partial
            factorization has the form:

            A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
                  ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

            A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
                  ( L21  I ) ( 0   A22 ) (  0       I    )

            where the order of D is at most NB. The actual order is returned in
            the argument KB, and is either NB or NB-1, or N if N <= NB.
            Note that U**T denotes the transpose of U.

            ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
            (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
            A22 (if UPLO = 'L').

       Parameters:
           UPLO

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

           N

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

           NB

                     NB is INTEGER
                     The maximum number of columns of the matrix A that should be
                     factored.  NB should be at least 2 to allow for 2-by-2 pivot
                     blocks.

           KB

                     KB is INTEGER
                     The number of columns of A that were actually factored.
                     KB is either NB-1 or NB, or N if N <= NB.

           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, A contains details of the partial factorization.

           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) = 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':
                        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) = 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.

           W

                     W is COMPLEX*16 array, dimension (LDW,NB)

           LDW

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

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2013

       Contributors:

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

   subroutine zlasyf_aa (character UPLO, integer J1, integer M, integer NB, complex*16,
       dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension(
       ldh, * ) H, integer LDH, complex*16, dimension( * ) WORK)
       ZLASYF_AA

       Purpose:

            DLATRF_AA factorizes a panel of a complex symmetric matrix A using
            the Aasen's algorithm. The panel consists of a set of NB rows of A
            when UPLO is U, or a set of NB columns when UPLO is L.

            In order to factorize the panel, the Aasen's algorithm requires the
            last row, or column, of the previous panel. The first row, or column,
            of A is set to be the first row, or column, of an identity matrix,
            which is used to factorize the first panel.

            The resulting J-th row of U, or J-th column of L, is stored in the
            (J-1)-th row, or column, of A (without the unit diagonals), while
            the diagonal and subdiagonal of A are overwritten by those of T.

       Parameters:
           UPLO

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

           J1

                     J1 is INTEGER
                     The location of the first row, or column, of the panel
                     within the submatrix of A, passed to this routine, e.g.,
                     when called by ZSYTRF_AA, for the first panel, J1 is 1,
                     while for the remaining panels, J1 is 2.

           M

                     M is INTEGER
                     The dimension of the submatrix. M >= 0.

           NB

                     NB is INTEGER
                     The dimension of the panel to be facotorized.

           A

                     A is COMPLEX*16 array, dimension (LDA,M) for
                     the first panel, while dimension (LDA,M+1) for the
                     remaining panels.

                     On entry, A contains the last row, or column, of
                     the previous panel, and the trailing submatrix of A
                     to be factorized, except for the first panel, only
                     the panel is passed.

                     On exit, the leading panel is factorized.

           LDA

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

           IPIV

                     IPIV is INTEGER array, dimension (M)
                     Details of the row and column interchanges,
                     the row and column k were interchanged with the row and
                     column IPIV(k).

           H

                     H is COMPLEX*16 workspace, dimension (LDH,NB).

           LDH

                     LDH is INTEGER
                     The leading dimension of the workspace H. LDH >= max(1,M).

           WORK

                     WORK is COMPLEX*16 workspace, dimension (M).

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zlasyf_rk (character UPLO, integer N, integer NB, integer KB, complex*16,
       dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * )
       IPIV, complex*16, dimension( ldw, * ) W, integer LDW, integer INFO)
       ZLASYF_RK computes a partial factorization of a complex symmetric indefinite matrix using
       bounded Bunch-Kaufman (rook) diagonal pivoting method.

       Purpose:

            ZLASYF_RK computes a partial factorization of a complex symmetric
            matrix A using the bounded Bunch-Kaufman (rook) diagonal
            pivoting method. The partial factorization has the form:

            A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
                  ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

            A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L',
                  ( L21  I ) (  0  A22 ) (  0       I    )

            where the order of D is at most NB. The actual order is returned in
            the argument KB, and is either NB or NB-1, or N if N <= NB.

            ZLASYF_RK is an auxiliary routine called by ZSYTRF_RK. It uses
            blocked code (calling Level 3 BLAS) to update the submatrix
            A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

       Parameters:
           UPLO

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

           N

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

           NB

                     NB is INTEGER
                     The maximum number of columns of the matrix A that should be
                     factored.  NB should be at least 2 to allow for 2-by-2 pivot
                     blocks.

           KB

                     KB is INTEGER
                     The number of columns of A that were actually factored.
                     KB is either NB-1 or NB, or N if N <= NB.

           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, contains:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On exit, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is set to 0 in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     IPIV describes the permutation matrix P in the factorization
                     of matrix A as follows. The absolute value of IPIV(k)
                     represents the index of row and column that were
                     interchanged with the k-th row and column. The value of UPLO
                     describes the order in which the interchanges were applied.
                     Also, the sign of IPIV represents the block structure of
                     the symmetric block diagonal matrix D with 1-by-1 or 2-by-2
                     diagonal blocks which correspond to 1 or 2 interchanges
                     at each factorization step.

                     If UPLO = 'U',
                     ( in factorization order, k decreases from N to 1 ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the submatrix A(1:N,N-KB+1:N);
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k-1) < 0 means:
                          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the matrix A(1:N,N-KB+1:N).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k-1) != k-1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the submatrix A(1:N,N-KB+1:N).
                             If -IPIV(k-1) = k-1, no interchange occurred.

                       c) In both cases a) and b) is always ABS( IPIV(k) ) <= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

                     If UPLO = 'L',
                     ( in factorization order, k increases from 1 to N ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the submatrix A(1:N,1:KB).
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k+1) < 0 means:
                          D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the submatrix A(1:N,1:KB).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k+1) != k+1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the submatrix A(1:N,1:KB).
                             If -IPIV(k+1) = k+1, no interchange occurred.

                       c) In both cases a) and b) is always ABS( IPIV(k) ) >= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

           W

                     W is COMPLEX*16 array, dimension (LDW,NB)

           LDW

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

           INFO

                     INFO is INTEGER
                     = 0: successful exit

                     < 0: If INFO = -k, the k-th argument had an illegal value

                     > 0: If INFO = k, the matrix A is singular, because:
                            If UPLO = 'U': column k in the upper
                            triangular part of A contains all zeros.
                            If UPLO = 'L': column k in the lower
                            triangular part of A contains all zeros.

                          Therefore D(k,k) is exactly zero, and superdiagonal
                          elements of column k of U (or subdiagonal elements of
                          column k of L ) are all zeros. 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.

                          NOTE: INFO only stores the first occurrence of
                          a singularity, any subsequent occurrence of singularity
                          is not stored in INFO even though the factorization
                          always completes.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:

             December 2016,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine zlasyf_rook (character UPLO, integer N, integer NB, integer KB, complex*16,
       dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension(
       ldw, * ) W, integer LDW, integer INFO)
       ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix using the
       bounded Bunch-Kaufman ('rook') diagonal pivoting method.

       Purpose:

            ZLASYF_ROOK computes a partial factorization of a complex symmetric
            matrix A using the bounded Bunch-Kaufman ("rook") diagonal
            pivoting method. The partial factorization has the form:

            A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
                  ( 0  U22 ) (  0   D  ) ( U12**T U22**T )

            A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
                  ( L21  I ) (  0  A22 ) (  0       I    )

            where the order of D is at most NB. The actual order is returned in
            the argument KB, and is either NB or NB-1, or N if N <= NB.

            ZLASYF_ROOK is an auxiliary routine called by ZSYTRF_ROOK. It uses
            blocked code (calling Level 3 BLAS) to update the submatrix
            A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

       Parameters:
           UPLO

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

           N

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

           NB

                     NB is INTEGER
                     The maximum number of columns of the matrix A that should be
                     factored.  NB should be at least 2 to allow for 2-by-2 pivot
                     blocks.

           KB

                     KB is INTEGER
                     The number of columns of A that were actually factored.
                     KB is either NB-1 or NB, or N if N <= NB.

           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, A contains details of the partial factorization.

           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.

           W

                     W is COMPLEX*16 array, dimension (LDW,NB)

           LDW

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

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2013

       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

   subroutine zsycon (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16,
       dimension( * ) WORK, integer INFO)
       ZSYCON

       Purpose:

            ZSYCON estimates the reciprocal of the condition number (in the
            1-norm) of a complex symmetric matrix A using the factorization
            A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF.

           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
                     as determined by ZSYTRF.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
                     estimate of the 1-norm of inv(A) computed in this routine.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zsycon_3 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, double precision ANORM,
       double precision RCOND, complex*16, dimension( * ) WORK, integer INFO)
       ZSYCON_3

       Purpose:

            ZSYCON_3 estimates the reciprocal of the condition number (in the
            1-norm) of a complex symmetric matrix A using the factorization
            computed by ZSYTRF_RK or ZSYTRF_BK:

               A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, and D is symmetric and block
            diagonal with 1-by-1 and 2-by-2 diagonal blocks.

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
            This routine uses BLAS3 solver ZSYTRS_3.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix:
                     = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
                     = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     Diagonal of the block diagonal matrix D and factors U or L
                     as computed by ZSYTRF_RK and ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           should be provided on entry in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is not referenced in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZSYTRF_RK or ZSYTRF_BK.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
                     estimate of the 1-norm of inv(A) computed in this routine.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           IWORK

                     IWORK is INTEGER array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

       Contributors:

       June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

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

   subroutine zsycon_rook (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND,
       complex*16, dimension( * ) WORK, integer INFO)
       ZSYCON_ROOK

       Purpose:

            ZSYCON_ROOK estimates the reciprocal of the condition number (in the
            1-norm) of a complex symmetric matrix A using the factorization
            A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK.

            An estimate is obtained for norm(inv(A)), and the reciprocal of the
            condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF_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
                     as determined by ZSYTRF_ROOK.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is DOUBLE PRECISION
                     The reciprocal of the condition number of the matrix A,
                     computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
                     estimate of the 1-norm of inv(A) computed in this routine.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:

       December 2016, Igor Kozachenko, Computer Science Division, University of California,
       Berkeley

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

   subroutine zsyconv (character UPLO, character WAY, integer N, complex*16, dimension( lda, * )
       A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( * ) E, integer INFO)
       ZSYCONV

       Purpose:

            ZSYCONV converts A given by ZHETRF into L and D or vice-versa.
            Get nondiagonal elements of D (returned in workspace) and
            apply or reverse permutation done in TRF.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF.

           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
                     as determined by ZSYTRF.

           E

                     E is COMPLEX*16 array, dimension (N)
                     E stores the supdiagonal/subdiagonal of the symmetric 1-by-1
                     or 2-by-2 block diagonal matrix D in LDLT.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zsyconvf (character UPLO, character WAY, integer N, complex*16, dimension( lda, * )
       A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, integer INFO)
       ZSYCONVF

       Purpose:

            If parameter WAY = 'C':
            ZSYCONVF converts the factorization output format used in
            ZSYTRF provided on entry in parameter A into the factorization
            output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
            on exit in parameters A and E. It also coverts in place details of
            the intechanges stored in IPIV from the format used in ZSYTRF into
            the format used in ZSYTRF_RK (or ZSYTRF_BK).

            If parameter WAY = 'R':
            ZSYCONVF performs the conversion in reverse direction, i.e.
            converts the factorization output format used in ZSYTRF_RK
            (or ZSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in ZSYTRF that is stored
            on exit in parameter A. It also coverts in place details of
            the intechanges stored in IPIV from the format used in ZSYTRF_RK
            (or ZSYTRF_BK) into the format used in ZSYTRF.

            ZSYCONVF can also convert in Hermitian matrix case, i.e. between
            formats used in ZHETRF and ZHETRF_RK (or ZHETRF_BK).

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix A.
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     ZSYTRF:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     ZSYTRF_RK or ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     ZSYTRF_RK or ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     On exit, contains factorization details in format used in
                     ZSYTRF:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)

                     1) If WAY ='C':
                     On entry, details of the interchanges and the block
                     structure of D in the format used in ZSYTRF.
                     On exit, details of the interchanges and the block
                     structure of D in the format used in ZSYTRF_RK
                     ( or ZSYTRF_BK).

                     1) If WAY ='R':
                     On entry, details of the interchanges and the block
                     structure of D in the format used in ZSYTRF_RK
                     ( or ZSYTRF_BK).
                     On exit, details of the interchanges and the block
                     structure of D in the format used in ZSYTRF.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine zsyconvf_rook (character UPLO, character WAY, integer N, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV,
       integer INFO)
       ZSYCONVF_ROOK

       Purpose:

            If parameter WAY = 'C':
            ZSYCONVF_ROOK converts the factorization output format used in
            ZSYTRF_ROOK provided on entry in parameter A into the factorization
            output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
            on exit in parameters A and E. IPIV format for ZSYTRF_ROOK and
            ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

            If parameter WAY = 'R':
            ZSYCONVF_ROOK performs the conversion in reverse direction, i.e.
            converts the factorization output format used in ZSYTRF_RK
            (or ZSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in ZSYTRF_ROOK that is stored
            on exit in parameter A. IPIV format for ZSYTRF_ROOK and
            ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

            ZSYCONVF_ROOK can also convert in Hermitian matrix case, i.e. between
            formats used in ZHETRF_ROOK and ZHETRF_RK (or ZHETRF_BK).

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix A.
                     = 'U':  Upper triangular
                     = 'L':  Lower triangular

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     ZSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     ZSYTRF_RK or ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     ZSYTRF_RK or ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     On exit, contains factorization details in format used in
                     ZSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On entry, details of the interchanges and the block
                     structure of D as determined:
                     1) by ZSYTRF_ROOK, if WAY ='C';
                     2) by ZSYTRF_RK (or ZSYTRF_BK), if WAY ='R'.
                     The IPIV format is the same for all these routines.

                     On exit, is not changed.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine zsyequb (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       double precision, dimension( * ) S, double precision SCOND, double precision AMAX,
       complex*16, dimension( * ) WORK, integer INFO)
       ZSYEQUB

       Purpose:

            ZSYEQUB computes row and column scalings intended to equilibrate a
            symmetric matrix A (with respect to the Euclidean norm) and reduce
            its condition number. The scale factors S are computed by the BIN
            algorithm (see references) so that the scaled matrix B with elements
            B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
            the smallest possible condition number over all possible diagonal
            scalings.

       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)
                     The N-by-N symmetric matrix whose scaling factors are to be
                     computed.

           LDA

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

           S

                     S is DOUBLE PRECISION array, dimension (N)
                     If INFO = 0, S contains the scale factors for A.

           SCOND

                     SCOND is DOUBLE PRECISION
                     If INFO = 0, S contains the ratio of the smallest S(i) to
                     the largest S(i). If SCOND >= 0.1 and AMAX is neither too
                     large nor too small, it is not worth scaling by S.

           AMAX

                     AMAX is DOUBLE PRECISION
                     Largest absolute value of any matrix element. If AMAX is
                     very close to overflow or very close to underflow, the
                     matrix should be scaled.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, the i-th diagonal element is nonpositive.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

       References:
           Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
            Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
            DOI 10.1023/B:NUMA.0000016606.32820.69
            Tech report version: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

   subroutine zsyrfs (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A,
       integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * )
       IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X,
       integer LDX, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR,
       complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)
       ZSYRFS

       Purpose:

            ZSYRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is symmetric indefinite, and
            provides error bounds and backward error estimates for the solution.

       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.

           NRHS

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     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.

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                     The factored form of the matrix A.  AF contains the block
                     diagonal matrix D and the multipliers used to obtain the
                     factor U or L from the factorization A = U*D*U**T or
                     A = L*D*L**T as computed by ZSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZSYTRF.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB

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

           X

                     X is COMPLEX*16 array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by ZSYTRS.
                     On exit, the improved solution matrix X.

           LDX

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

           FERR

                     FERR is DOUBLE PRECISION array, dimension (NRHS)
                     The estimated forward error bound for each solution vector
                     X(j) (the j-th column of the solution matrix X).
                     If XTRUE is the true solution corresponding to X(j), FERR(j)
                     is an estimated upper bound for the magnitude of the largest
                     element in (X(j) - XTRUE) divided by the magnitude of the
                     largest element in X(j).  The estimate is as reliable as
                     the estimate for RCOND, and is almost always a slight
                     overestimate of the true error.

           BERR

                     BERR is DOUBLE PRECISION array, dimension (NRHS)
                     The componentwise relative backward error of each solution
                     vector X(j) (i.e., the smallest relative change in
                     any element of A or B that makes X(j) an exact solution).

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Internal Parameters:

             ITMAX is the maximum number of steps of iterative refinement.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zsyrfsx (character UPLO, character EQUED, integer N, integer NRHS, complex*16,
       dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF,
       integer, dimension( * ) IPIV, double precision, dimension( * ) S, complex*16, dimension(
       ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X, integer LDX, double precision
       RCOND, double precision, dimension( * ) BERR, integer N_ERR_BNDS, double precision,
       dimension( nrhs, * ) ERR_BNDS_NORM, double precision, dimension( nrhs, * ) ERR_BNDS_COMP,
       integer NPARAMS, double precision, dimension( * ) PARAMS, complex*16, dimension( * ) WORK,
       double precision, dimension( * ) RWORK, integer INFO)
       ZSYRFSX

       Purpose:

               ZSYRFSX improves the computed solution to a system of linear
               equations when the coefficient matrix is symmetric indefinite, and
               provides error bounds and backward error estimates for the
               solution.  In addition to normwise error bound, the code provides
               maximum componentwise error bound if possible.  See comments for
               ERR_BNDS_NORM and ERR_BNDS_COMP for details of the error bounds.

               The original system of linear equations may have been equilibrated
               before calling this routine, as described by arguments EQUED and S
               below. In this case, the solution and error bounds returned are
               for the original unequilibrated system.

                Some optional parameters are bundled in the PARAMS array.  These
                settings determine how refinement is performed, but often the
                defaults are acceptable.  If the defaults are acceptable, users
                can pass NPARAMS = 0 which prevents the source code from accessing
                the PARAMS argument.

       Parameters:
           UPLO

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

           EQUED

                     EQUED is CHARACTER*1
                Specifies the form of equilibration that was done to A
                before calling this routine. This is needed to compute
                the solution and error bounds correctly.
                  = 'N':  No equilibration
                  = 'Y':  Both row and column equilibration, i.e., A has been
                          replaced by diag(S) * A * diag(S).
                          The right hand side B has been changed accordingly.

           N

                     N is INTEGER
                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 matrices B and X.  NRHS >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                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.

           LDA

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

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The factored form of the matrix A.  AF contains the block
                diagonal matrix D and the multipliers used to obtain the
                factor U or L from the factorization A = U*D*U**T or A =
                L*D*L**T as computed by DSYTRF.

           LDAF

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D
                as determined by DSYTRF.

           S

                     S is DOUBLE PRECISION array, dimension (N)
                The scale factors for A.  If EQUED = 'Y', A is multiplied on
                the left and right by diag(S).  S is an input argument if FACT =
                'F'; otherwise, S is an output argument.  If FACT = 'F' and EQUED
                = 'Y', each element of S must be positive.  If S is output, each
                element of S is a power of the radix. If S is input, each element
                of S should be a power of the radix to ensure a reliable solution
                and error estimates. Scaling by powers of the radix does not cause
                rounding errors unless the result underflows or overflows.
                Rounding errors during scaling lead to refining with a matrix that
                is not equivalent to the input matrix, producing error estimates
                that may not be reliable.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                The right hand side matrix B.

           LDB

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

           X

                     X is COMPLEX*16 array, dimension (LDX,NRHS)
                On entry, the solution matrix X, as computed by DGETRS.
                On exit, the improved solution matrix X.

           LDX

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

           RCOND

                     RCOND is DOUBLE PRECISION
                Reciprocal scaled condition number.  This is an estimate of the
                reciprocal Skeel condition number of the matrix A after
                equilibration (if done).  If this is less than the machine
                precision (in particular, if it is zero), the matrix is singular
                to working precision.  Note that the error may still be small even
                if this number is very small and the matrix appears ill-
                conditioned.

           BERR

                     BERR is DOUBLE PRECISION array, dimension (NRHS)
                Componentwise relative backward error.  This is the
                componentwise relative backward error of each solution vector X(j)
                (i.e., the smallest relative change in any element of A or B that
                makes X(j) an exact solution).

           N_ERR_BNDS

                     N_ERR_BNDS is INTEGER
                Number of error bounds to return for each right hand side
                and each type (normwise or componentwise).  See ERR_BNDS_NORM and
                ERR_BNDS_COMP below.

           ERR_BNDS_NORM

                     ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                normwise relative error, which is defined as follows:

                Normwise relative error in the ith solution vector:
                        max_j (abs(XTRUE(j,i) - X(j,i)))
                       ------------------------------
                             max_j abs(X(j,i))

                The array is indexed by the type of error information as described
                below. There currently are up to three pieces of information
                returned.

                The first index in ERR_BNDS_NORM(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_NORM(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * dlamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * dlamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated normwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * dlamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*A, where S scales each row by a power of the
                         radix so all absolute row sums of Z are approximately 1.

                See Lapack Working Note 165 for further details and extra
                cautions.

           ERR_BNDS_COMP

                     ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
                For each right-hand side, this array contains information about
                various error bounds and condition numbers corresponding to the
                componentwise relative error, which is defined as follows:

                Componentwise relative error in the ith solution vector:
                               abs(XTRUE(j,i) - X(j,i))
                        max_j ----------------------
                                    abs(X(j,i))

                The array is indexed by the right-hand side i (on which the
                componentwise relative error depends), and the type of error
                information as described below. There currently are up to three
                pieces of information returned for each right-hand side. If
                componentwise accuracy is not requested (PARAMS(3) = 0.0), then
                ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
                the first (:,N_ERR_BNDS) entries are returned.

                The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
                right-hand side.

                The second index in ERR_BNDS_COMP(:,err) contains the following
                three fields:
                err = 1 "Trust/don't trust" boolean. Trust the answer if the
                         reciprocal condition number is less than the threshold
                         sqrt(n) * dlamch('Epsilon').

                err = 2 "Guaranteed" error bound: The estimated forward error,
                         almost certainly within a factor of 10 of the true error
                         so long as the next entry is greater than the threshold
                         sqrt(n) * dlamch('Epsilon'). This error bound should only
                         be trusted if the previous boolean is true.

                err = 3  Reciprocal condition number: Estimated componentwise
                         reciprocal condition number.  Compared with the threshold
                         sqrt(n) * dlamch('Epsilon') to determine if the error
                         estimate is "guaranteed". These reciprocal condition
                         numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some
                         appropriately scaled matrix Z.
                         Let Z = S*(A*diag(x)), where x is the solution for the
                         current right-hand side and S scales each row of
                         A*diag(x) by a power of the radix so all absolute row
                         sums of Z are approximately 1.

                See Lapack Working Note 165 for further details and extra
                cautions.

           NPARAMS

                     NPARAMS is INTEGER
                Specifies the number of parameters set in PARAMS.  If .LE. 0, the
                PARAMS array is never referenced and default values are used.

           PARAMS

                     PARAMS is DOUBLE PRECISION array, dimension NPARAMS
                Specifies algorithm parameters.  If an entry is .LT. 0.0, then
                that entry will be filled with default value used for that
                parameter.  Only positions up to NPARAMS are accessed; defaults
                are used for higher-numbered parameters.

                  PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
                       refinement or not.
                    Default: 1.0D+0
                       = 0.0 : No refinement is performed, and no error bounds are
                               computed.
                       = 1.0 : Use the double-precision refinement algorithm,
                               possibly with doubled-single computations if the
                               compilation environment does not support DOUBLE
                               PRECISION.
                         (other values are reserved for future use)

                  PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
                       computations allowed for refinement.
                    Default: 10
                    Aggressive: Set to 100 to permit convergence using approximate
                                factorizations or factorizations other than LU. If
                                the factorization uses a technique other than
                                Gaussian elimination, the guarantees in
                                err_bnds_norm and err_bnds_comp may no longer be
                                trustworthy.

                  PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code
                       will attempt to find a solution with small componentwise
                       relative error in the double-precision algorithm.  Positive
                       is true, 0.0 is false.
                    Default: 1.0 (attempt componentwise convergence)

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (2*N)

           INFO

                     INFO is INTEGER
                  = 0:  Successful exit. The solution to every right-hand side is
                    guaranteed.
                  < 0:  If INFO = -i, the i-th argument had an illegal value
                  > 0 and <= N:  U(INFO,INFO) is exactly zero.  The factorization
                    has been completed, but the factor U is exactly singular, so
                    the solution and error bounds could not be computed. RCOND = 0
                    is returned.
                  = N+J: The solution corresponding to the Jth right-hand side is
                    not guaranteed. The solutions corresponding to other right-
                    hand sides K with K > J may not be guaranteed as well, but
                    only the first such right-hand side is reported. If a small
                    componentwise error is not requested (PARAMS(3) = 0.0) then
                    the Jth right-hand side is the first with a normwise error
                    bound that is not guaranteed (the smallest J such
                    that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0)
                    the Jth right-hand side is the first with either a normwise or
                    componentwise error bound that is not guaranteed (the smallest
                    J such that either ERR_BNDS_NORM(J,1) = 0.0 or
                    ERR_BNDS_COMP(J,1) = 0.0). See the definition of
                    ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information
                    about all of the right-hand sides check ERR_BNDS_NORM or
                    ERR_BNDS_COMP.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           April 2012

   subroutine zsysv_aa_2stage (character UPLO, integer N, integer NRHS, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( *
       ) IPIV, integer, dimension( * ) IPIV2, complex*16, dimension( ldb, * ) B, integer LDB,
       complex*16, dimension( * ) WORK, integer LWORK, integer INFO)
        ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY
       matrices

       Purpose:

            ZSYSV_AA_2STAGE computes the solution to a complex system of
            linear equations
               A * X = B,
            where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
            matrices.

            Aasen's 2-stage algorithm is used to factor A as
               A = U * T * U**H,  if UPLO = 'U', or
               A = L * T * L**H,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is symmetric and band. The matrix T is
            then LU-factored with partial pivoting. The factored form of A
            is then used to solve the system of equations A * X = B.

            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.

           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 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, L is stored below (or above) the subdiaonal blocks,
                     when UPLO  is 'L' (or 'U').

           LDA

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

           TB

                     TB is COMPLEX*16 array, dimension (LTB)
                     On exit, details of the LU factorization of the band matrix.

           LTB

                     The size of the array TB. LTB >= 4*N, internally
                     used to select NB such that LTB >= (3*NB+1)*N.

                     If LTB = -1, then a workspace query is assumed; the
                     routine only calculates the optimal size of LTB,
                     returns this value as the first entry of TB, and
                     no error message related to LTB is issued by XERBLA.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           IPIV2

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of T were interchanged with the
                     row and column IPIV(k).

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           WORK

                     WORK is COMPLEX*16 workspace of size LWORK

           LWORK

                     The size of WORK. LWORK >= N, internally used to select NB
                     such that LWORK >= N*NB.

                     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, band LU factorization failed on i-th column

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytf2 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       integer, dimension( * ) IPIV, integer INFO)
       ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the
       diagonal pivoting method (unblocked algorithm).

       Purpose:

            ZSYTF2 computes the factorization of a complex symmetric matrix A
            using the Bunch-Kaufman diagonal pivoting method:

               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, U**T is the transpose of U, and D is symmetric 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
                     symmetric 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*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 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) = 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':
                        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) = 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.

           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:
           December 2016

       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).

       Contributors:

             09-29-06 - patch from
               Bobby Cheng, MathWorks

               Replace l.209 and l.377
                    IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
               by
                    IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN

             1-96 - Based on modifications by J. Lewis, Boeing Computer Services
                    Company

   subroutine zsytf2_rk (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, integer INFO)
       ZSYTF2_RK computes the factorization of a complex symmetric indefinite matrix using the
       bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS2 unblocked algorithm).

       Purpose:

            ZSYTF2_RK computes the factorization of a complex symmetric matrix A
            using the bounded Bunch-Kaufman (rook) diagonal pivoting method:

               A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, and D is symmetric 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.
            For more information see Further Details section.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     symmetric 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*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, contains:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On exit, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is set to 0 in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     IPIV describes the permutation matrix P in the factorization
                     of matrix A as follows. The absolute value of IPIV(k)
                     represents the index of row and column that were
                     interchanged with the k-th row and column. The value of UPLO
                     describes the order in which the interchanges were applied.
                     Also, the sign of IPIV represents the block structure of
                     the symmetric block diagonal matrix D with 1-by-1 or 2-by-2
                     diagonal blocks which correspond to 1 or 2 interchanges
                     at each factorization step. For more info see Further
                     Details section.

                     If UPLO = 'U',
                     ( in factorization order, k decreases from N to 1 ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the matrix A(1:N,1:N);
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k-1) < 0 means:
                          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k-1) != k-1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k-1) = k-1, no interchange occurred.

                       c) In both cases a) and b), always ABS( IPIV(k) ) <= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

                     If UPLO = 'L',
                     ( in factorization order, k increases from 1 to N ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the matrix A(1:N,1:N).
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k+1) < 0 means:
                          D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k+1) != k+1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k+1) = k+1, no interchange occurred.

                       c) In both cases a) and b), always ABS( IPIV(k) ) >= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

           INFO

                     INFO is INTEGER
                     = 0: successful exit

                     < 0: If INFO = -k, the k-th argument had an illegal value

                     > 0: If INFO = k, the matrix A is singular, because:
                            If UPLO = 'U': column k in the upper
                            triangular part of A contains all zeros.
                            If UPLO = 'L': column k in the lower
                            triangular part of A contains all zeros.

                          Therefore D(k,k) is exactly zero, and superdiagonal
                          elements of column k of U (or subdiagonal elements of
                          column k of L ) are all zeros. 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.

                          NOTE: INFO only stores the first occurrence of
                          a singularity, any subsequent occurrence of singularity
                          is not stored in INFO even though the factorization
                          always completes.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Further Details:

            TODO: put further details

       Contributors:

             December 2016,  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 abd , USA

   subroutine zsytf2_rook (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, integer INFO)
       ZSYTF2_ROOK computes the factorization of a complex symmetric indefinite matrix using the
       bounded Bunch-Kaufman ('rook') diagonal pivoting method (unblocked algorithm).

       Purpose:

            ZSYTF2_ROOK computes the factorization of a complex symmetric matrix A
            using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:

               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, U**T is the transpose of U, and D is symmetric 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
                     symmetric 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*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 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**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).

       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 abd , USA

   subroutine zsytrf (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       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:
           December 2016

       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).

   subroutine zsytrf_aa (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       ZSYTRF_AA

       Purpose:

            ZSYTRF_AA computes the factorization of a complex symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U*T*U**T  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a complex symmetric tridiagonal matrix.

            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 tridiagonal matrix is stored in the diagonals
                     and the subdiagonals of A just below (or above) the diagonals,
                     and L is stored below (or above) the subdiaonals, when UPLO
                     is 'L' (or 'U').

           LDA

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

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           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 >=MAX(1,2*N). For optimum performance
                     LWORK >= N*(1+NB), where NB is the optimal blocksize.

                     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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytrf_aa_2stage (character UPLO, integer N, complex*16, dimension( lda, * ) A,
       integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( * ) IPIV,
       integer, dimension( * ) IPIV2, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       ZSYTRF_AA_2STAGE

       Purpose:

            ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
            using the Aasen's algorithm.  The form of the factorization is

               A = U*T*U**T  or  A = L*T*L**T

            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and T is a complex symmetric band matrix with the
            bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
            LU factorized with partial pivoting).

            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 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, L is stored below (or above) the subdiaonal blocks,
                     when UPLO  is 'L' (or 'U').

           LDA

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

           TB

                     TB is COMPLEX*16 array, dimension (LTB)
                     On exit, details of the LU factorization of the band matrix.

           LTB

                     The size of the array TB. LTB >= 4*N, internally
                     used to select NB such that LTB >= (3*NB+1)*N.

                     If LTB = -1, then a workspace query is assumed; the
                     routine only calculates the optimal size of LTB,
                     returns this value as the first entry of TB, and
                     no error message related to LTB is issued by XERBLA.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of A were interchanged with the
                     row and column IPIV(k).

           IPIV2

                     IPIV is INTEGER array, dimension (N)
                     On exit, it contains the details of the interchanges, i.e.,
                     the row and column k of T were interchanged with the
                     row and column IPIV(k).

           WORK

                     WORK is COMPLEX*16 workspace of size LWORK

           LWORK

                     The size of WORK. LWORK >= N, internally used to select NB
                     such that LWORK >= N*NB.

                     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, band LU factorization failed on i-th column

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytrf_rk (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( *
       ) WORK, integer LWORK, integer INFO)
       ZSYTRF_RK computes the factorization of a complex symmetric indefinite matrix using the
       bounded Bunch-Kaufman (rook) diagonal pivoting method (BLAS3 blocked algorithm).

       Purpose:

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

               A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, 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.
            For more information see Further Details section.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     symmetric 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*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, contains:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           are stored on exit in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On exit, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is set to 0 in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     IPIV describes the permutation matrix P in the factorization
                     of matrix A as follows. The absolute value of IPIV(k)
                     represents the index of row and column that were
                     interchanged with the k-th row and column. The value of UPLO
                     describes the order in which the interchanges were applied.
                     Also, the sign of IPIV represents the block structure of
                     the symmetric block diagonal matrix D with 1-by-1 or 2-by-2
                     diagonal blocks which correspond to 1 or 2 interchanges
                     at each factorization step. For more info see Further
                     Details section.

                     If UPLO = 'U',
                     ( in factorization order, k decreases from N to 1 ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the matrix A(1:N,1:N);
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k-1) < 0 means:
                          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k-1) != k-1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k-1) = k-1, no interchange occurred.

                       c) In both cases a) and b), always ABS( IPIV(k) ) <= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

                     If UPLO = 'L',
                     ( in factorization order, k increases from 1 to N ):
                       a) A single positive entry IPIV(k) > 0 means:
                          D(k,k) is a 1-by-1 diagonal block.
                          If IPIV(k) != k, rows and columns k and IPIV(k) were
                          interchanged in the matrix A(1:N,1:N).
                          If IPIV(k) = k, no interchange occurred.

                       b) A pair of consecutive negative entries
                          IPIV(k) < 0 and IPIV(k+1) < 0 means:
                          D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
                          (NOTE: negative entries in IPIV appear ONLY in pairs).
                          1) If -IPIV(k) != k, rows and columns
                             k and -IPIV(k) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k) = k, no interchange occurred.
                          2) If -IPIV(k+1) != k+1, rows and columns
                             k-1 and -IPIV(k-1) were interchanged
                             in the matrix A(1:N,1:N).
                             If -IPIV(k+1) = k+1, no interchange occurred.

                       c) In both cases a) and b), always ABS( IPIV(k) ) >= k.

                       d) NOTE: Any entry IPIV(k) is always NONZERO on output.

           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 = -k, the k-th argument had an illegal value

                     > 0: If INFO = k, the matrix A is singular, because:
                            If UPLO = 'U': column k in the upper
                            triangular part of A contains all zeros.
                            If UPLO = 'L': column k in the lower
                            triangular part of A contains all zeros.

                          Therefore D(k,k) is exactly zero, and superdiagonal
                          elements of column k of U (or subdiagonal elements of
                          column k of L ) are all zeros. 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.

                          NOTE: INFO only stores the first occurrence of
                          a singularity, any subsequent occurrence of singularity
                          is not stored in INFO even though the factorization
                          always completes.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Further Details:

            TODO: put correct description

       Contributors:

             December 2016,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine zsytrf_rook (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       ZSYTRF_ROOK

       Purpose:

            ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A
            using the bounded Bunch-Kaufman ("rook") 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
            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 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.

           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:
           June 2016

       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).

       Contributors:

              June 2016, Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine zsytri (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer INFO)
       ZSYTRI

       Purpose:

            ZSYTRI computes the inverse of a complex symmetric indefinite matrix
            A using the factorization A = U*D*U**T or A = L*D*L**T computed by
            ZSYTRF.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the block diagonal matrix D and the multipliers
                     used to obtain the factor U or L as computed by ZSYTRF.

                     On exit, if INFO = 0, the (symmetric) inverse of the original
                     matrix.  If UPLO = 'U', the upper triangular part of the
                     inverse is formed and the part of A below the diagonal is not
                     referenced; if UPLO = 'L' the lower triangular part of the
                     inverse is formed and the part of A above the diagonal is
                     not referenced.

           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
                     as determined by ZSYTRF.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zsytri2 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA,
       integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer
       INFO)
       ZSYTRI2

       Purpose:

            ZSYTRI2 computes the inverse of a COMPLEX*16 symmetric indefinite matrix
            A using the factorization A = U*D*U**T or A = L*D*L**T computed by
            ZSYTRF. ZSYTRI2 sets the LEADING DIMENSION of the workspace
            before calling ZSYTRI2X that actually computes the inverse.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the NB diagonal matrix D and the multipliers
                     used to obtain the factor U or L as computed by ZSYTRF.

                     On exit, if INFO = 0, the (symmetric) inverse of the original
                     matrix.  If UPLO = 'U', the upper triangular part of the
                     inverse is formed and the part of A below the diagonal is not
                     referenced; if UPLO = 'L' the lower triangular part of the
                     inverse is formed and the part of A above the diagonal is
                     not referenced.

           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 NB structure of D
                     as determined by ZSYTRF.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3)

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     WORK is size >= (N+NB+1)*(NB+3)
                     If LDWORK = -1, then a workspace query is assumed; the routine
                      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 LDWORK 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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytri2x (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, complex*16, dimension( n+nb+1,* ) WORK, integer NB,
       integer INFO)
       ZSYTRI2X

       Purpose:

            ZSYTRI2X computes the inverse of a complex symmetric indefinite matrix
            A using the factorization A = U*D*U**T or A = L*D*L**T computed by
            ZSYTRF.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the NNB diagonal matrix D and the multipliers
                     used to obtain the factor U or L as computed by ZSYTRF.

                     On exit, if INFO = 0, the (symmetric) inverse of the original
                     matrix.  If UPLO = 'U', the upper triangular part of the
                     inverse is formed and the part of A below the diagonal is not
                     referenced; if UPLO = 'L' the lower triangular part of the
                     inverse is formed and the part of A above the diagonal is
                     not referenced.

           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 NNB structure of D
                     as determined by ZSYTRF.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3)

           NB

                     NB is INTEGER
                     Block size

           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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

   subroutine zsytri_3 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( *
       ) WORK, integer LWORK, integer INFO)
       ZSYTRI_3

       Purpose:

            ZSYTRI_3 computes the inverse of a complex symmetric indefinite
            matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

                A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, and D is symmetric and block
            diagonal with 1-by-1 and 2-by-2 diagonal blocks.

            ZSYTRI_3 sets the leading dimension of the workspace  before calling
            ZSYTRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = '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, diagonal of the block diagonal matrix D and
                     factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           should be provided on entry in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is not referenced in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZSYTRF_RK or ZSYTRF_BK.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of 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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

       Contributors:

       November 2017, Igor Kozachenko, Computer Science Division, University of California,
       Berkeley

   subroutine zsytri_3x (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension(
       n+nb+1, * ) WORK, integer NB, integer INFO)
       ZSYTRI_3X

       Purpose:

            ZSYTRI_3X computes the inverse of a complex symmetric indefinite
            matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:

                A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, 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.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = '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, diagonal of the block diagonal matrix D and
                     factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           should be provided on entry in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) not referenced.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is not referenced in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZSYTRF_RK or ZSYTRF_BK.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1,NB+3).

           NB

                     NB is INTEGER
                     Block size.

           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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

       Contributors:

       June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

   subroutine zsytri_rook (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer
       LDA, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer INFO)
       ZSYTRI_ROOK

       Purpose:

            ZSYTRI_ROOK computes the inverse of a complex symmetric
            matrix A using the factorization A = U*D*U**T or A = L*D*L**T
            computed by ZSYTRF_ROOK.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the block diagonal matrix D and the multipliers
                     used to obtain the factor U or L as computed by ZSYTRF_ROOK.

                     On exit, if INFO = 0, the (symmetric) inverse of the original
                     matrix.  If UPLO = 'U', the upper triangular part of the
                     inverse is formed and the part of A below the diagonal is not
                     referenced; if UPLO = 'L' the lower triangular part of the
                     inverse is formed and the part of A above the diagonal is
                     not referenced.

           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
                     as determined by ZSYTRF_ROOK.

           WORK

                     WORK is COMPLEX*16 array, dimension (N)

           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) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:

              December 2016, Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine zsytrs (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * ) A,
       integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB,
       integer INFO)
       ZSYTRS

       Purpose:

            ZSYTRS solves a system of linear equations A*X = B with a complex
            symmetric matrix A using the factorization A = U*D*U**T or
            A = L*D*L**T computed by ZSYTRF.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

                     N is INTEGER
                     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)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF.

           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
                     as determined by ZSYTRF.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zsytrs2 (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 INFO)
       ZSYTRS2

       Purpose:

            ZSYTRS2 solves a system of linear equations A*X = B with a real
            symmetric matrix A using the factorization A = U*D*U**T or
            A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

                     N is INTEGER
                     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)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF.
                     Note that A is input / output. This might be counter-intuitive,
                     and one may think that A is input only. A is input / output. This
                     is because, at the start of the subroutine, we permute A in a
                     "better" form and then we permute A back to its original form at
                     the end.

           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
                     as determined by ZSYTRF.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the 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 (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2016

   subroutine zsytrs_3 (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, * )
       A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16,
       dimension( ldb, * ) B, integer LDB, integer INFO)
       ZSYTRS_3

       Purpose:

            ZSYTRS_3 solves a system of linear equations A * X = B with a complex
            symmetric matrix A using the factorization computed
            by ZSYTRF_RK or ZSYTRF_BK:

               A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

            where U (or L) is unit upper (or lower) triangular matrix,
            U**T (or L**T) is the transpose of U (or L), P is a permutation
            matrix, P**T is the transpose of P, and D is symmetric and block
            diagonal with 1-by-1 and 2-by-2 diagonal blocks.

            This algorithm is using Level 3 BLAS.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix:
                     = 'U':  Upper triangular, form is A = P*U*D*(U**T)*(P**T);
                     = 'L':  Lower triangular, form is A = P*L*D*(L**T)*(P**T).

           N

                     N is INTEGER
                     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)
                     Diagonal of the block diagonal matrix D and factors U or L
                     as computed by ZSYTRF_RK and ZSYTRF_BK:
                       a) ONLY diagonal elements of the symmetric block diagonal
                          matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
                          (superdiagonal (or subdiagonal) elements of D
                           should be provided on entry in array E), and
                       b) If UPLO = 'U': factor U in the superdiagonal part of A.
                          If UPLO = 'L': factor L in the subdiagonal part of A.

           LDA

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

           E

                     E is COMPLEX*16 array, dimension (N)
                     On entry, contains the superdiagonal (or subdiagonal)
                     elements of the symmetric block diagonal matrix D
                     with 1-by-1 or 2-by-2 diagonal blocks, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is not referenced in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZSYTRF_RK or ZSYTRF_BK.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           June 2017

       Contributors:

             June 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine zsytrs_aa (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)
       ZSYTRS_AA

       Purpose:

            ZSYTRS_AA solves a system of linear equations A*X = B with a complex
            symmetric matrix A using the factorization A = U*T*U**T or
            A = L*T*L**T computed by ZSYTRF_AA.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*T*U**T;
                     = 'L':  Lower triangular, form is A = L*T*L**T.

           N

                     N is INTEGER
                     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)
                     Details of factors computed by ZSYTRF_AA.

           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 as computed by ZSYTRF_AA.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           WORK

                     WORK is DOUBLE array, dimension (MAX(1,LWORK))

           LWORK

                     LWORK is INTEGER, LWORK >= MAX(1,3*N-2).

            aram[out] INFO
            batim
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytrs_aa_2stage (character UPLO, integer N, integer NRHS, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( * ) TB, integer LTB, integer, dimension( *
       ) IPIV, integer, dimension( * ) IPIV2, complex*16, dimension( ldb, * ) B, integer LDB,
       integer INFO)
       ZSYTRS_AA_2STAGE

       Purpose:

            ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex
            symmetric matrix A using the factorization A = U*T*U**T or
            A = L*T*L**T computed by ZSYTRF_AA_2STAGE.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*T*U**T;
                     = 'L':  Lower triangular, form is A = L*T*L**T.

           N

                     N is INTEGER
                     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)
                     Details of factors computed by ZSYTRF_AA_2STAGE.

           LDA

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

           TB

                     TB is COMPLEX*16 array, dimension (LTB)
                     Details of factors computed by ZSYTRF_AA_2STAGE.

           LTB

                     The size of the array TB. LTB >= 4*N.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges as computed by
                     ZSYTRF_AA_2STAGE.

           IPIV2

                     IPIV2 is INTEGER array, dimension (N)
                     Details of the interchanges as computed by
                     ZSYTRF_AA_2STAGE.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2017

   subroutine zsytrs_rook (character UPLO, integer N, integer NRHS, complex*16, dimension( lda, *
       ) A, integer LDA, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer
       LDB, integer INFO)
       ZSYTRS_ROOK

       Purpose:

            ZSYTRS_ROOK solves a system of linear equations A*X = B with
            a complex symmetric matrix A using the factorization A = U*D*U**T or
            A = L*D*L**T computed by ZSYTRF_ROOK.

       Parameters:
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are stored
                     as an upper or lower triangular matrix.
                     = 'U':  Upper triangular, form is A = U*D*U**T;
                     = 'L':  Lower triangular, form is A = L*D*L**T.

           N

                     N is INTEGER
                     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)
                     The block diagonal matrix D and the multipliers used to
                     obtain the factor U or L as computed by ZSYTRF_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
                     as determined by ZSYTRF_ROOK.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the right hand side matrix B.
                     On exit, the solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:

              December 2016, Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

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

   subroutine ztgsyl (character TRANS, integer IJOB, integer M, integer N, complex*16, dimension(
       lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16,
       dimension( ldc, * ) C, integer LDC, complex*16, dimension( ldd, * ) D, integer LDD,
       complex*16, dimension( lde, * ) E, integer LDE, complex*16, dimension( ldf, * ) F, integer
       LDF, double precision SCALE, double precision DIF, complex*16, dimension( * ) WORK,
       integer LWORK, integer, dimension( * ) IWORK, integer INFO)
       ZTGSYL

       Purpose:

            ZTGSYL solves the generalized Sylvester equation:

                        A * R - L * B = scale * C            (1)
                        D * R - L * E = scale * F

            where R and L are unknown m-by-n matrices, (A, D), (B, E) and
            (C, F) are given matrix pairs of size m-by-m, n-by-n and m-by-n,
            respectively, with complex entries. A, B, D and E are upper
            triangular (i.e., (A,D) and (B,E) in generalized Schur form).

            The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1
            is an output scaling factor chosen to avoid overflow.

            In matrix notation (1) is equivalent to solve Zx = scale*b, where Z
            is defined as

                   Z = [ kron(In, A)  -kron(B**H, Im) ]        (2)
                       [ kron(In, D)  -kron(E**H, Im) ],

            Here Ix is the identity matrix of size x and X**H is the conjugate
            transpose of X. Kron(X, Y) is the Kronecker product between the
            matrices X and Y.

            If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
            is solved for, which is equivalent to solve for R and L in

                        A**H * R + D**H * L = scale * C           (3)
                        R * B**H + L * E**H = scale * -F

            This case (TRANS = 'C') is used to compute an one-norm-based estimate
            of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
            and (B,E), using ZLACON.

            If IJOB >= 1, ZTGSYL computes a Frobenius norm-based estimate of
            Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
            reciprocal of the smallest singular value of Z.

            This is a level-3 BLAS algorithm.

       Parameters:
           TRANS

                     TRANS is CHARACTER*1
                     = 'N': solve the generalized sylvester equation (1).
                     = 'C': solve the "conjugate transposed" system (3).

           IJOB

                     IJOB is INTEGER
                     Specifies what kind of functionality to be performed.
                     =0: solve (1) only.
                     =1: The functionality of 0 and 3.
                     =2: The functionality of 0 and 4.
                     =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
                         (look ahead strategy is used).
                     =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
                         (ZGECON on sub-systems is used).
                     Not referenced if TRANS = 'C'.

           M

                     M is INTEGER
                     The order of the matrices A and D, and the row dimension of
                     the matrices C, F, R and L.

           N

                     N is INTEGER
                     The order of the matrices B and E, and the column dimension
                     of the matrices C, F, R and L.

           A

                     A is COMPLEX*16 array, dimension (LDA, M)
                     The upper triangular matrix A.

           LDA

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

           B

                     B is COMPLEX*16 array, dimension (LDB, N)
                     The upper triangular matrix B.

           LDB

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

           C

                     C is COMPLEX*16 array, dimension (LDC, N)
                     On entry, C contains the right-hand-side of the first matrix
                     equation in (1) or (3).
                     On exit, if IJOB = 0, 1 or 2, C has been overwritten by
                     the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
                     the solution achieved during the computation of the
                     Dif-estimate.

           LDC

                     LDC is INTEGER
                     The leading dimension of the array C. LDC >= max(1, M).

           D

                     D is COMPLEX*16 array, dimension (LDD, M)
                     The upper triangular matrix D.

           LDD

                     LDD is INTEGER
                     The leading dimension of the array D. LDD >= max(1, M).

           E

                     E is COMPLEX*16 array, dimension (LDE, N)
                     The upper triangular matrix E.

           LDE

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

           F

                     F is COMPLEX*16 array, dimension (LDF, N)
                     On entry, F contains the right-hand-side of the second matrix
                     equation in (1) or (3).
                     On exit, if IJOB = 0, 1 or 2, F has been overwritten by
                     the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
                     the solution achieved during the computation of the
                     Dif-estimate.

           LDF

                     LDF is INTEGER
                     The leading dimension of the array F. LDF >= max(1, M).

           DIF

                     DIF is DOUBLE PRECISION
                     On exit DIF is the reciprocal of a lower bound of the
                     reciprocal of the Dif-function, i.e. DIF is an upper bound of
                     Dif[(A,D), (B,E)] = sigma-min(Z), where Z as in (2).
                     IF IJOB = 0 or TRANS = 'C', DIF is not referenced.

           SCALE

                     SCALE is DOUBLE PRECISION
                     On exit SCALE is the scaling factor in (1) or (3).
                     If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
                     to a slightly perturbed system but the input matrices A, B,
                     D and E have not been changed. If SCALE = 0, R and L will
                     hold the solutions to the homogenious system with C = F = 0.

           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 dimension of the array WORK. LWORK > = 1.
                     If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N).

                     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.

           IWORK

                     IWORK is INTEGER array, dimension (M+N+2)

           INFO

                     INFO is INTEGER
                       =0: successful exit
                       <0: If INFO = -i, the i-th argument had an illegal value.
                       >0: (A, D) and (B, E) have common or very close
                           eigenvalues.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

       Contributors:
           Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
           87 Umea, Sweden.

       References:
           [1] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the
           Generalized Sylvester Equation and Estimating the Separation between Regular Matrix
           Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901
           87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK Working Note 75. To
           appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.
            [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester Equation (AR -
           LB, DR - LE ) = (C, F), SIAM J. Matrix Anal. Appl., 15(4):1045-1060, 1994.
            [3] B. Kagstrom and L. Westin, Generalized Schur Methods with Condition Estimators
           for Solving the Generalized Sylvester Equation, IEEE Transactions on Automatic
           Control, Vol. 34, No. 7, July 1989, pp 745-751.

   subroutine ztrsyl (character TRANA, character TRANB, integer ISGN, integer M, integer N,
       complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer
       LDB, complex*16, dimension( ldc, * ) C, integer LDC, double precision SCALE, integer INFO)
       ZTRSYL

       Purpose:

            ZTRSYL solves the complex Sylvester matrix equation:

               op(A)*X + X*op(B) = scale*C or
               op(A)*X - X*op(B) = scale*C,

            where op(A) = A or A**H, and A and B are both upper triangular. A is
            M-by-M and B is N-by-N; the right hand side C and the solution X are
            M-by-N; and scale is an output scale factor, set <= 1 to avoid
            overflow in X.

       Parameters:
           TRANA

                     TRANA is CHARACTER*1
                     Specifies the option op(A):
                     = 'N': op(A) = A    (No transpose)
                     = 'C': op(A) = A**H (Conjugate transpose)

           TRANB

                     TRANB is CHARACTER*1
                     Specifies the option op(B):
                     = 'N': op(B) = B    (No transpose)
                     = 'C': op(B) = B**H (Conjugate transpose)

           ISGN

                     ISGN is INTEGER
                     Specifies the sign in the equation:
                     = +1: solve op(A)*X + X*op(B) = scale*C
                     = -1: solve op(A)*X - X*op(B) = scale*C

           M

                     M is INTEGER
                     The order of the matrix A, and the number of rows in the
                     matrices X and C. M >= 0.

           N

                     N is INTEGER
                     The order of the matrix B, and the number of columns in the
                     matrices X and C. N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,M)
                     The upper triangular matrix A.

           LDA

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

           B

                     B is COMPLEX*16 array, dimension (LDB,N)
                     The upper triangular matrix B.

           LDB

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

           C

                     C is COMPLEX*16 array, dimension (LDC,N)
                     On entry, the M-by-N right hand side matrix C.
                     On exit, C is overwritten by the solution matrix X.

           LDC

                     LDC is INTEGER
                     The leading dimension of the array C. LDC >= max(1,M)

           SCALE

                     SCALE is DOUBLE PRECISION
                     The scale factor, scale, set <= 1 to avoid overflow in X.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     = 1: A and B have common or very close eigenvalues; perturbed
                          values were used to solve the equation (but the matrices
                          A and B are unchanged).

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

Author

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