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NAME

       complex16GTsolve

SYNOPSIS

   Functions
       subroutine zgtsv (N, NRHS, DL, D, DU, B, LDB, INFO)
            ZGTSV computes the solution to system of linear equations A * X = B for GT matrices
       subroutine zgtsvx (FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X,
           LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
            ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices

Detailed Description

       This is the group of complex16 solve driver functions for GT matrices

Function Documentation

   subroutine zgtsv (integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16,
       dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( ldb, * ) B,
       integer LDB, integer INFO)
        ZGTSV computes the solution to system of linear equations A * X = B for GT matrices

       Purpose:

            ZGTSV  solves the equation

               A*X = B,

            where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
            partial pivoting.

            Note that the equation  A**T *X = B  may be solved by interchanging the
            order of the arguments DU and DL.

       Parameters:
           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.

           DL

                     DL is COMPLEX*16 array, dimension (N-1)
                     On entry, DL must contain the (n-1) subdiagonal elements of
                     A.
                     On exit, DL is overwritten by the (n-2) elements of the
                     second superdiagonal of the upper triangular matrix U from
                     the LU factorization of A, in DL(1), ..., DL(n-2).

           D

                     D is COMPLEX*16 array, dimension (N)
                     On entry, D must contain the diagonal elements of A.
                     On exit, D is overwritten by the n diagonal elements of U.

           DU

                     DU is COMPLEX*16 array, dimension (N-1)
                     On entry, DU must contain the (n-1) superdiagonal elements
                     of A.
                     On exit, DU is overwritten by the (n-1) elements of the first
                     superdiagonal of U.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

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

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
                           has not been computed.  The factorization has not been
                           completed unless i = N.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

   subroutine zgtsvx (character FACT, character TRANS, integer N, integer NRHS, complex*16,
       dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU,
       complex*16, dimension( * ) DLF, complex*16, dimension( * ) DF, complex*16, dimension( * )
       DUF, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension(
       ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X, integer LDX, double precision
       RCOND, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR,
       complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)
        ZGTSVX computes the solution to system of linear equations A * X = B for GT matrices

       Purpose:

            ZGTSVX uses the LU factorization to compute the solution to a complex
            system of linear equations A * X = B, A**T * X = B, or A**H * X = B,
            where A is a tridiagonal matrix of order N and X and B are N-by-NRHS
            matrices.

            Error bounds on the solution and a condition estimate are also
            provided.

       Description:

            The following steps are performed:

            1. If FACT = 'N', the LU decomposition is used to factor the matrix A
               as A = L * U, where L is a product of permutation and unit lower
               bidiagonal matrices and U is upper triangular with nonzeros in
               only the main diagonal and first two superdiagonals.

            2. If some U(i,i)=0, so that U is exactly singular, then the routine
               returns with INFO = i. Otherwise, the factored form of A is used
               to estimate the condition number of the matrix A.  If the
               reciprocal of the condition number is less than machine precision,
               INFO = N+1 is returned as a warning, but the routine still goes on
               to solve for X and compute error bounds as described below.

            3. The system of equations is solved for X using the factored form
               of A.

            4. Iterative refinement is applied to improve the computed solution
               matrix and calculate error bounds and backward error estimates
               for it.

       Parameters:
           FACT

                     FACT is CHARACTER*1
                     Specifies whether or not the factored form of A has been
                     supplied on entry.
                     = 'F':  DLF, DF, DUF, DU2, and IPIV contain the factored form
                             of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV will not
                             be modified.
                     = 'N':  The matrix will be copied to DLF, DF, and DUF
                             and factored.

           TRANS

                     TRANS is CHARACTER*1
                     Specifies the form of the system of equations:
                     = 'N':  A * X = B     (No transpose)
                     = 'T':  A**T * X = B  (Transpose)
                     = 'C':  A**H * X = B  (Conjugate transpose)

           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.

           DL

                     DL is COMPLEX*16 array, dimension (N-1)
                     The (n-1) subdiagonal elements of A.

           D

                     D is COMPLEX*16 array, dimension (N)
                     The n diagonal elements of A.

           DU

                     DU is COMPLEX*16 array, dimension (N-1)
                     The (n-1) superdiagonal elements of A.

           DLF

                     DLF is COMPLEX*16 array, dimension (N-1)
                     If FACT = 'F', then DLF is an input argument and on entry
                     contains the (n-1) multipliers that define the matrix L from
                     the LU factorization of A as computed by ZGTTRF.

                     If FACT = 'N', then DLF is an output argument and on exit
                     contains the (n-1) multipliers that define the matrix L from
                     the LU factorization of A.

           DF

                     DF is COMPLEX*16 array, dimension (N)
                     If FACT = 'F', then DF is an input argument and on entry
                     contains the n diagonal elements of the upper triangular
                     matrix U from the LU factorization of A.

                     If FACT = 'N', then DF is an output argument and on exit
                     contains the n diagonal elements of the upper triangular
                     matrix U from the LU factorization of A.

           DUF

                     DUF is COMPLEX*16 array, dimension (N-1)
                     If FACT = 'F', then DUF is an input argument and on entry
                     contains the (n-1) elements of the first superdiagonal of U.

                     If FACT = 'N', then DUF is an output argument and on exit
                     contains the (n-1) elements of the first superdiagonal of U.

           DU2

                     DU2 is COMPLEX*16 array, dimension (N-2)
                     If FACT = 'F', then DU2 is an input argument and on entry
                     contains the (n-2) elements of the second superdiagonal of
                     U.

                     If FACT = 'N', then DU2 is an output argument and on exit
                     contains the (n-2) elements of the second superdiagonal of
                     U.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     If FACT = 'F', then IPIV is an input argument and on entry
                     contains the pivot indices from the LU factorization of A as
                     computed by ZGTTRF.

                     If FACT = 'N', then IPIV is an output argument and on exit
                     contains the pivot indices from the LU factorization of A;
                     row i of the matrix was interchanged with row IPIV(i).
                     IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
                     a row interchange was not required.

           B

                     B is COMPLEX*16 array, dimension (LDB,NRHS)
                     The N-by-NRHS 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)
                     If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.

           LDX

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

           RCOND

                     RCOND is DOUBLE PRECISION
                     The estimate of the reciprocal condition number of the matrix
                     A.  If RCOND is less than the machine precision (in
                     particular, if RCOND = 0), the matrix is singular to working
                     precision.  This condition is indicated by a return code of
                     INFO > 0.

           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
                     > 0:  if INFO = i, and i is
                           <= N:  U(i,i) is exactly zero.  The factorization
                                  has not been completed unless i = N, but the
                                  factor U is exactly singular, so the solution
                                  and error bounds could not be computed.
                                  RCOND = 0 is returned.
                           = N+1: U is nonsingular, but RCOND is less than machine
                                  precision, meaning that the matrix is singular
                                  to working precision.  Nevertheless, the
                                  solution and error bounds are computed because
                                  there are a number of situations where the
                                  computed solution can be more accurate than the
                                  value of RCOND would suggest.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           December 2016

Author

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