CPTSV - compute the solution to a complex system of linear
       equations A*X = B, where A is an N-by-N Hermitian positive
       definite  tridiagonal  matrix,  and  X and B are N-by-NRHS
       matrices


SYNOPSIS

       SUBROUTINE CPTSV( N, NRHS, D, E, B, LDB, INFO )

           INTEGER       INFO, LDB, N, NRHS

           REAL          D( * )

           COMPLEX       B( LDB, * ), E( * )


PURPOSE

       CPTSV computes the solution to a complex system of  linear
       equations A*X = B, where A is an N-by-N Hermitian positive
       definite tridiagonal matrix, and X  and  B  are  N-by-NRHS
       matrices.  A is factored as A = L*D*L**H, and the factored
       form of A is then used to solve the system of equations.


ARGUMENTS

       N       (input) INTEGER
               The order of the matrix A.  N >= 0.

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

       D       (input/output) REAL array, dimension (N)
               On entry, the n diagonal elements of the tridiago­
               nal matrix A.  On exit, the n diagonal elements of
               the  diagonal  matrix D from the factorization A =
               L*D*L**H.

       E       (input/output) COMPLEX array, dimension (N-1)
               On entry, the (n-1) subdiagonal  elements  of  the
               tridiagonal matrix A.  On exit, the (n-1) subdiag­
               onal elements of the unit bidiagonal factor L from
               the  L*D*L**H  factorization  of A.  E can also be
               regarded as the superdiagonal of the unit bidiago­
               nal factor U from the U**H*D*U factorization of A.

       B       (input/output) COMPLEX 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     (input) INTEGER
               The  leading  dimension  of  the  array B.  LDB >=
               max(1,N).

               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value
               > 0:  if INFO = i, the leading minor of order i is
               not positive definite, and the  solution  has  not
               been  computed.   The  factorization  has not been
               completed unless i = N.


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