ZPTTRS  - solve a tridiagonal system of the form A * X = B
       using the factorization A = U'*D*U or A = L*D*L'  computed
       by ZPTTRF


SYNOPSIS

       SUBROUTINE ZPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDB, N, NRHS

           DOUBLE         PRECISION D( * )

           COMPLEX*16     B( LDB, * ), E( * )


PURPOSE

       ZPTTRS  solves  a tridiagonal system of the form A * X = B
       using the factorization A = U'*D*U or A = L*D*L'  computed
       by  ZPTTRF. D is a diagonal matrix specified in the vector
       D, U (or L) is a unit bidiagonal matrix whose  superdiago­
       nal  (subdiagonal) is specified in the vector E, and X and
       B are N by NRHS matrices.


ARGUMENTS

       UPLO    (input) CHARACTER*1
               Specifies  the  form  of  the  factorization   and
               whether  the  vector E is the superdiagonal of the
               upper bidiagonal factor U or  the  subdiagonal  of
               the  lower  bidiagonal  factor  L.   =  'U':   A =
               U'*D*U, E is the superdiagonal of U
               = 'L':  A = L*D*L', E is the subdiagonal of L

       N       (input) INTEGER
               The order of the tridiagonal 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) DOUBLE PRECISION array, dimension (N)
               The  n  diagonal elements of the diagonal matrix D
               from the factorization A = U'*D*U or A = L*D*L'.

       E       (input) COMPLEX*16 array, dimension (N-1)
               If UPLO = 'U', the (n-1) superdiagonal elements of
               the  unit  bidiagonal factor U from the factoriza­
               tion A = U'*D*U.  If UPLO = 'L', the (n-1)  subdi­
               agonal  elements  of  the unit bidiagonal factor L
               from the factorization A = L*D*L'.

       B        (input/output)   DOUBLE   PRECISION   array,
               dimension (LDB,NRHS)

               system of linear equations.  On exit, the solution
               vectors, X.

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

       INFO    (output) INTEGER
               = 0: successful exit
               <  0: if INFO = -k, the k-th argument had an ille­
               gal value


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