CPTSVX(l)		LAPACK routine (version	1.1)		    CPTSVX(l)

NAME
  CPTSVX - use the factorization A = L*D*L**H to 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 CPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND,
		     FERR, BERR, WORK, RWORK, INFO )

      CHARACTER	     FACT

      INTEGER	     INFO, LDB,	LDX, N,	NRHS

      REAL	     RCOND

      REAL	     BERR( * ),	D( * ),	DF( * ), FERR( * ), RWORK( * )

      COMPLEX	     B(	LDB, * ), E( * ), EF( *	), WORK( * ), X( LDX, *	)

PURPOSE
  CPTSVX uses the factorization	A = L*D*L**H to	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.

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

DESCRIPTION
  The following	steps are performed:

  1. If	FACT = 'N', the	matrix A is factored as	A = L*D*L**H, where L
     is	a unit lower bidiagonal	matrix and D is	diagonal.  The
     factorization can also be regarded	as having the form
     A = U**H*D*U.

  2. The factored form of A is used to compute the condition number
     of	the matrix A.  If the reciprocal of the	condition number is
     less than machine precision, steps	3 and 4	are skipped.

  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.

ARGUMENTS

  FACT	  (input) CHARACTER*1
	  Specifies whether or not the factored	form of	the matrix A is	sup-
	  plied	on entry.  = 'F':  On entry, DF	and EF contain the factored
	  form of A.  D, E, DF,	and EF will not	be modified.  =	'N':  The
	  matrix A will	be copied to DF	and EF and factored.

  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
	  matrices B and X.  NRHS >= 0.

  D	  (input) REAL array, dimension	(N)
	  The n	diagonal elements of the tridiagonal matrix A.

  E	  (input) COMPLEX array, dimension (N-1)
	  The (n-1) subdiagonal	elements of the	tridiagonal matrix A.

  DF	  (input or output) REAL array,	dimension (N)
	  If FACT = 'F', then DF is an input argument and on entry contains
	  the n	diagonal elements of the diagonal matrix D from	the L*D*L**H
	  factorization	of A.  If FACT = 'N', then DF is an output argument
	  and on exit contains the n diagonal elements of the diagonal matrix
	  D from the L*D*L**H factorization of A.

  EF	  (input or output) COMPLEX array, dimension (N-1)
	  If FACT = 'F', then EF is an input argument and on entry contains
	  the (n-1) subdiagonal	elements of the	unit bidiagonal	factor L from
	  the L*D*L**H factorization of	A.  If FACT = 'N', then	EF is an out-
	  put argument and on exit contains the	(n-1) subdiagonal elements of
	  the unit bidiagonal factor L from the	L*D*L**H factorization of A.

  B	  (input) COMPLEX array, dimension (LDB,NRHS)
	  The N-by-NRHS	right hand side	matrix B.

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

  X	  (output) COMPLEX array, dimension (LDX,NRHS)
	  If INFO = 0, the N-by-NRHS solution matrix X.

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

  RCOND	  (output) REAL
	  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 indi-
	  cated	by a return code of INFO > 0, and the solution and error
	  bounds are not computed.

  FERR	  (output) REAL	array, dimension (NRHS)
	  The estimated	forward	error bounds 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) bounds the magnitude of the
	  largest element in (X(j) - XTRUE) divided by the magnitude of	the
	  largest element in X(j).

  BERR	  (output) REAL	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	  (workspace) COMPLEX array, dimension (N)

  RWORK	  (workspace) REAL array, dimension (N)

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO	= -i, the i-th argument	had an illegal value
	  > 0:	if INFO	= i, and i is <= N  the	leading	minor of order i of A
	  is not positive definite, so the factorization could not be com-
	  pleted unless	i = N, and the solution	and error bounds could not be
	  computed.  = N+1 RCOND is less than machine precision.  The
	  factorization	has been completed, but	the matrix is singular to
	  working precision, and the solution and error	bounds have not	been
	  computed.