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CPTSVX(l)			       )			     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 Her‐
       mitian  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  Her‐
       mitian  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. If the leading i-by-i principal minor is not positive definite,
	  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.

ARGUMENTS
       FACT    (input) CHARACTER*1
	       Specifies  whether  or not the factored form of the matrix A is
	       supplied 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 con‐
	       tains 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 out‐
	       put 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 con‐
	       tains 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 output 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 or INFO = N+1, 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
	       indicated by a return code of INFO > 0.

       FERR    (output) REAL array, dimension (NRHS)
	       The forward error bound for each solution vector X(j) (the j-th
	       column of the solution matrix X).  If XTRUE is the  true	 solu‐
	       tion 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).

       BERR    (output) REAL array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor 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 defi‐
	       nite, so the factorization could	 not  be  completed,  and  the
	       solution	 has not been 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.  Nev‐
	       ertheless, 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.

LAPACK version 3.0		 15 June 2000			     CPTSVX(l)
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