SPTSVX(l)								 )								 SPTSVX(l)

NAME

       SPTSVX - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N sym-
       metric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

SYNOPSIS

       SUBROUTINE SPTSVX( FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, INFO )

	   CHARACTER	  FACT

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   REAL 	  RCOND

	   REAL 	  B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

       SPTSVX uses the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N-by-N  sym-
       metric  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**T, where L
	  is a unit lower bidiagonal matrix and D is diagonal.	The
	  factorization can also be regarded as having the form
	  A = U**T*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 A has been 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) REAL 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**T 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**T factorization of A.

       EF      (input or output) REAL 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**T factorization of A.  If FACT = 'N', then EF is an output argument and on exit contains the (n-1) subdiagonal ele-
	       ments of the unit bidiagonal factor L from the L*D*L**T factorization of A.

       B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
	       If INFO = 0 of 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  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).

       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) REAL array, dimension (2*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 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.  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.

LAPACK version 3.0						   15 June 2000 							 SPTSVX(l)