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RedHat 9 (Linux i386) - man page for sptsvx (redhat section l)

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  symmetric  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  symmetric  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) subdi-
	       agonal 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  elements of the unit bidiagonal factor L from the L*D*L**T factoriza-
	       tion 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  solu-
	       tion).

       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 factor-
	       ization 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 solu-
	       tion  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)


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