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sptsvx.f

sptsvx.f(3)							      LAPACK							       sptsvx.f(3)

NAME

       sptsvx.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sptsvx (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, INFO)
	    SPTSVX computes the solution to system of linear equations A * X = B for PT matrices

Function/Subroutine Documentation
   subroutine sptsvx (characterFACT, integerN, integerNRHS, real, dimension( * )D, real, dimension( * )E, real, dimension( * )DF, real, dimension(
       * )EF, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, realRCOND, real, dimension( * )FERR, real,
       dimension( * )BERR, real, dimension( * )WORK, integerINFO)
	SPTSVX computes the solution to system of linear equations A * X = B for PT matrices

       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.

       Parameters:
	   FACT

		     FACT is 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

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of columns
		     of the matrices B and X.  NRHS >= 0.

	   D

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

	   E

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

	   DF

		     DF is 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

		     EF is 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 elements of the unit
		     bidiagonal factor L from the L*D*L**T factorization of A.

	   B

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

	   LDB

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

	   X

		     X is REAL array, dimension (LDX,NRHS)
		     If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.

	   LDX

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

	   RCOND

		     RCOND is 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

		     FERR is 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

		     BERR is 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

		     WORK is REAL array, dimension (2*N)

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 228 of file sptsvx.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sptsvx.f(3)