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sgtsvx.f(3)				      LAPACK				      sgtsvx.f(3)

NAME
       sgtsvx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sgtsvx (FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X,
	   LDX, RCOND, FERR, BERR, WORK, IWORK, INFO)
	    SGTSVX computes the solution to system of linear equations A * X = B for GT matrices

Function/Subroutine Documentation
   subroutine sgtsvx (characterFACT, characterTRANS, integerN, integerNRHS, real, dimension( *
       )DL, real, dimension( * )D, real, dimension( * )DU, real, dimension( * )DLF, real,
       dimension( * )DF, real, dimension( * )DUF, real, dimension( * )DU2, integer, dimension( *
       )IPIV, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX,
       realRCOND, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( * )WORK,
       integer, dimension( * )IWORK, integerINFO)
	SGTSVX computes the solution to system of linear equations A * X = B for GT matrices

       Purpose:

	    SGTSVX uses the LU factorization to compute the solution to a real
	    system of linear equations A * X = B or A**T * X = B,
	    where A is a tridiagonal matrix of order N 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 LU decomposition is used to factor the matrix A
	       as A = L * U, where L is a product of permutation and unit lower
	       bidiagonal matrices and U is upper triangular with nonzeros in
	       only the main diagonal and first two superdiagonals.

	    2. If some U(i,i)=0, so that U is exactly singular, 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':  DLF, DF, DUF, DU2, and IPIV contain the factored
			     form of A; DL, D, DU, DLF, DF, DUF, DU2 and IPIV
			     will not be modified.
		     = 'N':  The matrix will be copied to DLF, DF, and DUF
			     and factored.

	   TRANS

		     TRANS is CHARACTER*1
		     Specifies the form of the system of equations:
		     = 'N':  A * X = B	   (No transpose)
		     = 'T':  A**T * X = B  (Transpose)
		     = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

	   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 matrix B.  NRHS >= 0.

	   DL

		     DL is REAL array, dimension (N-1)
		     The (n-1) subdiagonal elements of A.

	   D

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

	   DU

		     DU is REAL array, dimension (N-1)
		     The (n-1) superdiagonal elements of A.

	   DLF

		     DLF is REAL array, dimension (N-1)
		     If FACT = 'F', then DLF is an input argument and on entry
		     contains the (n-1) multipliers that define the matrix L from
		     the LU factorization of A as computed by SGTTRF.

		     If FACT = 'N', then DLF is an output argument and on exit
		     contains the (n-1) multipliers that define the matrix L from
		     the LU factorization of 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 upper triangular
		     matrix U from the LU factorization of A.

		     If FACT = 'N', then DF is an output argument and on exit
		     contains the n diagonal elements of the upper triangular
		     matrix U from the LU factorization of A.

	   DUF

		     DUF is REAL array, dimension (N-1)
		     If FACT = 'F', then DUF is an input argument and on entry
		     contains the (n-1) elements of the first superdiagonal of U.

		     If FACT = 'N', then DUF is an output argument and on exit
		     contains the (n-1) elements of the first superdiagonal of U.

	   DU2

		     DU2 is REAL array, dimension (N-2)
		     If FACT = 'F', then DU2 is an input argument and on entry
		     contains the (n-2) elements of the second superdiagonal of
		     U.

		     If FACT = 'N', then DU2 is an output argument and on exit
		     contains the (n-2) elements of the second superdiagonal of
		     U.

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     If FACT = 'F', then IPIV is an input argument and on entry
		     contains the pivot indices from the LU factorization of A as
		     computed by SGTTRF.

		     If FACT = 'N', then IPIV is an output argument and on exit
		     contains the pivot indices from the LU factorization of A;
		     row i of the matrix was interchanged with row IPIV(i).
		     IPIV(i) will always be either i or i+1; IPIV(i) = i indicates
		     a row interchange was not required.

	   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 or 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 estimate of 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 estimated 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).  The estimate is as reliable as
		     the estimate for RCOND, and is almost always a slight
		     overestimate of the true error.

	   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 (3*N)

	   IWORK

		     IWORK is INTEGER array, dimension (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:  U(i,i) is exactly zero.  The factorization
				  has not been completed unless i = N, but the
				  factor U is exactly singular, so the solution
				  and error bounds could not be 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 292 of file sgtsvx.f.

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

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