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DGTSVX(3F)							    DGTSVX(3F)

NAME
     DGTSVX - use the LU factorization to compute the solution to a real
     system of linear equations A * X = B or A**T * X = B,

SYNOPSIS
     SUBROUTINE DGTSVX( FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2,
			IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK,
			INFO )

	 CHARACTER	FACT, TRANS

	 INTEGER	INFO, LDB, LDX, N, NRHS

	 DOUBLE		PRECISION RCOND

	 INTEGER	IPIV( * ), IWORK( * )

	 DOUBLE		PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), DL(
			* ), DLF( * ), DU( * ), DU2( * ), DUF( * ), FERR( * ),
			WORK( * ), X( LDX, * )

PURPOSE
     DGTSVX 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. 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, steps 3 and 4 are skipped.

     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.

									Page 1

DGTSVX(3F)							    DGTSVX(3F)

ARGUMENTS
     FACT    (input) 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   (input) 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	     (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 matrix B.  NRHS >= 0.

     DL	     (input) DOUBLE PRECISION array, dimension (N-1)
	     The (n-1) subdiagonal elements of A.

     D	     (input) DOUBLE PRECISION array, dimension (N)
	     The n diagonal elements of A.

     DU	     (input) DOUBLE PRECISION array, dimension (N-1)
	     The (n-1) superdiagonal elements of A.

     DLF     (input or output) DOUBLE PRECISION 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 DGTTRF.

	     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	     (input or output) DOUBLE PRECISION 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     (input or output) DOUBLE PRECISION 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.

									Page 2

DGTSVX(3F)							    DGTSVX(3F)

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

     DU2     (input or output) DOUBLE PRECISION 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    (input or output) 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 DGTTRF.

	     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	     (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
	     If INFO = 0, the N-by-NRHS solution matrix X.

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

     RCOND   (output) DOUBLE PRECISION
	     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, and the
	     solution and error bounds are not computed.

     FERR    (output) DOUBLE PRECISION 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    (output) DOUBLE PRECISION 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

									Page 3

DGTSVX(3F)							    DGTSVX(3F)

	     that makes X(j) an exact solution).

     WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

     IWORK   (workspace) INTEGER 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:  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.  = N+1:
	     RCOND is less than machine precision.  The factorization has been
	     completed, but the matrix is singular to working precision, and
	     the solution and error bounds have not been computed.

									Page 4

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