dgtrfs()

subroutine dgtrfs	(	character	trans,
		integer	n,
		integer	nrhs,
		double precision, dimension( * )	dl,
		double precision, dimension( * )	d,
		double precision, dimension( * )	du,
		double precision, dimension( * )	dlf,
		double precision, dimension( * )	df,
		double precision, dimension( * )	duf,
		double precision, dimension( * )	du2,
		integer, dimension( * )	ipiv,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( ldx, * )	x,
		integer	ldx,
		double precision, dimension( * )	ferr,
		double precision, dimension( * )	berr,
		double precision, dimension( * )	work,
		integer, dimension( * )	iwork,
		integer	info )

DGTRFS

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Purpose:

!>
!> DGTRFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is tridiagonal, and provides
!> error bounds and backward error estimates for the solution.
!> 

Parameters

[in]	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) !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>
[in]	DL	!> DL is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) subdiagonal elements of A. !>
[in]	D	!> D is DOUBLE PRECISION array, dimension (N) !> The diagonal elements of A. !>
[in]	DU	!> DU is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) superdiagonal elements of A. !>
[in]	DLF	!> DLF is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A as computed by DGTTRF. !>
[in]	DF	!> DF is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !>
[in]	DUF	!> DUF is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) elements of the first superdiagonal of U. !>
[in]	DU2	!> DU2 is DOUBLE PRECISION array, dimension (N-2) !> The (n-2) elements of the second superdiagonal of U. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices; for 1 <= i <= n, 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. !>
[in]	B	!> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> The right hand side matrix B. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[in,out]	X	!> X is DOUBLE PRECISION array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by DGTTRS. !> On exit, the improved solution matrix X. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N). !>
[out]	FERR	!> FERR is 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. !>
[out]	BERR	!> BERR is 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 that makes X(j) an exact solution). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (3*N) !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N) !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Internal Parameters:

!>  ITMAX is the maximum number of steps of iterative refinement.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.