zptrfs()

subroutine zptrfs	(	character	uplo,
		integer	n,
		integer	nrhs,
		double precision, dimension( * )	d,
		complex*16, dimension( * )	e,
		double precision, dimension( * )	df,
		complex*16, dimension( * )	ef,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( ldx, * )	x,
		integer	ldx,
		double precision, dimension( * )	ferr,
		double precision, dimension( * )	berr,
		complex*16, dimension( * )	work,
		double precision, dimension( * )	rwork,
		integer	info )

ZPTRFS

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Purpose:

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

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> Specifies whether the superdiagonal or the subdiagonal of the !> tridiagonal matrix A is stored and the form of the !> factorization: !> = 'U': E is the superdiagonal of A, and A = U**H*D*U; !> = 'L': E is the subdiagonal of A, and A = L*D*L**H. !> (The two forms are equivalent if A is real.) !>
[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]	D	!> D is DOUBLE PRECISION array, dimension (N) !> The n real diagonal elements of the tridiagonal matrix A. !>
[in]	E	!> E is COMPLEX*16 array, dimension (N-1) !> The (n-1) off-diagonal elements of the tridiagonal matrix A !> (see UPLO). !>
[in]	DF	!> DF is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the diagonal matrix D from !> the factorization computed by ZPTTRF. !>
[in]	EF	!> EF is COMPLEX*16 array, dimension (N-1) !> The (n-1) off-diagonal elements of the unit bidiagonal !> factor U or L from the factorization computed by ZPTTRF !> (see UPLO). !>
[in]	B	!> B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) !> On entry, the solution matrix X, as computed by ZPTTRS. !> 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 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). !>
[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 COMPLEX*16 array, dimension (N) !>
[out]	RWORK	!> RWORK is DOUBLE PRECISION 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.