zgtrfs(3)

NAME

ZGTRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is tridiagonal, and

provides error bounds and backward error estimates for the solu

tion

SYNOPSIS

SUBROUTINE  ZGTRFS(  TRANS,  N,  NRHS, DL, D, DU, DLF, DF,
DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
    CHARACTER      TRANS
    INTEGER        INFO, LDB, LDX, N, NRHS
    INTEGER        IPIV( * )
    DOUBLE         PRECISION BERR( * ), FERR( * ),  RWORK(
* )
    COMPLEX*16      B( LDB, * ), D( * ), DF( * ), DL( * ),
DLF( * ), DU( * ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )

PURPOSE

ZGTRFS improves the computed solution to a system of lin

ear equations when the coefficient matrix is tridiagonal, and

provides error bounds and backward error estimates for the solu

tion.

ARGUMENTS

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)

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) COMPLEX*16 array, dimension (N-1)

The (n-1) subdiagonal elements of A.

D (input) COMPLEX*16 array, dimension (N)

The diagonal elements of A.

DU (input) COMPLEX*16 array, dimension (N-1)

The (n-1) superdiagonal elements of A.

DLF (input) COMPLEX*16 array, dimension (N-1)

The (n-1) multipliers that define the matrix L

from the LU factorization of A as computed by ZGTTRF.

DF (input) COMPLEX*16 array, dimension (N)

The n diagonal elements of the upper triangular

matrix U from the LU factorization of A.

DUF (input) COMPLEX*16 array, dimension (N-1)

The (n-1) elements of the first superdiagonal of

U.

DU2 (input) COMPLEX*16 array, dimension (N-2)

The (n-2) elements of the second superdiagonal of

U.

IPIV (input) 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.

B (input) COMPLEX*16 array, dimension (LDB,NRHS)

The right hand side matrix B.

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

X (input/output) COMPLEX*16 array, dimension

(LDX,NRHS)

On entry, the solution matrix X, as computed by

ZGTTRS. On exit, the improved solution matrix X.

LDX (input) INTEGER

The leading dimension of the array X. LDX >=

max(1,N).

FERR (output) DOUBLE PRECISION array, dimension (NRHS)

The estimated forward error bound for each solu

tion 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 that makes X(j) an exact solution).

WORK (workspace) COMPLEX*16 array, dimension (2*N)

RWORK (workspace) DOUBLE PRECISION array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

ZGTRFS(3)