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ztbrfs.f(3) LAPACK ztbrfs.f(3)

NAME

ztbrfs.f

SYNOPSIS

Functions/Subroutines


subroutine ztbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZTBRFS

Function/Subroutine Documentation

subroutine ztbrfs (character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex*16, dimension( ldab, * ) AB, integer LDAB, 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)

ZTBRFS

Purpose:


ZTBRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by ZTBTRS or some other
means before entering this routine. ZTBRFS does not do iterative
refinement because doing so cannot improve the backward error.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.

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)

DIAG


DIAG is CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.

N


N is INTEGER
The order of the matrix A. N >= 0.

KD


KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.

NRHS


NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.

AB


AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

B


B is COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X


X is COMPLEX*16 array, dimension (LDX,NRHS)
The solution matrix X.

LDX


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

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.

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).

WORK


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

RWORK


RWORK is DOUBLE PRECISION array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 190 of file ztbrfs.f.

Author

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Tue Nov 14 2017 Version 3.8.0