# Ubuntu Feisty 7.04 manual page repository

Ubuntu is a free computer operating system based on the Linux kernel. Many IT companies, like DeployIS is using it to provide an up-to-date, stable operating system.

Provided by: lapack3-doc_3.0.20000531a-6ubuntu3_all

` `

### NAME

```        ZGBRFS  - improve the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides  error  bounds  and
backward error estimates for the solution
```

### SYNOPSIS

```        SUBROUTINE ZGBRFS( TRANS,  N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )

CHARACTER      TRANS

INTEGER        INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS

INTEGER        IPIV( * )

DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( * )

COMPLEX*16     AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( *
), X( LDX, * )
```

### PURPOSE

```        ZGBRFS  improves  the computed solution to a system of linear equations
when the coefficient matrix is banded, and provides  error  bounds  and
backward error estimates for the solution.
```

### 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.

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

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

AB      (input) COMPLEX*16 array, dimension (LDAB,N)
The original band matrix A, stored in rows 1 to  KL+KU+1.   The
j-th  column  of A is stored in the j-th column of the array AB
as   follows:   AB(ku+1+i-j,j)   =    A(i,j)    for    max(1,j-
ku)<=i<=min(n,j+kl).

LDAB    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.

AFB     (input) COMPLEX*16 array, dimension (LDAFB,N)
Details  of  the LU factorization of the band matrix A, as com‐
puted by ZGBTRF.  U is  stored  as  an  upper  triangular  band
matrix  with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
multipliers used during the factorization are  stored  in  rows
KL+KU+2 to 2*KL+KU+1.

LDAFB   (input) INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices from ZGBTRF; for 1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).

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  ZGBTRS.   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 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 vec‐
tor 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 illegal value
```

### PARAMETERS

```        ITMAX is the maximum number of steps of iterative refinement.

```
Sections

What does Ubuntu mean?
Ubuntu is an African word meaning 'Humanity to others', or 'I am what I am because of who we all are'. The Ubuntu distribution brings the spirit of Ubuntu to the software world.