# zpbrfs.f man page

zpbrfs.f —

## Synopsis

### Functions/Subroutines

subroutinezpbrfs(UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)ZPBRFS

## Function/Subroutine Documentation

### subroutine zpbrfs (characterUPLO, integerN, integerKD, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldafb, * )AFB, integerLDAFB, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

**ZPBRFS**

**Purpose:**

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

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
```

*N*

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

*KD*

```
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. 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 DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the Hermitian 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).
```

*LDAB*

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

*AFB*

```
AFB is COMPLEX*16 array, dimension (LDAFB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A as computed by
ZPBTRF, in the same storage format as A (see AB).
```

*LDAFB*

```
LDAFB is INTEGER
The leading dimension of the array AFB. LDAFB >= 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)
On entry, the solution matrix X, as computed by ZPBTRS.
On exit, the improved 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
```

**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.

**Date:**

November 2011

Definition at line 189 of file zpbrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zpbrfs(3) is an alias of zpbrfs.f(3).