# zpbrfs.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine zpbrfs (character UPLO, integer N, integer KD, integer NRHS, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldafb, * ) AFB, integer LDAFB, 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)

**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 COMPLEX*16 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:**June 2016

Definition at line 191 of file zpbrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zpbrfs(3) is an alias of zpbrfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK