# zpbt05.f - Man Page

TESTING/LIN/zpbt05.f

## Synopsis

### Functions/Subroutines

subroutine **zpbt05** (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)**ZPBT05**

## Function/Subroutine Documentation

### subroutine zpbt05 (character uplo, 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, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

**ZPBT05**

**Purpose:**

ZPBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a Hermitian band matrix. RESLTS(1) = test of the error bound = norm(X - XACT) / ( norm(X) * FERR ) A large value is returned if this ratio is not less than one. RESLTS(2) = residual from the iterative refinement routine = the maximum of BERR / ( NZ*EPS + (*) ), where (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) and NZ = max. number of nonzeros in any row of A, plus 1

**Parameters***UPLO*UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular

*N*N is INTEGER The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.

*KD*KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.

*NRHS*NRHS is INTEGER The number of columns of the matrices X, B, and XACT. 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.

*B*B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.

*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 computed solution vectors. Each vector is stored as a column of the matrix X.

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

*XACT*XACT is COMPLEX*16 array, dimension (LDX,NRHS) The exact solution vectors. Each vector is stored as a column of the matrix XACT.

*LDXACT*LDXACT is INTEGER The leading dimension of the array XACT. LDXACT >= max(1,N).

*FERR*FERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.

*BERR*BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).

*RESLTS*RESLTS is DOUBLE PRECISION array, dimension (2) The maximum over the NRHS solution vectors of the ratios: RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR ) RESLTS(2) = BERR / ( NZ*EPS + (*) )

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **169** of file **zpbt05.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zpbt05(3) is an alias of zpbt05.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK