 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zpbt02()

 subroutine zpbt02 ( character UPLO, integer N, integer KD, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

ZPBT02

Purpose:
``` ZPBT02 computes the residual for a solution of a Hermitian banded
system of equations  A*x = b:
RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
where EPS is the machine precision.```
Parameters
 [in] 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``` [in] N ``` N is INTEGER The number of rows and columns of the matrix A. N >= 0.``` [in] 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.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides. NRHS >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The original Hermitian band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See ZPBTRF for further details.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).```

Definition at line 134 of file zpbt02.f.

136*
137* -- LAPACK test routine --
138* -- LAPACK is a software package provided by Univ. of Tennessee, --
139* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140*
141* .. Scalar Arguments ..
142 CHARACTER UPLO
143 INTEGER KD, LDA, LDB, LDX, N, NRHS
144 DOUBLE PRECISION RESID
145* ..
146* .. Array Arguments ..
147 DOUBLE PRECISION RWORK( * )
148 COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
149* ..
150*
151* =====================================================================
152*
153* .. Parameters ..
154 DOUBLE PRECISION ZERO, ONE
155 parameter( zero = 0.0d+0, one = 1.0d+0 )
156 COMPLEX*16 CONE
157 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
158* ..
159* .. Local Scalars ..
160 INTEGER J
161 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
162* ..
163* .. External Functions ..
164 DOUBLE PRECISION DLAMCH, DZASUM, ZLANHB
165 EXTERNAL dlamch, dzasum, zlanhb
166* ..
167* .. External Subroutines ..
168 EXTERNAL zhbmv
169* ..
170* .. Intrinsic Functions ..
171 INTRINSIC max
172* ..
173* .. Executable Statements ..
174*
175* Quick exit if N = 0 or NRHS = 0.
176*
177 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
178 resid = zero
179 RETURN
180 END IF
181*
182* Exit with RESID = 1/EPS if ANORM = 0.
183*
184 eps = dlamch( 'Epsilon' )
185 anorm = zlanhb( '1', uplo, n, kd, a, lda, rwork )
186 IF( anorm.LE.zero ) THEN
187 resid = one / eps
188 RETURN
189 END IF
190*
191* Compute B - A*X
192*
193 DO 10 j = 1, nrhs
194 CALL zhbmv( uplo, n, kd, -cone, a, lda, x( 1, j ), 1, cone,
195 \$ b( 1, j ), 1 )
196 10 CONTINUE
197*
198* Compute the maximum over the number of right hand sides of
199* norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
200*
201 resid = zero
202 DO 20 j = 1, nrhs
203 bnorm = dzasum( n, b( 1, j ), 1 )
204 xnorm = dzasum( n, x( 1, j ), 1 )
205 IF( xnorm.LE.zero ) THEN
206 resid = one / eps
207 ELSE
208 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
209 END IF
210 20 CONTINUE
211*
212 RETURN
213*
214* End of ZPBT02
215*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zhbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHBMV
Definition: zhbmv.f:187
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhb.f:132
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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