 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dpbt02()

 subroutine dpbt02 ( character UPLO, integer N, integer KD, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision RESID )

DPBT02

Purpose:
``` DPBT02 computes the residual for a solution of a symmetric 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 symmetric 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 DOUBLE PRECISION array, dimension (LDA,N) The original symmetric 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 DPBTRF for further details.``` [in] LDA ``` LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).``` [in] X ``` X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dpbt02.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 A( LDA, * ), B( LDB, * ), RWORK( * ),
148 \$ X( LDX, * )
149* ..
150*
151* =====================================================================
152*
153* .. Parameters ..
154 DOUBLE PRECISION ZERO, ONE
155 parameter( zero = 0.0d+0, one = 1.0d+0 )
156* ..
157* .. Local Scalars ..
158 INTEGER J
159 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
160* ..
161* .. External Functions ..
162 DOUBLE PRECISION DASUM, DLAMCH, DLANSB
163 EXTERNAL dasum, dlamch, dlansb
164* ..
165* .. External Subroutines ..
166 EXTERNAL dsbmv
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max
170* ..
171* .. Executable Statements ..
172*
173* Quick exit if N = 0 or NRHS = 0.
174*
175 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
176 resid = zero
177 RETURN
178 END IF
179*
180* Exit with RESID = 1/EPS if ANORM = 0.
181*
182 eps = dlamch( 'Epsilon' )
183 anorm = dlansb( '1', uplo, n, kd, a, lda, rwork )
184 IF( anorm.LE.zero ) THEN
185 resid = one / eps
186 RETURN
187 END IF
188*
189* Compute B - A*X
190*
191 DO 10 j = 1, nrhs
192 CALL dsbmv( uplo, n, kd, -one, a, lda, x( 1, j ), 1, one,
193 \$ b( 1, j ), 1 )
194 10 CONTINUE
195*
196* Compute the maximum over the number of right hand sides of
197* norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
198*
199 resid = zero
200 DO 20 j = 1, nrhs
201 bnorm = dasum( n, b( 1, j ), 1 )
202 xnorm = dasum( n, x( 1, j ), 1 )
203 IF( xnorm.LE.zero ) THEN
204 resid = one / eps
205 ELSE
206 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
207 END IF
208 20 CONTINUE
209*
210 RETURN
211*
212* End of DPBT02
213*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine dsbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV
Definition: dsbmv.f:184
double precision function dlansb(NORM, UPLO, N, K, AB, LDAB, WORK)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansb.f:129
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