LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 ).```
Date
December 2016

Definition at line 138 of file dpbt02.f.

138 *
139 * -- LAPACK test routine (version 3.7.0) --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 * December 2016
143 *
144 * .. Scalar Arguments ..
145  CHARACTER uplo
146  INTEGER kd, lda, ldb, ldx, n, nrhs
147  DOUBLE PRECISION resid
148 * ..
149 * .. Array Arguments ..
150  DOUBLE PRECISION a( lda, * ), b( ldb, * ), rwork( * ),
151  \$ x( ldx, * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  DOUBLE PRECISION zero, one
158  parameter( zero = 0.0d+0, one = 1.0d+0 )
159 * ..
160 * .. Local Scalars ..
161  INTEGER j
162  DOUBLE PRECISION anorm, bnorm, eps, xnorm
163 * ..
164 * .. External Functions ..
165  DOUBLE PRECISION dasum, dlamch, dlansb
166  EXTERNAL dasum, dlamch, dlansb
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL dsbmv
170 * ..
171 * .. Intrinsic Functions ..
172  INTRINSIC max
173 * ..
174 * .. Executable Statements ..
175 *
176 * Quick exit if N = 0 or NRHS = 0.
177 *
178  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
179  resid = zero
180  RETURN
181  END IF
182 *
183 * Exit with RESID = 1/EPS if ANORM = 0.
184 *
185  eps = dlamch( 'Epsilon' )
186  anorm = dlansb( '1', uplo, n, kd, a, lda, rwork )
187  IF( anorm.LE.zero ) THEN
188  resid = one / eps
189  RETURN
190  END IF
191 *
192 * Compute B - A*X
193 *
194  DO 10 j = 1, nrhs
195  CALL dsbmv( uplo, n, kd, -one, a, lda, x( 1, j ), 1, one,
196  \$ b( 1, j ), 1 )
197  10 CONTINUE
198 *
199 * Compute the maximum over the number of right hand sides of
200 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
201 *
202  resid = zero
203  DO 20 j = 1, nrhs
204  bnorm = dasum( n, b( 1, j ), 1 )
205  xnorm = dasum( n, x( 1, j ), 1 )
206  IF( xnorm.LE.zero ) THEN
207  resid = one / eps
208  ELSE
209  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
210  END IF
211  20 CONTINUE
212 *
213  RETURN
214 *
215 * End of DPBT02
216 *
subroutine dsbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV
Definition: dsbmv.f:186
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
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, or the element of largest absolute value of a symmetric band matrix.
Definition: dlansb.f:131
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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