 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgbt02()

 subroutine cgbt02 ( character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID )

CGBT02

Purpose:
``` CGBT02 computes the residual for a solution of a banded system of
equations op(A)*X = B:
RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
machine epsilon.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose)``` [in] M ``` M is INTEGER The number of rows of the matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix A. N >= 0.``` [in] KL ``` KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.``` [in] KU ``` KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of columns of B. NRHS >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The original matrix A in band storage, stored in rows 1 to KL+KU+1.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,KL+KU+1).``` [in] X ``` X is COMPLEX 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. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).``` [in,out] B ``` B is COMPLEX 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. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).``` [out] RWORK ``` RWORK is REAL array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.``` [out] RESID ``` RESID is REAL The maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).```

Definition at line 146 of file cgbt02.f.

148*
149* -- LAPACK test routine --
150* -- LAPACK is a software package provided by Univ. of Tennessee, --
151* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152*
153* .. Scalar Arguments ..
154 CHARACTER TRANS
155 INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS
156 REAL RESID
157* ..
158* .. Array Arguments ..
159 REAL RWORK( * )
160 COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
161* ..
162*
163* =====================================================================
164*
165* .. Parameters ..
166 REAL ZERO, ONE
167 parameter( zero = 0.0e+0, one = 1.0e+0 )
168 COMPLEX CONE
169 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
170* ..
171* .. Local Scalars ..
172 INTEGER I1, I2, J, KD, N1
173 REAL ANORM, BNORM, EPS, TEMP, XNORM
174 COMPLEX CDUM
175* ..
176* .. External Functions ..
177 LOGICAL LSAME, SISNAN
178 REAL SCASUM, SLAMCH
179 EXTERNAL lsame, scasum, sisnan, slamch
180* ..
181* .. External Subroutines ..
182 EXTERNAL cgbmv
183* ..
184* .. Statement Functions ..
185 REAL CABS1
186* ..
187* .. Intrinsic Functions ..
188 INTRINSIC abs, aimag, max, min, real
189* ..
190* .. Statement Function definitions ..
191 cabs1( cdum ) = abs( real( cdum ) ) + abs( aimag( cdum ) )
192* ..
193* .. Executable Statements ..
194*
195* Quick return if N = 0 pr NRHS = 0
196*
197 IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
198 resid = zero
199 RETURN
200 END IF
201*
202* Exit with RESID = 1/EPS if ANORM = 0.
203*
204 eps = slamch( 'Epsilon' )
205 anorm = zero
206 IF( lsame( trans, 'N' ) ) THEN
207*
208* Find norm1(A).
209*
210 kd = ku + 1
211 DO 10 j = 1, n
212 i1 = max( kd+1-j, 1 )
213 i2 = min( kd+m-j, kl+kd )
214 IF( i2.GE.i1 ) THEN
215 temp = scasum( i2-i1+1, a( i1, j ), 1 )
216 IF( anorm.LT.temp .OR. sisnan( temp ) ) anorm = temp
217 END IF
218 10 CONTINUE
219 ELSE
220*
221* Find normI(A).
222*
223 DO 12 i1 = 1, m
224 rwork( i1 ) = zero
225 12 CONTINUE
226 DO 16 j = 1, n
227 kd = ku + 1 - j
228 DO 14 i1 = max( 1, j-ku ), min( m, j+kl )
229 rwork( i1 ) = rwork( i1 ) + cabs1( a( kd+i1, j ) )
230 14 CONTINUE
231 16 CONTINUE
232 DO 18 i1 = 1, m
233 temp = rwork( i1 )
234 IF( anorm.LT.temp .OR. sisnan( temp ) ) anorm = temp
235 18 CONTINUE
236 END IF
237 IF( anorm.LE.zero ) THEN
238 resid = one / eps
239 RETURN
240 END IF
241*
242 IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
243 n1 = n
244 ELSE
245 n1 = m
246 END IF
247*
248* Compute B - op(A)*X
249*
250 DO 20 j = 1, nrhs
251 CALL cgbmv( trans, m, n, kl, ku, -cone, a, lda, x( 1, j ), 1,
252 \$ cone, b( 1, j ), 1 )
253 20 CONTINUE
254*
255* Compute the maximum over the number of right hand sides of
256* norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
257*
258 resid = zero
259 DO 30 j = 1, nrhs
260 bnorm = scasum( n1, b( 1, j ), 1 )
261 xnorm = scasum( n1, x( 1, j ), 1 )
262 IF( xnorm.LE.zero ) THEN
263 resid = one / eps
264 ELSE
265 resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
266 END IF
267 30 CONTINUE
268*
269 RETURN
270*
271* End of CGBT02
272*
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV
Definition: cgbmv.f:187
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:72
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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