 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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 RESID )

CGBT02

Purpose:
``` CGBT02 computes the residual for a solution of a banded system of
equations  A*x = b  or  A'*x = b:
RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
where EPS is the machine precision.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A *x = b = 'T': A'*x = b, where A' is the transpose of A = 'C': A'*x = b, where A' is the transpose of A``` [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] RESID ``` RESID is REAL 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 141 of file cgbt02.f.

141 *
142 * -- LAPACK test routine (version 3.7.0) --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 * December 2016
146 *
147 * .. Scalar Arguments ..
148  CHARACTER trans
149  INTEGER kl, ku, lda, ldb, ldx, m, n, nrhs
150  REAL resid
151 * ..
152 * .. Array Arguments ..
153  COMPLEX a( lda, * ), b( ldb, * ), x( ldx, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL zero, one
160  parameter( zero = 0.0e+0, one = 1.0e+0 )
161  COMPLEX cone
162  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
163 * ..
164 * .. Local Scalars ..
165  INTEGER i1, i2, j, kd, n1
166  REAL anorm, bnorm, eps, xnorm
167 * ..
168 * .. External Functions ..
169  LOGICAL lsame
170  REAL scasum, slamch
171  EXTERNAL lsame, scasum, slamch
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL cgbmv
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC max, min
178 * ..
179 * .. Executable Statements ..
180 *
181 * Quick return if N = 0 pr NRHS = 0
182 *
183  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
184  resid = zero
185  RETURN
186  END IF
187 *
188 * Exit with RESID = 1/EPS if ANORM = 0.
189 *
190  eps = slamch( 'Epsilon' )
191  kd = ku + 1
192  anorm = zero
193  DO 10 j = 1, n
194  i1 = max( kd+1-j, 1 )
195  i2 = min( kd+m-j, kl+kd )
196  anorm = max( anorm, scasum( i2-i1+1, a( i1, j ), 1 ) )
197  10 CONTINUE
198  IF( anorm.LE.zero ) THEN
199  resid = one / eps
200  RETURN
201  END IF
202 *
203  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
204  n1 = n
205  ELSE
206  n1 = m
207  END IF
208 *
209 * Compute B - A*X (or B - A'*X )
210 *
211  DO 20 j = 1, nrhs
212  CALL cgbmv( trans, m, n, kl, ku, -cone, a, lda, x( 1, j ), 1,
213  \$ cone, b( 1, j ), 1 )
214  20 CONTINUE
215 *
216 * Compute the maximum over the number of right hand sides of
217 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
218 *
219  resid = zero
220  DO 30 j = 1, nrhs
221  bnorm = scasum( n1, b( 1, j ), 1 )
222  xnorm = scasum( n1, x( 1, j ), 1 )
223  IF( xnorm.LE.zero ) THEN
224  resid = one / eps
225  ELSE
226  resid = max( resid, ( ( bnorm/anorm )/xnorm )/eps )
227  END IF
228  30 CONTINUE
229 *
230  RETURN
231 *
232 * End of CGBT02
233 *
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:74
subroutine cgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV
Definition: cgbmv.f:189
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
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