LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine sgbt02 ( character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real RESID )

SGBT02

Purpose:
``` SGBT02 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 REAL 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 REAL 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 REAL 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
November 2011

Definition at line 141 of file sgbt02.f.

141 *
142 * -- LAPACK test routine (version 3.4.0) --
143 * -- LAPACK is a software package provided by Univ. of Tennessee, --
144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145 * November 2011
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  REAL 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 * ..
162 * .. Local Scalars ..
163  INTEGER i1, i2, j, kd, n1
164  REAL anorm, bnorm, eps, xnorm
165 * ..
166 * .. External Functions ..
167  LOGICAL lsame
168  REAL sasum, slamch
169  EXTERNAL lsame, sasum, slamch
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL sgbmv
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC max, min
176 * ..
177 * .. Executable Statements ..
178 *
179 * Quick return if N = 0 pr NRHS = 0
180 *
181  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
182  resid = zero
183  RETURN
184  END IF
185 *
186 * Exit with RESID = 1/EPS if ANORM = 0.
187 *
188  eps = slamch( 'Epsilon' )
189  kd = ku + 1
190  anorm = zero
191  DO 10 j = 1, n
192  i1 = max( kd+1-j, 1 )
193  i2 = min( kd+m-j, kl+kd )
194  anorm = max( anorm, sasum( i2-i1+1, a( i1, j ), 1 ) )
195  10 CONTINUE
196  IF( anorm.LE.zero ) THEN
197  resid = one / eps
198  RETURN
199  END IF
200 *
201  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
202  n1 = n
203  ELSE
204  n1 = m
205  END IF
206 *
207 * Compute B - A*X (or B - A'*X )
208 *
209  DO 20 j = 1, nrhs
210  CALL sgbmv( trans, m, n, kl, ku, -one, a, lda, x( 1, j ), 1,
211  \$ one, b( 1, j ), 1 )
212  20 CONTINUE
213 *
214 * Compute the maximum over the number of right hand sides of
215 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
216 *
217  resid = zero
218  DO 30 j = 1, nrhs
219  bnorm = sasum( n1, b( 1, j ), 1 )
220  xnorm = sasum( n1, x( 1, j ), 1 )
221  IF( xnorm.LE.zero ) THEN
222  resid = one / eps
223  ELSE
224  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
225  END IF
226  30 CONTINUE
227 *
228  RETURN
229 *
230 * End of SGBT02
231 *
subroutine sgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
Definition: sgbmv.f:187
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:54
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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