 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sgbt02()

 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, dimension( * ) RWORK, real RESID )

SGBT02

Purpose:
``` SGBT02 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 or A**T, depending on TRANS, and EPS is the
machine epsilon.
The norm used is the 1-norm.```
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 = 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 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] 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 147 of file sgbt02.f.

149 *
150 * -- LAPACK test routine --
151 * -- LAPACK is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 *
154 * .. Scalar Arguments ..
155  CHARACTER TRANS
156  INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS
157  REAL RESID
158 * ..
159 * .. Array Arguments ..
160  REAL A( LDA, * ), B( LDB, * ), X( LDX, * ),
161  \$ RWORK( * )
162 * ..
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167  REAL ZERO, ONE
168  parameter( zero = 0.0e+0, one = 1.0e+0 )
169 * ..
170 * .. Local Scalars ..
171  INTEGER I1, I2, J, KD, N1
172  REAL ANORM, BNORM, EPS, TEMP, XNORM
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME, SISNAN
176  REAL SASUM, SLAMCH
177  EXTERNAL lsame, sasum, sisnan, slamch
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL sgbmv
181 * ..
182 * .. Intrinsic Functions ..
183  INTRINSIC abs, max, min
184 * ..
185 * .. Executable Statements ..
186 *
187 * Quick return if N = 0 pr NRHS = 0
188 *
189  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
190  resid = zero
191  RETURN
192  END IF
193 *
194 * Exit with RESID = 1/EPS if ANORM = 0.
195 *
196  eps = slamch( 'Epsilon' )
197  anorm = zero
198  IF( lsame( trans, 'N' ) ) THEN
199 *
200 * Find norm1(A).
201 *
202  kd = ku + 1
203  DO 10 j = 1, n
204  i1 = max( kd+1-j, 1 )
205  i2 = min( kd+m-j, kl+kd )
206  IF( i2.GE.i1 ) THEN
207  temp = sasum( i2-i1+1, a( i1, j ), 1 )
208  IF( anorm.LT.temp .OR. sisnan( temp ) ) anorm = temp
209  END IF
210  10 CONTINUE
211  ELSE
212 *
213 * Find normI(A).
214 *
215  DO 12 i1 = 1, m
216  rwork( i1 ) = zero
217  12 CONTINUE
218  DO 16 j = 1, n
219  kd = ku + 1 - j
220  DO 14 i1 = max( 1, j-ku ), min( m, j+kl )
221  rwork( i1 ) = rwork( i1 ) + abs( a( kd+i1, j ) )
222  14 CONTINUE
223  16 CONTINUE
224  DO 18 i1 = 1, m
225  temp = rwork( i1 )
226  IF( anorm.LT.temp .OR. sisnan( temp ) ) anorm = temp
227  18 CONTINUE
228  END IF
229  IF( anorm.LE.zero ) THEN
230  resid = one / eps
231  RETURN
232  END IF
233 *
234  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
235  n1 = n
236  ELSE
237  n1 = m
238  END IF
239 *
240 * Compute B - op(A)*X
241 *
242  DO 20 j = 1, nrhs
243  CALL sgbmv( trans, m, n, kl, ku, -one, a, lda, x( 1, j ), 1,
244  \$ one, b( 1, j ), 1 )
245  20 CONTINUE
246 *
247 * Compute the maximum over the number of right hand sides of
248 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
249 *
250  resid = zero
251  DO 30 j = 1, nrhs
252  bnorm = sasum( n1, b( 1, j ), 1 )
253  xnorm = sasum( n1, x( 1, j ), 1 )
254  IF( xnorm.LE.zero ) THEN
255  resid = one / eps
256  ELSE
257  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
258  END IF
259  30 CONTINUE
260 *
261  RETURN
262 *
263 * End of SGBT02
264 *
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine sgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGBMV
Definition: sgbmv.f:185
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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