 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sqrt17()

 real function sqrt17 ( character TRANS, integer IRESID, integer M, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( ldx, * ) X, integer LDX, real, dimension( ldb, * ) B, integer LDB, real, dimension( ldb, * ) C, real, dimension( lwork ) WORK, integer LWORK )

SQRT17

Purpose:
``` SQRT17 computes the ratio

norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),

where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS
is the machine epsilon, and

alpha = norm(B) if IRESID = 1 (zero-residual problem)
alpha = norm(R) if IRESID = 2 (otherwise).

The norm used is the 1-norm.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies whether or not the transpose of A is used. = 'N': No transpose, op(A) = A. = 'T': Transpose, op(A) = A**T.``` [in] IRESID ``` IRESID is INTEGER IRESID = 1 indicates zero-residual problem. IRESID = 2 indicates non-zero residual.``` [in] M ``` M is INTEGER The number of rows of the matrix A. If TRANS = 'N', the number of rows of the matrix B. If TRANS = 'T', the number of rows of the matrix X.``` [in] N ``` N is INTEGER The number of columns of the matrix A. If TRANS = 'N', the number of rows of the matrix X. If TRANS = 'T', the number of rows of the matrix B.``` [in] NRHS ``` NRHS is INTEGER The number of columns of the matrices X and B.``` [in] A ``` A is REAL array, dimension (LDA,N) The m-by-n matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= M.``` [in] X ``` X is REAL array, dimension (LDX,NRHS) If TRANS = 'N', the n-by-nrhs matrix X. If TRANS = 'T', the m-by-nrhs matrix X.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= N. If TRANS = 'T', LDX >= M.``` [in] B ``` B is REAL array, dimension (LDB,NRHS) If TRANS = 'N', the m-by-nrhs matrix B. If TRANS = 'T', the n-by-nrhs matrix B.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. If TRANS = 'N', LDB >= M. If TRANS = 'T', LDB >= N.``` [out] C ` C is REAL array, dimension (LDB,NRHS)` [out] WORK ` WORK is REAL array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= NRHS*(M+N).```

Definition at line 151 of file sqrt17.f.

153 *
154 * -- LAPACK test routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  CHARACTER TRANS
160  INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS
161 * ..
162 * .. Array Arguments ..
163  REAL A( LDA, * ), B( LDB, * ), C( LDB, * ),
164  \$ WORK( LWORK ), X( LDX, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  REAL ZERO, ONE
171  parameter( zero = 0.0e0, one = 1.0e0 )
172 * ..
173 * .. Local Scalars ..
174  INTEGER INFO, ISCL, NCOLS, NROWS
175  REAL ERR, NORMA, NORMB, NORMRS, SMLNUM
176 * ..
177 * .. Local Arrays ..
178  REAL RWORK( 1 )
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  REAL SLAMCH, SLANGE
183  EXTERNAL lsame, slamch, slange
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL sgemm, slacpy, slascl, xerbla
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC max, real
190 * ..
191 * .. Executable Statements ..
192 *
193  sqrt17 = zero
194 *
195  IF( lsame( trans, 'N' ) ) THEN
196  nrows = m
197  ncols = n
198  ELSE IF( lsame( trans, 'T' ) ) THEN
199  nrows = n
200  ncols = m
201  ELSE
202  CALL xerbla( 'SQRT17', 1 )
203  RETURN
204  END IF
205 *
206  IF( lwork.LT.ncols*nrhs ) THEN
207  CALL xerbla( 'SQRT17', 13 )
208  RETURN
209  END IF
210 *
211  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
212  RETURN
213  END IF
214 *
215  norma = slange( 'One-norm', m, n, a, lda, rwork )
216  smlnum = slamch( 'Safe minimum' ) / slamch( 'Precision' )
217  iscl = 0
218 *
219 * compute residual and scale it
220 *
221  CALL slacpy( 'All', nrows, nrhs, b, ldb, c, ldb )
222  CALL sgemm( trans, 'No transpose', nrows, nrhs, ncols, -one, a,
223  \$ lda, x, ldx, one, c, ldb )
224  normrs = slange( 'Max', nrows, nrhs, c, ldb, rwork )
225  IF( normrs.GT.smlnum ) THEN
226  iscl = 1
227  CALL slascl( 'General', 0, 0, normrs, one, nrows, nrhs, c, ldb,
228  \$ info )
229  END IF
230 *
231 * compute R**T * op(A)
232 *
233  CALL sgemm( 'Transpose', trans, nrhs, ncols, nrows, one, c, ldb,
234  \$ a, lda, zero, work, nrhs )
235 *
236 * compute and properly scale error
237 *
238  err = slange( 'One-norm', nrhs, ncols, work, nrhs, rwork )
239  IF( norma.NE.zero )
240  \$ err = err / norma
241 *
242  IF( iscl.EQ.1 )
243  \$ err = err*normrs
244 *
245  IF( iresid.EQ.1 ) THEN
246  normb = slange( 'One-norm', nrows, nrhs, b, ldb, rwork )
247  IF( normb.NE.zero )
248  \$ err = err / normb
249  ELSE
250  IF( normrs.NE.zero )
251  \$ err = err / normrs
252  END IF
253 *
254  sqrt17 = err / ( slamch( 'Epsilon' )*real( max( m, n, nrhs ) ) )
255  RETURN
256 *
257 * End of SQRT17
258 *
subroutine slascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: slascl.f:143
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slange(NORM, M, N, A, LDA, WORK)
SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slange.f:114
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
real function sqrt17(TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
SQRT17
Definition: sqrt17.f:153
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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