LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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 xerbla(srname, info)
Definition cblat2.f:3285
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
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
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
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 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
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sqrt17(trans, iresid, m, n, nrhs, a, lda, x, ldx, b, ldb, c, work, lwork)
SQRT17
Definition sqrt17.f:153
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