 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zqrt17()

 double precision function zqrt17 ( character TRANS, integer IRESID, integer M, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldb, * ) C, complex*16, dimension( lwork ) WORK, integer LWORK )

ZQRT17

Purpose:
``` ZQRT17 computes the ratio

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

where R = B - op(A)*X, op(A) is A or A**H, 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. = 'C': Conjugate transpose, op(A) = A**H.``` [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 = 'C', 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 = 'C', 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS) If TRANS = 'N', the n-by-nrhs matrix X. If TRANS = 'C', 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 = 'C', LDX >= M.``` [in] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) If TRANS = 'N', the m-by-nrhs matrix B. If TRANS = 'C', 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 = 'C', LDB >= N.``` [out] C ` C is COMPLEX*16 array, dimension (LDB,NRHS)` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= NRHS*(M+N).```

Definition at line 151 of file zqrt17.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  COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDB, * ),
164  \$ WORK( LWORK ), X( LDX, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  DOUBLE PRECISION ZERO, ONE
171  parameter( zero = 0.0d0, one = 1.0d0 )
172 * ..
173 * .. Local Scalars ..
174  INTEGER INFO, ISCL, NCOLS, NROWS
175  DOUBLE PRECISION ERR, NORMA, NORMB, NORMRS, SMLNUM
176 * ..
177 * .. Local Arrays ..
178  DOUBLE PRECISION RWORK( 1 )
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  DOUBLE PRECISION DLAMCH, ZLANGE
183  EXTERNAL lsame, dlamch, zlange
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL xerbla, zgemm, zlacpy, zlascl
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC dble, dcmplx, max
190 * ..
191 * .. Executable Statements ..
192 *
193  zqrt17 = zero
194 *
195  IF( lsame( trans, 'N' ) ) THEN
196  nrows = m
197  ncols = n
198  ELSE IF( lsame( trans, 'C' ) ) THEN
199  nrows = n
200  ncols = m
201  ELSE
202  CALL xerbla( 'ZQRT17', 1 )
203  RETURN
204  END IF
205 *
206  IF( lwork.LT.ncols*nrhs ) THEN
207  CALL xerbla( 'ZQRT17', 13 )
208  RETURN
209  END IF
210 *
211  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 )
212  \$ RETURN
213 *
214  norma = zlange( 'One-norm', m, n, a, lda, rwork )
215  smlnum = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
216  iscl = 0
217 *
218 * compute residual and scale it
219 *
220  CALL zlacpy( 'All', nrows, nrhs, b, ldb, c, ldb )
221  CALL zgemm( trans, 'No transpose', nrows, nrhs, ncols,
222  \$ dcmplx( -one ), a, lda, x, ldx, dcmplx( one ), c,
223  \$ ldb )
224  normrs = zlange( 'Max', nrows, nrhs, c, ldb, rwork )
225  IF( normrs.GT.smlnum ) THEN
226  iscl = 1
227  CALL zlascl( 'General', 0, 0, normrs, one, nrows, nrhs, c, ldb,
228  \$ info )
229  END IF
230 *
231 * compute R**H * op(A)
232 *
233  CALL zgemm( 'Conjugate transpose', trans, nrhs, ncols, nrows,
234  \$ dcmplx( one ), c, ldb, a, lda, dcmplx( zero ), work,
235  \$ nrhs )
236 *
237 * compute and properly scale error
238 *
239  err = zlange( 'One-norm', nrhs, ncols, work, nrhs, rwork )
240  IF( norma.NE.zero )
241  \$ err = err / norma
242 *
243  IF( iscl.EQ.1 )
244  \$ err = err*normrs
245 *
246  IF( iresid.EQ.1 ) THEN
247  normb = zlange( 'One-norm', nrows, nrhs, b, ldb, rwork )
248  IF( normb.NE.zero )
249  \$ err = err / normb
250  ELSE
251  IF( normrs.NE.zero )
252  \$ err = err / normrs
253  END IF
254 *
255  zqrt17 = err / ( dlamch( 'Epsilon' )*dble( max( m, n, nrhs ) ) )
256  RETURN
257 *
258 * End of ZQRT17
259 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
double precision function zqrt17(TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
ZQRT17
Definition: zqrt17.f:153
double precision function zlange(NORM, M, N, A, LDA, WORK)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlange.f:115
subroutine zlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: zlascl.f:143
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:103
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