LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
double precision function dqrt17 ( character  TRANS,
integer  IRESID,
integer  M,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldb, * )  C,
double precision, dimension( lwork )  WORK,
integer  LWORK 
)

DQRT17

Purpose: 
 DQRT17 computes the ratio

    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)

 where R = op(A)*X - B, op(A) is A or A', and

    alpha = ||B|| if IRESID = 1 (zero-residual problem)
    alpha = ||R|| if IRESID = 2 (otherwise).
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'.
[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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDB,NRHS)
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= NRHS*(M+N).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
November 2015

Definition at line 152 of file dqrt17.f.

152 *
153 * -- LAPACK test routine (version 3.6.0) --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 * November 2015
157 *
158 * .. Scalar Arguments ..
159  CHARACTER trans
160  INTEGER iresid, lda, ldb, ldx, lwork, m, n, nrhs
161 * ..
162 * .. Array Arguments ..
163  DOUBLE PRECISION 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 bignum, err, norma, normb, normrs, normx,
176  $ smlnum
177 * ..
178 * .. Local Arrays ..
179  DOUBLE PRECISION rwork( 1 )
180 * ..
181 * .. External Functions ..
182  LOGICAL lsame
183  DOUBLE PRECISION dlamch, dlange
184  EXTERNAL lsame, dlamch, dlange
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL dgemm, dlacpy, dlascl, xerbla
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC dble, max
191 * ..
192 * .. Executable Statements ..
193 *
194  dqrt17 = zero
195 *
196  IF( lsame( trans, 'N' ) ) THEN
197  nrows = m
198  ncols = n
199  ELSE IF( lsame( trans, 'T' ) ) THEN
200  nrows = n
201  ncols = m
202  ELSE
203  CALL xerbla( 'DQRT17', 1 )
204  RETURN
205  END IF
206 *
207  IF( lwork.LT.ncols*nrhs ) THEN
208  CALL xerbla( 'DQRT17', 13 )
209  RETURN
210  END IF
211 *
212  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.LE.0 ) THEN
213  RETURN
214  END IF
215 *
216  norma = dlange( 'One-norm', m, n, a, lda, rwork )
217  smlnum = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
218  bignum = one / smlnum
219  iscl = 0
220 *
221 * compute residual and scale it
222 *
223  CALL dlacpy( 'All', nrows, nrhs, b, ldb, c, ldb )
224  CALL dgemm( trans, 'No transpose', nrows, nrhs, ncols, -one, a,
225  $ lda, x, ldx, one, c, ldb )
226  normrs = dlange( 'Max', nrows, nrhs, c, ldb, rwork )
227  IF( normrs.GT.smlnum ) THEN
228  iscl = 1
229  CALL dlascl( 'General', 0, 0, normrs, one, nrows, nrhs, c, ldb,
230  $ info )
231  END IF
232 *
233 * compute R'*A
234 *
235  CALL dgemm( 'Transpose', trans, nrhs, ncols, nrows, one, c, ldb,
236  $ a, lda, zero, work, nrhs )
237 *
238 * compute and properly scale error
239 *
240  err = dlange( 'One-norm', nrhs, ncols, work, nrhs, rwork )
241  IF( norma.NE.zero )
242  $ err = err / norma
243 *
244  IF( iscl.EQ.1 )
245  $ err = err*normrs
246 *
247  IF( iresid.EQ.1 ) THEN
248  normb = dlange( 'One-norm', nrows, nrhs, b, ldb, rwork )
249  IF( normb.NE.zero )
250  $ err = err / normb
251  ELSE
252  IF( normrs.NE.zero )
253  $ err = err / normrs
254  END IF
255 *
256  dqrt17 = err / ( dlamch( 'Epsilon' )*dble( max( m, n, nrhs ) ) )
257  RETURN
258 *
259 * End of DQRT17
260 *
dlamch
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
dlacpy
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:105
dlascl
subroutine dlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: dlascl.f:145
dgemm
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
dlange
double precision function dlange(NORM, M, N, A, LDA, WORK)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: dlange.f:116
dqrt17
double precision function dqrt17(TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
DQRT17
Definition: dqrt17.f:152
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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