LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dqrt17.f
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1 *> \brief \b DQRT17
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * DOUBLE PRECISION FUNCTION DQRT17( TRANS, IRESID, M, N, NRHS, A,
12 * LDA, X, LDX, B, LDB, C, WORK, LWORK )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER TRANS
16 * INTEGER IRESID, LDA, LDB, LDX, LWORK, M, N, NRHS
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDB, * ),
20 * $ WORK( LWORK ), X( LDX, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DQRT17 computes the ratio
30 *>
31 *> norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),
32 *>
33 *> where R = B - op(A)*X, op(A) is A or A**T, depending on TRANS, EPS
34 *> is the machine epsilon, and
35 *>
36 *> alpha = norm(B) if IRESID = 1 (zero-residual problem)
37 *> alpha = norm(R) if IRESID = 2 (otherwise).
38 *>
39 *> The norm used is the 1-norm.
40 *> \endverbatim
41 *
42 * Arguments:
43 * ==========
44 *
45 *> \param[in] TRANS
46 *> \verbatim
47 *> TRANS is CHARACTER*1
48 *> Specifies whether or not the transpose of A is used.
49 *> = 'N': No transpose, op(A) = A.
50 *> = 'T': Transpose, op(A) = A**T.
51 *> \endverbatim
52 *>
53 *> \param[in] IRESID
54 *> \verbatim
55 *> IRESID is INTEGER
56 *> IRESID = 1 indicates zero-residual problem.
57 *> IRESID = 2 indicates non-zero residual.
58 *> \endverbatim
59 *>
60 *> \param[in] M
61 *> \verbatim
62 *> M is INTEGER
63 *> The number of rows of the matrix A.
64 *> If TRANS = 'N', the number of rows of the matrix B.
65 *> If TRANS = 'T', the number of rows of the matrix X.
66 *> \endverbatim
67 *>
68 *> \param[in] N
69 *> \verbatim
70 *> N is INTEGER
71 *> The number of columns of the matrix A.
72 *> If TRANS = 'N', the number of rows of the matrix X.
73 *> If TRANS = 'T', the number of rows of the matrix B.
74 *> \endverbatim
75 *>
76 *> \param[in] NRHS
77 *> \verbatim
78 *> NRHS is INTEGER
79 *> The number of columns of the matrices X and B.
80 *> \endverbatim
81 *>
82 *> \param[in] A
83 *> \verbatim
84 *> A is DOUBLE PRECISION array, dimension (LDA,N)
85 *> The m-by-n matrix A.
86 *> \endverbatim
87 *>
88 *> \param[in] LDA
89 *> \verbatim
90 *> LDA is INTEGER
91 *> The leading dimension of the array A. LDA >= M.
92 *> \endverbatim
93 *>
94 *> \param[in] X
95 *> \verbatim
96 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
97 *> If TRANS = 'N', the n-by-nrhs matrix X.
98 *> If TRANS = 'T', the m-by-nrhs matrix X.
99 *> \endverbatim
100 *>
101 *> \param[in] LDX
102 *> \verbatim
103 *> LDX is INTEGER
104 *> The leading dimension of the array X.
105 *> If TRANS = 'N', LDX >= N.
106 *> If TRANS = 'T', LDX >= M.
107 *> \endverbatim
108 *>
109 *> \param[in] B
110 *> \verbatim
111 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
112 *> If TRANS = 'N', the m-by-nrhs matrix B.
113 *> If TRANS = 'T', the n-by-nrhs matrix B.
114 *> \endverbatim
115 *>
116 *> \param[in] LDB
117 *> \verbatim
118 *> LDB is INTEGER
119 *> The leading dimension of the array B.
120 *> If TRANS = 'N', LDB >= M.
121 *> If TRANS = 'T', LDB >= N.
122 *> \endverbatim
123 *>
124 *> \param[out] C
125 *> \verbatim
126 *> C is DOUBLE PRECISION array, dimension (LDB,NRHS)
127 *> \endverbatim
128 *>
129 *> \param[out] WORK
130 *> \verbatim
131 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
132 *> \endverbatim
133 *>
134 *> \param[in] LWORK
135 *> \verbatim
136 *> LWORK is INTEGER
137 *> The length of the array WORK. LWORK >= NRHS*(M+N).
138 *> \endverbatim
139 *
140 * Authors:
141 * ========
142 *
143 *> \author Univ. of Tennessee
144 *> \author Univ. of California Berkeley
145 *> \author Univ. of Colorado Denver
146 *> \author NAG Ltd.
147 *
148 *> \ingroup double_lin
149 *
150 * =====================================================================
151  DOUBLE PRECISION FUNCTION dqrt17( TRANS, IRESID, M, N, NRHS, A,
152  $ LDA, X, LDX, B, LDB, C, WORK, LWORK )
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  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 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, dlange
183  EXTERNAL lsame, dlamch, dlange
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL dgemm, dlacpy, dlascl, xerbla
187 * ..
188 * .. Intrinsic Functions ..
189  INTRINSIC dble, max
190 * ..
191 * .. Executable Statements ..
192 *
193  dqrt17 = 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( 'DQRT17', 1 )
203  RETURN
204  END IF
205 *
206  IF( lwork.LT.ncols*nrhs ) THEN
207  CALL xerbla( 'DQRT17', 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 = dlange( 'One-norm', m, n, a, lda, rwork )
216  smlnum = dlamch( 'Safe minimum' ) / dlamch( 'Precision' )
217  iscl = 0
218 *
219 * compute residual and scale it
220 *
221  CALL dlacpy( 'All', nrows, nrhs, b, ldb, c, ldb )
222  CALL dgemm( trans, 'No transpose', nrows, nrhs, ncols, -one, a,
223  $ lda, x, ldx, one, c, ldb )
224  normrs = dlange( 'Max', nrows, nrhs, c, ldb, rwork )
225  IF( normrs.GT.smlnum ) THEN
226  iscl = 1
227  CALL dlascl( 'General', 0, 0, normrs, one, nrows, nrhs, c, ldb,
228  $ info )
229  END IF
230 *
231 * compute R**T * op(A)
232 *
233  CALL dgemm( 'Transpose', trans, nrhs, ncols, nrows, one, c, ldb,
234  $ a, lda, zero, work, nrhs )
235 *
236 * compute and properly scale error
237 *
238  err = dlange( '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 = dlange( '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  dqrt17 = err / ( dlamch( 'Epsilon' )*dble( max( m, n, nrhs ) ) )
255  RETURN
256 *
257 * End of DQRT17
258 *
259  END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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:143
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dqrt17(TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
DQRT17
Definition: dqrt17.f:153
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:114