summaryrefslogtreecommitdiff
path: root/TESTING/EIG/dlarhs.f
blob: bcf3e438d9577a433afa61dc0314a190d54ab042 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
*> \brief \b DLARHS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
*                          A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS, UPLO, XTYPE
*       CHARACTER*3        PATH
*       INTEGER            INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLARHS chooses a set of NRHS random solution vectors and sets
*> up the right hand sides for the linear system
*>    op( A ) * X = B,
*> where op( A ) may be A or A' (transpose of A).
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] PATH
*> \verbatim
*>          PATH is CHARACTER*3
*>          The type of the real matrix A.  PATH may be given in any
*>          combination of upper and lower case.  Valid types include
*>             xGE:  General m x n matrix
*>             xGB:  General banded matrix
*>             xPO:  Symmetric positive definite, 2-D storage
*>             xPP:  Symmetric positive definite packed
*>             xPB:  Symmetric positive definite banded
*>             xSY:  Symmetric indefinite, 2-D storage
*>             xSP:  Symmetric indefinite packed
*>             xSB:  Symmetric indefinite banded
*>             xTR:  Triangular
*>             xTP:  Triangular packed
*>             xTB:  Triangular banded
*>             xQR:  General m x n matrix
*>             xLQ:  General m x n matrix
*>             xQL:  General m x n matrix
*>             xRQ:  General m x n matrix
*>          where the leading character indicates the precision.
*> \endverbatim
*>
*> \param[in] XTYPE
*> \verbatim
*>          XTYPE is CHARACTER*1
*>          Specifies how the exact solution X will be determined:
*>          = 'N':  New solution; generate a random X.
*>          = 'C':  Computed; use value of X on entry.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          matrix A is stored, if A is symmetric.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the operation applied to the matrix A.
*>          = 'N':  System is  A * x = b
*>          = 'T':  System is  A'* x = b
*>          = 'C':  System is  A'* x = b
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number or rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] KL
*> \verbatim
*>          KL is INTEGER
*>          Used only if A is a band matrix; specifies the number of
*>          subdiagonals of A if A is a general band matrix or if A is
*>          symmetric or triangular and UPLO = 'L'; specifies the number
*>          of superdiagonals of A if A is symmetric or triangular and
*>          UPLO = 'U'.  0 <= KL <= M-1.
*> \endverbatim
*>
*> \param[in] KU
*> \verbatim
*>          KU is INTEGER
*>          Used only if A is a general band matrix or if A is
*>          triangular.
*>
*>          If PATH = xGB, specifies the number of superdiagonals of A,
*>          and 0 <= KU <= N-1.
*>
*>          If PATH = xTR, xTP, or xTB, specifies whether or not the
*>          matrix has unit diagonal:
*>          = 1:  matrix has non-unit diagonal (default)
*>          = 2:  matrix has unit diagonal
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of right hand side vectors in the system A*X = B.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The test matrix whose type is given by PATH.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If PATH = xGB, LDA >= KL+KU+1.
*>          If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
*>          Otherwise, LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is or output) DOUBLE PRECISION array, dimension(LDX,NRHS)
*>          On entry, if XTYPE = 'C' (for 'Computed'), then X contains
*>          the exact solution to the system of linear equations.
*>          On exit, if XTYPE = 'N' (for 'New'), then X is initialized
*>          with random values.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  If TRANS = 'N',
*>          LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          The right hand side vector(s) for the system of equations,
*>          computed from B = op(A) * X, where op(A) is determined by
*>          TRANS.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  If TRANS = 'N',
*>          LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          The seed vector for the random number generator (used in
*>          DLATMS).  Modified on exit.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_eig
*
*  =====================================================================
      SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
     $                   A, LDA, X, LDX, B, LDB, ISEED, INFO )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          TRANS, UPLO, XTYPE
      CHARACTER*3        PATH
      INTEGER            INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
      CHARACTER          C1, DIAG
      CHARACTER*2        C2
      INTEGER            J, MB, NX
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, LSAMEN
      EXTERNAL           LSAME, LSAMEN
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGBMV, DGEMM, DLACPY, DLARNV, DSBMV, DSPMV,
     $                   DSYMM, DTBMV, DTPMV, DTRMM, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      C1 = PATH( 1: 1 )
      C2 = PATH( 2: 3 )
      TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' )
      NOTRAN = .NOT.TRAN
      GEN = LSAME( PATH( 2: 2 ), 'G' )
      QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' )
      SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR. LSAME( PATH( 2: 2 ), 'S' )
      TRI = LSAME( PATH( 2: 2 ), 'T' )
      BAND = LSAME( PATH( 3: 3 ), 'B' )
      IF( .NOT.LSAME( C1, 'Double precision' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) )
     $          THEN
         INFO = -2
      ELSE IF( ( SYM .OR. TRI ) .AND. .NOT.
     $         ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN
         INFO = -3
      ELSE IF( ( GEN .OR. QRS ) .AND. .NOT.
     $         ( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN
         INFO = -4
      ELSE IF( M.LT.0 ) THEN
         INFO = -5
      ELSE IF( N.LT.0 ) THEN
         INFO = -6
      ELSE IF( BAND .AND. KL.LT.0 ) THEN
         INFO = -7
      ELSE IF( BAND .AND. KU.LT.0 ) THEN
         INFO = -8
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -9
      ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR.
     $         ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR.
     $         ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN
         INFO = -11
      ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR.
     $         ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN
         INFO = -13
      ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR.
     $         ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN
         INFO = -15
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DLARHS', -INFO )
         RETURN
      END IF
*
*     Initialize X to NRHS random vectors unless XTYPE = 'C'.
*
      IF( TRAN ) THEN
         NX = M
         MB = N
      ELSE
         NX = N
         MB = M
      END IF
      IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN
         DO 10 J = 1, NRHS
            CALL DLARNV( 2, ISEED, N, X( 1, J ) )
   10    CONTINUE
      END IF
*
*     Multiply X by op( A ) using an appropriate
*     matrix multiply routine.
*
      IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR.
     $    LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR.
     $    LSAMEN( 2, C2, 'RQ' ) ) THEN
*
*        General matrix
*
         CALL DGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX,
     $               ZERO, B, LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN
*
*        Symmetric matrix, 2-D storage
*
         CALL DSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO,
     $               B, LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN
*
*        General matrix, band storage
*
         DO 20 J = 1, NRHS
            CALL DGBMV( TRANS, MB, NX, KL, KU, ONE, A, LDA, X( 1, J ),
     $                  1, ZERO, B( 1, J ), 1 )
   20    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'PB' ) ) THEN
*
*        Symmetric matrix, band storage
*
         DO 30 J = 1, NRHS
            CALL DSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO,
     $                  B( 1, J ), 1 )
   30    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'SP' ) ) THEN
*
*        Symmetric matrix, packed storage
*
         DO 40 J = 1, NRHS
            CALL DSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ),
     $                  1 )
   40    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN
*
*        Triangular matrix.  Note that for triangular matrices,
*           KU = 1 => non-unit triangular
*           KU = 2 => unit triangular
*
         CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         CALL DTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
     $               LDB )
*
      ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN
*
*        Triangular matrix, packed storage
*
         CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         DO 50 J = 1, NRHS
            CALL DTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 )
   50    CONTINUE
*
      ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN
*
*        Triangular matrix, banded storage
*
         CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB )
         IF( KU.EQ.2 ) THEN
            DIAG = 'U'
         ELSE
            DIAG = 'N'
         END IF
         DO 60 J = 1, NRHS
            CALL DTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 )
   60    CONTINUE
*
      ELSE
*
*        If PATH is none of the above, return with an error code.
*
         INFO = -1
         CALL XERBLA( 'DLARHS', -INFO )
      END IF
*
      RETURN
*
*     End of DLARHS
*
      END