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
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
|
SUBROUTINE CTIMHR( LINE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL,
$ NLDA, LDAVAL, TIMMIN, A, TAU, B, WORK, RWORK,
$ RESLTS, LDR1, LDR2, LDR3, NOUT )
*
* -- LAPACK timing routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER*80 LINE
INTEGER LDR1, LDR2, LDR3, NLDA, NM, NN, NNB, NOUT
REAL TIMMIN
* ..
* .. Array Arguments ..
INTEGER LDAVAL( * ), MVAL( * ), NBVAL( * ), NVAL( * ),
$ NXVAL( * )
REAL RESLTS( LDR1, LDR2, LDR3, * ), RWORK( * )
COMPLEX A( * ), B( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CTIMHR times the LAPACK routines CGEHRD, CUNGHR, and CUNMHR.
*
* Arguments
* =========
*
* LINE (input) CHARACTER*80
* The input line that requested this routine. The first six
* characters contain either the name of a subroutine or a
* generic path name. The remaining characters may be used to
* specify the individual routines to be timed. See ATIMIN for
* a full description of the format of the input line.
*
* NM (input) INTEGER
* The number of values of M contained in the vector MVAL.
*
* MVAL (input) INTEGER array, dimension (NM)
* The values of the matrix size M.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix column dimension N.
*
* NNB (input) INTEGER
* The number of values of NB and NX contained in the
* vectors NBVAL and NXVAL. The blocking parameters are used
* in pairs (NB,NX).
*
* NBVAL (input) INTEGER array, dimension (NNB)
* The values of the blocksize NB.
*
* NXVAL (input) INTEGER array, dimension (NNB)
* The values of the crossover point NX.
*
* NLDA (input) INTEGER
* The number of values of LDA contained in the vector LDAVAL.
*
* LDAVAL (input) INTEGER array, dimension (NLDA)
* The values of the leading dimension of the array A.
*
* TIMMIN (input) REAL
* The minimum time a subroutine will be timed.
*
* A (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
* where LDAMAX and NMAX are the maximum values of LDA and N.
*
* TAU (workspace) COMPLEX array, dimension (min(M,N))
*
* B (workspace) COMPLEX array, dimension (LDAMAX*NMAX)
*
* WORK (workspace) COMPLEX array, dimension (LDAMAX*NBMAX)
* where NBMAX is the maximum value of NB.
*
* RWORK (workspace) REAL array, dimension
* (min(MMAX,NMAX))
*
* RESLTS (workspace) REAL array, dimension
* (LDR1,LDR2,LDR3,4*NN+3)
* The timing results for each subroutine over the relevant
* values of M, (NB,NX), LDA, and N.
*
* LDR1 (input) INTEGER
* The first dimension of RESLTS. LDR1 >= max(1,NNB).
*
* LDR2 (input) INTEGER
* The second dimension of RESLTS. LDR2 >= max(1,NM).
*
* LDR3 (input) INTEGER
* The third dimension of RESLTS. LDR3 >= max(1,NLDA).
*
* NOUT (input) INTEGER
* The unit number for output.
*
* Internal Parameters
* ===================
*
* MODE INTEGER
* The matrix type. MODE = 3 is a geometric distribution of
* eigenvalues. See CLATMS for further details.
*
* COND REAL
* The condition number of the matrix. The singular values are
* set to values from DMAX to DMAX/COND.
*
* DMAX REAL
* The magnitude of the largest singular value.
*
* =====================================================================
*
* .. Parameters ..
INTEGER NSUBS
PARAMETER ( NSUBS = 3 )
INTEGER MODE
REAL COND, DMAX
PARAMETER ( MODE = 3, COND = 100.0E0, DMAX = 1.0E0 )
* ..
* .. Local Scalars ..
CHARACTER LAB1, LAB2, SIDE, TRANS
CHARACTER*3 PATH
CHARACTER*6 CNAME
INTEGER I, I4, IC, ICL, IHI, ILDA, ILO, IM, IN, INB,
$ INFO, ISIDE, ISUB, ITOFF, ITRAN, LDA, LW, M,
$ M1, N, N1, NB, NX
REAL OPS, S1, S2, TIME, UNTIME
* ..
* .. Local Arrays ..
LOGICAL TIMSUB( NSUBS )
CHARACTER SIDES( 2 ), TRANSS( 2 )
CHARACTER*6 SUBNAM( NSUBS )
INTEGER ISEED( 4 ), RESEED( 4 )
* ..
* .. External Functions ..
REAL SECOND, SMFLOP, SOPLA
EXTERNAL SECOND, SMFLOP, SOPLA
* ..
* .. External Subroutines ..
EXTERNAL ATIMCK, ATIMIN, CGEHRD, CLACPY, CLATMS, CTIMMG,
$ CUNGHR, CUNMHR, ICOPY, SPRTB3, SPRTBL, XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL
* ..
* .. Data statements ..
DATA SUBNAM / 'CGEHRD', 'CUNGHR', 'CUNMHR' /
DATA SIDES / 'L', 'R' / , TRANSS / 'N', 'C' /
DATA ISEED / 0, 0, 0, 1 /
* ..
* .. Executable Statements ..
*
* Extract the timing request from the input line.
*
PATH( 1: 1 ) = 'Complex precision'
PATH( 2: 3 ) = 'HR'
CALL ATIMIN( PATH, LINE, NSUBS, SUBNAM, TIMSUB, NOUT, INFO )
IF( INFO.NE.0 )
$ GO TO 190
*
* Check that N <= LDA for the input values.
*
CNAME = LINE( 1: 6 )
CALL ATIMCK( 2, CNAME, NM, MVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )CNAME
GO TO 190
END IF
*
* Check that K <= LDA for CUNMHR
*
IF( TIMSUB( 3 ) ) THEN
CALL ATIMCK( 3, CNAME, NN, NVAL, NLDA, LDAVAL, NOUT, INFO )
IF( INFO.GT.0 ) THEN
WRITE( NOUT, FMT = 9999 )SUBNAM( 3 )
TIMSUB( 3 ) = .FALSE.
END IF
END IF
*
* Do for each value of M:
*
DO 120 IM = 1, NM
M = MVAL( IM )
ILO = 1
IHI = M
CALL ICOPY( 4, ISEED, 1, RESEED, 1 )
*
* Do for each value of LDA:
*
DO 110 ILDA = 1, NLDA
LDA = LDAVAL( ILDA )
*
* Do for each pair of values (NB, NX) in NBVAL and NXVAL.
*
DO 100 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
NX = NXVAL( INB )
CALL XLAENV( 3, NX )
LW = MAX( 1, M*MAX( 1, NB ) )
*
* Generate a test matrix of size M by M.
*
CALL ICOPY( 4, RESEED, 1, ISEED, 1 )
CALL CLATMS( M, M, 'Uniform', ISEED, 'Nonsymm', RWORK,
$ MODE, COND, DMAX, M, M, 'No packing', B,
$ LDA, WORK, INFO )
*
IF( TIMSUB( 1 ) ) THEN
*
* CGEHRD: Reduction to Hesenberg form
*
CALL CLACPY( 'Full', M, M, B, LDA, A, LDA )
IC = 0
S1 = SECOND( )
10 CONTINUE
CALL CGEHRD( M, ILO, IHI, A, LDA, TAU, WORK, LW,
$ INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CLACPY( 'Full', M, M, B, LDA, A, LDA )
GO TO 10
END IF
*
* Subtract the time used in CLACPY.
*
ICL = 1
S1 = SECOND( )
20 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CLACPY( 'Full', M, M, A, LDA, B, LDA )
GO TO 20
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
OPS = SOPLA( 'CGEHRD', M, ILO, IHI, 0, NB )
RESLTS( INB, IM, ILDA, 1 ) = SMFLOP( OPS, TIME, INFO )
ELSE
*
* If CGEHRD was not timed, generate a matrix and factor
* it using CGEHRD anyway so that the factored form of
* the matrix can be used in timing the other routines.
*
CALL CLACPY( 'Full', M, M, B, LDA, A, LDA )
CALL CGEHRD( M, ILO, IHI, A, LDA, TAU, WORK, LW,
$ INFO )
END IF
*
IF( TIMSUB( 2 ) ) THEN
*
* CUNGHR: Generate the orthogonal matrix Q from the
* reduction to Hessenberg form A = Q*H*Q'
*
CALL CLACPY( 'Full', M, M, A, LDA, B, LDA )
IC = 0
S1 = SECOND( )
30 CONTINUE
CALL CUNGHR( M, ILO, IHI, B, LDA, TAU, WORK, LW,
$ INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CLACPY( 'Full', M, M, A, LDA, B, LDA )
GO TO 30
END IF
*
* Subtract the time used in CLACPY.
*
ICL = 1
S1 = SECOND( )
40 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CLACPY( 'Full', M, M, A, LDA, B, LDA )
GO TO 40
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
*
* Op count for CUNGHR: same as
* CUNGQR( IHI-ILO, IHI-ILO, IHI-ILO, ... )
*
OPS = SOPLA( 'CUNGQR', IHI-ILO, IHI-ILO, IHI-ILO, 0,
$ NB )
RESLTS( INB, IM, ILDA, 2 ) = SMFLOP( OPS, TIME, INFO )
END IF
*
IF( TIMSUB( 3 ) ) THEN
*
* CUNMHR: Multiply by Q stored as a product of
* elementary transformations
*
I4 = 2
DO 90 ISIDE = 1, 2
SIDE = SIDES( ISIDE )
DO 80 IN = 1, NN
N = NVAL( IN )
LW = MAX( 1, MAX( 1, NB )*N )
IF( ISIDE.EQ.1 ) THEN
M1 = M
N1 = N
ELSE
M1 = N
N1 = M
END IF
ITOFF = 0
DO 70 ITRAN = 1, 2
TRANS = TRANSS( ITRAN )
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
IC = 0
S1 = SECOND( )
50 CONTINUE
CALL CUNMHR( SIDE, TRANS, M1, N1, ILO, IHI,
$ A, LDA, TAU, B, LDA, WORK, LW,
$ INFO )
S2 = SECOND( )
TIME = S2 - S1
IC = IC + 1
IF( TIME.LT.TIMMIN ) THEN
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 50
END IF
*
* Subtract the time used in CTIMMG.
*
ICL = 1
S1 = SECOND( )
60 CONTINUE
S2 = SECOND( )
UNTIME = S2 - S1
ICL = ICL + 1
IF( ICL.LE.IC ) THEN
CALL CTIMMG( 0, M1, N1, B, LDA, 0, 0 )
GO TO 60
END IF
*
TIME = ( TIME-UNTIME ) / REAL( IC )
*
* Op count for CUNMHR, SIDE='L': same as
* CUNMQR( 'L', TRANS, IHI-ILO, N, IHI-ILO, ...)
*
* Op count for CUNMHR, SIDE='R': same as
* CUNMQR( 'R', TRANS, M, IHI-ILO, IHI-ILO, ...)
*
IF( ISIDE.EQ.1 ) THEN
OPS = SOPLA( 'CUNMQR', IHI-ILO, N1,
$ IHI-ILO, -1, NB )
ELSE
OPS = SOPLA( 'CUNMQR', M1, IHI-ILO,
$ IHI-ILO, 1, NB )
END IF
*
RESLTS( INB, IM, ILDA,
$ I4+ITOFF+IN ) = SMFLOP( OPS, TIME, INFO )
ITOFF = NN
70 CONTINUE
80 CONTINUE
I4 = I4 + 2*NN
90 CONTINUE
END IF
*
100 CONTINUE
110 CONTINUE
120 CONTINUE
*
* Print tables of results for CGEHRD and CUNGHR
*
DO 140 ISUB = 1, NSUBS - 1
IF( .NOT.TIMSUB( ISUB ) )
$ GO TO 140
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
IF( NLDA.GT.1 ) THEN
DO 130 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
130 CONTINUE
END IF
WRITE( NOUT, FMT = 9995 )
CALL SPRTB3( '( NB, NX)', 'N', NNB, NBVAL, NXVAL, NM, MVAL,
$ NLDA, RESLTS( 1, 1, 1, ISUB ), LDR1, LDR2, NOUT )
140 CONTINUE
*
* Print tables of results for CUNMHR
*
ISUB = 3
IF( TIMSUB( ISUB ) ) THEN
I4 = 2
DO 180 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
LAB1 = 'M'
LAB2 = 'N'
IF( NLDA.GT.1 ) THEN
WRITE( NOUT, FMT = 9998 )SUBNAM( ISUB )
DO 150 I = 1, NLDA
WRITE( NOUT, FMT = 9997 )I, LDAVAL( I )
150 CONTINUE
WRITE( NOUT, FMT = 9994 )
END IF
ELSE
LAB1 = 'N'
LAB2 = 'M'
END IF
DO 170 ITRAN = 1, 2
DO 160 IN = 1, NN
WRITE( NOUT, FMT = 9996 )SUBNAM( ISUB ),
$ SIDES( ISIDE ), TRANSS( ITRAN ), LAB2, NVAL( IN )
CALL SPRTBL( 'NB', LAB1, NNB, NBVAL, NM, MVAL, NLDA,
$ RESLTS( 1, 1, 1, I4+IN ), LDR1, LDR2,
$ NOUT )
160 CONTINUE
I4 = I4 + NN
170 CONTINUE
180 CONTINUE
END IF
190 CONTINUE
*
* Print a table of results for each timed routine.
*
RETURN
9999 FORMAT( 1X, A6, ' timing run not attempted', / )
9998 FORMAT( / ' *** Speed of ', A6, ' in megaflops *** ' )
9997 FORMAT( 5X, 'line ', I2, ' with LDA = ', I5 )
9996 FORMAT( / 5X, A6, ' with SIDE = ''', A1, ''', TRANS = ''', A1,
$ ''', ', A1, ' =', I6, / )
9995 FORMAT( / 5X, 'ILO = 1, IHI = N', / )
9994 FORMAT( / 5X, 'ILO = 1, IHI = M if SIDE = ''L''', / 5X,
$ ' = N if SIDE = ''R''' )
*
* End of CTIMHR
*
END
|
