summaryrefslogtreecommitdiff
path: root/SRC/zla_syamv.f
blob: 02958bef3f3a3ee21f3e21ef14c350fda164bcc4 (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
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
*> \brief \b ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLA_SYAMV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_syamv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_syamv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_syamv.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
*                             INCY )
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION   ALPHA, BETA
*       INTEGER            INCX, INCY, LDA, N
*       INTEGER            UPLO
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * ), X( * )
*       DOUBLE PRECISION   Y( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLA_SYAMV  performs the matrix-vector operation
*>
*>         y := alpha*abs(A)*abs(x) + beta*abs(y),
*>
*> where alpha and beta are scalars, x and y are vectors and A is an
*> n by n symmetric matrix.
*>
*> This function is primarily used in calculating error bounds.
*> To protect against underflow during evaluation, components in
*> the resulting vector are perturbed away from zero by (N+1)
*> times the underflow threshold.  To prevent unnecessarily large
*> errors for block-structure embedded in general matrices,
*> "symbolically" zero components are not perturbed.  A zero
*> entry is considered "symbolic" if all multiplications involved
*> in computing that entry have at least one zero multiplicand.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is INTEGER
*>           On entry, UPLO specifies whether the upper or lower
*>           triangular part of the array A is to be referenced as
*>           follows:
*>
*>              UPLO = BLAS_UPPER   Only the upper triangular part of A
*>                                  is to be referenced.
*>
*>              UPLO = BLAS_LOWER   Only the lower triangular part of A
*>                                  is to be referenced.
*>
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry, N specifies the number of columns of the matrix A.
*>           N must be at least zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION .
*>           On entry, ALPHA specifies the scalar alpha.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array, dimension ( LDA, n ).
*>           Before entry, the leading m by n part of the array A must
*>           contain the matrix of coefficients.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           On entry, LDA specifies the first dimension of A as declared
*>           in the calling (sub) program. LDA must be at least
*>           max( 1, n ).
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension at least
*>           ( 1 + ( n - 1 )*abs( INCX ) )
*>           Before entry, the incremented array X must contain the
*>           vector x.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>           On entry, INCX specifies the increment for the elements of
*>           X. INCX must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is DOUBLE PRECISION .
*>           On entry, BETA specifies the scalar beta. When BETA is
*>           supplied as zero then Y need not be set on input.
*>           Unchanged on exit.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*>          Y is DOUBLE PRECISION array, dimension
*>           ( 1 + ( n - 1 )*abs( INCY ) )
*>           Before entry with BETA non-zero, the incremented array Y
*>           must contain the vector y. On exit, Y is overwritten by the
*>           updated vector y.
*> \endverbatim
*>
*> \param[in] INCY
*> \verbatim
*>          INCY is INTEGER
*>           On entry, INCY specifies the increment for the elements of
*>           Y. INCY must not be zero.
*>           Unchanged on exit.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2017
*
*> \ingroup complex16SYcomputational
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 2 Blas routine.
*>
*>  -- Written on 22-October-1986.
*>     Jack Dongarra, Argonne National Lab.
*>     Jeremy Du Croz, Nag Central Office.
*>     Sven Hammarling, Nag Central Office.
*>     Richard Hanson, Sandia National Labs.
*>  -- Modified for the absolute-value product, April 2006
*>     Jason Riedy, UC Berkeley
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE ZLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
     $                      INCY )
*
*  -- LAPACK computational routine (version 3.7.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2017
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, N
      INTEGER            UPLO
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), X( * )
      DOUBLE PRECISION   Y( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            SYMB_ZERO
      DOUBLE PRECISION   TEMP, SAFE1
      INTEGER            I, INFO, IY, J, JX, KX, KY
      COMPLEX*16         ZDUM
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, DLAMCH
      DOUBLE PRECISION   DLAMCH
*     ..
*     .. External Functions ..
      EXTERNAL           ILAUPLO
      INTEGER            ILAUPLO
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, ABS, SIGN, REAL, DIMAG
*     ..
*     .. Statement Functions ..
      DOUBLE PRECISION   CABS1
*     ..
*     .. Statement Function Definitions ..
      CABS1( ZDUM ) = ABS( DBLE ( ZDUM ) ) + ABS( DIMAG ( ZDUM ) )
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( UPLO.NE.ILAUPLO( 'U' ) .AND.
     $         UPLO.NE.ILAUPLO( 'L' ) )THEN
         INFO = 1
      ELSE IF( N.LT.0 )THEN
         INFO = 2
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
         INFO = 5
      ELSE IF( INCX.EQ.0 )THEN
         INFO = 7
      ELSE IF( INCY.EQ.0 )THEN
         INFO = 10
      END IF
      IF( INFO.NE.0 )THEN
         CALL XERBLA( 'DSYMV ', INFO )
         RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF( INCX.GT.0 )THEN
         KX = 1
      ELSE
         KX = 1 - ( N - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
         KY = 1
      ELSE
         KY = 1 - ( N - 1 )*INCY
      END IF
*
*     Set SAFE1 essentially to be the underflow threshold times the
*     number of additions in each row.
*
      SAFE1 = DLAMCH( 'Safe minimum' )
      SAFE1 = (N+1)*SAFE1
*
*     Form  y := alpha*abs(A)*abs(x) + beta*abs(y).
*
*     The O(N^2) SYMB_ZERO tests could be replaced by O(N) queries to
*     the inexact flag.  Still doesn't help change the iteration order
*     to per-column.
*
      IY = KY
      IF ( INCX.EQ.1 ) THEN
         IF ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN
            DO I = 1, N
               IF ( BETA .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
                  Y( IY ) = 0.0D+0
               ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
               ELSE
                  SYMB_ZERO = .FALSE.
                  Y( IY ) = BETA * ABS( Y( IY ) )
               END IF
               IF ( ALPHA .NE. ZERO ) THEN
                  DO J = 1, I
                     TEMP = CABS1( A( J, I ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
                  END DO
                  DO J = I+1, N
                     TEMP = CABS1( A( I, J ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
                  END DO
               END IF

               IF ( .NOT.SYMB_ZERO )
     $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )

               IY = IY + INCY
            END DO
         ELSE
            DO I = 1, N
               IF ( BETA .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
                  Y( IY ) = 0.0D+0
               ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
               ELSE
                  SYMB_ZERO = .FALSE.
                  Y( IY ) = BETA * ABS( Y( IY ) )
               END IF
               IF ( ALPHA .NE. ZERO ) THEN
                  DO J = 1, I
                     TEMP = CABS1( A( I, J ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
                  END DO
                  DO J = I+1, N
                     TEMP = CABS1( A( J, I ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
                  END DO
               END IF

               IF ( .NOT.SYMB_ZERO )
     $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )

               IY = IY + INCY
            END DO
         END IF
      ELSE
         IF ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN
            DO I = 1, N
               IF ( BETA .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
                  Y( IY ) = 0.0D+0
               ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
               ELSE
                  SYMB_ZERO = .FALSE.
                  Y( IY ) = BETA * ABS( Y( IY ) )
               END IF
               JX = KX
               IF ( ALPHA .NE. ZERO ) THEN
                  DO J = 1, I
                     TEMP = CABS1( A( J, I ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
                     JX = JX + INCX
                  END DO
                  DO J = I+1, N
                     TEMP = CABS1( A( I, J ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
                     JX = JX + INCX
                  END DO
               END IF

               IF ( .NOT.SYMB_ZERO )
     $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )

               IY = IY + INCY
            END DO
         ELSE
            DO I = 1, N
               IF ( BETA .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
                  Y( IY ) = 0.0D+0
               ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
                  SYMB_ZERO = .TRUE.
               ELSE
                  SYMB_ZERO = .FALSE.
                  Y( IY ) = BETA * ABS( Y( IY ) )
               END IF
               JX = KX
               IF ( ALPHA .NE. ZERO ) THEN
                  DO J = 1, I
                     TEMP = CABS1( A( I, J ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
                     JX = JX + INCX
                  END DO
                  DO J = I+1, N
                     TEMP = CABS1( A( J, I ) )
                     SYMB_ZERO = SYMB_ZERO .AND.
     $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )

                     Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
                     JX = JX + INCX
                  END DO
               END IF

               IF ( .NOT.SYMB_ZERO )
     $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )

               IY = IY + INCY
            END DO
         END IF

      END IF
*
      RETURN
*
*     End of ZLA_SYAMV
*
      END