LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zla_heamv.f
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1*> \brief \b ZLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_heamv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
22* INCY )
23*
24* .. Scalar Arguments ..
25* DOUBLE PRECISION ALPHA, BETA
26* INTEGER INCX, INCY, LDA, N, UPLO
27* ..
28* .. Array Arguments ..
29* COMPLEX*16 A( LDA, * ), X( * )
30* DOUBLE PRECISION Y( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> ZLA_SYAMV performs the matrix-vector operation
40*>
41*> y := alpha*abs(A)*abs(x) + beta*abs(y),
42*>
43*> where alpha and beta are scalars, x and y are vectors and A is an
44*> n by n symmetric matrix.
45*>
46*> This function is primarily used in calculating error bounds.
47*> To protect against underflow during evaluation, components in
48*> the resulting vector are perturbed away from zero by (N+1)
49*> times the underflow threshold. To prevent unnecessarily large
50*> errors for block-structure embedded in general matrices,
51*> "symbolically" zero components are not perturbed. A zero
52*> entry is considered "symbolic" if all multiplications involved
53*> in computing that entry have at least one zero multiplicand.
54*> \endverbatim
55*
56* Arguments:
57* ==========
58*
59*> \param[in] UPLO
60*> \verbatim
61*> UPLO is INTEGER
62*> On entry, UPLO specifies whether the upper or lower
63*> triangular part of the array A is to be referenced as
64*> follows:
65*>
66*> UPLO = BLAS_UPPER Only the upper triangular part of A
67*> is to be referenced.
68*>
69*> UPLO = BLAS_LOWER Only the lower triangular part of A
70*> is to be referenced.
71*>
72*> Unchanged on exit.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> On entry, N specifies the number of columns of the matrix A.
79*> N must be at least zero.
80*> Unchanged on exit.
81*> \endverbatim
82*>
83*> \param[in] ALPHA
84*> \verbatim
85*> ALPHA is DOUBLE PRECISION .
86*> On entry, ALPHA specifies the scalar alpha.
87*> Unchanged on exit.
88*> \endverbatim
89*>
90*> \param[in] A
91*> \verbatim
92*> A is COMPLEX*16 array, dimension ( LDA, n ).
93*> Before entry, the leading m by n part of the array A must
94*> contain the matrix of coefficients.
95*> Unchanged on exit.
96*> \endverbatim
97*>
98*> \param[in] LDA
99*> \verbatim
100*> LDA is INTEGER
101*> On entry, LDA specifies the first dimension of A as declared
102*> in the calling (sub) program. LDA must be at least
103*> max( 1, n ).
104*> Unchanged on exit.
105*> \endverbatim
106*>
107*> \param[in] X
108*> \verbatim
109*> X is COMPLEX*16 array, dimension at least
110*> ( 1 + ( n - 1 )*abs( INCX ) )
111*> Before entry, the incremented array X must contain the
112*> vector x.
113*> Unchanged on exit.
114*> \endverbatim
115*>
116*> \param[in] INCX
117*> \verbatim
118*> INCX is INTEGER
119*> On entry, INCX specifies the increment for the elements of
120*> X. INCX must not be zero.
121*> Unchanged on exit.
122*> \endverbatim
123*>
124*> \param[in] BETA
125*> \verbatim
126*> BETA is DOUBLE PRECISION .
127*> On entry, BETA specifies the scalar beta. When BETA is
128*> supplied as zero then Y need not be set on input.
129*> Unchanged on exit.
130*> \endverbatim
131*>
132*> \param[in,out] Y
133*> \verbatim
134*> Y is DOUBLE PRECISION array, dimension
135*> ( 1 + ( n - 1 )*abs( INCY ) )
136*> Before entry with BETA non-zero, the incremented array Y
137*> must contain the vector y. On exit, Y is overwritten by the
138*> updated vector y.
139*> \endverbatim
140*>
141*> \param[in] INCY
142*> \verbatim
143*> INCY is INTEGER
144*> On entry, INCY specifies the increment for the elements of
145*> Y. INCY must not be zero.
146*> Unchanged on exit.
147*> \endverbatim
148*
149* Authors:
150* ========
151*
152*> \author Univ. of Tennessee
153*> \author Univ. of California Berkeley
154*> \author Univ. of Colorado Denver
155*> \author NAG Ltd.
156*
157*> \ingroup complex16HEcomputational
158*
159*> \par Further Details:
160* =====================
161*>
162*> \verbatim
163*>
164*> Level 2 Blas routine.
165*>
166*> -- Written on 22-October-1986.
167*> Jack Dongarra, Argonne National Lab.
168*> Jeremy Du Croz, Nag Central Office.
169*> Sven Hammarling, Nag Central Office.
170*> Richard Hanson, Sandia National Labs.
171*> -- Modified for the absolute-value product, April 2006
172*> Jason Riedy, UC Berkeley
173*> \endverbatim
174*>
175* =====================================================================
176 SUBROUTINE zla_heamv( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
177 \$ INCY )
178*
179* -- LAPACK computational routine --
180* -- LAPACK is a software package provided by Univ. of Tennessee, --
181* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182*
183* .. Scalar Arguments ..
184 DOUBLE PRECISION ALPHA, BETA
185 INTEGER INCX, INCY, LDA, N, UPLO
186* ..
187* .. Array Arguments ..
188 COMPLEX*16 A( LDA, * ), X( * )
189 DOUBLE PRECISION Y( * )
190* ..
191*
192* =====================================================================
193*
194* .. Parameters ..
195 DOUBLE PRECISION ONE, ZERO
196 parameter( one = 1.0d+0, zero = 0.0d+0 )
197* ..
198* .. Local Scalars ..
199 LOGICAL SYMB_ZERO
200 DOUBLE PRECISION TEMP, SAFE1
201 INTEGER I, INFO, IY, J, JX, KX, KY
202 COMPLEX*16 ZDUM
203* ..
204* .. External Subroutines ..
205 EXTERNAL xerbla, dlamch
206 DOUBLE PRECISION DLAMCH
207* ..
208* .. External Functions ..
209 EXTERNAL ilauplo
210 INTEGER ILAUPLO
211* ..
212* .. Intrinsic Functions ..
213 INTRINSIC max, abs, sign, real, dimag
214* ..
215* .. Statement Functions ..
216 DOUBLE PRECISION CABS1
217* ..
218* .. Statement Function Definitions ..
219 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
220* ..
221* .. Executable Statements ..
222*
223* Test the input parameters.
224*
225 info = 0
226 IF ( uplo.NE.ilauplo( 'U' ) .AND.
227 \$ uplo.NE.ilauplo( 'L' ) )THEN
228 info = 1
229 ELSE IF( n.LT.0 )THEN
230 info = 2
231 ELSE IF( lda.LT.max( 1, n ) )THEN
232 info = 5
233 ELSE IF( incx.EQ.0 )THEN
234 info = 7
235 ELSE IF( incy.EQ.0 )THEN
236 info = 10
237 END IF
238 IF( info.NE.0 )THEN
239 CALL xerbla( 'ZHEMV ', info )
240 RETURN
241 END IF
242*
243* Quick return if possible.
244*
245 IF( ( n.EQ.0 ).OR.( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
246 \$ RETURN
247*
248* Set up the start points in X and Y.
249*
250 IF( incx.GT.0 )THEN
251 kx = 1
252 ELSE
253 kx = 1 - ( n - 1 )*incx
254 END IF
255 IF( incy.GT.0 )THEN
256 ky = 1
257 ELSE
258 ky = 1 - ( n - 1 )*incy
259 END IF
260*
261* Set SAFE1 essentially to be the underflow threshold times the
262* number of additions in each row.
263*
264 safe1 = dlamch( 'Safe minimum' )
265 safe1 = (n+1)*safe1
266*
267* Form y := alpha*abs(A)*abs(x) + beta*abs(y).
268*
269* The O(N^2) SYMB_ZERO tests could be replaced by O(N) queries to
270* the inexact flag. Still doesn't help change the iteration order
271* to per-column.
272*
273 iy = ky
274 IF ( incx.EQ.1 ) THEN
275 IF ( uplo .EQ. ilauplo( 'U' ) ) THEN
276 DO i = 1, n
277 IF ( beta .EQ. zero ) THEN
278 symb_zero = .true.
279 y( iy ) = 0.0d+0
280 ELSE IF ( y( iy ) .EQ. zero ) THEN
281 symb_zero = .true.
282 ELSE
283 symb_zero = .false.
284 y( iy ) = beta * abs( y( iy ) )
285 END IF
286 IF ( alpha .NE. zero ) THEN
287 DO j = 1, i
288 temp = cabs1( a( j, i ) )
289 symb_zero = symb_zero .AND.
290 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
291
292 y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
293 END DO
294 DO j = i+1, n
295 temp = cabs1( a( i, j ) )
296 symb_zero = symb_zero .AND.
297 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
298
299 y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
300 END DO
301 END IF
302
303 IF (.NOT.symb_zero)
304 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
305
306 iy = iy + incy
307 END DO
308 ELSE
309 DO i = 1, n
310 IF ( beta .EQ. zero ) THEN
311 symb_zero = .true.
312 y( iy ) = 0.0d+0
313 ELSE IF ( y( iy ) .EQ. zero ) THEN
314 symb_zero = .true.
315 ELSE
316 symb_zero = .false.
317 y( iy ) = beta * abs( y( iy ) )
318 END IF
319 IF ( alpha .NE. zero ) THEN
320 DO j = 1, i
321 temp = cabs1( a( i, j ) )
322 symb_zero = symb_zero .AND.
323 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
324
325 y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
326 END DO
327 DO j = i+1, n
328 temp = cabs1( a( j, i ) )
329 symb_zero = symb_zero .AND.
330 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
331
332 y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
333 END DO
334 END IF
335
336 IF (.NOT.symb_zero)
337 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
338
339 iy = iy + incy
340 END DO
341 END IF
342 ELSE
343 IF ( uplo .EQ. ilauplo( 'U' ) ) THEN
344 DO i = 1, n
345 IF ( beta .EQ. zero ) THEN
346 symb_zero = .true.
347 y( iy ) = 0.0d+0
348 ELSE IF ( y( iy ) .EQ. zero ) THEN
349 symb_zero = .true.
350 ELSE
351 symb_zero = .false.
352 y( iy ) = beta * abs( y( iy ) )
353 END IF
354 jx = kx
355 IF ( alpha .NE. zero ) THEN
356 DO j = 1, i
357 temp = cabs1( a( j, i ) )
358 symb_zero = symb_zero .AND.
359 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
360
361 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
362 jx = jx + incx
363 END DO
364 DO j = i+1, n
365 temp = cabs1( a( i, j ) )
366 symb_zero = symb_zero .AND.
367 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
368
369 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
370 jx = jx + incx
371 END DO
372 END IF
373
374 IF ( .NOT.symb_zero )
375 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
376
377 iy = iy + incy
378 END DO
379 ELSE
380 DO i = 1, n
381 IF ( beta .EQ. zero ) THEN
382 symb_zero = .true.
383 y( iy ) = 0.0d+0
384 ELSE IF ( y( iy ) .EQ. zero ) THEN
385 symb_zero = .true.
386 ELSE
387 symb_zero = .false.
388 y( iy ) = beta * abs( y( iy ) )
389 END IF
390 jx = kx
391 IF ( alpha .NE. zero ) THEN
392 DO j = 1, i
393 temp = cabs1( a( i, j ) )
394 symb_zero = symb_zero .AND.
395 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
396
397 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
398 jx = jx + incx
399 END DO
400 DO j = i+1, n
401 temp = cabs1( a( j, i ) )
402 symb_zero = symb_zero .AND.
403 \$ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
404
405 y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
406 jx = jx + incx
407 END DO
408 END IF
409
410 IF ( .NOT.symb_zero )
411 \$ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
412
413 iy = iy + incy
414 END DO
415 END IF
416
417 END IF
418*
419 RETURN
420*
421* End of ZLA_HEAMV
422*
423 END
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function ilauplo(UPLO)
ILAUPLO
Definition: ilauplo.f:58
subroutine zla_heamv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bou...
Definition: zla_heamv.f:178