1: *> \brief \b ZLA_HEAMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_HEAMV + dependencies
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11: *> [TGZ]</a>
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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: *> \date November 2011
158: *
159: *> \ingroup complex16HEcomputational
160: *
161: *> \par Further Details:
162: * =====================
163: *>
164: *> \verbatim
165: *>
166: *> Level 2 Blas routine.
167: *>
168: *> -- Written on 22-October-1986.
169: *> Jack Dongarra, Argonne National Lab.
170: *> Jeremy Du Croz, Nag Central Office.
171: *> Sven Hammarling, Nag Central Office.
172: *> Richard Hanson, Sandia National Labs.
173: *> -- Modified for the absolute-value product, April 2006
174: *> Jason Riedy, UC Berkeley
175: *> \endverbatim
176: *>
177: * =====================================================================
178: SUBROUTINE ZLA_HEAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y,
179: $ INCY )
180: *
181: * -- LAPACK computational routine (version 3.4.0) --
182: * -- LAPACK is a software package provided by Univ. of Tennessee, --
183: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
184: * November 2011
185: *
186: * .. Scalar Arguments ..
187: DOUBLE PRECISION ALPHA, BETA
188: INTEGER INCX, INCY, LDA, N, UPLO
189: * ..
190: * .. Array Arguments ..
191: COMPLEX*16 A( LDA, * ), X( * )
192: DOUBLE PRECISION Y( * )
193: * ..
194: *
195: * =====================================================================
196: *
197: * .. Parameters ..
198: DOUBLE PRECISION ONE, ZERO
199: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
200: * ..
201: * .. Local Scalars ..
202: LOGICAL SYMB_ZERO
203: DOUBLE PRECISION TEMP, SAFE1
204: INTEGER I, INFO, IY, J, JX, KX, KY
205: COMPLEX*16 ZDUM
206: * ..
207: * .. External Subroutines ..
208: EXTERNAL XERBLA, DLAMCH
209: DOUBLE PRECISION DLAMCH
210: * ..
211: * .. External Functions ..
212: EXTERNAL ILAUPLO
213: INTEGER ILAUPLO
214: * ..
215: * .. Intrinsic Functions ..
216: INTRINSIC MAX, ABS, SIGN, REAL, DIMAG
217: * ..
218: * .. Statement Functions ..
219: DOUBLE PRECISION CABS1
220: * ..
221: * .. Statement Function Definitions ..
222: CABS1( ZDUM ) = ABS( DBLE ( ZDUM ) ) + ABS( DIMAG ( ZDUM ) )
223: * ..
224: * .. Executable Statements ..
225: *
226: * Test the input parameters.
227: *
228: INFO = 0
229: IF ( UPLO.NE.ILAUPLO( 'U' ) .AND.
230: $ UPLO.NE.ILAUPLO( 'L' ) )THEN
231: INFO = 1
232: ELSE IF( N.LT.0 )THEN
233: INFO = 2
234: ELSE IF( LDA.LT.MAX( 1, N ) )THEN
235: INFO = 5
236: ELSE IF( INCX.EQ.0 )THEN
237: INFO = 7
238: ELSE IF( INCY.EQ.0 )THEN
239: INFO = 10
240: END IF
241: IF( INFO.NE.0 )THEN
242: CALL XERBLA( 'ZHEMV ', INFO )
243: RETURN
244: END IF
245: *
246: * Quick return if possible.
247: *
248: IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
249: $ RETURN
250: *
251: * Set up the start points in X and Y.
252: *
253: IF( INCX.GT.0 )THEN
254: KX = 1
255: ELSE
256: KX = 1 - ( N - 1 )*INCX
257: END IF
258: IF( INCY.GT.0 )THEN
259: KY = 1
260: ELSE
261: KY = 1 - ( N - 1 )*INCY
262: END IF
263: *
264: * Set SAFE1 essentially to be the underflow threshold times the
265: * number of additions in each row.
266: *
267: SAFE1 = DLAMCH( 'Safe minimum' )
268: SAFE1 = (N+1)*SAFE1
269: *
270: * Form y := alpha*abs(A)*abs(x) + beta*abs(y).
271: *
272: * The O(N^2) SYMB_ZERO tests could be replaced by O(N) queries to
273: * the inexact flag. Still doesn't help change the iteration order
274: * to per-column.
275: *
276: IY = KY
277: IF ( INCX.EQ.1 ) THEN
278: IF ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN
279: DO I = 1, N
280: IF ( BETA .EQ. ZERO ) THEN
281: SYMB_ZERO = .TRUE.
282: Y( IY ) = 0.0D+0
283: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
284: SYMB_ZERO = .TRUE.
285: ELSE
286: SYMB_ZERO = .FALSE.
287: Y( IY ) = BETA * ABS( Y( IY ) )
288: END IF
289: IF ( ALPHA .NE. ZERO ) THEN
290: DO J = 1, I
291: TEMP = CABS1( A( J, I ) )
292: SYMB_ZERO = SYMB_ZERO .AND.
293: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
294:
295: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
296: END DO
297: DO J = I+1, N
298: TEMP = CABS1( A( I, J ) )
299: SYMB_ZERO = SYMB_ZERO .AND.
300: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
301:
302: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
303: END DO
304: END IF
305:
306: IF (.NOT.SYMB_ZERO)
307: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
308:
309: IY = IY + INCY
310: END DO
311: ELSE
312: DO I = 1, N
313: IF ( BETA .EQ. ZERO ) THEN
314: SYMB_ZERO = .TRUE.
315: Y( IY ) = 0.0D+0
316: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
317: SYMB_ZERO = .TRUE.
318: ELSE
319: SYMB_ZERO = .FALSE.
320: Y( IY ) = BETA * ABS( Y( IY ) )
321: END IF
322: IF ( ALPHA .NE. ZERO ) THEN
323: DO J = 1, I
324: TEMP = CABS1( A( I, J ) )
325: SYMB_ZERO = SYMB_ZERO .AND.
326: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
327:
328: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
329: END DO
330: DO J = I+1, N
331: TEMP = CABS1( A( J, I ) )
332: SYMB_ZERO = SYMB_ZERO .AND.
333: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
334:
335: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( J ) )*TEMP
336: END DO
337: END IF
338:
339: IF (.NOT.SYMB_ZERO)
340: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
341:
342: IY = IY + INCY
343: END DO
344: END IF
345: ELSE
346: IF ( UPLO .EQ. ILAUPLO( 'U' ) ) THEN
347: DO I = 1, N
348: IF ( BETA .EQ. ZERO ) THEN
349: SYMB_ZERO = .TRUE.
350: Y( IY ) = 0.0D+0
351: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
352: SYMB_ZERO = .TRUE.
353: ELSE
354: SYMB_ZERO = .FALSE.
355: Y( IY ) = BETA * ABS( Y( IY ) )
356: END IF
357: JX = KX
358: IF ( ALPHA .NE. ZERO ) THEN
359: DO J = 1, I
360: TEMP = CABS1( A( J, I ) )
361: SYMB_ZERO = SYMB_ZERO .AND.
362: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
363:
364: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
365: JX = JX + INCX
366: END DO
367: DO J = I+1, N
368: TEMP = CABS1( A( I, J ) )
369: SYMB_ZERO = SYMB_ZERO .AND.
370: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
371:
372: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
373: JX = JX + INCX
374: END DO
375: END IF
376:
377: IF ( .NOT.SYMB_ZERO )
378: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
379:
380: IY = IY + INCY
381: END DO
382: ELSE
383: DO I = 1, N
384: IF ( BETA .EQ. ZERO ) THEN
385: SYMB_ZERO = .TRUE.
386: Y( IY ) = 0.0D+0
387: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
388: SYMB_ZERO = .TRUE.
389: ELSE
390: SYMB_ZERO = .FALSE.
391: Y( IY ) = BETA * ABS( Y( IY ) )
392: END IF
393: JX = KX
394: IF ( ALPHA .NE. ZERO ) THEN
395: DO J = 1, I
396: TEMP = CABS1( A( I, J ) )
397: SYMB_ZERO = SYMB_ZERO .AND.
398: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
399:
400: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
401: JX = JX + INCX
402: END DO
403: DO J = I+1, N
404: TEMP = CABS1( A( J, I ) )
405: SYMB_ZERO = SYMB_ZERO .AND.
406: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
407:
408: Y( IY ) = Y( IY ) + ALPHA*CABS1( X( JX ) )*TEMP
409: JX = JX + INCX
410: END DO
411: END IF
412:
413: IF ( .NOT.SYMB_ZERO )
414: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
415:
416: IY = IY + INCY
417: END DO
418: END IF
419:
420: END IF
421: *
422: RETURN
423: *
424: * End of ZLA_HEAMV
425: *
426: END
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