Annotation of rpl/lapack/lapack/dla_geamv.f, revision 1.12
1.9 bertrand 1: *> \brief \b DLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.
1.6 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLA_GEAMV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_geamv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_geamv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_geamv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
22: * Y, INCY )
23: *
24: * .. Scalar Arguments ..
25: * DOUBLE PRECISION ALPHA, BETA
26: * INTEGER INCX, INCY, LDA, M, N, TRANS
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLA_GEAMV performs one of the matrix-vector operations
39: *>
40: *> y := alpha*abs(A)*abs(x) + beta*abs(y),
41: *> or y := alpha*abs(A)**T*abs(x) + beta*abs(y),
42: *>
43: *> where alpha and beta are scalars, x and y are vectors and A is an
44: *> m by n 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] TRANS
60: *> \verbatim
61: *> TRANS is INTEGER
62: *> On entry, TRANS specifies the operation to be performed as
63: *> follows:
64: *>
65: *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
66: *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
67: *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
68: *>
69: *> Unchanged on exit.
70: *> \endverbatim
71: *>
72: *> \param[in] M
73: *> \verbatim
74: *> M is INTEGER
75: *> On entry, M specifies the number of rows of the matrix A.
76: *> M must be at least zero.
77: *> Unchanged on exit.
78: *> \endverbatim
79: *>
80: *> \param[in] N
81: *> \verbatim
82: *> N is INTEGER
83: *> On entry, N specifies the number of columns of the matrix A.
84: *> N must be at least zero.
85: *> Unchanged on exit.
86: *> \endverbatim
87: *>
88: *> \param[in] ALPHA
89: *> \verbatim
90: *> ALPHA is DOUBLE PRECISION
91: *> On entry, ALPHA specifies the scalar alpha.
92: *> Unchanged on exit.
93: *> \endverbatim
94: *>
95: *> \param[in] A
96: *> \verbatim
97: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n )
98: *> Before entry, the leading m by n part of the array A must
99: *> contain the matrix of coefficients.
100: *> Unchanged on exit.
101: *> \endverbatim
102: *>
103: *> \param[in] LDA
104: *> \verbatim
105: *> LDA is INTEGER
106: *> On entry, LDA specifies the first dimension of A as declared
107: *> in the calling (sub) program. LDA must be at least
108: *> max( 1, m ).
109: *> Unchanged on exit.
110: *> \endverbatim
111: *>
112: *> \param[in] X
113: *> \verbatim
114: *> X is DOUBLE PRECISION array, dimension
115: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
116: *> and at least
117: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
118: *> Before entry, the incremented array X must contain the
119: *> vector x.
120: *> Unchanged on exit.
121: *> \endverbatim
122: *>
123: *> \param[in] INCX
124: *> \verbatim
125: *> INCX is INTEGER
126: *> On entry, INCX specifies the increment for the elements of
127: *> X. INCX must not be zero.
128: *> Unchanged on exit.
129: *> \endverbatim
130: *>
131: *> \param[in] BETA
132: *> \verbatim
133: *> BETA is DOUBLE PRECISION
134: *> On entry, BETA specifies the scalar beta. When BETA is
135: *> supplied as zero then Y need not be set on input.
136: *> Unchanged on exit.
137: *> \endverbatim
138: *>
139: *> \param[in,out] Y
140: *> \verbatim
141: *> Y is DOUBLE PRECISION
142: *> Array of DIMENSION at least
143: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
144: *> and at least
145: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
146: *> Before entry with BETA non-zero, the incremented array Y
147: *> must contain the vector y. On exit, Y is overwritten by the
148: *> updated vector y.
149: *> \endverbatim
150: *>
151: *> \param[in] INCY
152: *> \verbatim
153: *> INCY is INTEGER
154: *> On entry, INCY specifies the increment for the elements of
155: *> Y. INCY must not be zero.
156: *> Unchanged on exit.
157: *>
158: *> Level 2 Blas routine.
159: *> \endverbatim
160: *
161: * Authors:
162: * ========
163: *
164: *> \author Univ. of Tennessee
165: *> \author Univ. of California Berkeley
166: *> \author Univ. of Colorado Denver
167: *> \author NAG Ltd.
168: *
1.9 bertrand 169: *> \date September 2012
1.6 bertrand 170: *
171: *> \ingroup doubleGEcomputational
172: *
173: * =====================================================================
1.1 bertrand 174: SUBROUTINE DLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
175: $ Y, INCY )
176: *
1.9 bertrand 177: * -- LAPACK computational routine (version 3.4.2) --
1.6 bertrand 178: * -- LAPACK is a software package provided by Univ. of Tennessee, --
179: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 180: * September 2012
1.1 bertrand 181: *
182: * .. Scalar Arguments ..
183: DOUBLE PRECISION ALPHA, BETA
184: INTEGER INCX, INCY, LDA, M, N, TRANS
185: * ..
186: * .. Array Arguments ..
187: DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
188: * ..
189: *
190: * =====================================================================
191: *
192: * .. Parameters ..
193: DOUBLE PRECISION ONE, ZERO
194: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
195: * ..
196: * .. Local Scalars ..
197: LOGICAL SYMB_ZERO
198: DOUBLE PRECISION TEMP, SAFE1
199: INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY
200: * ..
201: * .. External Subroutines ..
202: EXTERNAL XERBLA, DLAMCH
203: DOUBLE PRECISION DLAMCH
204: * ..
205: * .. External Functions ..
206: EXTERNAL ILATRANS
207: INTEGER ILATRANS
208: * ..
209: * .. Intrinsic Functions ..
210: INTRINSIC MAX, ABS, SIGN
211: * ..
212: * .. Executable Statements ..
213: *
214: * Test the input parameters.
215: *
216: INFO = 0
217: IF ( .NOT.( ( TRANS.EQ.ILATRANS( 'N' ) )
218: $ .OR. ( TRANS.EQ.ILATRANS( 'T' ) )
219: $ .OR. ( TRANS.EQ.ILATRANS( 'C' )) ) ) THEN
220: INFO = 1
221: ELSE IF( M.LT.0 )THEN
222: INFO = 2
223: ELSE IF( N.LT.0 )THEN
224: INFO = 3
225: ELSE IF( LDA.LT.MAX( 1, M ) )THEN
226: INFO = 6
227: ELSE IF( INCX.EQ.0 )THEN
228: INFO = 8
229: ELSE IF( INCY.EQ.0 )THEN
230: INFO = 11
231: END IF
232: IF( INFO.NE.0 )THEN
233: CALL XERBLA( 'DLA_GEAMV ', INFO )
234: RETURN
235: END IF
236: *
237: * Quick return if possible.
238: *
239: IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
240: $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
241: $ RETURN
242: *
243: * Set LENX and LENY, the lengths of the vectors x and y, and set
244: * up the start points in X and Y.
245: *
246: IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
247: LENX = N
248: LENY = M
249: ELSE
250: LENX = M
251: LENY = N
252: END IF
253: IF( INCX.GT.0 )THEN
254: KX = 1
255: ELSE
256: KX = 1 - ( LENX - 1 )*INCX
257: END IF
258: IF( INCY.GT.0 )THEN
259: KY = 1
260: ELSE
261: KY = 1 - ( LENY - 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(M*N) 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( TRANS.EQ.ILATRANS( 'N' ) )THEN
279: DO I = 1, LENY
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, LENX
291: TEMP = ABS( A( I, J ) )
292: SYMB_ZERO = SYMB_ZERO .AND.
293: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
294:
295: Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
296: END DO
297: END IF
298:
299: IF ( .NOT.SYMB_ZERO )
300: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
301:
302: IY = IY + INCY
303: END DO
304: ELSE
305: DO I = 1, LENY
306: IF ( BETA .EQ. ZERO ) THEN
307: SYMB_ZERO = .TRUE.
308: Y( IY ) = 0.0D+0
309: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
310: SYMB_ZERO = .TRUE.
311: ELSE
312: SYMB_ZERO = .FALSE.
313: Y( IY ) = BETA * ABS( Y( IY ) )
314: END IF
315: IF ( ALPHA .NE. ZERO ) THEN
316: DO J = 1, LENX
317: TEMP = ABS( A( J, I ) )
318: SYMB_ZERO = SYMB_ZERO .AND.
319: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
320:
321: Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
322: END DO
323: END IF
324:
325: IF ( .NOT.SYMB_ZERO )
326: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
327:
328: IY = IY + INCY
329: END DO
330: END IF
331: ELSE
332: IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
333: DO I = 1, LENY
334: IF ( BETA .EQ. ZERO ) THEN
335: SYMB_ZERO = .TRUE.
336: Y( IY ) = 0.0D+0
337: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
338: SYMB_ZERO = .TRUE.
339: ELSE
340: SYMB_ZERO = .FALSE.
341: Y( IY ) = BETA * ABS( Y( IY ) )
342: END IF
343: IF ( ALPHA .NE. ZERO ) THEN
344: JX = KX
345: DO J = 1, LENX
346: TEMP = ABS( A( I, J ) )
347: SYMB_ZERO = SYMB_ZERO .AND.
348: $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
349:
350: Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
351: JX = JX + INCX
352: END DO
353: END IF
354:
355: IF (.NOT.SYMB_ZERO)
356: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
357:
358: IY = IY + INCY
359: END DO
360: ELSE
361: DO I = 1, LENY
362: IF ( BETA .EQ. ZERO ) THEN
363: SYMB_ZERO = .TRUE.
364: Y( IY ) = 0.0D+0
365: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
366: SYMB_ZERO = .TRUE.
367: ELSE
368: SYMB_ZERO = .FALSE.
369: Y( IY ) = BETA * ABS( Y( IY ) )
370: END IF
371: IF ( ALPHA .NE. ZERO ) THEN
372: JX = KX
373: DO J = 1, LENX
374: TEMP = ABS( A( J, I ) )
375: SYMB_ZERO = SYMB_ZERO .AND.
376: $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
377:
378: Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
379: JX = JX + INCX
380: END DO
381: END IF
382:
383: IF (.NOT.SYMB_ZERO)
384: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
385:
386: IY = IY + INCY
387: END DO
388: END IF
389:
390: END IF
391: *
392: RETURN
393: *
394: * End of DLA_GEAMV
395: *
396: END
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