Annotation of rpl/lapack/lapack/dla_gbamv.f, revision 1.16
1.9 bertrand 1: *> \brief \b DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
1.6 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.6 bertrand 7: *
8: *> \htmlonly
1.13 bertrand 9: *> Download DLA_GBAMV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbamv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbamv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbamv.f">
1.6 bertrand 15: *> [TXT]</a>
1.13 bertrand 16: *> \endhtmlonly
1.6 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
22: * INCX, BETA, Y, INCY )
1.13 bertrand 23: *
1.6 bertrand 24: * .. Scalar Arguments ..
25: * DOUBLE PRECISION ALPHA, BETA
26: * INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
30: * ..
1.13 bertrand 31: *
1.6 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLA_GBAMV 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] KL
89: *> \verbatim
90: *> KL is INTEGER
91: *> The number of subdiagonals within the band of A. KL >= 0.
92: *> \endverbatim
93: *>
94: *> \param[in] KU
95: *> \verbatim
96: *> KU is INTEGER
97: *> The number of superdiagonals within the band of A. KU >= 0.
98: *> \endverbatim
99: *>
100: *> \param[in] ALPHA
101: *> \verbatim
102: *> ALPHA is DOUBLE PRECISION
103: *> On entry, ALPHA specifies the scalar alpha.
104: *> Unchanged on exit.
105: *> \endverbatim
106: *>
107: *> \param[in] AB
108: *> \verbatim
1.15 bertrand 109: *> AB is DOUBLE PRECISION array, dimension ( LDAB, n )
1.6 bertrand 110: *> Before entry, the leading m by n part of the array AB must
111: *> contain the matrix of coefficients.
112: *> Unchanged on exit.
113: *> \endverbatim
114: *>
115: *> \param[in] LDAB
116: *> \verbatim
117: *> LDAB is INTEGER
118: *> On entry, LDA specifies the first dimension of AB as declared
119: *> in the calling (sub) program. LDAB must be at least
120: *> max( 1, m ).
121: *> Unchanged on exit.
122: *> \endverbatim
123: *>
124: *> \param[in] X
125: *> \verbatim
126: *> X is DOUBLE PRECISION array, dimension
127: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
128: *> and at least
129: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
130: *> Before entry, the incremented array X must contain the
131: *> vector x.
132: *> Unchanged on exit.
133: *> \endverbatim
134: *>
135: *> \param[in] INCX
136: *> \verbatim
137: *> INCX is INTEGER
138: *> On entry, INCX specifies the increment for the elements of
139: *> X. INCX must not be zero.
140: *> Unchanged on exit.
141: *> \endverbatim
142: *>
143: *> \param[in] BETA
144: *> \verbatim
145: *> BETA is DOUBLE PRECISION
146: *> On entry, BETA specifies the scalar beta. When BETA is
147: *> supplied as zero then Y need not be set on input.
148: *> Unchanged on exit.
149: *> \endverbatim
150: *>
151: *> \param[in,out] Y
152: *> \verbatim
153: *> Y is DOUBLE PRECISION array, dimension
154: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
155: *> and at least
156: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
157: *> Before entry with BETA non-zero, the incremented array Y
158: *> must contain the vector y. On exit, Y is overwritten by the
159: *> updated vector y.
160: *> \endverbatim
161: *>
162: *> \param[in] INCY
163: *> \verbatim
164: *> INCY is INTEGER
165: *> On entry, INCY specifies the increment for the elements of
166: *> Y. INCY must not be zero.
167: *> Unchanged on exit.
168: *>
169: *> Level 2 Blas routine.
170: *> \endverbatim
171: *
172: * Authors:
173: * ========
174: *
1.13 bertrand 175: *> \author Univ. of Tennessee
176: *> \author Univ. of California Berkeley
177: *> \author Univ. of Colorado Denver
178: *> \author NAG Ltd.
1.6 bertrand 179: *
1.15 bertrand 180: *> \date June 2017
1.6 bertrand 181: *
182: *> \ingroup doubleGBcomputational
183: *
184: * =====================================================================
1.1 bertrand 185: SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
186: $ INCX, BETA, Y, INCY )
187: *
1.15 bertrand 188: * -- LAPACK computational routine (version 3.7.1) --
1.6 bertrand 189: * -- LAPACK is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 191: * June 2017
1.1 bertrand 192: *
193: * .. Scalar Arguments ..
194: DOUBLE PRECISION ALPHA, BETA
195: INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
196: * ..
197: * .. Array Arguments ..
198: DOUBLE PRECISION AB( LDAB, * ), X( * ), Y( * )
199: * ..
200: *
201: * =====================================================================
1.5 bertrand 202: *
1.1 bertrand 203: * .. Parameters ..
204: DOUBLE PRECISION ONE, ZERO
205: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
206: * ..
207: * .. Local Scalars ..
208: LOGICAL SYMB_ZERO
209: DOUBLE PRECISION TEMP, SAFE1
210: INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
211: * ..
212: * .. External Subroutines ..
213: EXTERNAL XERBLA, DLAMCH
214: DOUBLE PRECISION DLAMCH
215: * ..
216: * .. External Functions ..
217: EXTERNAL ILATRANS
218: INTEGER ILATRANS
219: * ..
220: * .. Intrinsic Functions ..
221: INTRINSIC MAX, ABS, SIGN
222: * ..
223: * .. Executable Statements ..
224: *
225: * Test the input parameters.
226: *
227: INFO = 0
228: IF ( .NOT.( ( TRANS.EQ.ILATRANS( 'N' ) )
229: $ .OR. ( TRANS.EQ.ILATRANS( 'T' ) )
230: $ .OR. ( TRANS.EQ.ILATRANS( 'C' ) ) ) ) THEN
231: INFO = 1
232: ELSE IF( M.LT.0 )THEN
233: INFO = 2
234: ELSE IF( N.LT.0 )THEN
235: INFO = 3
236: ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
237: INFO = 4
238: ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
239: INFO = 5
240: ELSE IF( LDAB.LT.KL+KU+1 )THEN
241: INFO = 6
242: ELSE IF( INCX.EQ.0 )THEN
243: INFO = 8
244: ELSE IF( INCY.EQ.0 )THEN
245: INFO = 11
246: END IF
247: IF( INFO.NE.0 )THEN
248: CALL XERBLA( 'DLA_GBAMV ', INFO )
249: RETURN
250: END IF
251: *
252: * Quick return if possible.
253: *
254: IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
255: $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
256: $ RETURN
257: *
258: * Set LENX and LENY, the lengths of the vectors x and y, and set
259: * up the start points in X and Y.
260: *
261: IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
262: LENX = N
263: LENY = M
264: ELSE
265: LENX = M
266: LENY = N
267: END IF
268: IF( INCX.GT.0 )THEN
269: KX = 1
270: ELSE
271: KX = 1 - ( LENX - 1 )*INCX
272: END IF
273: IF( INCY.GT.0 )THEN
274: KY = 1
275: ELSE
276: KY = 1 - ( LENY - 1 )*INCY
277: END IF
278: *
279: * Set SAFE1 essentially to be the underflow threshold times the
280: * number of additions in each row.
281: *
282: SAFE1 = DLAMCH( 'Safe minimum' )
283: SAFE1 = (N+1)*SAFE1
284: *
285: * Form y := alpha*abs(A)*abs(x) + beta*abs(y).
286: *
287: * The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
288: * the inexact flag. Still doesn't help change the iteration order
289: * to per-column.
290: *
291: KD = KU + 1
292: KE = KL + 1
293: IY = KY
294: IF ( INCX.EQ.1 ) THEN
295: IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
296: DO I = 1, LENY
297: IF ( BETA .EQ. ZERO ) THEN
298: SYMB_ZERO = .TRUE.
299: Y( IY ) = 0.0D+0
300: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
301: SYMB_ZERO = .TRUE.
302: ELSE
303: SYMB_ZERO = .FALSE.
304: Y( IY ) = BETA * ABS( Y( IY ) )
305: END IF
306: IF ( ALPHA .NE. ZERO ) THEN
307: DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
308: TEMP = ABS( AB( KD+I-J, J ) )
309: SYMB_ZERO = SYMB_ZERO .AND.
310: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
311:
312: Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
313: END DO
314: END IF
315:
316: IF ( .NOT.SYMB_ZERO )
317: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
318: IY = IY + INCY
319: END DO
320: ELSE
321: DO I = 1, LENY
322: IF ( BETA .EQ. ZERO ) THEN
323: SYMB_ZERO = .TRUE.
324: Y( IY ) = 0.0D+0
325: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
326: SYMB_ZERO = .TRUE.
327: ELSE
328: SYMB_ZERO = .FALSE.
329: Y( IY ) = BETA * ABS( Y( IY ) )
330: END IF
331: IF ( ALPHA .NE. ZERO ) THEN
332: DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
333: TEMP = ABS( AB( KE-I+J, I ) )
334: SYMB_ZERO = SYMB_ZERO .AND.
335: $ ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
336:
337: Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
338: END DO
339: END IF
340:
341: IF ( .NOT.SYMB_ZERO )
342: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
343: IY = IY + INCY
344: END DO
345: END IF
346: ELSE
347: IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
348: DO I = 1, LENY
349: IF ( BETA .EQ. ZERO ) THEN
350: SYMB_ZERO = .TRUE.
351: Y( IY ) = 0.0D+0
352: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
353: SYMB_ZERO = .TRUE.
354: ELSE
355: SYMB_ZERO = .FALSE.
356: Y( IY ) = BETA * ABS( Y( IY ) )
357: END IF
358: IF ( ALPHA .NE. ZERO ) THEN
359: JX = KX
360: DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
361: TEMP = ABS( AB( KD+I-J, J ) )
362: SYMB_ZERO = SYMB_ZERO .AND.
363: $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
364:
365: Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
366: JX = JX + INCX
367: END DO
368: END IF
369:
370: IF ( .NOT.SYMB_ZERO )
371: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
372:
373: IY = IY + INCY
374: END DO
375: ELSE
376: DO I = 1, LENY
377: IF ( BETA .EQ. ZERO ) THEN
378: SYMB_ZERO = .TRUE.
379: Y( IY ) = 0.0D+0
380: ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
381: SYMB_ZERO = .TRUE.
382: ELSE
383: SYMB_ZERO = .FALSE.
384: Y( IY ) = BETA * ABS( Y( IY ) )
385: END IF
386: IF ( ALPHA .NE. ZERO ) THEN
387: JX = KX
388: DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
389: TEMP = ABS( AB( KE-I+J, I ) )
390: SYMB_ZERO = SYMB_ZERO .AND.
391: $ ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
392:
393: Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
394: JX = JX + INCX
395: END DO
396: END IF
397:
398: IF ( .NOT.SYMB_ZERO )
399: $ Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
400:
401: IY = IY + INCY
402: END DO
403: END IF
404:
405: END IF
406: *
407: RETURN
408: *
409: * End of DLA_GBAMV
410: *
411: END
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