LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
dla_gbamv.f
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1 *> \brief \b DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
22 * INCX, BETA, Y, INCY )
23 *
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 * ..
31 *
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
109 *> AB is DOUBLE PRECISION array, dimension ( LDAB, n )
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 *
175 *> \author Univ. of Tennessee
176 *> \author Univ. of California Berkeley
177 *> \author Univ. of Colorado Denver
178 *> \author NAG Ltd.
179 *
180 *> \date June 2017
181 *
182 *> \ingroup doubleGBcomputational
183 *
184 * =====================================================================
185  SUBROUTINE dla_gbamv( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
186  \$ INCX, BETA, Y, INCY )
187 *
188 * -- LAPACK computational routine (version 3.7.1) --
189 * -- LAPACK is a software package provided by Univ. of Tennessee, --
190 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191 * June 2017
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 * =====================================================================
202 *
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
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine dla_gbamv(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY)
DLA_GBAMV performs a matrix-vector operation to calculate error bounds.
Definition: dla_gbamv.f:187
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62