LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
sla_gbamv.f
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1 *> \brief \b SLA_GBAMV performs a matrix-vector operation to calculate error bounds.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
22 * INCX, BETA, Y, INCY )
23 *
24 * .. Scalar Arguments ..
25 * REAL ALPHA, BETA
26 * INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
27 * ..
28 * .. Array Arguments ..
29 * REAL AB( LDAB, * ), X( * ), Y( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SLA_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 REAL
103 *> On entry, ALPHA specifies the scalar alpha.
104 *> Unchanged on exit.
105 *> \endverbatim
106 *>
107 *> \param[in] AB
108 *> \verbatim
109 *> AB is REAL array of 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 REAL 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 REAL
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 REAL 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 September 2012
181 *
182 *> \ingroup realGBcomputational
183 *
184 * =====================================================================
185  SUBROUTINE sla_gbamv( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
186  $ incx, beta, y, incy )
187 *
188 * -- LAPACK computational routine (version 3.4.2) --
189 * -- LAPACK is a software package provided by Univ. of Tennessee, --
190 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191 * September 2012
192 *
193 * .. Scalar Arguments ..
194  REAL ALPHA, BETA
195  INTEGER INCX, INCY, LDAB, M, N, KL, KU, TRANS
196 * ..
197 * .. Array Arguments ..
198  REAL AB( ldab, * ), X( * ), Y( * )
199 * ..
200 *
201 * =====================================================================
202 * .. Parameters ..
203  REAL ONE, ZERO
204  parameter ( one = 1.0e+0, zero = 0.0e+0 )
205 * ..
206 * .. Local Scalars ..
207  LOGICAL SYMB_ZERO
208  REAL TEMP, SAFE1
209  INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL xerbla, slamch
213  REAL SLAMCH
214 * ..
215 * .. External Functions ..
216  EXTERNAL ilatrans
217  INTEGER ILATRANS
218 * ..
219 * .. Intrinsic Functions ..
220  INTRINSIC max, abs, sign
221 * ..
222 * .. Executable Statements ..
223 *
224 * Test the input parameters.
225 *
226  info = 0
227  IF ( .NOT.( ( trans.EQ.ilatrans( 'N' ) )
228  $ .OR. ( trans.EQ.ilatrans( 'T' ) )
229  $ .OR. ( trans.EQ.ilatrans( 'C' ) ) ) ) THEN
230  info = 1
231  ELSE IF( m.LT.0 )THEN
232  info = 2
233  ELSE IF( n.LT.0 )THEN
234  info = 3
235  ELSE IF( kl.LT.0 .OR. kl.GT.m-1 ) THEN
236  info = 4
237  ELSE IF( ku.LT.0 .OR. ku.GT.n-1 ) THEN
238  info = 5
239  ELSE IF( ldab.LT.kl+ku+1 )THEN
240  info = 6
241  ELSE IF( incx.EQ.0 )THEN
242  info = 8
243  ELSE IF( incy.EQ.0 )THEN
244  info = 11
245  END IF
246  IF( info.NE.0 )THEN
247  CALL xerbla( 'SLA_GBAMV ', info )
248  RETURN
249  END IF
250 *
251 * Quick return if possible.
252 *
253  IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
254  $ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
255  $ RETURN
256 *
257 * Set LENX and LENY, the lengths of the vectors x and y, and set
258 * up the start points in X and Y.
259 *
260  IF( trans.EQ.ilatrans( 'N' ) )THEN
261  lenx = n
262  leny = m
263  ELSE
264  lenx = m
265  leny = n
266  END IF
267  IF( incx.GT.0 )THEN
268  kx = 1
269  ELSE
270  kx = 1 - ( lenx - 1 )*incx
271  END IF
272  IF( incy.GT.0 )THEN
273  ky = 1
274  ELSE
275  ky = 1 - ( leny - 1 )*incy
276  END IF
277 *
278 * Set SAFE1 essentially to be the underflow threshold times the
279 * number of additions in each row.
280 *
281  safe1 = slamch( 'Safe minimum' )
282  safe1 = (n+1)*safe1
283 *
284 * Form y := alpha*abs(A)*abs(x) + beta*abs(y).
285 *
286 * The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
287 * the inexact flag. Still doesn't help change the iteration order
288 * to per-column.
289 *
290  kd = ku + 1
291  ke = kl + 1
292  iy = ky
293  IF ( incx.EQ.1 ) THEN
294  IF( trans.EQ.ilatrans( 'N' ) )THEN
295  DO i = 1, leny
296  IF ( beta .EQ. zero ) THEN
297  symb_zero = .true.
298  y( iy ) = 0.0
299  ELSE IF ( y( iy ) .EQ. zero ) THEN
300  symb_zero = .true.
301  ELSE
302  symb_zero = .false.
303  y( iy ) = beta * abs( y( iy ) )
304  END IF
305  IF ( alpha .NE. zero ) THEN
306  DO j = max( i-kl, 1 ), min( i+ku, lenx )
307  temp = abs( ab( kd+i-j, j ) )
308  symb_zero = symb_zero .AND.
309  $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
310 
311  y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
312  END DO
313  END IF
314 
315  IF ( .NOT.symb_zero )
316  $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
317  iy = iy + incy
318  END DO
319  ELSE
320  DO i = 1, leny
321  IF ( beta .EQ. zero ) THEN
322  symb_zero = .true.
323  y( iy ) = 0.0
324  ELSE IF ( y( iy ) .EQ. zero ) THEN
325  symb_zero = .true.
326  ELSE
327  symb_zero = .false.
328  y( iy ) = beta * abs( y( iy ) )
329  END IF
330  IF ( alpha .NE. zero ) THEN
331  DO j = max( i-kl, 1 ), min( i+ku, lenx )
332  temp = abs( ab( ke-i+j, i ) )
333  symb_zero = symb_zero .AND.
334  $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
335 
336  y( iy ) = y( iy ) + alpha*abs( x( j ) )*temp
337  END DO
338  END IF
339 
340  IF ( .NOT.symb_zero )
341  $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
342  iy = iy + incy
343  END DO
344  END IF
345  ELSE
346  IF( trans.EQ.ilatrans( 'N' ) )THEN
347  DO i = 1, leny
348  IF ( beta .EQ. zero ) THEN
349  symb_zero = .true.
350  y( iy ) = 0.0
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  IF ( alpha .NE. zero ) THEN
358  jx = kx
359  DO j = max( i-kl, 1 ), min( i+ku, lenx )
360  temp = abs( ab( kd+i-j, j ) )
361  symb_zero = symb_zero .AND.
362  $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
363 
364  y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
365  jx = jx + incx
366  END DO
367  END IF
368 
369  IF ( .NOT.symb_zero )
370  $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
371 
372  iy = iy + incy
373  END DO
374  ELSE
375  DO i = 1, leny
376  IF ( beta .EQ. zero ) THEN
377  symb_zero = .true.
378  y( iy ) = 0.0
379  ELSE IF ( y( iy ) .EQ. zero ) THEN
380  symb_zero = .true.
381  ELSE
382  symb_zero = .false.
383  y( iy ) = beta * abs( y( iy ) )
384  END IF
385  IF ( alpha .NE. zero ) THEN
386  jx = kx
387  DO j = max( i-kl, 1 ), min( i+ku, lenx )
388  temp = abs( ab( ke-i+j, i ) )
389  symb_zero = symb_zero .AND.
390  $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
391 
392  y( iy ) = y( iy ) + alpha*abs( x( jx ) )*temp
393  jx = jx + incx
394  END DO
395  END IF
396 
397  IF ( .NOT.symb_zero )
398  $ y( iy ) = y( iy ) + sign( safe1, y( iy ) )
399 
400  iy = iy + incy
401  END DO
402  END IF
403 
404  END IF
405 *
406  RETURN
407 *
408 * End of SLA_GBAMV
409 *
410  END
ilatrans
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
sla_gbamv
subroutine sla_gbamv(TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X, INCX, BETA, Y, INCY)
SLA_GBAMV performs a matrix-vector operation to calculate error bounds.
Definition: sla_gbamv.f:187
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
slamch
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69