LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
cla_geamv.f
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1 *> \brief \b CLA_GEAMV computes a matrix-vector product using a general matrix 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 CLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
22 * Y, INCY )
23 *
24 * .. Scalar Arguments ..
25 * REAL ALPHA, BETA
26 * INTEGER INCX, INCY, LDA, M, N
27 * INTEGER TRANS
28 * ..
29 * .. Array Arguments ..
30 * COMPLEX A( LDA, * ), X( * )
31 * REAL Y( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CLA_GEAMV performs one of the matrix-vector operations
41 *>
42 *> y := alpha*abs(A)*abs(x) + beta*abs(y),
43 *> or y := alpha*abs(A)**T*abs(x) + beta*abs(y),
44 *>
45 *> where alpha and beta are scalars, x and y are vectors and A is an
46 *> m by n matrix.
47 *>
48 *> This function is primarily used in calculating error bounds.
49 *> To protect against underflow during evaluation, components in
50 *> the resulting vector are perturbed away from zero by (N+1)
51 *> times the underflow threshold. To prevent unnecessarily large
52 *> errors for block-structure embedded in general matrices,
53 *> "symbolically" zero components are not perturbed. A zero
54 *> entry is considered "symbolic" if all multiplications involved
55 *> in computing that entry have at least one zero multiplicand.
56 *> \endverbatim
57 *
58 * Arguments:
59 * ==========
60 *
61 *> \param[in] TRANS
62 *> \verbatim
63 *> TRANS is INTEGER
64 *> On entry, TRANS specifies the operation to be performed as
65 *> follows:
66 *>
67 *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y)
68 *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
69 *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y)
70 *>
71 *> Unchanged on exit.
72 *> \endverbatim
73 *>
74 *> \param[in] M
75 *> \verbatim
76 *> M is INTEGER
77 *> On entry, M specifies the number of rows of the matrix A.
78 *> M must be at least zero.
79 *> Unchanged on exit.
80 *> \endverbatim
81 *>
82 *> \param[in] N
83 *> \verbatim
84 *> N is INTEGER
85 *> On entry, N specifies the number of columns of the matrix A.
86 *> N must be at least zero.
87 *> Unchanged on exit.
88 *> \endverbatim
89 *>
90 *> \param[in] ALPHA
91 *> \verbatim
92 *> ALPHA is REAL
93 *> On entry, ALPHA specifies the scalar alpha.
94 *> Unchanged on exit.
95 *> \endverbatim
96 *>
97 *> \param[in] A
98 *> \verbatim
99 *> A is COMPLEX array, dimension (LDA,n)
100 *> Before entry, the leading m by n part of the array A must
101 *> contain the matrix of coefficients.
102 *> Unchanged on exit.
103 *> \endverbatim
104 *>
105 *> \param[in] LDA
106 *> \verbatim
107 *> LDA is INTEGER
108 *> On entry, LDA specifies the first dimension of A as declared
109 *> in the calling (sub) program. LDA must be at least
110 *> max( 1, m ).
111 *> Unchanged on exit.
112 *> \endverbatim
113 *>
114 *> \param[in] X
115 *> \verbatim
116 *> X is COMPLEX array, dimension
117 *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
118 *> and at least
119 *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
120 *> Before entry, the incremented array X must contain the
121 *> vector x.
122 *> Unchanged on exit.
123 *> \endverbatim
124 *>
125 *> \param[in] INCX
126 *> \verbatim
127 *> INCX is INTEGER
128 *> On entry, INCX specifies the increment for the elements of
129 *> X. INCX must not be zero.
130 *> Unchanged on exit.
131 *> \endverbatim
132 *>
133 *> \param[in] BETA
134 *> \verbatim
135 *> BETA is REAL
136 *> On entry, BETA specifies the scalar beta. When BETA is
137 *> supplied as zero then Y need not be set on input.
138 *> Unchanged on exit.
139 *> \endverbatim
140 *>
141 *> \param[in,out] Y
142 *> \verbatim
143 *> Y is REAL array, dimension
144 *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
145 *> and at least
146 *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
147 *> Before entry with BETA non-zero, the incremented array Y
148 *> must contain the vector y. On exit, Y is overwritten by the
149 *> updated vector y.
150 *> \endverbatim
151 *>
152 *> \param[in] INCY
153 *> \verbatim
154 *> INCY is INTEGER
155 *> On entry, INCY specifies the increment for the elements of
156 *> Y. INCY must not be zero.
157 *> Unchanged on exit.
158 *>
159 *> Level 2 Blas routine.
160 *> \endverbatim
161 *
162 * Authors:
163 * ========
164 *
165 *> \author Univ. of Tennessee
166 *> \author Univ. of California Berkeley
167 *> \author Univ. of Colorado Denver
168 *> \author NAG Ltd.
169 *
170 *> \date December 2016
171 *
172 *> \ingroup complexGEcomputational
173 *
174 * =====================================================================
175  SUBROUTINE cla_geamv ( TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA,
176  $ Y, INCY )
177 *
178 * -- LAPACK computational routine (version 3.7.0) --
179 * -- LAPACK is a software package provided by Univ. of Tennessee, --
180 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181 * December 2016
182 *
183 * .. Scalar Arguments ..
184  REAL ALPHA, BETA
185  INTEGER INCX, INCY, LDA, M, N
186  INTEGER TRANS
187 * ..
188 * .. Array Arguments ..
189  COMPLEX A( lda, * ), X( * )
190  REAL Y( * )
191 * ..
192 *
193 * =====================================================================
194 *
195 * .. Parameters ..
196  COMPLEX ONE, ZERO
197  parameter( one = 1.0e+0, zero = 0.0e+0 )
198 * ..
199 * .. Local Scalars ..
200  LOGICAL SYMB_ZERO
201  REAL TEMP, SAFE1
202  INTEGER I, INFO, IY, J, JX, KX, KY, LENX, LENY
203  COMPLEX CDUM
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL xerbla, slamch
207  REAL SLAMCH
208 * ..
209 * .. External Functions ..
210  EXTERNAL ilatrans
211  INTEGER ILATRANS
212 * ..
213 * .. Intrinsic Functions ..
214  INTRINSIC max, abs, REAL, AIMAG, SIGN
215 * ..
216 * .. Statement Functions ..
217  REAL CABS1
218 * ..
219 * .. Statement Function Definitions ..
220  cabs1( cdum ) = abs( REAL( CDUM ) ) + abs( AIMAG( cdum ) )
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( lda.LT.max( 1, m ) )THEN
236  info = 6
237  ELSE IF( incx.EQ.0 )THEN
238  info = 8
239  ELSE IF( incy.EQ.0 )THEN
240  info = 11
241  END IF
242  IF( info.NE.0 )THEN
243  CALL xerbla( 'CLA_GEAMV ', info )
244  RETURN
245  END IF
246 *
247 * Quick return if possible.
248 *
249  IF( ( m.EQ.0 ).OR.( n.EQ.0 ).OR.
250  $ ( ( alpha.EQ.zero ).AND.( beta.EQ.one ) ) )
251  $ RETURN
252 *
253 * Set LENX and LENY, the lengths of the vectors x and y, and set
254 * up the start points in X and Y.
255 *
256  IF( trans.EQ.ilatrans( 'N' ) )THEN
257  lenx = n
258  leny = m
259  ELSE
260  lenx = m
261  leny = n
262  END IF
263  IF( incx.GT.0 )THEN
264  kx = 1
265  ELSE
266  kx = 1 - ( lenx - 1 )*incx
267  END IF
268  IF( incy.GT.0 )THEN
269  ky = 1
270  ELSE
271  ky = 1 - ( leny - 1 )*incy
272  END IF
273 *
274 * Set SAFE1 essentially to be the underflow threshold times the
275 * number of additions in each row.
276 *
277  safe1 = slamch( 'Safe minimum' )
278  safe1 = (n+1)*safe1
279 *
280 * Form y := alpha*abs(A)*abs(x) + beta*abs(y).
281 *
282 * The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
283 * the inexact flag. Still doesn't help change the iteration order
284 * to per-column.
285 *
286  iy = ky
287  IF ( incx.EQ.1 ) THEN
288  IF( trans.EQ.ilatrans( 'N' ) )THEN
289  DO i = 1, leny
290  IF ( beta .EQ. 0.0 ) THEN
291  symb_zero = .true.
292  y( iy ) = 0.0
293  ELSE IF ( y( iy ) .EQ. 0.0 ) THEN
294  symb_zero = .true.
295  ELSE
296  symb_zero = .false.
297  y( iy ) = beta * abs( y( iy ) )
298  END IF
299  IF ( alpha .NE. 0.0 ) THEN
300  DO j = 1, lenx
301  temp = cabs1( a( i, j ) )
302  symb_zero = symb_zero .AND.
303  $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
304 
305  y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
306  END DO
307  END IF
308 
309  IF ( .NOT.symb_zero ) y( iy ) =
310  $ y( iy ) + sign( safe1, y( iy ) )
311 
312  iy = iy + incy
313  END DO
314  ELSE
315  DO i = 1, leny
316  IF ( beta .EQ. 0.0 ) THEN
317  symb_zero = .true.
318  y( iy ) = 0.0
319  ELSE IF ( y( iy ) .EQ. 0.0 ) THEN
320  symb_zero = .true.
321  ELSE
322  symb_zero = .false.
323  y( iy ) = beta * abs( y( iy ) )
324  END IF
325  IF ( alpha .NE. 0.0 ) THEN
326  DO j = 1, lenx
327  temp = cabs1( a( j, i ) )
328  symb_zero = symb_zero .AND.
329  $ ( x( j ) .EQ. zero .OR. temp .EQ. zero )
330 
331  y( iy ) = y( iy ) + alpha*cabs1( x( j ) )*temp
332  END DO
333  END IF
334 
335  IF ( .NOT.symb_zero ) y( iy ) =
336  $ y( iy ) + sign( safe1, y( iy ) )
337 
338  iy = iy + incy
339  END DO
340  END IF
341  ELSE
342  IF( trans.EQ.ilatrans( 'N' ) )THEN
343  DO i = 1, leny
344  IF ( beta .EQ. 0.0 ) THEN
345  symb_zero = .true.
346  y( iy ) = 0.0
347  ELSE IF ( y( iy ) .EQ. 0.0 ) THEN
348  symb_zero = .true.
349  ELSE
350  symb_zero = .false.
351  y( iy ) = beta * abs( y( iy ) )
352  END IF
353  IF ( alpha .NE. 0.0 ) THEN
354  jx = kx
355  DO j = 1, lenx
356  temp = cabs1( a( i, j ) )
357  symb_zero = symb_zero .AND.
358  $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
359 
360  y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
361  jx = jx + incx
362  END DO
363  END IF
364 
365  IF ( .NOT.symb_zero ) y( iy ) =
366  $ y( iy ) + sign( safe1, y( iy ) )
367 
368  iy = iy + incy
369  END DO
370  ELSE
371  DO i = 1, leny
372  IF ( beta .EQ. 0.0 ) THEN
373  symb_zero = .true.
374  y( iy ) = 0.0
375  ELSE IF ( y( iy ) .EQ. 0.0 ) THEN
376  symb_zero = .true.
377  ELSE
378  symb_zero = .false.
379  y( iy ) = beta * abs( y( iy ) )
380  END IF
381  IF ( alpha .NE. 0.0 ) THEN
382  jx = kx
383  DO j = 1, lenx
384  temp = cabs1( a( j, i ) )
385  symb_zero = symb_zero .AND.
386  $ ( x( jx ) .EQ. zero .OR. temp .EQ. zero )
387 
388  y( iy ) = y( iy ) + alpha*cabs1( x( jx ) )*temp
389  jx = jx + incx
390  END DO
391  END IF
392 
393  IF ( .NOT.symb_zero ) y( iy ) =
394  $ y( iy ) + sign( safe1, y( iy ) )
395 
396  iy = iy + incy
397  END DO
398  END IF
399 
400  END IF
401 *
402  RETURN
403 *
404 * End of CLA_GEAMV
405 *
406  END
ilatrans
integer function ilatrans(TRANS)
ILATRANS
Definition: ilatrans.f:60
cla_geamv
subroutine cla_geamv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds...
Definition: cla_geamv.f:177
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
slamch
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69