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dtrmv.f
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1 *> \brief \b DTRMV
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
12 *
13 * .. Scalar Arguments ..
14 * INTEGER INCX,LDA,N
15 * CHARACTER DIAG,TRANS,UPLO
16 * ..
17 * .. Array Arguments ..
18 * DOUBLE PRECISION A(LDA,*),X(*)
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> DTRMV performs one of the matrix-vector operations
28 *>
29 *> x := A*x, or x := A**T*x,
30 *>
31 *> where x is an n element vector and A is an n by n unit, or non-unit,
32 *> upper or lower triangular matrix.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] UPLO
39 *> \verbatim
40 *> UPLO is CHARACTER*1
41 *> On entry, UPLO specifies whether the matrix is an upper or
42 *> lower triangular matrix as follows:
43 *>
44 *> UPLO = 'U' or 'u' A is an upper triangular matrix.
45 *>
46 *> UPLO = 'L' or 'l' A is a lower triangular matrix.
47 *> \endverbatim
48 *>
49 *> \param[in] TRANS
50 *> \verbatim
51 *> TRANS is CHARACTER*1
52 *> On entry, TRANS specifies the operation to be performed as
53 *> follows:
54 *>
55 *> TRANS = 'N' or 'n' x := A*x.
56 *>
57 *> TRANS = 'T' or 't' x := A**T*x.
58 *>
59 *> TRANS = 'C' or 'c' x := A**T*x.
60 *> \endverbatim
61 *>
62 *> \param[in] DIAG
63 *> \verbatim
64 *> DIAG is CHARACTER*1
65 *> On entry, DIAG specifies whether or not A is unit
66 *> triangular as follows:
67 *>
68 *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
69 *>
70 *> DIAG = 'N' or 'n' A is not assumed to be unit
71 *> triangular.
72 *> \endverbatim
73 *>
74 *> \param[in] N
75 *> \verbatim
76 *> N is INTEGER
77 *> On entry, N specifies the order of the matrix A.
78 *> N must be at least zero.
79 *> \endverbatim
80 *>
81 *> \param[in] A
82 *> \verbatim
83 *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
84 *> Before entry with UPLO = 'U' or 'u', the leading n by n
85 *> upper triangular part of the array A must contain the upper
86 *> triangular matrix and the strictly lower triangular part of
87 *> A is not referenced.
88 *> Before entry with UPLO = 'L' or 'l', the leading n by n
89 *> lower triangular part of the array A must contain the lower
90 *> triangular matrix and the strictly upper triangular part of
91 *> A is not referenced.
92 *> Note that when DIAG = 'U' or 'u', the diagonal elements of
93 *> A are not referenced either, but are assumed to be unity.
94 *> \endverbatim
95 *>
96 *> \param[in] LDA
97 *> \verbatim
98 *> LDA is INTEGER
99 *> On entry, LDA specifies the first dimension of A as declared
100 *> in the calling (sub) program. LDA must be at least
101 *> max( 1, n ).
102 *> \endverbatim
103 *>
104 *> \param[in,out] X
105 *> \verbatim
106 *> X is DOUBLE PRECISION array of dimension at least
107 *> ( 1 + ( n - 1 )*abs( INCX ) ).
108 *> Before entry, the incremented array X must contain the n
109 *> element vector x. On exit, X is overwritten with the
110 *> tranformed vector x.
111 *> \endverbatim
112 *>
113 *> \param[in] INCX
114 *> \verbatim
115 *> INCX is INTEGER
116 *> On entry, INCX specifies the increment for the elements of
117 *> X. INCX must not be zero.
118 *> \endverbatim
119 *
120 * Authors:
121 * ========
122 *
123 *> \author Univ. of Tennessee
124 *> \author Univ. of California Berkeley
125 *> \author Univ. of Colorado Denver
126 *> \author NAG Ltd.
127 *
128 *> \date November 2011
129 *
130 *> \ingroup double_blas_level2
131 *
132 *> \par Further Details:
133 * =====================
134 *>
135 *> \verbatim
136 *>
137 *> Level 2 Blas routine.
138 *> The vector and matrix arguments are not referenced when N = 0, or M = 0
139 *>
140 *> -- Written on 22-October-1986.
141 *> Jack Dongarra, Argonne National Lab.
142 *> Jeremy Du Croz, Nag Central Office.
143 *> Sven Hammarling, Nag Central Office.
144 *> Richard Hanson, Sandia National Labs.
145 *> \endverbatim
146 *>
147 * =====================================================================
148  SUBROUTINE dtrmv(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
149 *
150 * -- Reference BLAS level2 routine (version 3.4.0) --
151 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153 * November 2011
154 *
155 * .. Scalar Arguments ..
156  INTEGER incx,lda,n
157  CHARACTER diag,trans,uplo
158 * ..
159 * .. Array Arguments ..
160  DOUBLE PRECISION a(lda,*),x(*)
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  DOUBLE PRECISION zero
167  parameter(zero=0.0d+0)
168 * ..
169 * .. Local Scalars ..
170  DOUBLE PRECISION temp
171  INTEGER i,info,ix,j,jx,kx
172  LOGICAL nounit
173 * ..
174 * .. External Functions ..
175  LOGICAL lsame
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL xerbla
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC max
183 * ..
184 *
185 * Test the input parameters.
186 *
187  info = 0
188  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
189  info = 1
190  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
191  + .NOT.lsame(trans,'C')) THEN
192  info = 2
193  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
194  info = 3
195  ELSE IF (n.LT.0) THEN
196  info = 4
197  ELSE IF (lda.LT.max(1,n)) THEN
198  info = 6
199  ELSE IF (incx.EQ.0) THEN
200  info = 8
201  END IF
202  IF (info.NE.0) THEN
203  CALL xerbla('DTRMV ',info)
204  RETURN
205  END IF
206 *
207 * Quick return if possible.
208 *
209  IF (n.EQ.0) RETURN
210 *
211  nounit = lsame(diag,'N')
212 *
213 * Set up the start point in X if the increment is not unity. This
214 * will be ( N - 1 )*INCX too small for descending loops.
215 *
216  IF (incx.LE.0) THEN
217  kx = 1 - (n-1)*incx
218  ELSE IF (incx.NE.1) THEN
219  kx = 1
220  END IF
221 *
222 * Start the operations. In this version the elements of A are
223 * accessed sequentially with one pass through A.
224 *
225  IF (lsame(trans,'N')) THEN
226 *
227 * Form x := A*x.
228 *
229  IF (lsame(uplo,'U')) THEN
230  IF (incx.EQ.1) THEN
231  DO 20 j = 1,n
232  IF (x(j).NE.zero) THEN
233  temp = x(j)
234  DO 10 i = 1,j - 1
235  x(i) = x(i) + temp*a(i,j)
236  10 CONTINUE
237  IF (nounit) x(j) = x(j)*a(j,j)
238  END IF
239  20 CONTINUE
240  ELSE
241  jx = kx
242  DO 40 j = 1,n
243  IF (x(jx).NE.zero) THEN
244  temp = x(jx)
245  ix = kx
246  DO 30 i = 1,j - 1
247  x(ix) = x(ix) + temp*a(i,j)
248  ix = ix + incx
249  30 CONTINUE
250  IF (nounit) x(jx) = x(jx)*a(j,j)
251  END IF
252  jx = jx + incx
253  40 CONTINUE
254  END IF
255  ELSE
256  IF (incx.EQ.1) THEN
257  DO 60 j = n,1,-1
258  IF (x(j).NE.zero) THEN
259  temp = x(j)
260  DO 50 i = n,j + 1,-1
261  x(i) = x(i) + temp*a(i,j)
262  50 CONTINUE
263  IF (nounit) x(j) = x(j)*a(j,j)
264  END IF
265  60 CONTINUE
266  ELSE
267  kx = kx + (n-1)*incx
268  jx = kx
269  DO 80 j = n,1,-1
270  IF (x(jx).NE.zero) THEN
271  temp = x(jx)
272  ix = kx
273  DO 70 i = n,j + 1,-1
274  x(ix) = x(ix) + temp*a(i,j)
275  ix = ix - incx
276  70 CONTINUE
277  IF (nounit) x(jx) = x(jx)*a(j,j)
278  END IF
279  jx = jx - incx
280  80 CONTINUE
281  END IF
282  END IF
283  ELSE
284 *
285 * Form x := A**T*x.
286 *
287  IF (lsame(uplo,'U')) THEN
288  IF (incx.EQ.1) THEN
289  DO 100 j = n,1,-1
290  temp = x(j)
291  IF (nounit) temp = temp*a(j,j)
292  DO 90 i = j - 1,1,-1
293  temp = temp + a(i,j)*x(i)
294  90 CONTINUE
295  x(j) = temp
296  100 CONTINUE
297  ELSE
298  jx = kx + (n-1)*incx
299  DO 120 j = n,1,-1
300  temp = x(jx)
301  ix = jx
302  IF (nounit) temp = temp*a(j,j)
303  DO 110 i = j - 1,1,-1
304  ix = ix - incx
305  temp = temp + a(i,j)*x(ix)
306  110 CONTINUE
307  x(jx) = temp
308  jx = jx - incx
309  120 CONTINUE
310  END IF
311  ELSE
312  IF (incx.EQ.1) THEN
313  DO 140 j = 1,n
314  temp = x(j)
315  IF (nounit) temp = temp*a(j,j)
316  DO 130 i = j + 1,n
317  temp = temp + a(i,j)*x(i)
318  130 CONTINUE
319  x(j) = temp
320  140 CONTINUE
321  ELSE
322  jx = kx
323  DO 160 j = 1,n
324  temp = x(jx)
325  ix = jx
326  IF (nounit) temp = temp*a(j,j)
327  DO 150 i = j + 1,n
328  ix = ix + incx
329  temp = temp + a(i,j)*x(ix)
330  150 CONTINUE
331  x(jx) = temp
332  jx = jx + incx
333  160 CONTINUE
334  END IF
335  END IF
336  END IF
337 *
338  RETURN
339 *
340 * End of DTRMV .
341 *
342  END