LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dtpmv.f
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1*> \brief \b DTPMV
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 DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
12*
13* .. Scalar Arguments ..
14* INTEGER INCX,N
15* CHARACTER DIAG,TRANS,UPLO
16* ..
17* .. Array Arguments ..
18* DOUBLE PRECISION AP(*),X(*)
19* ..
20*
21*
22*> \par Purpose:
23* =============
24*>
25*> \verbatim
26*>
27*> DTPMV 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, supplied in packed form.
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] AP
82*> \verbatim
83*> AP is DOUBLE PRECISION array, dimension at least
84*> ( ( n*( n + 1 ) )/2 ).
85*> Before entry with UPLO = 'U' or 'u', the array AP must
86*> contain the upper triangular matrix packed sequentially,
87*> column by column, so that AP( 1 ) contains a( 1, 1 ),
88*> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
89*> respectively, and so on.
90*> Before entry with UPLO = 'L' or 'l', the array AP must
91*> contain the lower triangular matrix packed sequentially,
92*> column by column, so that AP( 1 ) contains a( 1, 1 ),
93*> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
94*> respectively, and so on.
95*> Note that when DIAG = 'U' or 'u', the diagonal elements of
96*> A are not referenced, but are assumed to be unity.
97*> \endverbatim
98*>
99*> \param[in,out] X
100*> \verbatim
101*> X is DOUBLE PRECISION array, dimension at least
102*> ( 1 + ( n - 1 )*abs( INCX ) ).
103*> Before entry, the incremented array X must contain the n
104*> element vector x. On exit, X is overwritten with the
105*> transformed vector x.
106*> \endverbatim
107*>
108*> \param[in] INCX
109*> \verbatim
110*> INCX is INTEGER
111*> On entry, INCX specifies the increment for the elements of
112*> X. INCX must not be zero.
113*> \endverbatim
114*
115* Authors:
116* ========
117*
118*> \author Univ. of Tennessee
119*> \author Univ. of California Berkeley
120*> \author Univ. of Colorado Denver
121*> \author NAG Ltd.
122*
123*> \ingroup double_blas_level2
124*
125*> \par Further Details:
126* =====================
127*>
128*> \verbatim
129*>
130*> Level 2 Blas routine.
131*> The vector and matrix arguments are not referenced when N = 0, or M = 0
132*>
133*> -- Written on 22-October-1986.
134*> Jack Dongarra, Argonne National Lab.
135*> Jeremy Du Croz, Nag Central Office.
136*> Sven Hammarling, Nag Central Office.
137*> Richard Hanson, Sandia National Labs.
138*> \endverbatim
139*>
140* =====================================================================
141 SUBROUTINE dtpmv(UPLO,TRANS,DIAG,N,AP,X,INCX)
142*
143* -- Reference BLAS level2 routine --
144* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
145* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146*
147* .. Scalar Arguments ..
148 INTEGER INCX,N
149 CHARACTER DIAG,TRANS,UPLO
150* ..
151* .. Array Arguments ..
152 DOUBLE PRECISION AP(*),X(*)
153* ..
154*
155* =====================================================================
156*
157* .. Parameters ..
158 DOUBLE PRECISION ZERO
159 parameter(zero=0.0d+0)
160* ..
161* .. Local Scalars ..
162 DOUBLE PRECISION TEMP
163 INTEGER I,INFO,IX,J,JX,K,KK,KX
164 LOGICAL NOUNIT
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 EXTERNAL lsame
169* ..
170* .. External Subroutines ..
171 EXTERNAL xerbla
172* ..
173*
174* Test the input parameters.
175*
176 info = 0
177 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
178 info = 1
179 ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
180 + .NOT.lsame(trans,'C')) THEN
181 info = 2
182 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
183 info = 3
184 ELSE IF (n.LT.0) THEN
185 info = 4
186 ELSE IF (incx.EQ.0) THEN
187 info = 7
188 END IF
189 IF (info.NE.0) THEN
190 CALL xerbla('DTPMV ',info)
191 RETURN
192 END IF
193*
194* Quick return if possible.
195*
196 IF (n.EQ.0) RETURN
197*
198 nounit = lsame(diag,'N')
199*
200* Set up the start point in X if the increment is not unity. This
201* will be ( N - 1 )*INCX too small for descending loops.
202*
203 IF (incx.LE.0) THEN
204 kx = 1 - (n-1)*incx
205 ELSE IF (incx.NE.1) THEN
206 kx = 1
207 END IF
208*
209* Start the operations. In this version the elements of AP are
210* accessed sequentially with one pass through AP.
211*
212 IF (lsame(trans,'N')) THEN
213*
214* Form x:= A*x.
215*
216 IF (lsame(uplo,'U')) THEN
217 kk = 1
218 IF (incx.EQ.1) THEN
219 DO 20 j = 1,n
220 IF (x(j).NE.zero) THEN
221 temp = x(j)
222 k = kk
223 DO 10 i = 1,j - 1
224 x(i) = x(i) + temp*ap(k)
225 k = k + 1
226 10 CONTINUE
227 IF (nounit) x(j) = x(j)*ap(kk+j-1)
228 END IF
229 kk = kk + j
230 20 CONTINUE
231 ELSE
232 jx = kx
233 DO 40 j = 1,n
234 IF (x(jx).NE.zero) THEN
235 temp = x(jx)
236 ix = kx
237 DO 30 k = kk,kk + j - 2
238 x(ix) = x(ix) + temp*ap(k)
239 ix = ix + incx
240 30 CONTINUE
241 IF (nounit) x(jx) = x(jx)*ap(kk+j-1)
242 END IF
243 jx = jx + incx
244 kk = kk + j
245 40 CONTINUE
246 END IF
247 ELSE
248 kk = (n* (n+1))/2
249 IF (incx.EQ.1) THEN
250 DO 60 j = n,1,-1
251 IF (x(j).NE.zero) THEN
252 temp = x(j)
253 k = kk
254 DO 50 i = n,j + 1,-1
255 x(i) = x(i) + temp*ap(k)
256 k = k - 1
257 50 CONTINUE
258 IF (nounit) x(j) = x(j)*ap(kk-n+j)
259 END IF
260 kk = kk - (n-j+1)
261 60 CONTINUE
262 ELSE
263 kx = kx + (n-1)*incx
264 jx = kx
265 DO 80 j = n,1,-1
266 IF (x(jx).NE.zero) THEN
267 temp = x(jx)
268 ix = kx
269 DO 70 k = kk,kk - (n- (j+1)),-1
270 x(ix) = x(ix) + temp*ap(k)
271 ix = ix - incx
272 70 CONTINUE
273 IF (nounit) x(jx) = x(jx)*ap(kk-n+j)
274 END IF
275 jx = jx - incx
276 kk = kk - (n-j+1)
277 80 CONTINUE
278 END IF
279 END IF
280 ELSE
281*
282* Form x := A**T*x.
283*
284 IF (lsame(uplo,'U')) THEN
285 kk = (n* (n+1))/2
286 IF (incx.EQ.1) THEN
287 DO 100 j = n,1,-1
288 temp = x(j)
289 IF (nounit) temp = temp*ap(kk)
290 k = kk - 1
291 DO 90 i = j - 1,1,-1
292 temp = temp + ap(k)*x(i)
293 k = k - 1
294 90 CONTINUE
295 x(j) = temp
296 kk = kk - j
297 100 CONTINUE
298 ELSE
299 jx = kx + (n-1)*incx
300 DO 120 j = n,1,-1
301 temp = x(jx)
302 ix = jx
303 IF (nounit) temp = temp*ap(kk)
304 DO 110 k = kk - 1,kk - j + 1,-1
305 ix = ix - incx
306 temp = temp + ap(k)*x(ix)
307 110 CONTINUE
308 x(jx) = temp
309 jx = jx - incx
310 kk = kk - j
311 120 CONTINUE
312 END IF
313 ELSE
314 kk = 1
315 IF (incx.EQ.1) THEN
316 DO 140 j = 1,n
317 temp = x(j)
318 IF (nounit) temp = temp*ap(kk)
319 k = kk + 1
320 DO 130 i = j + 1,n
321 temp = temp + ap(k)*x(i)
322 k = k + 1
323 130 CONTINUE
324 x(j) = temp
325 kk = kk + (n-j+1)
326 140 CONTINUE
327 ELSE
328 jx = kx
329 DO 160 j = 1,n
330 temp = x(jx)
331 ix = jx
332 IF (nounit) temp = temp*ap(kk)
333 DO 150 k = kk + 1,kk + n - j
334 ix = ix + incx
335 temp = temp + ap(k)*x(ix)
336 150 CONTINUE
337 x(jx) = temp
338 jx = jx + incx
339 kk = kk + (n-j+1)
340 160 CONTINUE
341 END IF
342 END IF
343 END IF
344*
345 RETURN
346*
347* End of DTPMV
348*
349 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142