LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dtpmv()

subroutine dtpmv ( character uplo,
character trans,
character diag,
integer n,
double precision, dimension(*) ap,
double precision, dimension(*) x,
integer incx )

DTPMV

Purpose:
!>
!> DTPMV  performs one of the matrix-vector operations
!>
!>    x := A*x,   or   x := A**T*x,
!>
!> where x is an n element vector and  A is an n by n unit, or non-unit,
!> upper or lower triangular matrix, supplied in packed form.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the matrix is an upper or
!>           lower triangular matrix as follows:
!>
!>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
!>
!>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
!>
[in]TRANS
!>          TRANS is CHARACTER*1
!>           On entry, TRANS specifies the operation to be performed as
!>           follows:
!>
!>              TRANS = 'N' or 'n'   x := A*x.
!>
!>              TRANS = 'T' or 't'   x := A**T*x.
!>
!>              TRANS = 'C' or 'c'   x := A**T*x.
!>
[in]DIAG
!>          DIAG is CHARACTER*1
!>           On entry, DIAG specifies whether or not A is unit
!>           triangular as follows:
!>
!>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
!>
!>              DIAG = 'N' or 'n'   A is not assumed to be unit
!>                                  triangular.
!>
[in]N
!>          N is INTEGER
!>           On entry, N specifies the order of the matrix A.
!>           N must be at least zero.
!>
[in]AP
!>          AP is DOUBLE PRECISION array, dimension at least
!>           ( ( n*( n + 1 ) )/2 ).
!>           Before entry with  UPLO = 'U' or 'u', the array AP must
!>           contain the upper triangular matrix packed sequentially,
!>           column by column, so that AP( 1 ) contains a( 1, 1 ),
!>           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
!>           respectively, and so on.
!>           Before entry with UPLO = 'L' or 'l', the array AP must
!>           contain the lower triangular matrix packed sequentially,
!>           column by column, so that AP( 1 ) contains a( 1, 1 ),
!>           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
!>           respectively, and so on.
!>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
!>           A are not referenced, but are assumed to be unity.
!>
[in,out]X
!>          X is DOUBLE PRECISION array, dimension at least
!>           ( 1 + ( n - 1 )*abs( INCX ) ).
!>           Before entry, the incremented array X must contain the n
!>           element vector x. On exit, X is overwritten with the
!>           transformed vector x.
!>
[in]INCX
!>          INCX is INTEGER
!>           On entry, INCX specifies the increment for the elements of
!>           X. INCX must not be zero.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  Level 2 Blas routine.
!>  The vector and matrix arguments are not referenced when N = 0, or M = 0
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>

Definition at line 141 of file dtpmv.f.

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.
180 + .NOT.lsame(trans,'T') .AND.
181 + .NOT.lsame(trans,'C')) THEN
182 info = 2
183 ELSE IF (.NOT.lsame(diag,'U') .AND.
184 + .NOT.lsame(diag,'N')) THEN
185 info = 3
186 ELSE IF (n.LT.0) THEN
187 info = 4
188 ELSE IF (incx.EQ.0) THEN
189 info = 7
190 END IF
191 IF (info.NE.0) THEN
192 CALL xerbla('DTPMV ',info)
193 RETURN
194 END IF
195*
196* Quick return if possible.
197*
198 IF (n.EQ.0) RETURN
199*
200 nounit = lsame(diag,'N')
201*
202* Set up the start point in X if the increment is not unity. This
203* will be ( N - 1 )*INCX too small for descending loops.
204*
205 IF (incx.LE.0) THEN
206 kx = 1 - (n-1)*incx
207 ELSE IF (incx.NE.1) THEN
208 kx = 1
209 END IF
210*
211* Start the operations. In this version the elements of AP are
212* accessed sequentially with one pass through AP.
213*
214 IF (lsame(trans,'N')) THEN
215*
216* Form x:= A*x.
217*
218 IF (lsame(uplo,'U')) THEN
219 kk = 1
220 IF (incx.EQ.1) THEN
221 DO 20 j = 1,n
222 IF (x(j).NE.zero) THEN
223 temp = x(j)
224 k = kk
225 DO 10 i = 1,j - 1
226 x(i) = x(i) + temp*ap(k)
227 k = k + 1
228 10 CONTINUE
229 IF (nounit) x(j) = x(j)*ap(kk+j-1)
230 END IF
231 kk = kk + j
232 20 CONTINUE
233 ELSE
234 jx = kx
235 DO 40 j = 1,n
236 IF (x(jx).NE.zero) THEN
237 temp = x(jx)
238 ix = kx
239 DO 30 k = kk,kk + j - 2
240 x(ix) = x(ix) + temp*ap(k)
241 ix = ix + incx
242 30 CONTINUE
243 IF (nounit) x(jx) = x(jx)*ap(kk+j-1)
244 END IF
245 jx = jx + incx
246 kk = kk + j
247 40 CONTINUE
248 END IF
249 ELSE
250 kk = (n* (n+1))/2
251 IF (incx.EQ.1) THEN
252 DO 60 j = n,1,-1
253 IF (x(j).NE.zero) THEN
254 temp = x(j)
255 k = kk
256 DO 50 i = n,j + 1,-1
257 x(i) = x(i) + temp*ap(k)
258 k = k - 1
259 50 CONTINUE
260 IF (nounit) x(j) = x(j)*ap(kk-n+j)
261 END IF
262 kk = kk - (n-j+1)
263 60 CONTINUE
264 ELSE
265 kx = kx + (n-1)*incx
266 jx = kx
267 DO 80 j = n,1,-1
268 IF (x(jx).NE.zero) THEN
269 temp = x(jx)
270 ix = kx
271 DO 70 k = kk,kk - (n- (j+1)),-1
272 x(ix) = x(ix) + temp*ap(k)
273 ix = ix - incx
274 70 CONTINUE
275 IF (nounit) x(jx) = x(jx)*ap(kk-n+j)
276 END IF
277 jx = jx - incx
278 kk = kk - (n-j+1)
279 80 CONTINUE
280 END IF
281 END IF
282 ELSE
283*
284* Form x := A**T*x.
285*
286 IF (lsame(uplo,'U')) THEN
287 kk = (n* (n+1))/2
288 IF (incx.EQ.1) THEN
289 DO 100 j = n,1,-1
290 temp = x(j)
291 IF (nounit) temp = temp*ap(kk)
292 k = kk - 1
293 DO 90 i = j - 1,1,-1
294 temp = temp + ap(k)*x(i)
295 k = k - 1
296 90 CONTINUE
297 x(j) = temp
298 kk = kk - j
299 100 CONTINUE
300 ELSE
301 jx = kx + (n-1)*incx
302 DO 120 j = n,1,-1
303 temp = x(jx)
304 ix = jx
305 IF (nounit) temp = temp*ap(kk)
306 DO 110 k = kk - 1,kk - j + 1,-1
307 ix = ix - incx
308 temp = temp + ap(k)*x(ix)
309 110 CONTINUE
310 x(jx) = temp
311 jx = jx - incx
312 kk = kk - j
313 120 CONTINUE
314 END IF
315 ELSE
316 kk = 1
317 IF (incx.EQ.1) THEN
318 DO 140 j = 1,n
319 temp = x(j)
320 IF (nounit) temp = temp*ap(kk)
321 k = kk + 1
322 DO 130 i = j + 1,n
323 temp = temp + ap(k)*x(i)
324 k = k + 1
325 130 CONTINUE
326 x(j) = temp
327 kk = kk + (n-j+1)
328 140 CONTINUE
329 ELSE
330 jx = kx
331 DO 160 j = 1,n
332 temp = x(jx)
333 ix = jx
334 IF (nounit) temp = temp*ap(kk)
335 DO 150 k = kk + 1,kk + n - j
336 ix = ix + incx
337 temp = temp + ap(k)*x(ix)
338 150 CONTINUE
339 x(jx) = temp
340 jx = jx + incx
341 kk = kk + (n-j+1)
342 160 CONTINUE
343 END IF
344 END IF
345 END IF
346*
347 RETURN
348*
349* End of DTPMV
350*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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