LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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◆ ztpmv()

 subroutine ztpmv ( character UPLO, character TRANS, character DIAG, integer N, complex*16, dimension(*) AP, complex*16, dimension(*) X, integer INCX )

ZTPMV

Purpose:
``` ZTPMV  performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,   or   x := A**H*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**H*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 COMPLEX*16 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 COMPLEX*16 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.```
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 ztpmv.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 COMPLEX*16 AP(*),X(*)
153* ..
154*
155* =====================================================================
156*
157* .. Parameters ..
158 COMPLEX*16 ZERO
159 parameter(zero= (0.0d+0,0.0d+0))
160* ..
161* .. Local Scalars ..
162 COMPLEX*16 TEMP
163 INTEGER I,INFO,IX,J,JX,K,KK,KX
164 LOGICAL NOCONJ,NOUNIT
165* ..
166* .. External Functions ..
167 LOGICAL LSAME
168 EXTERNAL lsame
169* ..
170* .. External Subroutines ..
171 EXTERNAL xerbla
172* ..
173* .. Intrinsic Functions ..
174 INTRINSIC dconjg
175* ..
176*
177* Test the input parameters.
178*
179 info = 0
180 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
181 info = 1
182 ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
183 + .NOT.lsame(trans,'C')) THEN
184 info = 2
185 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
186 info = 3
187 ELSE IF (n.LT.0) THEN
188 info = 4
189 ELSE IF (incx.EQ.0) THEN
190 info = 7
191 END IF
192 IF (info.NE.0) THEN
193 CALL xerbla('ZTPMV ',info)
194 RETURN
195 END IF
196*
197* Quick return if possible.
198*
199 IF (n.EQ.0) RETURN
200*
201 noconj = lsame(trans,'T')
202 nounit = lsame(diag,'N')
203*
204* Set up the start point in X if the increment is not unity. This
205* will be ( N - 1 )*INCX too small for descending loops.
206*
207 IF (incx.LE.0) THEN
208 kx = 1 - (n-1)*incx
209 ELSE IF (incx.NE.1) THEN
210 kx = 1
211 END IF
212*
213* Start the operations. In this version the elements of AP are
214* accessed sequentially with one pass through AP.
215*
216 IF (lsame(trans,'N')) THEN
217*
218* Form x:= A*x.
219*
220 IF (lsame(uplo,'U')) THEN
221 kk = 1
222 IF (incx.EQ.1) THEN
223 DO 20 j = 1,n
224 IF (x(j).NE.zero) THEN
225 temp = x(j)
226 k = kk
227 DO 10 i = 1,j - 1
228 x(i) = x(i) + temp*ap(k)
229 k = k + 1
230 10 CONTINUE
231 IF (nounit) x(j) = x(j)*ap(kk+j-1)
232 END IF
233 kk = kk + j
234 20 CONTINUE
235 ELSE
236 jx = kx
237 DO 40 j = 1,n
238 IF (x(jx).NE.zero) THEN
239 temp = x(jx)
240 ix = kx
241 DO 30 k = kk,kk + j - 2
242 x(ix) = x(ix) + temp*ap(k)
243 ix = ix + incx
244 30 CONTINUE
245 IF (nounit) x(jx) = x(jx)*ap(kk+j-1)
246 END IF
247 jx = jx + incx
248 kk = kk + j
249 40 CONTINUE
250 END IF
251 ELSE
252 kk = (n* (n+1))/2
253 IF (incx.EQ.1) THEN
254 DO 60 j = n,1,-1
255 IF (x(j).NE.zero) THEN
256 temp = x(j)
257 k = kk
258 DO 50 i = n,j + 1,-1
259 x(i) = x(i) + temp*ap(k)
260 k = k - 1
261 50 CONTINUE
262 IF (nounit) x(j) = x(j)*ap(kk-n+j)
263 END IF
264 kk = kk - (n-j+1)
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 k = kk,kk - (n- (j+1)),-1
274 x(ix) = x(ix) + temp*ap(k)
275 ix = ix - incx
276 70 CONTINUE
277 IF (nounit) x(jx) = x(jx)*ap(kk-n+j)
278 END IF
279 jx = jx - incx
280 kk = kk - (n-j+1)
281 80 CONTINUE
282 END IF
283 END IF
284 ELSE
285*
286* Form x := A**T*x or x := A**H*x.
287*
288 IF (lsame(uplo,'U')) THEN
289 kk = (n* (n+1))/2
290 IF (incx.EQ.1) THEN
291 DO 110 j = n,1,-1
292 temp = x(j)
293 k = kk - 1
294 IF (noconj) THEN
295 IF (nounit) temp = temp*ap(kk)
296 DO 90 i = j - 1,1,-1
297 temp = temp + ap(k)*x(i)
298 k = k - 1
299 90 CONTINUE
300 ELSE
301 IF (nounit) temp = temp*dconjg(ap(kk))
302 DO 100 i = j - 1,1,-1
303 temp = temp + dconjg(ap(k))*x(i)
304 k = k - 1
305 100 CONTINUE
306 END IF
307 x(j) = temp
308 kk = kk - j
309 110 CONTINUE
310 ELSE
311 jx = kx + (n-1)*incx
312 DO 140 j = n,1,-1
313 temp = x(jx)
314 ix = jx
315 IF (noconj) THEN
316 IF (nounit) temp = temp*ap(kk)
317 DO 120 k = kk - 1,kk - j + 1,-1
318 ix = ix - incx
319 temp = temp + ap(k)*x(ix)
320 120 CONTINUE
321 ELSE
322 IF (nounit) temp = temp*dconjg(ap(kk))
323 DO 130 k = kk - 1,kk - j + 1,-1
324 ix = ix - incx
325 temp = temp + dconjg(ap(k))*x(ix)
326 130 CONTINUE
327 END IF
328 x(jx) = temp
329 jx = jx - incx
330 kk = kk - j
331 140 CONTINUE
332 END IF
333 ELSE
334 kk = 1
335 IF (incx.EQ.1) THEN
336 DO 170 j = 1,n
337 temp = x(j)
338 k = kk + 1
339 IF (noconj) THEN
340 IF (nounit) temp = temp*ap(kk)
341 DO 150 i = j + 1,n
342 temp = temp + ap(k)*x(i)
343 k = k + 1
344 150 CONTINUE
345 ELSE
346 IF (nounit) temp = temp*dconjg(ap(kk))
347 DO 160 i = j + 1,n
348 temp = temp + dconjg(ap(k))*x(i)
349 k = k + 1
350 160 CONTINUE
351 END IF
352 x(j) = temp
353 kk = kk + (n-j+1)
354 170 CONTINUE
355 ELSE
356 jx = kx
357 DO 200 j = 1,n
358 temp = x(jx)
359 ix = jx
360 IF (noconj) THEN
361 IF (nounit) temp = temp*ap(kk)
362 DO 180 k = kk + 1,kk + n - j
363 ix = ix + incx
364 temp = temp + ap(k)*x(ix)
365 180 CONTINUE
366 ELSE
367 IF (nounit) temp = temp*dconjg(ap(kk))
368 DO 190 k = kk + 1,kk + n - j
369 ix = ix + incx
370 temp = temp + dconjg(ap(k))*x(ix)
371 190 CONTINUE
372 END IF
373 x(jx) = temp
374 jx = jx + incx
375 kk = kk + (n-j+1)
376 200 CONTINUE
377 END IF
378 END IF
379 END IF
380*
381 RETURN
382*
383* End of ZTPMV
384*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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