LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ ztpsv()

 subroutine ztpsv ( character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx )

ZTPSV

Purpose:
``` ZTPSV  solves one of the systems of equations

A*x = b,   or   A**T*x = b,   or   A**H*x = b,

where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix, supplied in packed form.

No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.```
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 equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' A**T*x = b. TRANS = 'C' or 'c' A**H*x = b.``` [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 right-hand side vector b. On exit, X is overwritten with the solution 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.

-- 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 143 of file ztpsv.f.

144*
145* -- Reference BLAS level2 routine --
146* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
147* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148*
149* .. Scalar Arguments ..
150 INTEGER INCX,N
151 CHARACTER DIAG,TRANS,UPLO
152* ..
153* .. Array Arguments ..
154 COMPLEX*16 AP(*),X(*)
155* ..
156*
157* =====================================================================
158*
159* .. Parameters ..
160 COMPLEX*16 ZERO
161 parameter(zero= (0.0d+0,0.0d+0))
162* ..
163* .. Local Scalars ..
164 COMPLEX*16 TEMP
165 INTEGER I,INFO,IX,J,JX,K,KK,KX
166 LOGICAL NOCONJ,NOUNIT
167* ..
168* .. External Functions ..
169 LOGICAL LSAME
170 EXTERNAL lsame
171* ..
172* .. External Subroutines ..
173 EXTERNAL xerbla
174* ..
175* .. Intrinsic Functions ..
176 INTRINSIC dconjg
177* ..
178*
179* Test the input parameters.
180*
181 info = 0
182 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
183 info = 1
184 ELSE IF (.NOT.lsame(trans,'N') .AND.
185 + .NOT.lsame(trans,'T') .AND.
186 + .NOT.lsame(trans,'C')) THEN
187 info = 2
188 ELSE IF (.NOT.lsame(diag,'U') .AND.
189 + .NOT.lsame(diag,'N')) THEN
190 info = 3
191 ELSE IF (n.LT.0) THEN
192 info = 4
193 ELSE IF (incx.EQ.0) THEN
194 info = 7
195 END IF
196 IF (info.NE.0) THEN
197 CALL xerbla('ZTPSV ',info)
198 RETURN
199 END IF
200*
201* Quick return if possible.
202*
203 IF (n.EQ.0) RETURN
204*
205 noconj = lsame(trans,'T')
206 nounit = lsame(diag,'N')
207*
208* Set up the start point in X if the increment is not unity. This
209* will be ( N - 1 )*INCX too small for descending loops.
210*
211 IF (incx.LE.0) THEN
212 kx = 1 - (n-1)*incx
213 ELSE IF (incx.NE.1) THEN
214 kx = 1
215 END IF
216*
217* Start the operations. In this version the elements of AP are
218* accessed sequentially with one pass through AP.
219*
220 IF (lsame(trans,'N')) THEN
221*
222* Form x := inv( A )*x.
223*
224 IF (lsame(uplo,'U')) THEN
225 kk = (n* (n+1))/2
226 IF (incx.EQ.1) THEN
227 DO 20 j = n,1,-1
228 IF (x(j).NE.zero) THEN
229 IF (nounit) x(j) = x(j)/ap(kk)
230 temp = x(j)
231 k = kk - 1
232 DO 10 i = j - 1,1,-1
233 x(i) = x(i) - temp*ap(k)
234 k = k - 1
235 10 CONTINUE
236 END IF
237 kk = kk - j
238 20 CONTINUE
239 ELSE
240 jx = kx + (n-1)*incx
241 DO 40 j = n,1,-1
242 IF (x(jx).NE.zero) THEN
243 IF (nounit) x(jx) = x(jx)/ap(kk)
244 temp = x(jx)
245 ix = jx
246 DO 30 k = kk - 1,kk - j + 1,-1
247 ix = ix - incx
248 x(ix) = x(ix) - temp*ap(k)
249 30 CONTINUE
250 END IF
251 jx = jx - incx
252 kk = kk - j
253 40 CONTINUE
254 END IF
255 ELSE
256 kk = 1
257 IF (incx.EQ.1) THEN
258 DO 60 j = 1,n
259 IF (x(j).NE.zero) THEN
260 IF (nounit) x(j) = x(j)/ap(kk)
261 temp = x(j)
262 k = kk + 1
263 DO 50 i = j + 1,n
264 x(i) = x(i) - temp*ap(k)
265 k = k + 1
266 50 CONTINUE
267 END IF
268 kk = kk + (n-j+1)
269 60 CONTINUE
270 ELSE
271 jx = kx
272 DO 80 j = 1,n
273 IF (x(jx).NE.zero) THEN
274 IF (nounit) x(jx) = x(jx)/ap(kk)
275 temp = x(jx)
276 ix = jx
277 DO 70 k = kk + 1,kk + n - j
278 ix = ix + incx
279 x(ix) = x(ix) - temp*ap(k)
280 70 CONTINUE
281 END IF
282 jx = jx + incx
283 kk = kk + (n-j+1)
284 80 CONTINUE
285 END IF
286 END IF
287 ELSE
288*
289* Form x := inv( A**T )*x or x := inv( A**H )*x.
290*
291 IF (lsame(uplo,'U')) THEN
292 kk = 1
293 IF (incx.EQ.1) THEN
294 DO 110 j = 1,n
295 temp = x(j)
296 k = kk
297 IF (noconj) THEN
298 DO 90 i = 1,j - 1
299 temp = temp - ap(k)*x(i)
300 k = k + 1
301 90 CONTINUE
302 IF (nounit) temp = temp/ap(kk+j-1)
303 ELSE
304 DO 100 i = 1,j - 1
305 temp = temp - dconjg(ap(k))*x(i)
306 k = k + 1
307 100 CONTINUE
308 IF (nounit) temp = temp/dconjg(ap(kk+j-1))
309 END IF
310 x(j) = temp
311 kk = kk + j
312 110 CONTINUE
313 ELSE
314 jx = kx
315 DO 140 j = 1,n
316 temp = x(jx)
317 ix = kx
318 IF (noconj) THEN
319 DO 120 k = kk,kk + j - 2
320 temp = temp - ap(k)*x(ix)
321 ix = ix + incx
322 120 CONTINUE
323 IF (nounit) temp = temp/ap(kk+j-1)
324 ELSE
325 DO 130 k = kk,kk + j - 2
326 temp = temp - dconjg(ap(k))*x(ix)
327 ix = ix + incx
328 130 CONTINUE
329 IF (nounit) temp = temp/dconjg(ap(kk+j-1))
330 END IF
331 x(jx) = temp
332 jx = jx + incx
333 kk = kk + j
334 140 CONTINUE
335 END IF
336 ELSE
337 kk = (n* (n+1))/2
338 IF (incx.EQ.1) THEN
339 DO 170 j = n,1,-1
340 temp = x(j)
341 k = kk
342 IF (noconj) THEN
343 DO 150 i = n,j + 1,-1
344 temp = temp - ap(k)*x(i)
345 k = k - 1
346 150 CONTINUE
347 IF (nounit) temp = temp/ap(kk-n+j)
348 ELSE
349 DO 160 i = n,j + 1,-1
350 temp = temp - dconjg(ap(k))*x(i)
351 k = k - 1
352 160 CONTINUE
353 IF (nounit) temp = temp/dconjg(ap(kk-n+j))
354 END IF
355 x(j) = temp
356 kk = kk - (n-j+1)
357 170 CONTINUE
358 ELSE
359 kx = kx + (n-1)*incx
360 jx = kx
361 DO 200 j = n,1,-1
362 temp = x(jx)
363 ix = kx
364 IF (noconj) THEN
365 DO 180 k = kk,kk - (n- (j+1)),-1
366 temp = temp - ap(k)*x(ix)
367 ix = ix - incx
368 180 CONTINUE
369 IF (nounit) temp = temp/ap(kk-n+j)
370 ELSE
371 DO 190 k = kk,kk - (n- (j+1)),-1
372 temp = temp - dconjg(ap(k))*x(ix)
373 ix = ix - incx
374 190 CONTINUE
375 IF (nounit) temp = temp/dconjg(ap(kk-n+j))
376 END IF
377 x(jx) = temp
378 jx = jx - incx
379 kk = kk - (n-j+1)
380 200 CONTINUE
381 END IF
382 END IF
383 END IF
384*
385 RETURN
386*
387* End of ZTPSV
388*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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