 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ctpsv()

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

CTPSV

Purpose:
``` CTPSV  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 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 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 ctpsv.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 AP(*),X(*)
155* ..
156*
157* =====================================================================
158*
159* .. Parameters ..
160 COMPLEX ZERO
161 parameter(zero= (0.0e+0,0.0e+0))
162* ..
163* .. Local Scalars ..
164 COMPLEX 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 conjg
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. .NOT.lsame(trans,'T') .AND.
185 + .NOT.lsame(trans,'C')) THEN
186 info = 2
187 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
188 info = 3
189 ELSE IF (n.LT.0) THEN
190 info = 4
191 ELSE IF (incx.EQ.0) THEN
192 info = 7
193 END IF
194 IF (info.NE.0) THEN
195 CALL xerbla('CTPSV ',info)
196 RETURN
197 END IF
198*
199* Quick return if possible.
200*
201 IF (n.EQ.0) RETURN
202*
203 noconj = lsame(trans,'T')
204 nounit = lsame(diag,'N')
205*
206* Set up the start point in X if the increment is not unity. This
207* will be ( N - 1 )*INCX too small for descending loops.
208*
209 IF (incx.LE.0) THEN
210 kx = 1 - (n-1)*incx
211 ELSE IF (incx.NE.1) THEN
212 kx = 1
213 END IF
214*
215* Start the operations. In this version the elements of AP are
216* accessed sequentially with one pass through AP.
217*
218 IF (lsame(trans,'N')) THEN
219*
220* Form x := inv( A )*x.
221*
222 IF (lsame(uplo,'U')) THEN
223 kk = (n* (n+1))/2
224 IF (incx.EQ.1) THEN
225 DO 20 j = n,1,-1
226 IF (x(j).NE.zero) THEN
227 IF (nounit) x(j) = x(j)/ap(kk)
228 temp = x(j)
229 k = kk - 1
230 DO 10 i = j - 1,1,-1
231 x(i) = x(i) - temp*ap(k)
232 k = k - 1
233 10 CONTINUE
234 END IF
235 kk = kk - j
236 20 CONTINUE
237 ELSE
238 jx = kx + (n-1)*incx
239 DO 40 j = n,1,-1
240 IF (x(jx).NE.zero) THEN
241 IF (nounit) x(jx) = x(jx)/ap(kk)
242 temp = x(jx)
243 ix = jx
244 DO 30 k = kk - 1,kk - j + 1,-1
245 ix = ix - incx
246 x(ix) = x(ix) - temp*ap(k)
247 30 CONTINUE
248 END IF
249 jx = jx - incx
250 kk = kk - j
251 40 CONTINUE
252 END IF
253 ELSE
254 kk = 1
255 IF (incx.EQ.1) THEN
256 DO 60 j = 1,n
257 IF (x(j).NE.zero) THEN
258 IF (nounit) x(j) = x(j)/ap(kk)
259 temp = x(j)
260 k = kk + 1
261 DO 50 i = j + 1,n
262 x(i) = x(i) - temp*ap(k)
263 k = k + 1
264 50 CONTINUE
265 END IF
266 kk = kk + (n-j+1)
267 60 CONTINUE
268 ELSE
269 jx = kx
270 DO 80 j = 1,n
271 IF (x(jx).NE.zero) THEN
272 IF (nounit) x(jx) = x(jx)/ap(kk)
273 temp = x(jx)
274 ix = jx
275 DO 70 k = kk + 1,kk + n - j
276 ix = ix + incx
277 x(ix) = x(ix) - temp*ap(k)
278 70 CONTINUE
279 END IF
280 jx = jx + incx
281 kk = kk + (n-j+1)
282 80 CONTINUE
283 END IF
284 END IF
285 ELSE
286*
287* Form x := inv( A**T )*x or x := inv( A**H )*x.
288*
289 IF (lsame(uplo,'U')) THEN
290 kk = 1
291 IF (incx.EQ.1) THEN
292 DO 110 j = 1,n
293 temp = x(j)
294 k = kk
295 IF (noconj) THEN
296 DO 90 i = 1,j - 1
297 temp = temp - ap(k)*x(i)
298 k = k + 1
299 90 CONTINUE
300 IF (nounit) temp = temp/ap(kk+j-1)
301 ELSE
302 DO 100 i = 1,j - 1
303 temp = temp - conjg(ap(k))*x(i)
304 k = k + 1
305 100 CONTINUE
306 IF (nounit) temp = temp/conjg(ap(kk+j-1))
307 END IF
308 x(j) = temp
309 kk = kk + j
310 110 CONTINUE
311 ELSE
312 jx = kx
313 DO 140 j = 1,n
314 temp = x(jx)
315 ix = kx
316 IF (noconj) THEN
317 DO 120 k = kk,kk + j - 2
318 temp = temp - ap(k)*x(ix)
319 ix = ix + incx
320 120 CONTINUE
321 IF (nounit) temp = temp/ap(kk+j-1)
322 ELSE
323 DO 130 k = kk,kk + j - 2
324 temp = temp - conjg(ap(k))*x(ix)
325 ix = ix + incx
326 130 CONTINUE
327 IF (nounit) temp = temp/conjg(ap(kk+j-1))
328 END IF
329 x(jx) = temp
330 jx = jx + incx
331 kk = kk + j
332 140 CONTINUE
333 END IF
334 ELSE
335 kk = (n* (n+1))/2
336 IF (incx.EQ.1) THEN
337 DO 170 j = n,1,-1
338 temp = x(j)
339 k = kk
340 IF (noconj) THEN
341 DO 150 i = n,j + 1,-1
342 temp = temp - ap(k)*x(i)
343 k = k - 1
344 150 CONTINUE
345 IF (nounit) temp = temp/ap(kk-n+j)
346 ELSE
347 DO 160 i = n,j + 1,-1
348 temp = temp - conjg(ap(k))*x(i)
349 k = k - 1
350 160 CONTINUE
351 IF (nounit) temp = temp/conjg(ap(kk-n+j))
352 END IF
353 x(j) = temp
354 kk = kk - (n-j+1)
355 170 CONTINUE
356 ELSE
357 kx = kx + (n-1)*incx
358 jx = kx
359 DO 200 j = n,1,-1
360 temp = x(jx)
361 ix = kx
362 IF (noconj) THEN
363 DO 180 k = kk,kk - (n- (j+1)),-1
364 temp = temp - ap(k)*x(ix)
365 ix = ix - incx
366 180 CONTINUE
367 IF (nounit) temp = temp/ap(kk-n+j)
368 ELSE
369 DO 190 k = kk,kk - (n- (j+1)),-1
370 temp = temp - conjg(ap(k))*x(ix)
371 ix = ix - incx
372 190 CONTINUE
373 IF (nounit) temp = temp/conjg(ap(kk-n+j))
374 END IF
375 x(jx) = temp
376 jx = jx - incx
377 kk = kk - (n-j+1)
378 200 CONTINUE
379 END IF
380 END IF
381 END IF
382*
383 RETURN
384*
385* End of CTPSV
386*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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