LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dtpsv()

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

DTPSV

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

A*x = b,   or   A**T*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**T*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 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 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 dtpsv.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 DOUBLE PRECISION AP(*),X(*)
155* ..
156*
157* =====================================================================
158*
159* .. Parameters ..
160 DOUBLE PRECISION ZERO
161 parameter(zero=0.0d+0)
162* ..
163* .. Local Scalars ..
164 DOUBLE PRECISION TEMP
165 INTEGER I,INFO,IX,J,JX,K,KK,KX
166 LOGICAL NOUNIT
167* ..
168* .. External Functions ..
169 LOGICAL LSAME
170 EXTERNAL lsame
171* ..
172* .. External Subroutines ..
173 EXTERNAL xerbla
174* ..
175*
176* Test the input parameters.
177*
178 info = 0
179 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
180 info = 1
181 ELSE IF (.NOT.lsame(trans,'N') .AND.
182 + .NOT.lsame(trans,'T') .AND.
183 + .NOT.lsame(trans,'C')) THEN
184 info = 2
185 ELSE IF (.NOT.lsame(diag,'U') .AND.
186 + .NOT.lsame(diag,'N')) THEN
187 info = 3
188 ELSE IF (n.LT.0) THEN
189 info = 4
190 ELSE IF (incx.EQ.0) THEN
191 info = 7
192 END IF
193 IF (info.NE.0) THEN
194 CALL xerbla('DTPSV ',info)
195 RETURN
196 END IF
197*
198* Quick return if possible.
199*
200 IF (n.EQ.0) RETURN
201*
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 := inv( A )*x.
219*
220 IF (lsame(uplo,'U')) THEN
221 kk = (n* (n+1))/2
222 IF (incx.EQ.1) THEN
223 DO 20 j = n,1,-1
224 IF (x(j).NE.zero) THEN
225 IF (nounit) x(j) = x(j)/ap(kk)
226 temp = x(j)
227 k = kk - 1
228 DO 10 i = j - 1,1,-1
229 x(i) = x(i) - temp*ap(k)
230 k = k - 1
231 10 CONTINUE
232 END IF
233 kk = kk - j
234 20 CONTINUE
235 ELSE
236 jx = kx + (n-1)*incx
237 DO 40 j = n,1,-1
238 IF (x(jx).NE.zero) THEN
239 IF (nounit) x(jx) = x(jx)/ap(kk)
240 temp = x(jx)
241 ix = jx
242 DO 30 k = kk - 1,kk - j + 1,-1
243 ix = ix - incx
244 x(ix) = x(ix) - temp*ap(k)
245 30 CONTINUE
246 END IF
247 jx = jx - incx
248 kk = kk - j
249 40 CONTINUE
250 END IF
251 ELSE
252 kk = 1
253 IF (incx.EQ.1) THEN
254 DO 60 j = 1,n
255 IF (x(j).NE.zero) THEN
256 IF (nounit) x(j) = x(j)/ap(kk)
257 temp = x(j)
258 k = kk + 1
259 DO 50 i = j + 1,n
260 x(i) = x(i) - temp*ap(k)
261 k = k + 1
262 50 CONTINUE
263 END IF
264 kk = kk + (n-j+1)
265 60 CONTINUE
266 ELSE
267 jx = kx
268 DO 80 j = 1,n
269 IF (x(jx).NE.zero) THEN
270 IF (nounit) x(jx) = x(jx)/ap(kk)
271 temp = x(jx)
272 ix = jx
273 DO 70 k = kk + 1,kk + n - j
274 ix = ix + incx
275 x(ix) = x(ix) - temp*ap(k)
276 70 CONTINUE
277 END IF
278 jx = jx + incx
279 kk = kk + (n-j+1)
280 80 CONTINUE
281 END IF
282 END IF
283 ELSE
284*
285* Form x := inv( A**T )*x.
286*
287 IF (lsame(uplo,'U')) THEN
288 kk = 1
289 IF (incx.EQ.1) THEN
290 DO 100 j = 1,n
291 temp = x(j)
292 k = kk
293 DO 90 i = 1,j - 1
294 temp = temp - ap(k)*x(i)
295 k = k + 1
296 90 CONTINUE
297 IF (nounit) temp = temp/ap(kk+j-1)
298 x(j) = temp
299 kk = kk + j
300 100 CONTINUE
301 ELSE
302 jx = kx
303 DO 120 j = 1,n
304 temp = x(jx)
305 ix = kx
306 DO 110 k = kk,kk + j - 2
307 temp = temp - ap(k)*x(ix)
308 ix = ix + incx
309 110 CONTINUE
310 IF (nounit) temp = temp/ap(kk+j-1)
311 x(jx) = temp
312 jx = jx + incx
313 kk = kk + j
314 120 CONTINUE
315 END IF
316 ELSE
317 kk = (n* (n+1))/2
318 IF (incx.EQ.1) THEN
319 DO 140 j = n,1,-1
320 temp = x(j)
321 k = kk
322 DO 130 i = n,j + 1,-1
323 temp = temp - ap(k)*x(i)
324 k = k - 1
325 130 CONTINUE
326 IF (nounit) temp = temp/ap(kk-n+j)
327 x(j) = temp
328 kk = kk - (n-j+1)
329 140 CONTINUE
330 ELSE
331 kx = kx + (n-1)*incx
332 jx = kx
333 DO 160 j = n,1,-1
334 temp = x(jx)
335 ix = kx
336 DO 150 k = kk,kk - (n- (j+1)),-1
337 temp = temp - ap(k)*x(ix)
338 ix = ix - incx
339 150 CONTINUE
340 IF (nounit) temp = temp/ap(kk-n+j)
341 x(jx) = temp
342 jx = jx - incx
343 kk = kk - (n-j+1)
344 160 CONTINUE
345 END IF
346 END IF
347 END IF
348*
349 RETURN
350*
351* End of DTPSV
352*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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