LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ ctrsv()

subroutine ctrsv ( character  UPLO,
character  TRANS,
character  DIAG,
integer  N,
complex, dimension(lda,*)  A,
integer  LDA,
complex, dimension(*)  X,
integer  INCX 
)

CTRSV

Purpose:
 CTRSV  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.

 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]A
          A is COMPLEX array, dimension ( LDA, N )
           Before entry with  UPLO = 'U' or 'u', the leading n by n
           upper triangular part of the array A must contain the upper
           triangular matrix and the strictly lower triangular part of
           A is not referenced.
           Before entry with UPLO = 'L' or 'l', the leading n by n
           lower triangular part of the array A must contain the lower
           triangular matrix and the strictly upper triangular part of
           A is not referenced.
           Note that when  DIAG = 'U' or 'u', the diagonal elements of
           A are not referenced either, but are assumed to be unity.
[in]LDA
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           max( 1, n ).
[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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 148 of file ctrsv.f.

149*
150* -- Reference BLAS level2 routine --
151* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*
154* .. Scalar Arguments ..
155 INTEGER INCX,LDA,N
156 CHARACTER DIAG,TRANS,UPLO
157* ..
158* .. Array Arguments ..
159 COMPLEX A(LDA,*),X(*)
160* ..
161*
162* =====================================================================
163*
164* .. Parameters ..
165 COMPLEX ZERO
166 parameter(zero= (0.0e+0,0.0e+0))
167* ..
168* .. Local Scalars ..
169 COMPLEX TEMP
170 INTEGER I,INFO,IX,J,JX,KX
171 LOGICAL NOCONJ,NOUNIT
172* ..
173* .. External Functions ..
174 LOGICAL LSAME
175 EXTERNAL lsame
176* ..
177* .. External Subroutines ..
178 EXTERNAL xerbla
179* ..
180* .. Intrinsic Functions ..
181 INTRINSIC conjg,max
182* ..
183*
184* Test the input parameters.
185*
186 info = 0
187 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
188 info = 1
189 ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
190 + .NOT.lsame(trans,'C')) THEN
191 info = 2
192 ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
193 info = 3
194 ELSE IF (n.LT.0) THEN
195 info = 4
196 ELSE IF (lda.LT.max(1,n)) THEN
197 info = 6
198 ELSE IF (incx.EQ.0) THEN
199 info = 8
200 END IF
201 IF (info.NE.0) THEN
202 CALL xerbla('CTRSV ',info)
203 RETURN
204 END IF
205*
206* Quick return if possible.
207*
208 IF (n.EQ.0) RETURN
209*
210 noconj = lsame(trans,'T')
211 nounit = lsame(diag,'N')
212*
213* Set up the start point in X if the increment is not unity. This
214* will be ( N - 1 )*INCX too small for descending loops.
215*
216 IF (incx.LE.0) THEN
217 kx = 1 - (n-1)*incx
218 ELSE IF (incx.NE.1) THEN
219 kx = 1
220 END IF
221*
222* Start the operations. In this version the elements of A are
223* accessed sequentially with one pass through A.
224*
225 IF (lsame(trans,'N')) THEN
226*
227* Form x := inv( A )*x.
228*
229 IF (lsame(uplo,'U')) THEN
230 IF (incx.EQ.1) THEN
231 DO 20 j = n,1,-1
232 IF (x(j).NE.zero) THEN
233 IF (nounit) x(j) = x(j)/a(j,j)
234 temp = x(j)
235 DO 10 i = j - 1,1,-1
236 x(i) = x(i) - temp*a(i,j)
237 10 CONTINUE
238 END IF
239 20 CONTINUE
240 ELSE
241 jx = kx + (n-1)*incx
242 DO 40 j = n,1,-1
243 IF (x(jx).NE.zero) THEN
244 IF (nounit) x(jx) = x(jx)/a(j,j)
245 temp = x(jx)
246 ix = jx
247 DO 30 i = j - 1,1,-1
248 ix = ix - incx
249 x(ix) = x(ix) - temp*a(i,j)
250 30 CONTINUE
251 END IF
252 jx = jx - incx
253 40 CONTINUE
254 END IF
255 ELSE
256 IF (incx.EQ.1) THEN
257 DO 60 j = 1,n
258 IF (x(j).NE.zero) THEN
259 IF (nounit) x(j) = x(j)/a(j,j)
260 temp = x(j)
261 DO 50 i = j + 1,n
262 x(i) = x(i) - temp*a(i,j)
263 50 CONTINUE
264 END IF
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)/a(j,j)
271 temp = x(jx)
272 ix = jx
273 DO 70 i = j + 1,n
274 ix = ix + incx
275 x(ix) = x(ix) - temp*a(i,j)
276 70 CONTINUE
277 END IF
278 jx = jx + incx
279 80 CONTINUE
280 END IF
281 END IF
282 ELSE
283*
284* Form x := inv( A**T )*x or x := inv( A**H )*x.
285*
286 IF (lsame(uplo,'U')) THEN
287 IF (incx.EQ.1) THEN
288 DO 110 j = 1,n
289 temp = x(j)
290 IF (noconj) THEN
291 DO 90 i = 1,j - 1
292 temp = temp - a(i,j)*x(i)
293 90 CONTINUE
294 IF (nounit) temp = temp/a(j,j)
295 ELSE
296 DO 100 i = 1,j - 1
297 temp = temp - conjg(a(i,j))*x(i)
298 100 CONTINUE
299 IF (nounit) temp = temp/conjg(a(j,j))
300 END IF
301 x(j) = temp
302 110 CONTINUE
303 ELSE
304 jx = kx
305 DO 140 j = 1,n
306 ix = kx
307 temp = x(jx)
308 IF (noconj) THEN
309 DO 120 i = 1,j - 1
310 temp = temp - a(i,j)*x(ix)
311 ix = ix + incx
312 120 CONTINUE
313 IF (nounit) temp = temp/a(j,j)
314 ELSE
315 DO 130 i = 1,j - 1
316 temp = temp - conjg(a(i,j))*x(ix)
317 ix = ix + incx
318 130 CONTINUE
319 IF (nounit) temp = temp/conjg(a(j,j))
320 END IF
321 x(jx) = temp
322 jx = jx + incx
323 140 CONTINUE
324 END IF
325 ELSE
326 IF (incx.EQ.1) THEN
327 DO 170 j = n,1,-1
328 temp = x(j)
329 IF (noconj) THEN
330 DO 150 i = n,j + 1,-1
331 temp = temp - a(i,j)*x(i)
332 150 CONTINUE
333 IF (nounit) temp = temp/a(j,j)
334 ELSE
335 DO 160 i = n,j + 1,-1
336 temp = temp - conjg(a(i,j))*x(i)
337 160 CONTINUE
338 IF (nounit) temp = temp/conjg(a(j,j))
339 END IF
340 x(j) = temp
341 170 CONTINUE
342 ELSE
343 kx = kx + (n-1)*incx
344 jx = kx
345 DO 200 j = n,1,-1
346 ix = kx
347 temp = x(jx)
348 IF (noconj) THEN
349 DO 180 i = n,j + 1,-1
350 temp = temp - a(i,j)*x(ix)
351 ix = ix - incx
352 180 CONTINUE
353 IF (nounit) temp = temp/a(j,j)
354 ELSE
355 DO 190 i = n,j + 1,-1
356 temp = temp - conjg(a(i,j))*x(ix)
357 ix = ix - incx
358 190 CONTINUE
359 IF (nounit) temp = temp/conjg(a(j,j))
360 END IF
361 x(jx) = temp
362 jx = jx - incx
363 200 CONTINUE
364 END IF
365 END IF
366 END IF
367*
368 RETURN
369*
370* End of CTRSV
371*
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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