LAPACK 3.12.0
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.
190 + .NOT.lsame(trans,'T') .AND.
191 + .NOT.lsame(trans,'C')) THEN
192 info = 2
193 ELSE IF (.NOT.lsame(diag,'U') .AND.
194 + .NOT.lsame(diag,'N')) THEN
195 info = 3
196 ELSE IF (n.LT.0) THEN
197 info = 4
198 ELSE IF (lda.LT.max(1,n)) THEN
199 info = 6
200 ELSE IF (incx.EQ.0) THEN
201 info = 8
202 END IF
203 IF (info.NE.0) THEN
204 CALL xerbla('CTRSV ',info)
205 RETURN
206 END IF
207*
208* Quick return if possible.
209*
210 IF (n.EQ.0) RETURN
211*
212 noconj = lsame(trans,'T')
213 nounit = lsame(diag,'N')
214*
215* Set up the start point in X if the increment is not unity. This
216* will be ( N - 1 )*INCX too small for descending loops.
217*
218 IF (incx.LE.0) THEN
219 kx = 1 - (n-1)*incx
220 ELSE IF (incx.NE.1) THEN
221 kx = 1
222 END IF
223*
224* Start the operations. In this version the elements of A are
225* accessed sequentially with one pass through A.
226*
227 IF (lsame(trans,'N')) THEN
228*
229* Form x := inv( A )*x.
230*
231 IF (lsame(uplo,'U')) THEN
232 IF (incx.EQ.1) THEN
233 DO 20 j = n,1,-1
234 IF (x(j).NE.zero) THEN
235 IF (nounit) x(j) = x(j)/a(j,j)
236 temp = x(j)
237 DO 10 i = j - 1,1,-1
238 x(i) = x(i) - temp*a(i,j)
239 10 CONTINUE
240 END IF
241 20 CONTINUE
242 ELSE
243 jx = kx + (n-1)*incx
244 DO 40 j = n,1,-1
245 IF (x(jx).NE.zero) THEN
246 IF (nounit) x(jx) = x(jx)/a(j,j)
247 temp = x(jx)
248 ix = jx
249 DO 30 i = j - 1,1,-1
250 ix = ix - incx
251 x(ix) = x(ix) - temp*a(i,j)
252 30 CONTINUE
253 END IF
254 jx = jx - incx
255 40 CONTINUE
256 END IF
257 ELSE
258 IF (incx.EQ.1) THEN
259 DO 60 j = 1,n
260 IF (x(j).NE.zero) THEN
261 IF (nounit) x(j) = x(j)/a(j,j)
262 temp = x(j)
263 DO 50 i = j + 1,n
264 x(i) = x(i) - temp*a(i,j)
265 50 CONTINUE
266 END IF
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)/a(j,j)
273 temp = x(jx)
274 ix = jx
275 DO 70 i = j + 1,n
276 ix = ix + incx
277 x(ix) = x(ix) - temp*a(i,j)
278 70 CONTINUE
279 END IF
280 jx = jx + incx
281 80 CONTINUE
282 END IF
283 END IF
284 ELSE
285*
286* Form x := inv( A**T )*x or x := inv( A**H )*x.
287*
288 IF (lsame(uplo,'U')) THEN
289 IF (incx.EQ.1) THEN
290 DO 110 j = 1,n
291 temp = x(j)
292 IF (noconj) THEN
293 DO 90 i = 1,j - 1
294 temp = temp - a(i,j)*x(i)
295 90 CONTINUE
296 IF (nounit) temp = temp/a(j,j)
297 ELSE
298 DO 100 i = 1,j - 1
299 temp = temp - conjg(a(i,j))*x(i)
300 100 CONTINUE
301 IF (nounit) temp = temp/conjg(a(j,j))
302 END IF
303 x(j) = temp
304 110 CONTINUE
305 ELSE
306 jx = kx
307 DO 140 j = 1,n
308 ix = kx
309 temp = x(jx)
310 IF (noconj) THEN
311 DO 120 i = 1,j - 1
312 temp = temp - a(i,j)*x(ix)
313 ix = ix + incx
314 120 CONTINUE
315 IF (nounit) temp = temp/a(j,j)
316 ELSE
317 DO 130 i = 1,j - 1
318 temp = temp - conjg(a(i,j))*x(ix)
319 ix = ix + incx
320 130 CONTINUE
321 IF (nounit) temp = temp/conjg(a(j,j))
322 END IF
323 x(jx) = temp
324 jx = jx + incx
325 140 CONTINUE
326 END IF
327 ELSE
328 IF (incx.EQ.1) THEN
329 DO 170 j = n,1,-1
330 temp = x(j)
331 IF (noconj) THEN
332 DO 150 i = n,j + 1,-1
333 temp = temp - a(i,j)*x(i)
334 150 CONTINUE
335 IF (nounit) temp = temp/a(j,j)
336 ELSE
337 DO 160 i = n,j + 1,-1
338 temp = temp - conjg(a(i,j))*x(i)
339 160 CONTINUE
340 IF (nounit) temp = temp/conjg(a(j,j))
341 END IF
342 x(j) = temp
343 170 CONTINUE
344 ELSE
345 kx = kx + (n-1)*incx
346 jx = kx
347 DO 200 j = n,1,-1
348 ix = kx
349 temp = x(jx)
350 IF (noconj) THEN
351 DO 180 i = n,j + 1,-1
352 temp = temp - a(i,j)*x(ix)
353 ix = ix - incx
354 180 CONTINUE
355 IF (nounit) temp = temp/a(j,j)
356 ELSE
357 DO 190 i = n,j + 1,-1
358 temp = temp - conjg(a(i,j))*x(ix)
359 ix = ix - incx
360 190 CONTINUE
361 IF (nounit) temp = temp/conjg(a(j,j))
362 END IF
363 x(jx) = temp
364 jx = jx - incx
365 200 CONTINUE
366 END IF
367 END IF
368 END IF
369*
370 RETURN
371*
372* End of CTRSV
373*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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