LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dtrsv()

subroutine dtrsv ( character  uplo,
character  trans,
character  diag,
integer  n,
double precision, dimension(lda,*)  a,
integer  lda,
double precision, dimension(*)  x,
integer  incx 
)

DTRSV

Purpose:
 DTRSV  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.

 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]A
          A is DOUBLE PRECISION 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 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.

  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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 142 of file dtrsv.f.

143*
144* -- Reference BLAS level2 routine --
145* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
146* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147*
148* .. Scalar Arguments ..
149 INTEGER INCX,LDA,N
150 CHARACTER DIAG,TRANS,UPLO
151* ..
152* .. Array Arguments ..
153 DOUBLE PRECISION A(LDA,*),X(*)
154* ..
155*
156* =====================================================================
157*
158* .. Parameters ..
159 DOUBLE PRECISION ZERO
160 parameter(zero=0.0d+0)
161* ..
162* .. Local Scalars ..
163 DOUBLE PRECISION TEMP
164 INTEGER I,INFO,IX,J,JX,KX
165 LOGICAL NOUNIT
166* ..
167* .. External Functions ..
168 LOGICAL LSAME
169 EXTERNAL lsame
170* ..
171* .. External Subroutines ..
172 EXTERNAL xerbla
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC max
176* ..
177*
178* Test the input parameters.
179*
180 info = 0
181 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
182 info = 1
183 ELSE IF (.NOT.lsame(trans,'N') .AND.
184 + .NOT.lsame(trans,'T') .AND.
185 + .NOT.lsame(trans,'C')) THEN
186 info = 2
187 ELSE IF (.NOT.lsame(diag,'U') .AND.
188 + .NOT.lsame(diag,'N')) THEN
189 info = 3
190 ELSE IF (n.LT.0) THEN
191 info = 4
192 ELSE IF (lda.LT.max(1,n)) THEN
193 info = 6
194 ELSE IF (incx.EQ.0) THEN
195 info = 8
196 END IF
197 IF (info.NE.0) THEN
198 CALL xerbla('DTRSV ',info)
199 RETURN
200 END IF
201*
202* Quick return if possible.
203*
204 IF (n.EQ.0) RETURN
205*
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 A are
218* accessed sequentially with one pass through A.
219*
220 IF (lsame(trans,'N')) THEN
221*
222* Form x := inv( A )*x.
223*
224 IF (lsame(uplo,'U')) THEN
225 IF (incx.EQ.1) THEN
226 DO 20 j = n,1,-1
227 IF (x(j).NE.zero) THEN
228 IF (nounit) x(j) = x(j)/a(j,j)
229 temp = x(j)
230 DO 10 i = j - 1,1,-1
231 x(i) = x(i) - temp*a(i,j)
232 10 CONTINUE
233 END IF
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)/a(j,j)
240 temp = x(jx)
241 ix = jx
242 DO 30 i = j - 1,1,-1
243 ix = ix - incx
244 x(ix) = x(ix) - temp*a(i,j)
245 30 CONTINUE
246 END IF
247 jx = jx - incx
248 40 CONTINUE
249 END IF
250 ELSE
251 IF (incx.EQ.1) THEN
252 DO 60 j = 1,n
253 IF (x(j).NE.zero) THEN
254 IF (nounit) x(j) = x(j)/a(j,j)
255 temp = x(j)
256 DO 50 i = j + 1,n
257 x(i) = x(i) - temp*a(i,j)
258 50 CONTINUE
259 END IF
260 60 CONTINUE
261 ELSE
262 jx = kx
263 DO 80 j = 1,n
264 IF (x(jx).NE.zero) THEN
265 IF (nounit) x(jx) = x(jx)/a(j,j)
266 temp = x(jx)
267 ix = jx
268 DO 70 i = j + 1,n
269 ix = ix + incx
270 x(ix) = x(ix) - temp*a(i,j)
271 70 CONTINUE
272 END IF
273 jx = jx + incx
274 80 CONTINUE
275 END IF
276 END IF
277 ELSE
278*
279* Form x := inv( A**T )*x.
280*
281 IF (lsame(uplo,'U')) THEN
282 IF (incx.EQ.1) THEN
283 DO 100 j = 1,n
284 temp = x(j)
285 DO 90 i = 1,j - 1
286 temp = temp - a(i,j)*x(i)
287 90 CONTINUE
288 IF (nounit) temp = temp/a(j,j)
289 x(j) = temp
290 100 CONTINUE
291 ELSE
292 jx = kx
293 DO 120 j = 1,n
294 temp = x(jx)
295 ix = kx
296 DO 110 i = 1,j - 1
297 temp = temp - a(i,j)*x(ix)
298 ix = ix + incx
299 110 CONTINUE
300 IF (nounit) temp = temp/a(j,j)
301 x(jx) = temp
302 jx = jx + incx
303 120 CONTINUE
304 END IF
305 ELSE
306 IF (incx.EQ.1) THEN
307 DO 140 j = n,1,-1
308 temp = x(j)
309 DO 130 i = n,j + 1,-1
310 temp = temp - a(i,j)*x(i)
311 130 CONTINUE
312 IF (nounit) temp = temp/a(j,j)
313 x(j) = temp
314 140 CONTINUE
315 ELSE
316 kx = kx + (n-1)*incx
317 jx = kx
318 DO 160 j = n,1,-1
319 temp = x(jx)
320 ix = kx
321 DO 150 i = n,j + 1,-1
322 temp = temp - a(i,j)*x(ix)
323 ix = ix - incx
324 150 CONTINUE
325 IF (nounit) temp = temp/a(j,j)
326 x(jx) = temp
327 jx = jx - incx
328 160 CONTINUE
329 END IF
330 END IF
331 END IF
332*
333 RETURN
334*
335* End of DTRSV
336*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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