LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ strsv()

subroutine strsv ( character uplo,
character trans,
character diag,
integer n,
real, dimension(lda,*) a,
integer lda,
real, dimension(*) x,
integer incx )

STRSV

Purpose:
!>
!> STRSV  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 REAL 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 REAL 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 strsv.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 REAL A(LDA,*),X(*)
160* ..
161*
162* =====================================================================
163*
164* .. Parameters ..
165 REAL ZERO
166 parameter(zero=0.0e+0)
167* ..
168* .. Local Scalars ..
169 REAL TEMP
170 INTEGER I,INFO,IX,J,JX,KX
171 LOGICAL NOUNIT
172* ..
173* .. External Functions ..
174 LOGICAL LSAME
175 EXTERNAL lsame
176* ..
177* .. External Subroutines ..
178 EXTERNAL xerbla
179* ..
180* .. Intrinsic Functions ..
181 INTRINSIC 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('STRSV ',info)
205 RETURN
206 END IF
207*
208* Quick return if possible.
209*
210 IF (n.EQ.0) RETURN
211*
212 nounit = lsame(diag,'N')
213*
214* Set up the start point in X if the increment is not unity. This
215* will be ( N - 1 )*INCX too small for descending loops.
216*
217 IF (incx.LE.0) THEN
218 kx = 1 - (n-1)*incx
219 ELSE IF (incx.NE.1) THEN
220 kx = 1
221 END IF
222*
223* Start the operations. In this version the elements of A are
224* accessed sequentially with one pass through A.
225*
226 IF (lsame(trans,'N')) THEN
227*
228* Form x := inv( A )*x.
229*
230 IF (lsame(uplo,'U')) THEN
231 IF (incx.EQ.1) THEN
232 DO 20 j = n,1,-1
233 IF (x(j).NE.zero) THEN
234 IF (nounit) x(j) = x(j)/a(j,j)
235 temp = x(j)
236 DO 10 i = j - 1,1,-1
237 x(i) = x(i) - temp*a(i,j)
238 10 CONTINUE
239 END IF
240 20 CONTINUE
241 ELSE
242 jx = kx + (n-1)*incx
243 DO 40 j = n,1,-1
244 IF (x(jx).NE.zero) THEN
245 IF (nounit) x(jx) = x(jx)/a(j,j)
246 temp = x(jx)
247 ix = jx
248 DO 30 i = j - 1,1,-1
249 ix = ix - incx
250 x(ix) = x(ix) - temp*a(i,j)
251 30 CONTINUE
252 END IF
253 jx = jx - incx
254 40 CONTINUE
255 END IF
256 ELSE
257 IF (incx.EQ.1) THEN
258 DO 60 j = 1,n
259 IF (x(j).NE.zero) THEN
260 IF (nounit) x(j) = x(j)/a(j,j)
261 temp = x(j)
262 DO 50 i = j + 1,n
263 x(i) = x(i) - temp*a(i,j)
264 50 CONTINUE
265 END IF
266 60 CONTINUE
267 ELSE
268 jx = kx
269 DO 80 j = 1,n
270 IF (x(jx).NE.zero) THEN
271 IF (nounit) x(jx) = x(jx)/a(j,j)
272 temp = x(jx)
273 ix = jx
274 DO 70 i = j + 1,n
275 ix = ix + incx
276 x(ix) = x(ix) - temp*a(i,j)
277 70 CONTINUE
278 END IF
279 jx = jx + incx
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 IF (incx.EQ.1) THEN
289 DO 100 j = 1,n
290 temp = x(j)
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 x(j) = temp
296 100 CONTINUE
297 ELSE
298 jx = kx
299 DO 120 j = 1,n
300 temp = x(jx)
301 ix = kx
302 DO 110 i = 1,j - 1
303 temp = temp - a(i,j)*x(ix)
304 ix = ix + incx
305 110 CONTINUE
306 IF (nounit) temp = temp/a(j,j)
307 x(jx) = temp
308 jx = jx + incx
309 120 CONTINUE
310 END IF
311 ELSE
312 IF (incx.EQ.1) THEN
313 DO 140 j = n,1,-1
314 temp = x(j)
315 DO 130 i = n,j + 1,-1
316 temp = temp - a(i,j)*x(i)
317 130 CONTINUE
318 IF (nounit) temp = temp/a(j,j)
319 x(j) = temp
320 140 CONTINUE
321 ELSE
322 kx = kx + (n-1)*incx
323 jx = kx
324 DO 160 j = n,1,-1
325 temp = x(jx)
326 ix = kx
327 DO 150 i = n,j + 1,-1
328 temp = temp - a(i,j)*x(ix)
329 ix = ix - incx
330 150 CONTINUE
331 IF (nounit) temp = temp/a(j,j)
332 x(jx) = temp
333 jx = jx - incx
334 160 CONTINUE
335 END IF
336 END IF
337 END IF
338*
339 RETURN
340*
341* End of STRSV
342*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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