 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```

Definition at line 142 of file dtrsv.f.

143 *
144 * -- Reference BLAS level1 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. .NOT.lsame(trans,'T') .AND.
184  + .NOT.lsame(trans,'C')) THEN
185  info = 2
186  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
187  info = 3
188  ELSE IF (n.LT.0) THEN
189  info = 4
190  ELSE IF (lda.LT.max(1,n)) THEN
191  info = 6
192  ELSE IF (incx.EQ.0) THEN
193  info = 8
194  END IF
195  IF (info.NE.0) THEN
196  CALL xerbla('DTRSV ',info)
197  RETURN
198  END IF
199 *
200 * Quick return if possible.
201 *
202  IF (n.EQ.0) RETURN
203 *
204  nounit = lsame(diag,'N')
205 *
206 * Set up the start point in X if the increment is not unity. This
207 * will be ( N - 1 )*INCX too small for descending loops.
208 *
209  IF (incx.LE.0) THEN
210  kx = 1 - (n-1)*incx
211  ELSE IF (incx.NE.1) THEN
212  kx = 1
213  END IF
214 *
215 * Start the operations. In this version the elements of A are
216 * accessed sequentially with one pass through A.
217 *
218  IF (lsame(trans,'N')) THEN
219 *
220 * Form x := inv( A )*x.
221 *
222  IF (lsame(uplo,'U')) THEN
223  IF (incx.EQ.1) THEN
224  DO 20 j = n,1,-1
225  IF (x(j).NE.zero) THEN
226  IF (nounit) x(j) = x(j)/a(j,j)
227  temp = x(j)
228  DO 10 i = j - 1,1,-1
229  x(i) = x(i) - temp*a(i,j)
230  10 CONTINUE
231  END IF
232  20 CONTINUE
233  ELSE
234  jx = kx + (n-1)*incx
235  DO 40 j = n,1,-1
236  IF (x(jx).NE.zero) THEN
237  IF (nounit) x(jx) = x(jx)/a(j,j)
238  temp = x(jx)
239  ix = jx
240  DO 30 i = j - 1,1,-1
241  ix = ix - incx
242  x(ix) = x(ix) - temp*a(i,j)
243  30 CONTINUE
244  END IF
245  jx = jx - incx
246  40 CONTINUE
247  END IF
248  ELSE
249  IF (incx.EQ.1) THEN
250  DO 60 j = 1,n
251  IF (x(j).NE.zero) THEN
252  IF (nounit) x(j) = x(j)/a(j,j)
253  temp = x(j)
254  DO 50 i = j + 1,n
255  x(i) = x(i) - temp*a(i,j)
256  50 CONTINUE
257  END IF
258  60 CONTINUE
259  ELSE
260  jx = kx
261  DO 80 j = 1,n
262  IF (x(jx).NE.zero) THEN
263  IF (nounit) x(jx) = x(jx)/a(j,j)
264  temp = x(jx)
265  ix = jx
266  DO 70 i = j + 1,n
267  ix = ix + incx
268  x(ix) = x(ix) - temp*a(i,j)
269  70 CONTINUE
270  END IF
271  jx = jx + incx
272  80 CONTINUE
273  END IF
274  END IF
275  ELSE
276 *
277 * Form x := inv( A**T )*x.
278 *
279  IF (lsame(uplo,'U')) THEN
280  IF (incx.EQ.1) THEN
281  DO 100 j = 1,n
282  temp = x(j)
283  DO 90 i = 1,j - 1
284  temp = temp - a(i,j)*x(i)
285  90 CONTINUE
286  IF (nounit) temp = temp/a(j,j)
287  x(j) = temp
288  100 CONTINUE
289  ELSE
290  jx = kx
291  DO 120 j = 1,n
292  temp = x(jx)
293  ix = kx
294  DO 110 i = 1,j - 1
295  temp = temp - a(i,j)*x(ix)
296  ix = ix + incx
297  110 CONTINUE
298  IF (nounit) temp = temp/a(j,j)
299  x(jx) = temp
300  jx = jx + incx
301  120 CONTINUE
302  END IF
303  ELSE
304  IF (incx.EQ.1) THEN
305  DO 140 j = n,1,-1
306  temp = x(j)
307  DO 130 i = n,j + 1,-1
308  temp = temp - a(i,j)*x(i)
309  130 CONTINUE
310  IF (nounit) temp = temp/a(j,j)
311  x(j) = temp
312  140 CONTINUE
313  ELSE
314  kx = kx + (n-1)*incx
315  jx = kx
316  DO 160 j = n,1,-1
317  temp = x(jx)
318  ix = kx
319  DO 150 i = n,j + 1,-1
320  temp = temp - a(i,j)*x(ix)
321  ix = ix - incx
322  150 CONTINUE
323  IF (nounit) temp = temp/a(j,j)
324  x(jx) = temp
325  jx = jx - incx
326  160 CONTINUE
327  END IF
328  END IF
329  END IF
330 *
331  RETURN
332 *
333 * End of DTRSV
334 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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