 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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.```
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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
Here is the call graph for this function:
Here is the caller graph for this function: