 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ztrmv()

 subroutine ztrmv ( character UPLO, character TRANS, character DIAG, integer N, complex*16, dimension(lda,*) A, integer LDA, complex*16, dimension(*) X, integer INCX )

ZTRMV

Purpose:
``` ZTRMV  performs one of the matrix-vector operations

x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and  A is an n by n unit, or non-unit,
upper or lower triangular matrix.```
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 operation to be performed as follows: TRANS = 'N' or 'n' x := A*x. TRANS = 'T' or 't' x := A**T*x. TRANS = 'C' or 'c' x := A**H*x.``` [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*16 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*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.```
Date
December 2016
Further Details:
```  Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- 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 149 of file ztrmv.f.

149 *
150 * -- Reference BLAS level2 routine (version 3.7.0) --
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 * December 2016
154 *
155 * .. Scalar Arguments ..
156  INTEGER incx,lda,n
157  CHARACTER diag,trans,uplo
158 * ..
159 * .. Array Arguments ..
160  COMPLEX*16 a(lda,*),x(*)
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  COMPLEX*16 zero
167  parameter(zero= (0.0d+0,0.0d+0))
168 * ..
169 * .. Local Scalars ..
170  COMPLEX*16 temp
171  INTEGER i,info,ix,j,jx,kx
172  LOGICAL noconj,nounit
173 * ..
174 * .. External Functions ..
175  LOGICAL lsame
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL xerbla
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC dconjg,max
183 * ..
184 *
185 * Test the input parameters.
186 *
187  info = 0
188  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
189  info = 1
190  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
191  + .NOT.lsame(trans,'C')) THEN
192  info = 2
193  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
194  info = 3
195  ELSE IF (n.LT.0) THEN
196  info = 4
197  ELSE IF (lda.LT.max(1,n)) THEN
198  info = 6
199  ELSE IF (incx.EQ.0) THEN
200  info = 8
201  END IF
202  IF (info.NE.0) THEN
203  CALL xerbla('ZTRMV ',info)
204  RETURN
205  END IF
206 *
207 * Quick return if possible.
208 *
209  IF (n.EQ.0) RETURN
210 *
211  noconj = lsame(trans,'T')
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 := A*x.
229 *
230  IF (lsame(uplo,'U')) THEN
231  IF (incx.EQ.1) THEN
232  DO 20 j = 1,n
233  IF (x(j).NE.zero) THEN
234  temp = x(j)
235  DO 10 i = 1,j - 1
236  x(i) = x(i) + temp*a(i,j)
237  10 CONTINUE
238  IF (nounit) x(j) = x(j)*a(j,j)
239  END IF
240  20 CONTINUE
241  ELSE
242  jx = kx
243  DO 40 j = 1,n
244  IF (x(jx).NE.zero) THEN
245  temp = x(jx)
246  ix = kx
247  DO 30 i = 1,j - 1
248  x(ix) = x(ix) + temp*a(i,j)
249  ix = ix + incx
250  30 CONTINUE
251  IF (nounit) x(jx) = x(jx)*a(j,j)
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 = n,1,-1
259  IF (x(j).NE.zero) THEN
260  temp = x(j)
261  DO 50 i = n,j + 1,-1
262  x(i) = x(i) + temp*a(i,j)
263  50 CONTINUE
264  IF (nounit) x(j) = x(j)*a(j,j)
265  END IF
266  60 CONTINUE
267  ELSE
268  kx = kx + (n-1)*incx
269  jx = kx
270  DO 80 j = n,1,-1
271  IF (x(jx).NE.zero) THEN
272  temp = x(jx)
273  ix = kx
274  DO 70 i = n,j + 1,-1
275  x(ix) = x(ix) + temp*a(i,j)
276  ix = ix - incx
277  70 CONTINUE
278  IF (nounit) x(jx) = x(jx)*a(j,j)
279  END IF
280  jx = jx - incx
281  80 CONTINUE
282  END IF
283  END IF
284  ELSE
285 *
286 * Form x := A**T*x or x := A**H*x.
287 *
288  IF (lsame(uplo,'U')) THEN
289  IF (incx.EQ.1) THEN
290  DO 110 j = n,1,-1
291  temp = x(j)
292  IF (noconj) THEN
293  IF (nounit) temp = temp*a(j,j)
294  DO 90 i = j - 1,1,-1
295  temp = temp + a(i,j)*x(i)
296  90 CONTINUE
297  ELSE
298  IF (nounit) temp = temp*dconjg(a(j,j))
299  DO 100 i = j - 1,1,-1
300  temp = temp + dconjg(a(i,j))*x(i)
301  100 CONTINUE
302  END IF
303  x(j) = temp
304  110 CONTINUE
305  ELSE
306  jx = kx + (n-1)*incx
307  DO 140 j = n,1,-1
308  temp = x(jx)
309  ix = jx
310  IF (noconj) THEN
311  IF (nounit) temp = temp*a(j,j)
312  DO 120 i = j - 1,1,-1
313  ix = ix - incx
314  temp = temp + a(i,j)*x(ix)
315  120 CONTINUE
316  ELSE
317  IF (nounit) temp = temp*dconjg(a(j,j))
318  DO 130 i = j - 1,1,-1
319  ix = ix - incx
320  temp = temp + dconjg(a(i,j))*x(ix)
321  130 CONTINUE
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 = 1,n
330  temp = x(j)
331  IF (noconj) THEN
332  IF (nounit) temp = temp*a(j,j)
333  DO 150 i = j + 1,n
334  temp = temp + a(i,j)*x(i)
335  150 CONTINUE
336  ELSE
337  IF (nounit) temp = temp*dconjg(a(j,j))
338  DO 160 i = j + 1,n
339  temp = temp + dconjg(a(i,j))*x(i)
340  160 CONTINUE
341  END IF
342  x(j) = temp
343  170 CONTINUE
344  ELSE
345  jx = kx
346  DO 200 j = 1,n
347  temp = x(jx)
348  ix = jx
349  IF (noconj) THEN
350  IF (nounit) temp = temp*a(j,j)
351  DO 180 i = j + 1,n
352  ix = ix + incx
353  temp = temp + a(i,j)*x(ix)
354  180 CONTINUE
355  ELSE
356  IF (nounit) temp = temp*dconjg(a(j,j))
357  DO 190 i = j + 1,n
358  ix = ix + incx
359  temp = temp + dconjg(a(i,j))*x(ix)
360  190 CONTINUE
361  END IF
362  x(jx) = temp
363  jx = jx + incx
364  200 CONTINUE
365  END IF
366  END IF
367  END IF
368 *
369  RETURN
370 *
371 * End of ZTRMV .
372 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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