 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ strmv()

 subroutine strmv ( character UPLO, character TRANS, character DIAG, integer N, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX )

STRMV

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

x := A*x,   or   x := A**T*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**T*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 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 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.```
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 146 of file strmv.f.

147 *
148 * -- Reference BLAS level2 routine --
149 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  INTEGER INCX,LDA,N
154  CHARACTER DIAG,TRANS,UPLO
155 * ..
156 * .. Array Arguments ..
157  REAL A(LDA,*),X(*)
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Parameters ..
163  REAL ZERO
164  parameter(zero=0.0e+0)
165 * ..
166 * .. Local Scalars ..
167  REAL TEMP
168  INTEGER I,INFO,IX,J,JX,KX
169  LOGICAL NOUNIT
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  EXTERNAL lsame
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL xerbla
177 * ..
178 * .. Intrinsic Functions ..
179  INTRINSIC max
180 * ..
181 *
182 * Test the input parameters.
183 *
184  info = 0
185  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
186  info = 1
187  ELSE IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
188  + .NOT.lsame(trans,'C')) THEN
189  info = 2
190  ELSE IF (.NOT.lsame(diag,'U') .AND. .NOT.lsame(diag,'N')) THEN
191  info = 3
192  ELSE IF (n.LT.0) THEN
193  info = 4
194  ELSE IF (lda.LT.max(1,n)) THEN
195  info = 6
196  ELSE IF (incx.EQ.0) THEN
197  info = 8
198  END IF
199  IF (info.NE.0) THEN
200  CALL xerbla('STRMV ',info)
201  RETURN
202  END IF
203 *
204 * Quick return if possible.
205 *
206  IF (n.EQ.0) RETURN
207 *
208  nounit = lsame(diag,'N')
209 *
210 * Set up the start point in X if the increment is not unity. This
211 * will be ( N - 1 )*INCX too small for descending loops.
212 *
213  IF (incx.LE.0) THEN
214  kx = 1 - (n-1)*incx
215  ELSE IF (incx.NE.1) THEN
216  kx = 1
217  END IF
218 *
219 * Start the operations. In this version the elements of A are
220 * accessed sequentially with one pass through A.
221 *
222  IF (lsame(trans,'N')) THEN
223 *
224 * Form x := A*x.
225 *
226  IF (lsame(uplo,'U')) THEN
227  IF (incx.EQ.1) THEN
228  DO 20 j = 1,n
229  IF (x(j).NE.zero) THEN
230  temp = x(j)
231  DO 10 i = 1,j - 1
232  x(i) = x(i) + temp*a(i,j)
233  10 CONTINUE
234  IF (nounit) x(j) = x(j)*a(j,j)
235  END IF
236  20 CONTINUE
237  ELSE
238  jx = kx
239  DO 40 j = 1,n
240  IF (x(jx).NE.zero) THEN
241  temp = x(jx)
242  ix = kx
243  DO 30 i = 1,j - 1
244  x(ix) = x(ix) + temp*a(i,j)
245  ix = ix + incx
246  30 CONTINUE
247  IF (nounit) x(jx) = x(jx)*a(j,j)
248  END IF
249  jx = jx + incx
250  40 CONTINUE
251  END IF
252  ELSE
253  IF (incx.EQ.1) THEN
254  DO 60 j = n,1,-1
255  IF (x(j).NE.zero) THEN
256  temp = x(j)
257  DO 50 i = n,j + 1,-1
258  x(i) = x(i) + temp*a(i,j)
259  50 CONTINUE
260  IF (nounit) x(j) = x(j)*a(j,j)
261  END IF
262  60 CONTINUE
263  ELSE
264  kx = kx + (n-1)*incx
265  jx = kx
266  DO 80 j = n,1,-1
267  IF (x(jx).NE.zero) THEN
268  temp = x(jx)
269  ix = kx
270  DO 70 i = n,j + 1,-1
271  x(ix) = x(ix) + temp*a(i,j)
272  ix = ix - incx
273  70 CONTINUE
274  IF (nounit) x(jx) = x(jx)*a(j,j)
275  END IF
276  jx = jx - incx
277  80 CONTINUE
278  END IF
279  END IF
280  ELSE
281 *
282 * Form x := A**T*x.
283 *
284  IF (lsame(uplo,'U')) THEN
285  IF (incx.EQ.1) THEN
286  DO 100 j = n,1,-1
287  temp = x(j)
288  IF (nounit) temp = temp*a(j,j)
289  DO 90 i = j - 1,1,-1
290  temp = temp + a(i,j)*x(i)
291  90 CONTINUE
292  x(j) = temp
293  100 CONTINUE
294  ELSE
295  jx = kx + (n-1)*incx
296  DO 120 j = n,1,-1
297  temp = x(jx)
298  ix = jx
299  IF (nounit) temp = temp*a(j,j)
300  DO 110 i = j - 1,1,-1
301  ix = ix - incx
302  temp = temp + a(i,j)*x(ix)
303  110 CONTINUE
304  x(jx) = temp
305  jx = jx - incx
306  120 CONTINUE
307  END IF
308  ELSE
309  IF (incx.EQ.1) THEN
310  DO 140 j = 1,n
311  temp = x(j)
312  IF (nounit) temp = temp*a(j,j)
313  DO 130 i = j + 1,n
314  temp = temp + a(i,j)*x(i)
315  130 CONTINUE
316  x(j) = temp
317  140 CONTINUE
318  ELSE
319  jx = kx
320  DO 160 j = 1,n
321  temp = x(jx)
322  ix = jx
323  IF (nounit) temp = temp*a(j,j)
324  DO 150 i = j + 1,n
325  ix = ix + incx
326  temp = temp + a(i,j)*x(ix)
327  150 CONTINUE
328  x(jx) = temp
329  jx = jx + incx
330  160 CONTINUE
331  END IF
332  END IF
333  END IF
334 *
335  RETURN
336 *
337 * End of STRMV
338 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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