 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cgbmv()

 subroutine cgbmv ( character TRANS, integer M, integer N, integer KL, integer KU, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY )

CGBMV

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

y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or

y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero.``` [in] KL ``` KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.``` [in] KU ``` KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX array, dimension ( LDA, N ) Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE``` [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 ( kl + ku + 1 ).``` [in] X ``` X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.``` [in,out] Y ``` Y is COMPLEX array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY 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 186 of file cgbmv.f.

187*
188* -- Reference BLAS level2 routine --
189* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192* .. Scalar Arguments ..
193 COMPLEX ALPHA,BETA
194 INTEGER INCX,INCY,KL,KU,LDA,M,N
195 CHARACTER TRANS
196* ..
197* .. Array Arguments ..
198 COMPLEX A(LDA,*),X(*),Y(*)
199* ..
200*
201* =====================================================================
202*
203* .. Parameters ..
204 COMPLEX ONE
205 parameter(one= (1.0e+0,0.0e+0))
206 COMPLEX ZERO
207 parameter(zero= (0.0e+0,0.0e+0))
208* ..
209* .. Local Scalars ..
210 COMPLEX TEMP
211 INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
212 LOGICAL NOCONJ
213* ..
214* .. External Functions ..
215 LOGICAL LSAME
216 EXTERNAL lsame
217* ..
218* .. External Subroutines ..
219 EXTERNAL xerbla
220* ..
221* .. Intrinsic Functions ..
222 INTRINSIC conjg,max,min
223* ..
224*
225* Test the input parameters.
226*
227 info = 0
228 IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
229 + .NOT.lsame(trans,'C')) THEN
230 info = 1
231 ELSE IF (m.LT.0) THEN
232 info = 2
233 ELSE IF (n.LT.0) THEN
234 info = 3
235 ELSE IF (kl.LT.0) THEN
236 info = 4
237 ELSE IF (ku.LT.0) THEN
238 info = 5
239 ELSE IF (lda.LT. (kl+ku+1)) THEN
240 info = 8
241 ELSE IF (incx.EQ.0) THEN
242 info = 10
243 ELSE IF (incy.EQ.0) THEN
244 info = 13
245 END IF
246 IF (info.NE.0) THEN
247 CALL xerbla('CGBMV ',info)
248 RETURN
249 END IF
250*
251* Quick return if possible.
252*
253 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
254 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
255*
256 noconj = lsame(trans,'T')
257*
258* Set LENX and LENY, the lengths of the vectors x and y, and set
259* up the start points in X and Y.
260*
261 IF (lsame(trans,'N')) THEN
262 lenx = n
263 leny = m
264 ELSE
265 lenx = m
266 leny = n
267 END IF
268 IF (incx.GT.0) THEN
269 kx = 1
270 ELSE
271 kx = 1 - (lenx-1)*incx
272 END IF
273 IF (incy.GT.0) THEN
274 ky = 1
275 ELSE
276 ky = 1 - (leny-1)*incy
277 END IF
278*
279* Start the operations. In this version the elements of A are
280* accessed sequentially with one pass through the band part of A.
281*
282* First form y := beta*y.
283*
284 IF (beta.NE.one) THEN
285 IF (incy.EQ.1) THEN
286 IF (beta.EQ.zero) THEN
287 DO 10 i = 1,leny
288 y(i) = zero
289 10 CONTINUE
290 ELSE
291 DO 20 i = 1,leny
292 y(i) = beta*y(i)
293 20 CONTINUE
294 END IF
295 ELSE
296 iy = ky
297 IF (beta.EQ.zero) THEN
298 DO 30 i = 1,leny
299 y(iy) = zero
300 iy = iy + incy
301 30 CONTINUE
302 ELSE
303 DO 40 i = 1,leny
304 y(iy) = beta*y(iy)
305 iy = iy + incy
306 40 CONTINUE
307 END IF
308 END IF
309 END IF
310 IF (alpha.EQ.zero) RETURN
311 kup1 = ku + 1
312 IF (lsame(trans,'N')) THEN
313*
314* Form y := alpha*A*x + y.
315*
316 jx = kx
317 IF (incy.EQ.1) THEN
318 DO 60 j = 1,n
319 temp = alpha*x(jx)
320 k = kup1 - j
321 DO 50 i = max(1,j-ku),min(m,j+kl)
322 y(i) = y(i) + temp*a(k+i,j)
323 50 CONTINUE
324 jx = jx + incx
325 60 CONTINUE
326 ELSE
327 DO 80 j = 1,n
328 temp = alpha*x(jx)
329 iy = ky
330 k = kup1 - j
331 DO 70 i = max(1,j-ku),min(m,j+kl)
332 y(iy) = y(iy) + temp*a(k+i,j)
333 iy = iy + incy
334 70 CONTINUE
335 jx = jx + incx
336 IF (j.GT.ku) ky = ky + incy
337 80 CONTINUE
338 END IF
339 ELSE
340*
341* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
342*
343 jy = ky
344 IF (incx.EQ.1) THEN
345 DO 110 j = 1,n
346 temp = zero
347 k = kup1 - j
348 IF (noconj) THEN
349 DO 90 i = max(1,j-ku),min(m,j+kl)
350 temp = temp + a(k+i,j)*x(i)
351 90 CONTINUE
352 ELSE
353 DO 100 i = max(1,j-ku),min(m,j+kl)
354 temp = temp + conjg(a(k+i,j))*x(i)
355 100 CONTINUE
356 END IF
357 y(jy) = y(jy) + alpha*temp
358 jy = jy + incy
359 110 CONTINUE
360 ELSE
361 DO 140 j = 1,n
362 temp = zero
363 ix = kx
364 k = kup1 - j
365 IF (noconj) THEN
366 DO 120 i = max(1,j-ku),min(m,j+kl)
367 temp = temp + a(k+i,j)*x(ix)
368 ix = ix + incx
369 120 CONTINUE
370 ELSE
371 DO 130 i = max(1,j-ku),min(m,j+kl)
372 temp = temp + conjg(a(k+i,j))*x(ix)
373 ix = ix + incx
374 130 CONTINUE
375 END IF
376 y(jy) = y(jy) + alpha*temp
377 jy = jy + incy
378 IF (j.GT.ku) kx = kx + incx
379 140 CONTINUE
380 END IF
381 END IF
382*
383 RETURN
384*
385* End of CGBMV
386*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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