LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ zgbmv()

subroutine zgbmv ( character  trans,
integer  m,
integer  n,
integer  kl,
integer  ku,
complex*16  alpha,
complex*16, dimension(lda,*)  a,
integer  lda,
complex*16, dimension(*)  x,
integer  incx,
complex*16  beta,
complex*16, dimension(*)  y,
integer  incy 
)

ZGBMV

Purpose:
 ZGBMV  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*16
           On entry, ALPHA specifies the scalar alpha.
[in]A
          A is COMPLEX*16 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*16 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*16
           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*16 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.
           If either m or n is zero, then Y not referenced and the function
           performs a quick return.
[in]INCY
          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 188 of file zgbmv.f.

190*
191* -- Reference BLAS level2 routine --
192* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
193* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
194*
195* .. Scalar Arguments ..
196 COMPLEX*16 ALPHA,BETA
197 INTEGER INCX,INCY,KL,KU,LDA,M,N
198 CHARACTER TRANS
199* ..
200* .. Array Arguments ..
201 COMPLEX*16 A(LDA,*),X(*),Y(*)
202* ..
203*
204* =====================================================================
205*
206* .. Parameters ..
207 COMPLEX*16 ONE
208 parameter(one= (1.0d+0,0.0d+0))
209 COMPLEX*16 ZERO
210 parameter(zero= (0.0d+0,0.0d+0))
211* ..
212* .. Local Scalars ..
213 COMPLEX*16 TEMP
214 INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
215 LOGICAL NOCONJ
216* ..
217* .. External Functions ..
218 LOGICAL LSAME
219 EXTERNAL lsame
220* ..
221* .. External Subroutines ..
222 EXTERNAL xerbla
223* ..
224* .. Intrinsic Functions ..
225 INTRINSIC dconjg,max,min
226* ..
227*
228* Test the input parameters.
229*
230 info = 0
231 IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
232 + .NOT.lsame(trans,'C')) THEN
233 info = 1
234 ELSE IF (m.LT.0) THEN
235 info = 2
236 ELSE IF (n.LT.0) THEN
237 info = 3
238 ELSE IF (kl.LT.0) THEN
239 info = 4
240 ELSE IF (ku.LT.0) THEN
241 info = 5
242 ELSE IF (lda.LT. (kl+ku+1)) THEN
243 info = 8
244 ELSE IF (incx.EQ.0) THEN
245 info = 10
246 ELSE IF (incy.EQ.0) THEN
247 info = 13
248 END IF
249 IF (info.NE.0) THEN
250 CALL xerbla('ZGBMV ',info)
251 RETURN
252 END IF
253*
254* Quick return if possible.
255*
256 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
257 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
258*
259 noconj = lsame(trans,'T')
260*
261* Set LENX and LENY, the lengths of the vectors x and y, and set
262* up the start points in X and Y.
263*
264 IF (lsame(trans,'N')) THEN
265 lenx = n
266 leny = m
267 ELSE
268 lenx = m
269 leny = n
270 END IF
271 IF (incx.GT.0) THEN
272 kx = 1
273 ELSE
274 kx = 1 - (lenx-1)*incx
275 END IF
276 IF (incy.GT.0) THEN
277 ky = 1
278 ELSE
279 ky = 1 - (leny-1)*incy
280 END IF
281*
282* Start the operations. In this version the elements of A are
283* accessed sequentially with one pass through the band part of A.
284*
285* First form y := beta*y.
286*
287 IF (beta.NE.one) THEN
288 IF (incy.EQ.1) THEN
289 IF (beta.EQ.zero) THEN
290 DO 10 i = 1,leny
291 y(i) = zero
292 10 CONTINUE
293 ELSE
294 DO 20 i = 1,leny
295 y(i) = beta*y(i)
296 20 CONTINUE
297 END IF
298 ELSE
299 iy = ky
300 IF (beta.EQ.zero) THEN
301 DO 30 i = 1,leny
302 y(iy) = zero
303 iy = iy + incy
304 30 CONTINUE
305 ELSE
306 DO 40 i = 1,leny
307 y(iy) = beta*y(iy)
308 iy = iy + incy
309 40 CONTINUE
310 END IF
311 END IF
312 END IF
313 IF (alpha.EQ.zero) RETURN
314 kup1 = ku + 1
315 IF (lsame(trans,'N')) THEN
316*
317* Form y := alpha*A*x + y.
318*
319 jx = kx
320 IF (incy.EQ.1) THEN
321 DO 60 j = 1,n
322 temp = alpha*x(jx)
323 k = kup1 - j
324 DO 50 i = max(1,j-ku),min(m,j+kl)
325 y(i) = y(i) + temp*a(k+i,j)
326 50 CONTINUE
327 jx = jx + incx
328 60 CONTINUE
329 ELSE
330 DO 80 j = 1,n
331 temp = alpha*x(jx)
332 iy = ky
333 k = kup1 - j
334 DO 70 i = max(1,j-ku),min(m,j+kl)
335 y(iy) = y(iy) + temp*a(k+i,j)
336 iy = iy + incy
337 70 CONTINUE
338 jx = jx + incx
339 IF (j.GT.ku) ky = ky + incy
340 80 CONTINUE
341 END IF
342 ELSE
343*
344* Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
345*
346 jy = ky
347 IF (incx.EQ.1) THEN
348 DO 110 j = 1,n
349 temp = zero
350 k = kup1 - j
351 IF (noconj) THEN
352 DO 90 i = max(1,j-ku),min(m,j+kl)
353 temp = temp + a(k+i,j)*x(i)
354 90 CONTINUE
355 ELSE
356 DO 100 i = max(1,j-ku),min(m,j+kl)
357 temp = temp + dconjg(a(k+i,j))*x(i)
358 100 CONTINUE
359 END IF
360 y(jy) = y(jy) + alpha*temp
361 jy = jy + incy
362 110 CONTINUE
363 ELSE
364 DO 140 j = 1,n
365 temp = zero
366 ix = kx
367 k = kup1 - j
368 IF (noconj) THEN
369 DO 120 i = max(1,j-ku),min(m,j+kl)
370 temp = temp + a(k+i,j)*x(ix)
371 ix = ix + incx
372 120 CONTINUE
373 ELSE
374 DO 130 i = max(1,j-ku),min(m,j+kl)
375 temp = temp + dconjg(a(k+i,j))*x(ix)
376 ix = ix + incx
377 130 CONTINUE
378 END IF
379 y(jy) = y(jy) + alpha*temp
380 jy = jy + incy
381 IF (j.GT.ku) kx = kx + incx
382 140 CONTINUE
383 END IF
384 END IF
385*
386 RETURN
387*
388* End of ZGBMV
389*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
Here is the call graph for this function:
Here is the caller graph for this function: