LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 189 of file cgbmv.f.

189 *
190 * -- Reference BLAS level2 routine (version 3.7.0) --
191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 * December 2016
194 *
195 * .. Scalar Arguments ..
196  COMPLEX alpha,beta
197  INTEGER incx,incy,kl,ku,lda,m,n
198  CHARACTER trans
199 * ..
200 * .. Array Arguments ..
201  COMPLEX a(lda,*),x(*),y(*)
202 * ..
203 *
204 * =====================================================================
205 *
206 * .. Parameters ..
207  COMPLEX one
208  parameter(one= (1.0e+0,0.0e+0))
209  COMPLEX zero
210  parameter(zero= (0.0e+0,0.0e+0))
211 * ..
212 * .. Local Scalars ..
213  COMPLEX 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 conjg,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('CGBMV ',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 + conjg(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 + conjg(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 CGBMV .
389 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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