LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dgbmv()

subroutine dgbmv ( character trans,
integer m,
integer n,
integer kl,
integer ku,
double precision alpha,
double precision, dimension(lda,*) a,
integer lda,
double precision, dimension(*) x,
integer incx,
double precision beta,
double precision, dimension(*) y,
integer incy )

DGBMV

Purpose:
!>
!> DGBMV  performs one of the matrix-vector operations
!>
!>    y := alpha*A*x + beta*y,   or   y := alpha*A**T*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**T*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 DOUBLE PRECISION.
!>           On entry, ALPHA specifies the scalar alpha.
!>
[in]A
!>          A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION.
!>           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 DOUBLE PRECISION 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 186 of file dgbmv.f.

188*
189* -- Reference BLAS level2 routine --
190* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
191* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192*
193* .. Scalar Arguments ..
194 DOUBLE PRECISION ALPHA,BETA
195 INTEGER INCX,INCY,KL,KU,LDA,M,N
196 CHARACTER TRANS
197* ..
198* .. Array Arguments ..
199 DOUBLE PRECISION A(LDA,*),X(*),Y(*)
200* ..
201*
202* =====================================================================
203*
204* .. Parameters ..
205 DOUBLE PRECISION ONE,ZERO
206 parameter(one=1.0d+0,zero=0.0d+0)
207* ..
208* .. Local Scalars ..
209 DOUBLE PRECISION TEMP
210 INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
211* ..
212* .. External Functions ..
213 LOGICAL LSAME
214 EXTERNAL lsame
215* ..
216* .. External Subroutines ..
217 EXTERNAL xerbla
218* ..
219* .. Intrinsic Functions ..
220 INTRINSIC max,min
221* ..
222*
223* Test the input parameters.
224*
225 info = 0
226 IF (.NOT.lsame(trans,'N') .AND. .NOT.lsame(trans,'T') .AND.
227 + .NOT.lsame(trans,'C')) THEN
228 info = 1
229 ELSE IF (m.LT.0) THEN
230 info = 2
231 ELSE IF (n.LT.0) THEN
232 info = 3
233 ELSE IF (kl.LT.0) THEN
234 info = 4
235 ELSE IF (ku.LT.0) THEN
236 info = 5
237 ELSE IF (lda.LT. (kl+ku+1)) THEN
238 info = 8
239 ELSE IF (incx.EQ.0) THEN
240 info = 10
241 ELSE IF (incy.EQ.0) THEN
242 info = 13
243 END IF
244 IF (info.NE.0) THEN
245 CALL xerbla('DGBMV ',info)
246 RETURN
247 END IF
248*
249* Quick return if possible.
250*
251 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
252 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
253*
254* Set LENX and LENY, the lengths of the vectors x and y, and set
255* up the start points in X and Y.
256*
257 IF (lsame(trans,'N')) THEN
258 lenx = n
259 leny = m
260 ELSE
261 lenx = m
262 leny = n
263 END IF
264 IF (incx.GT.0) THEN
265 kx = 1
266 ELSE
267 kx = 1 - (lenx-1)*incx
268 END IF
269 IF (incy.GT.0) THEN
270 ky = 1
271 ELSE
272 ky = 1 - (leny-1)*incy
273 END IF
274*
275* Start the operations. In this version the elements of A are
276* accessed sequentially with one pass through the band part of A.
277*
278* First form y := beta*y.
279*
280 IF (beta.NE.one) THEN
281 IF (incy.EQ.1) THEN
282 IF (beta.EQ.zero) THEN
283 DO 10 i = 1,leny
284 y(i) = zero
285 10 CONTINUE
286 ELSE
287 DO 20 i = 1,leny
288 y(i) = beta*y(i)
289 20 CONTINUE
290 END IF
291 ELSE
292 iy = ky
293 IF (beta.EQ.zero) THEN
294 DO 30 i = 1,leny
295 y(iy) = zero
296 iy = iy + incy
297 30 CONTINUE
298 ELSE
299 DO 40 i = 1,leny
300 y(iy) = beta*y(iy)
301 iy = iy + incy
302 40 CONTINUE
303 END IF
304 END IF
305 END IF
306 IF (alpha.EQ.zero) RETURN
307 kup1 = ku + 1
308 IF (lsame(trans,'N')) THEN
309*
310* Form y := alpha*A*x + y.
311*
312 jx = kx
313 IF (incy.EQ.1) THEN
314 DO 60 j = 1,n
315 temp = alpha*x(jx)
316 k = kup1 - j
317 DO 50 i = max(1,j-ku),min(m,j+kl)
318 y(i) = y(i) + temp*a(k+i,j)
319 50 CONTINUE
320 jx = jx + incx
321 60 CONTINUE
322 ELSE
323 DO 80 j = 1,n
324 temp = alpha*x(jx)
325 iy = ky
326 k = kup1 - j
327 DO 70 i = max(1,j-ku),min(m,j+kl)
328 y(iy) = y(iy) + temp*a(k+i,j)
329 iy = iy + incy
330 70 CONTINUE
331 jx = jx + incx
332 IF (j.GT.ku) ky = ky + incy
333 80 CONTINUE
334 END IF
335 ELSE
336*
337* Form y := alpha*A**T*x + y.
338*
339 jy = ky
340 IF (incx.EQ.1) THEN
341 DO 100 j = 1,n
342 temp = zero
343 k = kup1 - j
344 DO 90 i = max(1,j-ku),min(m,j+kl)
345 temp = temp + a(k+i,j)*x(i)
346 90 CONTINUE
347 y(jy) = y(jy) + alpha*temp
348 jy = jy + incy
349 100 CONTINUE
350 ELSE
351 DO 120 j = 1,n
352 temp = zero
353 ix = kx
354 k = kup1 - j
355 DO 110 i = max(1,j-ku),min(m,j+kl)
356 temp = temp + a(k+i,j)*x(ix)
357 ix = ix + incx
358 110 CONTINUE
359 y(jy) = y(jy) + alpha*temp
360 jy = jy + incy
361 IF (j.GT.ku) kx = kx + incx
362 120 CONTINUE
363 END IF
364 END IF
365*
366 RETURN
367*
368* End of DGBMV
369*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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