LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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chbmv.f
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1*> \brief \b CHBMV
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12*
13* .. Scalar Arguments ..
14* COMPLEX ALPHA,BETA
15* INTEGER INCX,INCY,K,LDA,N
16* CHARACTER UPLO
17* ..
18* .. Array Arguments ..
19* COMPLEX A(LDA,*),X(*),Y(*)
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> CHBMV performs the matrix-vector operation
29*>
30*> y := alpha*A*x + beta*y,
31*>
32*> where alpha and beta are scalars, x and y are n element vectors and
33*> A is an n by n hermitian band matrix, with k super-diagonals.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*> UPLO is CHARACTER*1
42*> On entry, UPLO specifies whether the upper or lower
43*> triangular part of the band matrix A is being supplied as
44*> follows:
45*>
46*> UPLO = 'U' or 'u' The upper triangular part of A is
47*> being supplied.
48*>
49*> UPLO = 'L' or 'l' The lower triangular part of A is
50*> being supplied.
51*> \endverbatim
52*>
53*> \param[in] N
54*> \verbatim
55*> N is INTEGER
56*> On entry, N specifies the order of the matrix A.
57*> N must be at least zero.
58*> \endverbatim
59*>
60*> \param[in] K
61*> \verbatim
62*> K is INTEGER
63*> On entry, K specifies the number of super-diagonals of the
64*> matrix A. K must satisfy 0 .le. K.
65*> \endverbatim
66*>
67*> \param[in] ALPHA
68*> \verbatim
69*> ALPHA is COMPLEX
70*> On entry, ALPHA specifies the scalar alpha.
71*> \endverbatim
72*>
73*> \param[in] A
74*> \verbatim
75*> A is COMPLEX array, dimension ( LDA, N )
76*> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
77*> by n part of the array A must contain the upper triangular
78*> band part of the hermitian matrix, supplied column by
79*> column, with the leading diagonal of the matrix in row
80*> ( k + 1 ) of the array, the first super-diagonal starting at
81*> position 2 in row k, and so on. The top left k by k triangle
82*> of the array A is not referenced.
83*> The following program segment will transfer the upper
84*> triangular part of a hermitian band matrix from conventional
85*> full matrix storage to band storage:
86*>
87*> DO 20, J = 1, N
88*> M = K + 1 - J
89*> DO 10, I = MAX( 1, J - K ), J
90*> A( M + I, J ) = matrix( I, J )
91*> 10 CONTINUE
92*> 20 CONTINUE
93*>
94*> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
95*> by n part of the array A must contain the lower triangular
96*> band part of the hermitian matrix, supplied column by
97*> column, with the leading diagonal of the matrix in row 1 of
98*> the array, the first sub-diagonal starting at position 1 in
99*> row 2, and so on. The bottom right k by k triangle of the
100*> array A is not referenced.
101*> The following program segment will transfer the lower
102*> triangular part of a hermitian band matrix from conventional
103*> full matrix storage to band storage:
104*>
105*> DO 20, J = 1, N
106*> M = 1 - J
107*> DO 10, I = J, MIN( N, J + K )
108*> A( M + I, J ) = matrix( I, J )
109*> 10 CONTINUE
110*> 20 CONTINUE
111*>
112*> Note that the imaginary parts of the diagonal elements need
113*> not be set and are assumed to be zero.
114*> \endverbatim
115*>
116*> \param[in] LDA
117*> \verbatim
118*> LDA is INTEGER
119*> On entry, LDA specifies the first dimension of A as declared
120*> in the calling (sub) program. LDA must be at least
121*> ( k + 1 ).
122*> \endverbatim
123*>
124*> \param[in] X
125*> \verbatim
126*> X is COMPLEX array, dimension at least
127*> ( 1 + ( n - 1 )*abs( INCX ) ).
128*> Before entry, the incremented array X must contain the
129*> vector x.
130*> \endverbatim
131*>
132*> \param[in] INCX
133*> \verbatim
134*> INCX is INTEGER
135*> On entry, INCX specifies the increment for the elements of
136*> X. INCX must not be zero.
137*> \endverbatim
138*>
139*> \param[in] BETA
140*> \verbatim
141*> BETA is COMPLEX
142*> On entry, BETA specifies the scalar beta.
143*> \endverbatim
144*>
145*> \param[in,out] Y
146*> \verbatim
147*> Y is COMPLEX array, dimension at least
148*> ( 1 + ( n - 1 )*abs( INCY ) ).
149*> Before entry, the incremented array Y must contain the
150*> vector y. On exit, Y is overwritten by the updated vector y.
151*> \endverbatim
152*>
153*> \param[in] INCY
154*> \verbatim
155*> INCY is INTEGER
156*> On entry, INCY specifies the increment for the elements of
157*> Y. INCY must not be zero.
158*> \endverbatim
159*
160* Authors:
161* ========
162*
163*> \author Univ. of Tennessee
164*> \author Univ. of California Berkeley
165*> \author Univ. of Colorado Denver
166*> \author NAG Ltd.
167*
168*> \ingroup hbmv
169*
170*> \par Further Details:
171* =====================
172*>
173*> \verbatim
174*>
175*> Level 2 Blas routine.
176*> The vector and matrix arguments are not referenced when N = 0, or M = 0
177*>
178*> -- Written on 22-October-1986.
179*> Jack Dongarra, Argonne National Lab.
180*> Jeremy Du Croz, Nag Central Office.
181*> Sven Hammarling, Nag Central Office.
182*> Richard Hanson, Sandia National Labs.
183*> \endverbatim
184*>
185* =====================================================================
186 SUBROUTINE chbmv(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
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,K,LDA,N
195 CHARACTER UPLO
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 TEMP1,TEMP2
211 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
212* ..
213* .. External Functions ..
214 LOGICAL LSAME
215 EXTERNAL lsame
216* ..
217* .. External Subroutines ..
218 EXTERNAL xerbla
219* ..
220* .. Intrinsic Functions ..
221 INTRINSIC conjg,max,min,real
222* ..
223*
224* Test the input parameters.
225*
226 info = 0
227 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
228 info = 1
229 ELSE IF (n.LT.0) THEN
230 info = 2
231 ELSE IF (k.LT.0) THEN
232 info = 3
233 ELSE IF (lda.LT. (k+1)) THEN
234 info = 6
235 ELSE IF (incx.EQ.0) THEN
236 info = 8
237 ELSE IF (incy.EQ.0) THEN
238 info = 11
239 END IF
240 IF (info.NE.0) THEN
241 CALL xerbla('CHBMV ',info)
242 RETURN
243 END IF
244*
245* Quick return if possible.
246*
247 IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
248*
249* Set up the start points in X and Y.
250*
251 IF (incx.GT.0) THEN
252 kx = 1
253 ELSE
254 kx = 1 - (n-1)*incx
255 END IF
256 IF (incy.GT.0) THEN
257 ky = 1
258 ELSE
259 ky = 1 - (n-1)*incy
260 END IF
261*
262* Start the operations. In this version the elements of the array A
263* are accessed sequentially with one pass through A.
264*
265* First form y := beta*y.
266*
267 IF (beta.NE.one) THEN
268 IF (incy.EQ.1) THEN
269 IF (beta.EQ.zero) THEN
270 DO 10 i = 1,n
271 y(i) = zero
272 10 CONTINUE
273 ELSE
274 DO 20 i = 1,n
275 y(i) = beta*y(i)
276 20 CONTINUE
277 END IF
278 ELSE
279 iy = ky
280 IF (beta.EQ.zero) THEN
281 DO 30 i = 1,n
282 y(iy) = zero
283 iy = iy + incy
284 30 CONTINUE
285 ELSE
286 DO 40 i = 1,n
287 y(iy) = beta*y(iy)
288 iy = iy + incy
289 40 CONTINUE
290 END IF
291 END IF
292 END IF
293 IF (alpha.EQ.zero) RETURN
294 IF (lsame(uplo,'U')) THEN
295*
296* Form y when upper triangle of A is stored.
297*
298 kplus1 = k + 1
299 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
300 DO 60 j = 1,n
301 temp1 = alpha*x(j)
302 temp2 = zero
303 l = kplus1 - j
304 DO 50 i = max(1,j-k),j - 1
305 y(i) = y(i) + temp1*a(l+i,j)
306 temp2 = temp2 + conjg(a(l+i,j))*x(i)
307 50 CONTINUE
308 y(j) = y(j) + temp1*real(a(kplus1,j)) + alpha*temp2
309 60 CONTINUE
310 ELSE
311 jx = kx
312 jy = ky
313 DO 80 j = 1,n
314 temp1 = alpha*x(jx)
315 temp2 = zero
316 ix = kx
317 iy = ky
318 l = kplus1 - j
319 DO 70 i = max(1,j-k),j - 1
320 y(iy) = y(iy) + temp1*a(l+i,j)
321 temp2 = temp2 + conjg(a(l+i,j))*x(ix)
322 ix = ix + incx
323 iy = iy + incy
324 70 CONTINUE
325 y(jy) = y(jy) + temp1*real(a(kplus1,j)) + alpha*temp2
326 jx = jx + incx
327 jy = jy + incy
328 IF (j.GT.k) THEN
329 kx = kx + incx
330 ky = ky + incy
331 END IF
332 80 CONTINUE
333 END IF
334 ELSE
335*
336* Form y when lower triangle of A is stored.
337*
338 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
339 DO 100 j = 1,n
340 temp1 = alpha*x(j)
341 temp2 = zero
342 y(j) = y(j) + temp1*real(a(1,j))
343 l = 1 - j
344 DO 90 i = j + 1,min(n,j+k)
345 y(i) = y(i) + temp1*a(l+i,j)
346 temp2 = temp2 + conjg(a(l+i,j))*x(i)
347 90 CONTINUE
348 y(j) = y(j) + alpha*temp2
349 100 CONTINUE
350 ELSE
351 jx = kx
352 jy = ky
353 DO 120 j = 1,n
354 temp1 = alpha*x(jx)
355 temp2 = zero
356 y(jy) = y(jy) + temp1*real(a(1,j))
357 l = 1 - j
358 ix = jx
359 iy = jy
360 DO 110 i = j + 1,min(n,j+k)
361 ix = ix + incx
362 iy = iy + incy
363 y(iy) = y(iy) + temp1*a(l+i,j)
364 temp2 = temp2 + conjg(a(l+i,j))*x(ix)
365 110 CONTINUE
366 y(jy) = y(jy) + alpha*temp2
367 jx = jx + incx
368 jy = jy + incy
369 120 CONTINUE
370 END IF
371 END IF
372*
373 RETURN
374*
375* End of CHBMV
376*
377 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chbmv(uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
CHBMV
Definition chbmv.f:187