LAPACK  3.11.0
LAPACK: Linear Algebra PACKage
dsbmv.f
1 *> \brief \b DSBMV
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 DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12 *
13 * .. Scalar Arguments ..
14 * DOUBLE PRECISION ALPHA,BETA
15 * INTEGER INCX,INCY,K,LDA,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> DSBMV 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 symmetric 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 DOUBLE PRECISION.
70 *> On entry, ALPHA specifies the scalar alpha.
71 *> \endverbatim
72 *>
73 *> \param[in] A
74 *> \verbatim
75 *> A is DOUBLE PRECISION 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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 *> \endverbatim
112 *>
113 *> \param[in] LDA
114 *> \verbatim
115 *> LDA is INTEGER
116 *> On entry, LDA specifies the first dimension of A as declared
117 *> in the calling (sub) program. LDA must be at least
118 *> ( k + 1 ).
119 *> \endverbatim
120 *>
121 *> \param[in] X
122 *> \verbatim
123 *> X is DOUBLE PRECISION array, dimension at least
124 *> ( 1 + ( n - 1 )*abs( INCX ) ).
125 *> Before entry, the incremented array X must contain the
126 *> vector x.
127 *> \endverbatim
128 *>
129 *> \param[in] INCX
130 *> \verbatim
131 *> INCX is INTEGER
132 *> On entry, INCX specifies the increment for the elements of
133 *> X. INCX must not be zero.
134 *> \endverbatim
135 *>
136 *> \param[in] BETA
137 *> \verbatim
138 *> BETA is DOUBLE PRECISION.
139 *> On entry, BETA specifies the scalar beta.
140 *> \endverbatim
141 *>
142 *> \param[in,out] Y
143 *> \verbatim
144 *> Y is DOUBLE PRECISION array, dimension at least
145 *> ( 1 + ( n - 1 )*abs( INCY ) ).
146 *> Before entry, the incremented array Y must contain the
147 *> vector y. On exit, Y is overwritten by the updated vector y.
148 *> \endverbatim
149 *>
150 *> \param[in] INCY
151 *> \verbatim
152 *> INCY is INTEGER
153 *> On entry, INCY specifies the increment for the elements of
154 *> Y. INCY must not be zero.
155 *> \endverbatim
156 *
157 * Authors:
158 * ========
159 *
160 *> \author Univ. of Tennessee
161 *> \author Univ. of California Berkeley
162 *> \author Univ. of Colorado Denver
163 *> \author NAG Ltd.
164 *
165 *> \ingroup hbmv
166 *
167 *> \par Further Details:
168 * =====================
169 *>
170 *> \verbatim
171 *>
172 *> Level 2 Blas routine.
173 *> The vector and matrix arguments are not referenced when N = 0, or M = 0
174 *>
175 *> -- Written on 22-October-1986.
176 *> Jack Dongarra, Argonne National Lab.
177 *> Jeremy Du Croz, Nag Central Office.
178 *> Sven Hammarling, Nag Central Office.
179 *> Richard Hanson, Sandia National Labs.
180 *> \endverbatim
181 *>
182 * =====================================================================
183  SUBROUTINE dsbmv(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
184 *
185 * -- Reference BLAS level2 routine --
186 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
187 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
188 *
189 * .. Scalar Arguments ..
190  DOUBLE PRECISION ALPHA,BETA
191  INTEGER INCX,INCY,K,LDA,N
192  CHARACTER UPLO
193 * ..
194 * .. Array Arguments ..
195  DOUBLE PRECISION A(lda,*),X(*),Y(*)
196 * ..
197 *
198 * =====================================================================
199 *
200 * .. Parameters ..
201  DOUBLE PRECISION ONE,ZERO
202  parameter(one=1.0d+0,zero=0.0d+0)
203 * ..
204 * .. Local Scalars ..
205  DOUBLE PRECISION TEMP1,TEMP2
206  INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
207 * ..
208 * .. External Functions ..
209  LOGICAL LSAME
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL xerbla
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max,min
217 * ..
218 *
219 * Test the input parameters.
220 *
221  info = 0
222  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
223  info = 1
224  ELSE IF (n.LT.0) THEN
225  info = 2
226  ELSE IF (k.LT.0) THEN
227  info = 3
228  ELSE IF (lda.LT. (k+1)) THEN
229  info = 6
230  ELSE IF (incx.EQ.0) THEN
231  info = 8
232  ELSE IF (incy.EQ.0) THEN
233  info = 11
234  END IF
235  IF (info.NE.0) THEN
236  CALL xerbla('DSBMV ',info)
237  RETURN
238  END IF
239 *
240 * Quick return if possible.
241 *
242  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
243 *
244 * Set up the start points in X and Y.
245 *
246  IF (incx.GT.0) THEN
247  kx = 1
248  ELSE
249  kx = 1 - (n-1)*incx
250  END IF
251  IF (incy.GT.0) THEN
252  ky = 1
253  ELSE
254  ky = 1 - (n-1)*incy
255  END IF
256 *
257 * Start the operations. In this version the elements of the array A
258 * are accessed sequentially with one pass through A.
259 *
260 * First form y := beta*y.
261 *
262  IF (beta.NE.one) THEN
263  IF (incy.EQ.1) THEN
264  IF (beta.EQ.zero) THEN
265  DO 10 i = 1,n
266  y(i) = zero
267  10 CONTINUE
268  ELSE
269  DO 20 i = 1,n
270  y(i) = beta*y(i)
271  20 CONTINUE
272  END IF
273  ELSE
274  iy = ky
275  IF (beta.EQ.zero) THEN
276  DO 30 i = 1,n
277  y(iy) = zero
278  iy = iy + incy
279  30 CONTINUE
280  ELSE
281  DO 40 i = 1,n
282  y(iy) = beta*y(iy)
283  iy = iy + incy
284  40 CONTINUE
285  END IF
286  END IF
287  END IF
288  IF (alpha.EQ.zero) RETURN
289  IF (lsame(uplo,'U')) THEN
290 *
291 * Form y when upper triangle of A is stored.
292 *
293  kplus1 = k + 1
294  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
295  DO 60 j = 1,n
296  temp1 = alpha*x(j)
297  temp2 = zero
298  l = kplus1 - j
299  DO 50 i = max(1,j-k),j - 1
300  y(i) = y(i) + temp1*a(l+i,j)
301  temp2 = temp2 + a(l+i,j)*x(i)
302  50 CONTINUE
303  y(j) = y(j) + temp1*a(kplus1,j) + alpha*temp2
304  60 CONTINUE
305  ELSE
306  jx = kx
307  jy = ky
308  DO 80 j = 1,n
309  temp1 = alpha*x(jx)
310  temp2 = zero
311  ix = kx
312  iy = ky
313  l = kplus1 - j
314  DO 70 i = max(1,j-k),j - 1
315  y(iy) = y(iy) + temp1*a(l+i,j)
316  temp2 = temp2 + a(l+i,j)*x(ix)
317  ix = ix + incx
318  iy = iy + incy
319  70 CONTINUE
320  y(jy) = y(jy) + temp1*a(kplus1,j) + alpha*temp2
321  jx = jx + incx
322  jy = jy + incy
323  IF (j.GT.k) THEN
324  kx = kx + incx
325  ky = ky + incy
326  END IF
327  80 CONTINUE
328  END IF
329  ELSE
330 *
331 * Form y when lower triangle of A is stored.
332 *
333  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
334  DO 100 j = 1,n
335  temp1 = alpha*x(j)
336  temp2 = zero
337  y(j) = y(j) + temp1*a(1,j)
338  l = 1 - j
339  DO 90 i = j + 1,min(n,j+k)
340  y(i) = y(i) + temp1*a(l+i,j)
341  temp2 = temp2 + a(l+i,j)*x(i)
342  90 CONTINUE
343  y(j) = y(j) + alpha*temp2
344  100 CONTINUE
345  ELSE
346  jx = kx
347  jy = ky
348  DO 120 j = 1,n
349  temp1 = alpha*x(jx)
350  temp2 = zero
351  y(jy) = y(jy) + temp1*a(1,j)
352  l = 1 - j
353  ix = jx
354  iy = jy
355  DO 110 i = j + 1,min(n,j+k)
356  ix = ix + incx
357  iy = iy + incy
358  y(iy) = y(iy) + temp1*a(l+i,j)
359  temp2 = temp2 + a(l+i,j)*x(ix)
360  110 CONTINUE
361  y(jy) = y(jy) + alpha*temp2
362  jx = jx + incx
363  jy = jy + incy
364  120 CONTINUE
365  END IF
366  END IF
367 *
368  RETURN
369 *
370 * End of DSBMV
371 *
372  END
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
dsbmv
subroutine dsbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DSBMV
Definition: dsbmv.f:184