LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dspmv()

 subroutine dspmv ( character UPLO, integer N, double precision ALPHA, double precision, dimension(*) AP, double precision, dimension(*) X, integer INCX, double precision BETA, double precision, dimension(*) Y, integer INCY )

DSPMV

Purpose:
``` DSPMV  performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix, supplied in packed form.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.``` [in] ALPHA ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.``` [in] AP ``` AP is DOUBLE PRECISION array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the symmetric matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.``` [in] X ``` X is DOUBLE PRECISION array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element 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 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element 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.```
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 146 of file dspmv.f.

147 *
148 * -- Reference BLAS level2 routine --
149 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  DOUBLE PRECISION ALPHA,BETA
154  INTEGER INCX,INCY,N
155  CHARACTER UPLO
156 * ..
157 * .. Array Arguments ..
158  DOUBLE PRECISION AP(*),X(*),Y(*)
159 * ..
160 *
161 * =====================================================================
162 *
163 * .. Parameters ..
164  DOUBLE PRECISION ONE,ZERO
165  parameter(one=1.0d+0,zero=0.0d+0)
166 * ..
167 * .. Local Scalars ..
168  DOUBLE PRECISION TEMP1,TEMP2
169  INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  EXTERNAL lsame
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL xerbla
177 * ..
178 *
179 * Test the input parameters.
180 *
181  info = 0
182  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
183  info = 1
184  ELSE IF (n.LT.0) THEN
185  info = 2
186  ELSE IF (incx.EQ.0) THEN
187  info = 6
188  ELSE IF (incy.EQ.0) THEN
189  info = 9
190  END IF
191  IF (info.NE.0) THEN
192  CALL xerbla('DSPMV ',info)
193  RETURN
194  END IF
195 *
196 * Quick return if possible.
197 *
198  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
199 *
200 * Set up the start points in X and Y.
201 *
202  IF (incx.GT.0) THEN
203  kx = 1
204  ELSE
205  kx = 1 - (n-1)*incx
206  END IF
207  IF (incy.GT.0) THEN
208  ky = 1
209  ELSE
210  ky = 1 - (n-1)*incy
211  END IF
212 *
213 * Start the operations. In this version the elements of the array AP
214 * are accessed sequentially with one pass through AP.
215 *
216 * First form y := beta*y.
217 *
218  IF (beta.NE.one) THEN
219  IF (incy.EQ.1) THEN
220  IF (beta.EQ.zero) THEN
221  DO 10 i = 1,n
222  y(i) = zero
223  10 CONTINUE
224  ELSE
225  DO 20 i = 1,n
226  y(i) = beta*y(i)
227  20 CONTINUE
228  END IF
229  ELSE
230  iy = ky
231  IF (beta.EQ.zero) THEN
232  DO 30 i = 1,n
233  y(iy) = zero
234  iy = iy + incy
235  30 CONTINUE
236  ELSE
237  DO 40 i = 1,n
238  y(iy) = beta*y(iy)
239  iy = iy + incy
240  40 CONTINUE
241  END IF
242  END IF
243  END IF
244  IF (alpha.EQ.zero) RETURN
245  kk = 1
246  IF (lsame(uplo,'U')) THEN
247 *
248 * Form y when AP contains the upper triangle.
249 *
250  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
251  DO 60 j = 1,n
252  temp1 = alpha*x(j)
253  temp2 = zero
254  k = kk
255  DO 50 i = 1,j - 1
256  y(i) = y(i) + temp1*ap(k)
257  temp2 = temp2 + ap(k)*x(i)
258  k = k + 1
259  50 CONTINUE
260  y(j) = y(j) + temp1*ap(kk+j-1) + alpha*temp2
261  kk = kk + j
262  60 CONTINUE
263  ELSE
264  jx = kx
265  jy = ky
266  DO 80 j = 1,n
267  temp1 = alpha*x(jx)
268  temp2 = zero
269  ix = kx
270  iy = ky
271  DO 70 k = kk,kk + j - 2
272  y(iy) = y(iy) + temp1*ap(k)
273  temp2 = temp2 + ap(k)*x(ix)
274  ix = ix + incx
275  iy = iy + incy
276  70 CONTINUE
277  y(jy) = y(jy) + temp1*ap(kk+j-1) + alpha*temp2
278  jx = jx + incx
279  jy = jy + incy
280  kk = kk + j
281  80 CONTINUE
282  END IF
283  ELSE
284 *
285 * Form y when AP contains the lower triangle.
286 *
287  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
288  DO 100 j = 1,n
289  temp1 = alpha*x(j)
290  temp2 = zero
291  y(j) = y(j) + temp1*ap(kk)
292  k = kk + 1
293  DO 90 i = j + 1,n
294  y(i) = y(i) + temp1*ap(k)
295  temp2 = temp2 + ap(k)*x(i)
296  k = k + 1
297  90 CONTINUE
298  y(j) = y(j) + alpha*temp2
299  kk = kk + (n-j+1)
300  100 CONTINUE
301  ELSE
302  jx = kx
303  jy = ky
304  DO 120 j = 1,n
305  temp1 = alpha*x(jx)
306  temp2 = zero
307  y(jy) = y(jy) + temp1*ap(kk)
308  ix = jx
309  iy = jy
310  DO 110 k = kk + 1,kk + n - j
311  ix = ix + incx
312  iy = iy + incy
313  y(iy) = y(iy) + temp1*ap(k)
314  temp2 = temp2 + ap(k)*x(ix)
315  110 CONTINUE
316  y(jy) = y(jy) + alpha*temp2
317  jx = jx + incx
318  jy = jy + incy
319  kk = kk + (n-j+1)
320  120 CONTINUE
321  END IF
322  END IF
323 *
324  RETURN
325 *
326 * End of DSPMV
327 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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