 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ ssymv()

 subroutine ssymv ( character UPLO, integer N, real ALPHA, real, dimension(lda,*) A, integer LDA, real, dimension(*) X, integer INCX, real BETA, real, dimension(*) Y, integer INCY )

SSYMV

Purpose:
``` SSYMV  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.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.``` [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 REAL On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is REAL array, dimension ( LDA, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.``` [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 max( 1, n ).``` [in] X ``` X is REAL 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 REAL 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 REAL 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 151 of file ssymv.f.

152 *
153 * -- Reference BLAS level2 routine --
154 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 *
157 * .. Scalar Arguments ..
158  REAL ALPHA,BETA
159  INTEGER INCX,INCY,LDA,N
160  CHARACTER UPLO
161 * ..
162 * .. Array Arguments ..
163  REAL A(LDA,*),X(*),Y(*)
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  REAL ONE,ZERO
170  parameter(one=1.0e+0,zero=0.0e+0)
171 * ..
172 * .. Local Scalars ..
173  REAL TEMP1,TEMP2
174  INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
175 * ..
176 * .. External Functions ..
177  LOGICAL LSAME
178  EXTERNAL lsame
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL xerbla
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 *
187 * Test the input parameters.
188 *
189  info = 0
190  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
191  info = 1
192  ELSE IF (n.LT.0) THEN
193  info = 2
194  ELSE IF (lda.LT.max(1,n)) THEN
195  info = 5
196  ELSE IF (incx.EQ.0) THEN
197  info = 7
198  ELSE IF (incy.EQ.0) THEN
199  info = 10
200  END IF
201  IF (info.NE.0) THEN
202  CALL xerbla('SSYMV ',info)
203  RETURN
204  END IF
205 *
206 * Quick return if possible.
207 *
208  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
209 *
210 * Set up the start points in X and Y.
211 *
212  IF (incx.GT.0) THEN
213  kx = 1
214  ELSE
215  kx = 1 - (n-1)*incx
216  END IF
217  IF (incy.GT.0) THEN
218  ky = 1
219  ELSE
220  ky = 1 - (n-1)*incy
221  END IF
222 *
223 * Start the operations. In this version the elements of A are
224 * accessed sequentially with one pass through the triangular part
225 * of A.
226 *
227 * First form y := beta*y.
228 *
229  IF (beta.NE.one) THEN
230  IF (incy.EQ.1) THEN
231  IF (beta.EQ.zero) THEN
232  DO 10 i = 1,n
233  y(i) = zero
234  10 CONTINUE
235  ELSE
236  DO 20 i = 1,n
237  y(i) = beta*y(i)
238  20 CONTINUE
239  END IF
240  ELSE
241  iy = ky
242  IF (beta.EQ.zero) THEN
243  DO 30 i = 1,n
244  y(iy) = zero
245  iy = iy + incy
246  30 CONTINUE
247  ELSE
248  DO 40 i = 1,n
249  y(iy) = beta*y(iy)
250  iy = iy + incy
251  40 CONTINUE
252  END IF
253  END IF
254  END IF
255  IF (alpha.EQ.zero) RETURN
256  IF (lsame(uplo,'U')) THEN
257 *
258 * Form y when A is stored in upper triangle.
259 *
260  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
261  DO 60 j = 1,n
262  temp1 = alpha*x(j)
263  temp2 = zero
264  DO 50 i = 1,j - 1
265  y(i) = y(i) + temp1*a(i,j)
266  temp2 = temp2 + a(i,j)*x(i)
267  50 CONTINUE
268  y(j) = y(j) + temp1*a(j,j) + alpha*temp2
269  60 CONTINUE
270  ELSE
271  jx = kx
272  jy = ky
273  DO 80 j = 1,n
274  temp1 = alpha*x(jx)
275  temp2 = zero
276  ix = kx
277  iy = ky
278  DO 70 i = 1,j - 1
279  y(iy) = y(iy) + temp1*a(i,j)
280  temp2 = temp2 + a(i,j)*x(ix)
281  ix = ix + incx
282  iy = iy + incy
283  70 CONTINUE
284  y(jy) = y(jy) + temp1*a(j,j) + alpha*temp2
285  jx = jx + incx
286  jy = jy + incy
287  80 CONTINUE
288  END IF
289  ELSE
290 *
291 * Form y when A is stored in lower triangle.
292 *
293  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
294  DO 100 j = 1,n
295  temp1 = alpha*x(j)
296  temp2 = zero
297  y(j) = y(j) + temp1*a(j,j)
298  DO 90 i = j + 1,n
299  y(i) = y(i) + temp1*a(i,j)
300  temp2 = temp2 + a(i,j)*x(i)
301  90 CONTINUE
302  y(j) = y(j) + alpha*temp2
303  100 CONTINUE
304  ELSE
305  jx = kx
306  jy = ky
307  DO 120 j = 1,n
308  temp1 = alpha*x(jx)
309  temp2 = zero
310  y(jy) = y(jy) + temp1*a(j,j)
311  ix = jx
312  iy = jy
313  DO 110 i = j + 1,n
314  ix = ix + incx
315  iy = iy + incy
316  y(iy) = y(iy) + temp1*a(i,j)
317  temp2 = temp2 + a(i,j)*x(ix)
318  110 CONTINUE
319  y(jy) = y(jy) + alpha*temp2
320  jx = jx + incx
321  jy = jy + incy
322  120 CONTINUE
323  END IF
324  END IF
325 *
326  RETURN
327 *
328 * End of SSYMV
329 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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