 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ csymv()

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

CSYMV computes a matrix-vector product for a complex symmetric matrix.

Purpose:
``` CSYMV  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. Unchanged on exit.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha. Unchanged on exit.``` [in] A ``` A is COMPLEX 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. Unchanged on exit.``` [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 ). Unchanged on exit.``` [in] X ``` X is COMPLEX array, dimension at least ( 1 + ( N - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the N- element vector x. Unchanged on exit.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.``` [in,out] Y ``` Y is COMPLEX 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. Unchanged on exit.```

Definition at line 156 of file csymv.f.

157*
158* -- LAPACK auxiliary routine --
159* -- LAPACK is a software package provided by Univ. of Tennessee, --
160* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161*
162* .. Scalar Arguments ..
163 CHARACTER UPLO
164 INTEGER INCX, INCY, LDA, N
165 COMPLEX ALPHA, BETA
166* ..
167* .. Array Arguments ..
168 COMPLEX A( LDA, * ), X( * ), Y( * )
169* ..
170*
171* =====================================================================
172*
173* .. Parameters ..
174 COMPLEX ONE
175 parameter( one = ( 1.0e+0, 0.0e+0 ) )
176 COMPLEX ZERO
177 parameter( zero = ( 0.0e+0, 0.0e+0 ) )
178* ..
179* .. Local Scalars ..
180 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
181 COMPLEX TEMP1, TEMP2
182* ..
183* .. External Functions ..
184 LOGICAL LSAME
185 EXTERNAL lsame
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 info = 0
198 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
199 info = 1
200 ELSE IF( n.LT.0 ) THEN
201 info = 2
202 ELSE IF( lda.LT.max( 1, n ) ) THEN
203 info = 5
204 ELSE IF( incx.EQ.0 ) THEN
205 info = 7
206 ELSE IF( incy.EQ.0 ) THEN
207 info = 10
208 END IF
209 IF( info.NE.0 ) THEN
210 CALL xerbla( 'CSYMV ', info )
211 RETURN
212 END IF
213*
214* Quick return if possible.
215*
216 IF( ( n.EQ.0 ) .OR. ( ( alpha.EQ.zero ) .AND. ( beta.EQ.one ) ) )
217 \$ RETURN
218*
219* Set up the start points in X and Y.
220*
221 IF( incx.GT.0 ) THEN
222 kx = 1
223 ELSE
224 kx = 1 - ( n-1 )*incx
225 END IF
226 IF( incy.GT.0 ) THEN
227 ky = 1
228 ELSE
229 ky = 1 - ( n-1 )*incy
230 END IF
231*
232* Start the operations. In this version the elements of A are
233* accessed sequentially with one pass through the triangular part
234* of A.
235*
236* First form y := beta*y.
237*
238 IF( beta.NE.one ) THEN
239 IF( incy.EQ.1 ) THEN
240 IF( beta.EQ.zero ) THEN
241 DO 10 i = 1, n
242 y( i ) = zero
243 10 CONTINUE
244 ELSE
245 DO 20 i = 1, n
246 y( i ) = beta*y( i )
247 20 CONTINUE
248 END IF
249 ELSE
250 iy = ky
251 IF( beta.EQ.zero ) THEN
252 DO 30 i = 1, n
253 y( iy ) = zero
254 iy = iy + incy
255 30 CONTINUE
256 ELSE
257 DO 40 i = 1, n
258 y( iy ) = beta*y( iy )
259 iy = iy + incy
260 40 CONTINUE
261 END IF
262 END IF
263 END IF
264 IF( alpha.EQ.zero )
265 \$ RETURN
266 IF( lsame( uplo, 'U' ) ) THEN
267*
268* Form y when A is stored in upper triangle.
269*
270 IF( ( incx.EQ.1 ) .AND. ( incy.EQ.1 ) ) THEN
271 DO 60 j = 1, n
272 temp1 = alpha*x( j )
273 temp2 = zero
274 DO 50 i = 1, j - 1
275 y( i ) = y( i ) + temp1*a( i, j )
276 temp2 = temp2 + a( i, j )*x( i )
277 50 CONTINUE
278 y( j ) = y( j ) + temp1*a( j, j ) + alpha*temp2
279 60 CONTINUE
280 ELSE
281 jx = kx
282 jy = ky
283 DO 80 j = 1, n
284 temp1 = alpha*x( jx )
285 temp2 = zero
286 ix = kx
287 iy = ky
288 DO 70 i = 1, j - 1
289 y( iy ) = y( iy ) + temp1*a( i, j )
290 temp2 = temp2 + a( i, j )*x( ix )
291 ix = ix + incx
292 iy = iy + incy
293 70 CONTINUE
294 y( jy ) = y( jy ) + temp1*a( j, j ) + alpha*temp2
295 jx = jx + incx
296 jy = jy + incy
297 80 CONTINUE
298 END IF
299 ELSE
300*
301* Form y when A is stored in lower triangle.
302*
303 IF( ( incx.EQ.1 ) .AND. ( incy.EQ.1 ) ) THEN
304 DO 100 j = 1, n
305 temp1 = alpha*x( j )
306 temp2 = zero
307 y( j ) = y( j ) + temp1*a( j, j )
308 DO 90 i = j + 1, n
309 y( i ) = y( i ) + temp1*a( i, j )
310 temp2 = temp2 + a( i, j )*x( i )
311 90 CONTINUE
312 y( j ) = y( j ) + alpha*temp2
313 100 CONTINUE
314 ELSE
315 jx = kx
316 jy = ky
317 DO 120 j = 1, n
318 temp1 = alpha*x( jx )
319 temp2 = zero
320 y( jy ) = y( jy ) + temp1*a( j, j )
321 ix = jx
322 iy = jy
323 DO 110 i = j + 1, n
324 ix = ix + incx
325 iy = iy + incy
326 y( iy ) = y( iy ) + temp1*a( i, j )
327 temp2 = temp2 + a( i, j )*x( ix )
328 110 CONTINUE
329 y( jy ) = y( jy ) + alpha*temp2
330 jx = jx + incx
331 jy = jy + incy
332 120 CONTINUE
333 END IF
334 END IF
335*
336 RETURN
337*
338* End of CSYMV
339*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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