LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zsyr.f
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1*> \brief \b ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsyr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
22*
23* .. Scalar Arguments ..
24* CHARACTER UPLO
25* INTEGER INCX, LDA, N
26* COMPLEX*16 ALPHA
27* ..
28* .. Array Arguments ..
29* COMPLEX*16 A( LDA, * ), X( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZSYR performs the symmetric rank 1 operation
39*>
40*> A := alpha*x*x**H + A,
41*>
42*> where alpha is a complex scalar, x is an n element vector and A is an
43*> n by n symmetric matrix.
44*> \endverbatim
45*
46* Arguments:
47* ==========
48*
49*> \param[in] UPLO
50*> \verbatim
51*> UPLO is CHARACTER*1
52*> On entry, UPLO specifies whether the upper or lower
53*> triangular part of the array A is to be referenced as
54*> follows:
55*>
56*> UPLO = 'U' or 'u' Only the upper triangular part of A
57*> is to be referenced.
58*>
59*> UPLO = 'L' or 'l' Only the lower triangular part of A
60*> is to be referenced.
61*>
62*> Unchanged on exit.
63*> \endverbatim
64*>
65*> \param[in] N
66*> \verbatim
67*> N is INTEGER
68*> On entry, N specifies the order of the matrix A.
69*> N must be at least zero.
70*> Unchanged on exit.
71*> \endverbatim
72*>
73*> \param[in] ALPHA
74*> \verbatim
75*> ALPHA is COMPLEX*16
76*> On entry, ALPHA specifies the scalar alpha.
77*> Unchanged on exit.
78*> \endverbatim
79*>
80*> \param[in] X
81*> \verbatim
82*> X is COMPLEX*16 array, dimension at least
83*> ( 1 + ( N - 1 )*abs( INCX ) ).
84*> Before entry, the incremented array X must contain the N-
85*> element vector x.
86*> Unchanged on exit.
87*> \endverbatim
88*>
89*> \param[in] INCX
90*> \verbatim
91*> INCX is INTEGER
92*> On entry, INCX specifies the increment for the elements of
93*> X. INCX must not be zero.
94*> Unchanged on exit.
95*> \endverbatim
96*>
97*> \param[in,out] A
98*> \verbatim
99*> A is COMPLEX*16 array, dimension ( LDA, N )
100*> Before entry, with UPLO = 'U' or 'u', the leading n by n
101*> upper triangular part of the array A must contain the upper
102*> triangular part of the symmetric matrix and the strictly
103*> lower triangular part of A is not referenced. On exit, the
104*> upper triangular part of the array A is overwritten by the
105*> upper triangular part of the updated matrix.
106*> Before entry, with UPLO = 'L' or 'l', the leading n by n
107*> lower triangular part of the array A must contain the lower
108*> triangular part of the symmetric matrix and the strictly
109*> upper triangular part of A is not referenced. On exit, the
110*> lower triangular part of the array A is overwritten by the
111*> lower triangular part of the updated matrix.
112*> \endverbatim
113*>
114*> \param[in] LDA
115*> \verbatim
116*> LDA is INTEGER
117*> On entry, LDA specifies the first dimension of A as declared
118*> in the calling (sub) program. LDA must be at least
119*> max( 1, N ).
120*> Unchanged on exit.
121*> \endverbatim
122*
123* Authors:
124* ========
125*
126*> \author Univ. of Tennessee
127*> \author Univ. of California Berkeley
128*> \author Univ. of Colorado Denver
129*> \author NAG Ltd.
130*
131*> \ingroup her
132*
133* =====================================================================
134 SUBROUTINE zsyr( UPLO, N, ALPHA, X, INCX, A, LDA )
135*
136* -- LAPACK auxiliary routine --
137* -- LAPACK is a software package provided by Univ. of Tennessee, --
138* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*
140* .. Scalar Arguments ..
141 CHARACTER UPLO
142 INTEGER INCX, LDA, N
143 COMPLEX*16 ALPHA
144* ..
145* .. Array Arguments ..
146 COMPLEX*16 A( LDA, * ), X( * )
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 COMPLEX*16 ZERO
153 parameter( zero = ( 0.0d+0, 0.0d+0 ) )
154* ..
155* .. Local Scalars ..
156 INTEGER I, INFO, IX, J, JX, KX
157 COMPLEX*16 TEMP
158* ..
159* .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL lsame
162* ..
163* .. External Subroutines ..
164 EXTERNAL xerbla
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC max
168* ..
169* .. Executable Statements ..
170*
171* Test the input parameters.
172*
173 info = 0
174 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
175 info = 1
176 ELSE IF( n.LT.0 ) THEN
177 info = 2
178 ELSE IF( incx.EQ.0 ) THEN
179 info = 5
180 ELSE IF( lda.LT.max( 1, n ) ) THEN
181 info = 7
182 END IF
183 IF( info.NE.0 ) THEN
184 CALL xerbla( 'ZSYR ', info )
185 RETURN
186 END IF
187*
188* Quick return if possible.
189*
190 IF( ( n.EQ.0 ) .OR. ( alpha.EQ.zero ) )
191 \$ RETURN
192*
193* Set the start point in X if the increment is not unity.
194*
195 IF( incx.LE.0 ) THEN
196 kx = 1 - ( n-1 )*incx
197 ELSE IF( incx.NE.1 ) THEN
198 kx = 1
199 END IF
200*
201* Start the operations. In this version the elements of A are
202* accessed sequentially with one pass through the triangular part
203* of A.
204*
205 IF( lsame( uplo, 'U' ) ) THEN
206*
207* Form A when A is stored in upper triangle.
208*
209 IF( incx.EQ.1 ) THEN
210 DO 20 j = 1, n
211 IF( x( j ).NE.zero ) THEN
212 temp = alpha*x( j )
213 DO 10 i = 1, j
214 a( i, j ) = a( i, j ) + x( i )*temp
215 10 CONTINUE
216 END IF
217 20 CONTINUE
218 ELSE
219 jx = kx
220 DO 40 j = 1, n
221 IF( x( jx ).NE.zero ) THEN
222 temp = alpha*x( jx )
223 ix = kx
224 DO 30 i = 1, j
225 a( i, j ) = a( i, j ) + x( ix )*temp
226 ix = ix + incx
227 30 CONTINUE
228 END IF
229 jx = jx + incx
230 40 CONTINUE
231 END IF
232 ELSE
233*
234* Form A when A is stored in lower triangle.
235*
236 IF( incx.EQ.1 ) THEN
237 DO 60 j = 1, n
238 IF( x( j ).NE.zero ) THEN
239 temp = alpha*x( j )
240 DO 50 i = j, n
241 a( i, j ) = a( i, j ) + x( i )*temp
242 50 CONTINUE
243 END IF
244 60 CONTINUE
245 ELSE
246 jx = kx
247 DO 80 j = 1, n
248 IF( x( jx ).NE.zero ) THEN
249 temp = alpha*x( jx )
250 ix = jx
251 DO 70 i = j, n
252 a( i, j ) = a( i, j ) + x( ix )*temp
253 ix = ix + incx
254 70 CONTINUE
255 END IF
256 jx = jx + incx
257 80 CONTINUE
258 END IF
259 END IF
260*
261 RETURN
262*
263* End of ZSYR
264*
265 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zsyr(uplo, n, alpha, x, incx, a, lda)
ZSYR performs the symmetric rank-1 update of a complex symmetric matrix.
Definition zsyr.f:135