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Mon Jan 27 09:28:42 2014 UTC (10 years, 3 months ago) by
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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
9: *> Download ZSYR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsyr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsyr.f">
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: *> \date September 2012
132: *
133: *> \ingroup complex16SYauxiliary
134: *
135: * =====================================================================
136: SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
137: *
138: * -- LAPACK auxiliary routine (version 3.4.2) --
139: * -- LAPACK is a software package provided by Univ. of Tennessee, --
140: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141: * September 2012
142: *
143: * .. Scalar Arguments ..
144: CHARACTER UPLO
145: INTEGER INCX, LDA, N
146: COMPLEX*16 ALPHA
147: * ..
148: * .. Array Arguments ..
149: COMPLEX*16 A( LDA, * ), X( * )
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: COMPLEX*16 ZERO
156: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
157: * ..
158: * .. Local Scalars ..
159: INTEGER I, INFO, IX, J, JX, KX
160: COMPLEX*16 TEMP
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: EXTERNAL LSAME
165: * ..
166: * .. External Subroutines ..
167: EXTERNAL XERBLA
168: * ..
169: * .. Intrinsic Functions ..
170: INTRINSIC MAX
171: * ..
172: * .. Executable Statements ..
173: *
174: * Test the input parameters.
175: *
176: INFO = 0
177: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
178: INFO = 1
179: ELSE IF( N.LT.0 ) THEN
180: INFO = 2
181: ELSE IF( INCX.EQ.0 ) THEN
182: INFO = 5
183: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
184: INFO = 7
185: END IF
186: IF( INFO.NE.0 ) THEN
187: CALL XERBLA( 'ZSYR ', INFO )
188: RETURN
189: END IF
190: *
191: * Quick return if possible.
192: *
193: IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
194: $ RETURN
195: *
196: * Set the start point in X if the increment is not unity.
197: *
198: IF( INCX.LE.0 ) THEN
199: KX = 1 - ( N-1 )*INCX
200: ELSE IF( INCX.NE.1 ) THEN
201: KX = 1
202: END IF
203: *
204: * Start the operations. In this version the elements of A are
205: * accessed sequentially with one pass through the triangular part
206: * of A.
207: *
208: IF( LSAME( UPLO, 'U' ) ) THEN
209: *
210: * Form A when A is stored in upper triangle.
211: *
212: IF( INCX.EQ.1 ) THEN
213: DO 20 J = 1, N
214: IF( X( J ).NE.ZERO ) THEN
215: TEMP = ALPHA*X( J )
216: DO 10 I = 1, J
217: A( I, J ) = A( I, J ) + X( I )*TEMP
218: 10 CONTINUE
219: END IF
220: 20 CONTINUE
221: ELSE
222: JX = KX
223: DO 40 J = 1, N
224: IF( X( JX ).NE.ZERO ) THEN
225: TEMP = ALPHA*X( JX )
226: IX = KX
227: DO 30 I = 1, J
228: A( I, J ) = A( I, J ) + X( IX )*TEMP
229: IX = IX + INCX
230: 30 CONTINUE
231: END IF
232: JX = JX + INCX
233: 40 CONTINUE
234: END IF
235: ELSE
236: *
237: * Form A when A is stored in lower triangle.
238: *
239: IF( INCX.EQ.1 ) THEN
240: DO 60 J = 1, N
241: IF( X( J ).NE.ZERO ) THEN
242: TEMP = ALPHA*X( J )
243: DO 50 I = J, N
244: A( I, J ) = A( I, J ) + X( I )*TEMP
245: 50 CONTINUE
246: END IF
247: 60 CONTINUE
248: ELSE
249: JX = KX
250: DO 80 J = 1, N
251: IF( X( JX ).NE.ZERO ) THEN
252: TEMP = ALPHA*X( JX )
253: IX = JX
254: DO 70 I = J, N
255: A( I, J ) = A( I, J ) + X( IX )*TEMP
256: IX = IX + INCX
257: 70 CONTINUE
258: END IF
259: JX = JX + INCX
260: 80 CONTINUE
261: END IF
262: END IF
263: *
264: RETURN
265: *
266: * End of ZSYR
267: *
268: END
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