1: *> \brief \b ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSPR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INCX, N
26: * COMPLEX*16 ALPHA
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 AP( * ), X( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSPR 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, supplied in packed form.
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 matrix A is supplied in the packed
54: *> array AP as follows:
55: *>
56: *> UPLO = 'U' or 'u' The upper triangular part of A is
57: *> supplied in AP.
58: *>
59: *> UPLO = 'L' or 'l' The lower triangular part of A is
60: *> supplied in AP.
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] AP
98: *> \verbatim
99: *> AP is COMPLEX*16 array, dimension at least
100: *> ( ( N*( N + 1 ) )/2 ).
101: *> Before entry, with UPLO = 'U' or 'u', the array AP must
102: *> contain the upper triangular part of the symmetric matrix
103: *> packed sequentially, column by column, so that AP( 1 )
104: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
105: *> and a( 2, 2 ) respectively, and so on. On exit, the array
106: *> AP is overwritten by the upper triangular part of the
107: *> updated matrix.
108: *> Before entry, with UPLO = 'L' or 'l', the array AP must
109: *> contain the lower triangular part of the symmetric matrix
110: *> packed sequentially, column by column, so that AP( 1 )
111: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
112: *> and a( 3, 1 ) respectively, and so on. On exit, the array
113: *> AP is overwritten by the lower triangular part of the
114: *> updated matrix.
115: *> Note that the imaginary parts of the diagonal elements need
116: *> not be set, they are assumed to be zero, and on exit they
117: *> are set to zero.
118: *> \endverbatim
119: *
120: * Authors:
121: * ========
122: *
123: *> \author Univ. of Tennessee
124: *> \author Univ. of California Berkeley
125: *> \author Univ. of Colorado Denver
126: *> \author NAG Ltd.
127: *
128: *> \ingroup complex16OTHERauxiliary
129: *
130: * =====================================================================
131: SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
132: *
133: * -- LAPACK auxiliary routine --
134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136: *
137: * .. Scalar Arguments ..
138: CHARACTER UPLO
139: INTEGER INCX, N
140: COMPLEX*16 ALPHA
141: * ..
142: * .. Array Arguments ..
143: COMPLEX*16 AP( * ), X( * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. Parameters ..
149: COMPLEX*16 ZERO
150: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
151: * ..
152: * .. Local Scalars ..
153: INTEGER I, INFO, IX, J, JX, K, KK, KX
154: COMPLEX*16 TEMP
155: * ..
156: * .. External Functions ..
157: LOGICAL LSAME
158: EXTERNAL LSAME
159: * ..
160: * .. External Subroutines ..
161: EXTERNAL XERBLA
162: * ..
163: * .. Executable Statements ..
164: *
165: * Test the input parameters.
166: *
167: INFO = 0
168: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
169: INFO = 1
170: ELSE IF( N.LT.0 ) THEN
171: INFO = 2
172: ELSE IF( INCX.EQ.0 ) THEN
173: INFO = 5
174: END IF
175: IF( INFO.NE.0 ) THEN
176: CALL XERBLA( 'ZSPR ', INFO )
177: RETURN
178: END IF
179: *
180: * Quick return if possible.
181: *
182: IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
183: $ RETURN
184: *
185: * Set the start point in X if the increment is not unity.
186: *
187: IF( INCX.LE.0 ) THEN
188: KX = 1 - ( N-1 )*INCX
189: ELSE IF( INCX.NE.1 ) THEN
190: KX = 1
191: END IF
192: *
193: * Start the operations. In this version the elements of the array AP
194: * are accessed sequentially with one pass through AP.
195: *
196: KK = 1
197: IF( LSAME( UPLO, 'U' ) ) THEN
198: *
199: * Form A when upper triangle is stored in AP.
200: *
201: IF( INCX.EQ.1 ) THEN
202: DO 20 J = 1, N
203: IF( X( J ).NE.ZERO ) THEN
204: TEMP = ALPHA*X( J )
205: K = KK
206: DO 10 I = 1, J - 1
207: AP( K ) = AP( K ) + X( I )*TEMP
208: K = K + 1
209: 10 CONTINUE
210: AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
211: ELSE
212: AP( KK+J-1 ) = AP( KK+J-1 )
213: END IF
214: KK = KK + J
215: 20 CONTINUE
216: ELSE
217: JX = KX
218: DO 40 J = 1, N
219: IF( X( JX ).NE.ZERO ) THEN
220: TEMP = ALPHA*X( JX )
221: IX = KX
222: DO 30 K = KK, KK + J - 2
223: AP( K ) = AP( K ) + X( IX )*TEMP
224: IX = IX + INCX
225: 30 CONTINUE
226: AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
227: ELSE
228: AP( KK+J-1 ) = AP( KK+J-1 )
229: END IF
230: JX = JX + INCX
231: KK = KK + J
232: 40 CONTINUE
233: END IF
234: ELSE
235: *
236: * Form A when lower triangle is stored in AP.
237: *
238: IF( INCX.EQ.1 ) THEN
239: DO 60 J = 1, N
240: IF( X( J ).NE.ZERO ) THEN
241: TEMP = ALPHA*X( J )
242: AP( KK ) = AP( KK ) + TEMP*X( J )
243: K = KK + 1
244: DO 50 I = J + 1, N
245: AP( K ) = AP( K ) + X( I )*TEMP
246: K = K + 1
247: 50 CONTINUE
248: ELSE
249: AP( KK ) = AP( KK )
250: END IF
251: KK = KK + N - J + 1
252: 60 CONTINUE
253: ELSE
254: JX = KX
255: DO 80 J = 1, N
256: IF( X( JX ).NE.ZERO ) THEN
257: TEMP = ALPHA*X( JX )
258: AP( KK ) = AP( KK ) + TEMP*X( JX )
259: IX = JX
260: DO 70 K = KK + 1, KK + N - J
261: IX = IX + INCX
262: AP( K ) = AP( K ) + X( IX )*TEMP
263: 70 CONTINUE
264: ELSE
265: AP( KK ) = AP( KK )
266: END IF
267: JX = JX + INCX
268: KK = KK + N - J + 1
269: 80 CONTINUE
270: END IF
271: END IF
272: *
273: RETURN
274: *
275: * End of ZSPR
276: *
277: END
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