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1.8 bertrand 1: *> \brief \b DSPR2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA
15: * INTEGER INCX,INCY,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION AP(*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DSPR2 performs the symmetric rank 2 operation
29: *>
30: *> A := alpha*x*y**T + alpha*y*x**T + A,
31: *>
32: *> where alpha is a scalar, x and y are n element vectors and A is an
33: *> n by n symmetric matrix, supplied in packed form.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] UPLO
40: *> \verbatim
41: *> UPLO is CHARACTER*1
42: *> On entry, UPLO specifies whether the upper or lower
43: *> triangular part of the matrix A is supplied in the packed
44: *> array AP as follows:
45: *>
46: *> UPLO = 'U' or 'u' The upper triangular part of A is
47: *> supplied in AP.
48: *>
49: *> UPLO = 'L' or 'l' The lower triangular part of A is
50: *> supplied in AP.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> On entry, N specifies the order of the matrix A.
57: *> N must be at least zero.
58: *> \endverbatim
59: *>
60: *> \param[in] ALPHA
61: *> \verbatim
62: *> ALPHA is DOUBLE PRECISION.
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] X
67: *> \verbatim
68: *> X is DOUBLE PRECISION array of dimension at least
69: *> ( 1 + ( n - 1 )*abs( INCX ) ).
70: *> Before entry, the incremented array X must contain the n
71: *> element vector x.
72: *> \endverbatim
73: *>
74: *> \param[in] INCX
75: *> \verbatim
76: *> INCX is INTEGER
77: *> On entry, INCX specifies the increment for the elements of
78: *> X. INCX must not be zero.
79: *> \endverbatim
80: *>
81: *> \param[in] Y
82: *> \verbatim
83: *> Y is DOUBLE PRECISION array of dimension at least
84: *> ( 1 + ( n - 1 )*abs( INCY ) ).
85: *> Before entry, the incremented array Y must contain the n
86: *> element vector y.
87: *> \endverbatim
88: *>
89: *> \param[in] INCY
90: *> \verbatim
91: *> INCY is INTEGER
92: *> On entry, INCY specifies the increment for the elements of
93: *> Y. INCY must not be zero.
94: *> \endverbatim
95: *>
96: *> \param[in,out] AP
97: *> \verbatim
98: *> AP is DOUBLE PRECISION array of DIMENSION at least
99: *> ( ( n*( n + 1 ) )/2 ).
100: *> Before entry with UPLO = 'U' or 'u', the array AP must
101: *> contain the upper triangular part of the symmetric matrix
102: *> packed sequentially, column by column, so that AP( 1 )
103: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
104: *> and a( 2, 2 ) respectively, and so on. On exit, the array
105: *> AP is overwritten by the upper triangular part of the
106: *> updated matrix.
107: *> Before entry with UPLO = 'L' or 'l', the array AP must
108: *> contain the lower triangular part of the symmetric matrix
109: *> packed sequentially, column by column, so that AP( 1 )
110: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
111: *> and a( 3, 1 ) respectively, and so on. On exit, the array
112: *> AP is overwritten by the lower triangular part of the
113: *> updated matrix.
114: *> \endverbatim
115: *
116: * Authors:
117: * ========
118: *
119: *> \author Univ. of Tennessee
120: *> \author Univ. of California Berkeley
121: *> \author Univ. of Colorado Denver
122: *> \author NAG Ltd.
123: *
124: *> \date November 2011
125: *
126: *> \ingroup double_blas_level2
127: *
128: *> \par Further Details:
129: * =====================
130: *>
131: *> \verbatim
132: *>
133: *> Level 2 Blas routine.
134: *>
135: *> -- Written on 22-October-1986.
136: *> Jack Dongarra, Argonne National Lab.
137: *> Jeremy Du Croz, Nag Central Office.
138: *> Sven Hammarling, Nag Central Office.
139: *> Richard Hanson, Sandia National Labs.
140: *> \endverbatim
141: *>
142: * =====================================================================
1.1 bertrand 143: SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
1.8 bertrand 144: *
145: * -- Reference BLAS level2 routine (version 3.4.0) --
146: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148: * November 2011
149: *
1.1 bertrand 150: * .. Scalar Arguments ..
151: DOUBLE PRECISION ALPHA
152: INTEGER INCX,INCY,N
153: CHARACTER UPLO
154: * ..
155: * .. Array Arguments ..
156: DOUBLE PRECISION AP(*),X(*),Y(*)
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ZERO
163: PARAMETER (ZERO=0.0D+0)
164: * ..
165: * .. Local Scalars ..
166: DOUBLE PRECISION TEMP1,TEMP2
167: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA
175: * ..
176: *
177: * Test the input parameters.
178: *
179: INFO = 0
180: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
181: INFO = 1
182: ELSE IF (N.LT.0) THEN
183: INFO = 2
184: ELSE IF (INCX.EQ.0) THEN
185: INFO = 5
186: ELSE IF (INCY.EQ.0) THEN
187: INFO = 7
188: END IF
189: IF (INFO.NE.0) THEN
190: CALL XERBLA('DSPR2 ',INFO)
191: RETURN
192: END IF
193: *
194: * Quick return if possible.
195: *
196: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
197: *
198: * Set up the start points in X and Y if the increments are not both
199: * unity.
200: *
201: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
202: IF (INCX.GT.0) THEN
203: KX = 1
204: ELSE
205: KX = 1 - (N-1)*INCX
206: END IF
207: IF (INCY.GT.0) THEN
208: KY = 1
209: ELSE
210: KY = 1 - (N-1)*INCY
211: END IF
212: JX = KX
213: JY = KY
214: END IF
215: *
216: * Start the operations. In this version the elements of the array AP
217: * are accessed sequentially with one pass through AP.
218: *
219: KK = 1
220: IF (LSAME(UPLO,'U')) THEN
221: *
222: * Form A when upper triangle is stored in AP.
223: *
224: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
225: DO 20 J = 1,N
226: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
227: TEMP1 = ALPHA*Y(J)
228: TEMP2 = ALPHA*X(J)
229: K = KK
230: DO 10 I = 1,J
231: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
232: K = K + 1
233: 10 CONTINUE
234: END IF
235: KK = KK + J
236: 20 CONTINUE
237: ELSE
238: DO 40 J = 1,N
239: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
240: TEMP1 = ALPHA*Y(JY)
241: TEMP2 = ALPHA*X(JX)
242: IX = KX
243: IY = KY
244: DO 30 K = KK,KK + J - 1
245: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
246: IX = IX + INCX
247: IY = IY + INCY
248: 30 CONTINUE
249: END IF
250: JX = JX + INCX
251: JY = JY + INCY
252: KK = KK + J
253: 40 CONTINUE
254: END IF
255: ELSE
256: *
257: * Form A when lower triangle is stored in AP.
258: *
259: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
260: DO 60 J = 1,N
261: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
262: TEMP1 = ALPHA*Y(J)
263: TEMP2 = ALPHA*X(J)
264: K = KK
265: DO 50 I = J,N
266: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
267: K = K + 1
268: 50 CONTINUE
269: END IF
270: KK = KK + N - J + 1
271: 60 CONTINUE
272: ELSE
273: DO 80 J = 1,N
274: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
275: TEMP1 = ALPHA*Y(JY)
276: TEMP2 = ALPHA*X(JX)
277: IX = JX
278: IY = JY
279: DO 70 K = KK,KK + N - J
280: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
281: IX = IX + INCX
282: IY = IY + INCY
283: 70 CONTINUE
284: END IF
285: JX = JX + INCX
286: JY = JY + INCY
287: KK = KK + N - J + 1
288: 80 CONTINUE
289: END IF
290: END IF
291: *
292: RETURN
293: *
294: * End of DSPR2 .
295: *
296: END