1: SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
2: * .. Scalar Arguments ..
3: DOUBLE PRECISION ALPHA
4: INTEGER INCX,INCY,N
5: CHARACTER UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE PRECISION AP(*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * DSPR2 performs the symmetric rank 2 operation
15: *
16: * A := alpha*x*y' + alpha*y*x' + A,
17: *
18: * where alpha is a scalar, x and y are n element vectors and A is an
19: * n by n symmetric matrix, supplied in packed form.
20: *
21: * Arguments
22: * ==========
23: *
24: * UPLO - CHARACTER*1.
25: * On entry, UPLO specifies whether the upper or lower
26: * triangular part of the matrix A is supplied in the packed
27: * array AP as follows:
28: *
29: * UPLO = 'U' or 'u' The upper triangular part of A is
30: * supplied in AP.
31: *
32: * UPLO = 'L' or 'l' The lower triangular part of A is
33: * supplied in AP.
34: *
35: * Unchanged on exit.
36: *
37: * N - INTEGER.
38: * On entry, N specifies the order of the matrix A.
39: * N must be at least zero.
40: * Unchanged on exit.
41: *
42: * ALPHA - DOUBLE PRECISION.
43: * On entry, ALPHA specifies the scalar alpha.
44: * Unchanged on exit.
45: *
46: * X - DOUBLE PRECISION array of dimension at least
47: * ( 1 + ( n - 1 )*abs( INCX ) ).
48: * Before entry, the incremented array X must contain the n
49: * element vector x.
50: * Unchanged on exit.
51: *
52: * INCX - INTEGER.
53: * On entry, INCX specifies the increment for the elements of
54: * X. INCX must not be zero.
55: * Unchanged on exit.
56: *
57: * Y - DOUBLE PRECISION array of dimension at least
58: * ( 1 + ( n - 1 )*abs( INCY ) ).
59: * Before entry, the incremented array Y must contain the n
60: * element vector y.
61: * Unchanged on exit.
62: *
63: * INCY - INTEGER.
64: * On entry, INCY specifies the increment for the elements of
65: * Y. INCY must not be zero.
66: * Unchanged on exit.
67: *
68: * AP - DOUBLE PRECISION array of DIMENSION at least
69: * ( ( n*( n + 1 ) )/2 ).
70: * Before entry with UPLO = 'U' or 'u', the array AP must
71: * contain the upper triangular part of the symmetric matrix
72: * packed sequentially, column by column, so that AP( 1 )
73: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
74: * and a( 2, 2 ) respectively, and so on. On exit, the array
75: * AP is overwritten by the upper triangular part of the
76: * updated matrix.
77: * Before entry with UPLO = 'L' or 'l', the array AP must
78: * contain the lower triangular part of the symmetric matrix
79: * packed sequentially, column by column, so that AP( 1 )
80: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
81: * and a( 3, 1 ) respectively, and so on. On exit, the array
82: * AP is overwritten by the lower triangular part of the
83: * updated matrix.
84: *
85: * Further Details
86: * ===============
87: *
88: * Level 2 Blas routine.
89: *
90: * -- Written on 22-October-1986.
91: * Jack Dongarra, Argonne National Lab.
92: * Jeremy Du Croz, Nag Central Office.
93: * Sven Hammarling, Nag Central Office.
94: * Richard Hanson, Sandia National Labs.
95: *
96: * =====================================================================
97: *
98: * .. Parameters ..
99: DOUBLE PRECISION ZERO
100: PARAMETER (ZERO=0.0D+0)
101: * ..
102: * .. Local Scalars ..
103: DOUBLE PRECISION TEMP1,TEMP2
104: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
105: * ..
106: * .. External Functions ..
107: LOGICAL LSAME
108: EXTERNAL LSAME
109: * ..
110: * .. External Subroutines ..
111: EXTERNAL XERBLA
112: * ..
113: *
114: * Test the input parameters.
115: *
116: INFO = 0
117: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
118: INFO = 1
119: ELSE IF (N.LT.0) THEN
120: INFO = 2
121: ELSE IF (INCX.EQ.0) THEN
122: INFO = 5
123: ELSE IF (INCY.EQ.0) THEN
124: INFO = 7
125: END IF
126: IF (INFO.NE.0) THEN
127: CALL XERBLA('DSPR2 ',INFO)
128: RETURN
129: END IF
130: *
131: * Quick return if possible.
132: *
133: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
134: *
135: * Set up the start points in X and Y if the increments are not both
136: * unity.
137: *
138: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
139: IF (INCX.GT.0) THEN
140: KX = 1
141: ELSE
142: KX = 1 - (N-1)*INCX
143: END IF
144: IF (INCY.GT.0) THEN
145: KY = 1
146: ELSE
147: KY = 1 - (N-1)*INCY
148: END IF
149: JX = KX
150: JY = KY
151: END IF
152: *
153: * Start the operations. In this version the elements of the array AP
154: * are accessed sequentially with one pass through AP.
155: *
156: KK = 1
157: IF (LSAME(UPLO,'U')) THEN
158: *
159: * Form A when upper triangle is stored in AP.
160: *
161: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
162: DO 20 J = 1,N
163: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
164: TEMP1 = ALPHA*Y(J)
165: TEMP2 = ALPHA*X(J)
166: K = KK
167: DO 10 I = 1,J
168: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
169: K = K + 1
170: 10 CONTINUE
171: END IF
172: KK = KK + J
173: 20 CONTINUE
174: ELSE
175: DO 40 J = 1,N
176: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
177: TEMP1 = ALPHA*Y(JY)
178: TEMP2 = ALPHA*X(JX)
179: IX = KX
180: IY = KY
181: DO 30 K = KK,KK + J - 1
182: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
183: IX = IX + INCX
184: IY = IY + INCY
185: 30 CONTINUE
186: END IF
187: JX = JX + INCX
188: JY = JY + INCY
189: KK = KK + J
190: 40 CONTINUE
191: END IF
192: ELSE
193: *
194: * Form A when lower triangle is stored in AP.
195: *
196: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
197: DO 60 J = 1,N
198: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
199: TEMP1 = ALPHA*Y(J)
200: TEMP2 = ALPHA*X(J)
201: K = KK
202: DO 50 I = J,N
203: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
204: K = K + 1
205: 50 CONTINUE
206: END IF
207: KK = KK + N - J + 1
208: 60 CONTINUE
209: ELSE
210: DO 80 J = 1,N
211: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
212: TEMP1 = ALPHA*Y(JY)
213: TEMP2 = ALPHA*X(JX)
214: IX = JX
215: IY = JY
216: DO 70 K = KK,KK + N - J
217: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
218: IX = IX + INCX
219: IY = IY + INCY
220: 70 CONTINUE
221: END IF
222: JX = JX + INCX
223: JY = JY + INCY
224: KK = KK + N - J + 1
225: 80 CONTINUE
226: END IF
227: END IF
228: *
229: RETURN
230: *
231: * End of DSPR2 .
232: *
233: END
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