1: SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE PRECISION ALPHA,BETA
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: * DSPMV performs the matrix-vector operation
15: *
16: * y := alpha*A*x + beta*y,
17: *
18: * where alpha and beta are scalars, x and y are n element vectors and
19: * A is an 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: * AP - DOUBLE PRECISION array of DIMENSION at least
47: * ( ( n*( n + 1 ) )/2 ).
48: * Before entry with UPLO = 'U' or 'u', the array AP must
49: * contain the upper triangular part of the symmetric matrix
50: * packed sequentially, column by column, so that AP( 1 )
51: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
52: * and a( 2, 2 ) respectively, and so on.
53: * Before entry with UPLO = 'L' or 'l', the array AP must
54: * contain the lower triangular part of the symmetric matrix
55: * packed sequentially, column by column, so that AP( 1 )
56: * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
57: * and a( 3, 1 ) respectively, and so on.
58: * Unchanged on exit.
59: *
60: * X - DOUBLE PRECISION array of dimension at least
61: * ( 1 + ( n - 1 )*abs( INCX ) ).
62: * Before entry, the incremented array X must contain the n
63: * element vector x.
64: * Unchanged on exit.
65: *
66: * INCX - INTEGER.
67: * On entry, INCX specifies the increment for the elements of
68: * X. INCX must not be zero.
69: * Unchanged on exit.
70: *
71: * BETA - DOUBLE PRECISION.
72: * On entry, BETA specifies the scalar beta. When BETA is
73: * supplied as zero then Y need not be set on input.
74: * Unchanged on exit.
75: *
76: * Y - DOUBLE PRECISION array of dimension at least
77: * ( 1 + ( n - 1 )*abs( INCY ) ).
78: * Before entry, the incremented array Y must contain the n
79: * element vector y. On exit, Y is overwritten by the updated
80: * vector y.
81: *
82: * INCY - INTEGER.
83: * On entry, INCY specifies the increment for the elements of
84: * Y. INCY must not be zero.
85: * Unchanged on exit.
86: *
87: * Further Details
88: * ===============
89: *
90: * Level 2 Blas routine.
91: *
92: * -- Written on 22-October-1986.
93: * Jack Dongarra, Argonne National Lab.
94: * Jeremy Du Croz, Nag Central Office.
95: * Sven Hammarling, Nag Central Office.
96: * Richard Hanson, Sandia National Labs.
97: *
98: * =====================================================================
99: *
100: * .. Parameters ..
101: DOUBLE PRECISION ONE,ZERO
102: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
103: * ..
104: * .. Local Scalars ..
105: DOUBLE PRECISION TEMP1,TEMP2
106: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
107: * ..
108: * .. External Functions ..
109: LOGICAL LSAME
110: EXTERNAL LSAME
111: * ..
112: * .. External Subroutines ..
113: EXTERNAL XERBLA
114: * ..
115: *
116: * Test the input parameters.
117: *
118: INFO = 0
119: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
120: INFO = 1
121: ELSE IF (N.LT.0) THEN
122: INFO = 2
123: ELSE IF (INCX.EQ.0) THEN
124: INFO = 6
125: ELSE IF (INCY.EQ.0) THEN
126: INFO = 9
127: END IF
128: IF (INFO.NE.0) THEN
129: CALL XERBLA('DSPMV ',INFO)
130: RETURN
131: END IF
132: *
133: * Quick return if possible.
134: *
135: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
136: *
137: * Set up the start points in X and Y.
138: *
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: *
150: * Start the operations. In this version the elements of the array AP
151: * are accessed sequentially with one pass through AP.
152: *
153: * First form y := beta*y.
154: *
155: IF (BETA.NE.ONE) THEN
156: IF (INCY.EQ.1) THEN
157: IF (BETA.EQ.ZERO) THEN
158: DO 10 I = 1,N
159: Y(I) = ZERO
160: 10 CONTINUE
161: ELSE
162: DO 20 I = 1,N
163: Y(I) = BETA*Y(I)
164: 20 CONTINUE
165: END IF
166: ELSE
167: IY = KY
168: IF (BETA.EQ.ZERO) THEN
169: DO 30 I = 1,N
170: Y(IY) = ZERO
171: IY = IY + INCY
172: 30 CONTINUE
173: ELSE
174: DO 40 I = 1,N
175: Y(IY) = BETA*Y(IY)
176: IY = IY + INCY
177: 40 CONTINUE
178: END IF
179: END IF
180: END IF
181: IF (ALPHA.EQ.ZERO) RETURN
182: KK = 1
183: IF (LSAME(UPLO,'U')) THEN
184: *
185: * Form y when AP contains the upper triangle.
186: *
187: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
188: DO 60 J = 1,N
189: TEMP1 = ALPHA*X(J)
190: TEMP2 = ZERO
191: K = KK
192: DO 50 I = 1,J - 1
193: Y(I) = Y(I) + TEMP1*AP(K)
194: TEMP2 = TEMP2 + AP(K)*X(I)
195: K = K + 1
196: 50 CONTINUE
197: Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
198: KK = KK + J
199: 60 CONTINUE
200: ELSE
201: JX = KX
202: JY = KY
203: DO 80 J = 1,N
204: TEMP1 = ALPHA*X(JX)
205: TEMP2 = ZERO
206: IX = KX
207: IY = KY
208: DO 70 K = KK,KK + J - 2
209: Y(IY) = Y(IY) + TEMP1*AP(K)
210: TEMP2 = TEMP2 + AP(K)*X(IX)
211: IX = IX + INCX
212: IY = IY + INCY
213: 70 CONTINUE
214: Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
215: JX = JX + INCX
216: JY = JY + INCY
217: KK = KK + J
218: 80 CONTINUE
219: END IF
220: ELSE
221: *
222: * Form y when AP contains the lower triangle.
223: *
224: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
225: DO 100 J = 1,N
226: TEMP1 = ALPHA*X(J)
227: TEMP2 = ZERO
228: Y(J) = Y(J) + TEMP1*AP(KK)
229: K = KK + 1
230: DO 90 I = J + 1,N
231: Y(I) = Y(I) + TEMP1*AP(K)
232: TEMP2 = TEMP2 + AP(K)*X(I)
233: K = K + 1
234: 90 CONTINUE
235: Y(J) = Y(J) + ALPHA*TEMP2
236: KK = KK + (N-J+1)
237: 100 CONTINUE
238: ELSE
239: JX = KX
240: JY = KY
241: DO 120 J = 1,N
242: TEMP1 = ALPHA*X(JX)
243: TEMP2 = ZERO
244: Y(JY) = Y(JY) + TEMP1*AP(KK)
245: IX = JX
246: IY = JY
247: DO 110 K = KK + 1,KK + N - J
248: IX = IX + INCX
249: IY = IY + INCY
250: Y(IY) = Y(IY) + TEMP1*AP(K)
251: TEMP2 = TEMP2 + AP(K)*X(IX)
252: 110 CONTINUE
253: Y(JY) = Y(JY) + ALPHA*TEMP2
254: JX = JX + INCX
255: JY = JY + INCY
256: KK = KK + (N-J+1)
257: 120 CONTINUE
258: END IF
259: END IF
260: *
261: RETURN
262: *
263: * End of DSPMV .
264: *
265: END
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