![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zsymv.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack|
Return to zsymv.f CVS log | Up to [local] / rpl / lapack / lapack |
1.1 bertrand 1: SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INCX, INCY, LDA, N
11: COMPLEX*16 ALPHA, BETA
12: * ..
13: * .. Array Arguments ..
14: COMPLEX*16 A( LDA, * ), X( * ), Y( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZSYMV performs the matrix-vector operation
21: *
22: * y := alpha*A*x + beta*y,
23: *
24: * where alpha and beta are scalars, x and y are n element vectors and
25: * A is an n by n symmetric matrix.
26: *
27: * Arguments
28: * ==========
29: *
30: * UPLO (input) CHARACTER*1
31: * On entry, UPLO specifies whether the upper or lower
32: * triangular part of the array A is to be referenced as
33: * follows:
34: *
35: * UPLO = 'U' or 'u' Only the upper triangular part of A
36: * is to be referenced.
37: *
38: * UPLO = 'L' or 'l' Only the lower triangular part of A
39: * is to be referenced.
40: *
41: * Unchanged on exit.
42: *
43: * N (input) INTEGER
44: * On entry, N specifies the order of the matrix A.
45: * N must be at least zero.
46: * Unchanged on exit.
47: *
48: * ALPHA (input) COMPLEX*16
49: * On entry, ALPHA specifies the scalar alpha.
50: * Unchanged on exit.
51: *
52: * A (input) COMPLEX*16 array, dimension ( LDA, N )
53: * Before entry, with UPLO = 'U' or 'u', the leading n by n
54: * upper triangular part of the array A must contain the upper
55: * triangular part of the symmetric matrix and the strictly
56: * lower triangular part of A is not referenced.
57: * Before entry, with UPLO = 'L' or 'l', the leading n by n
58: * lower triangular part of the array A must contain the lower
59: * triangular part of the symmetric matrix and the strictly
60: * upper triangular part of A is not referenced.
61: * Unchanged on exit.
62: *
63: * LDA (input) INTEGER
64: * On entry, LDA specifies the first dimension of A as declared
65: * in the calling (sub) program. LDA must be at least
66: * max( 1, N ).
67: * Unchanged on exit.
68: *
69: * X (input) COMPLEX*16 array, dimension at least
70: * ( 1 + ( N - 1 )*abs( INCX ) ).
71: * Before entry, the incremented array X must contain the N-
72: * element vector x.
73: * Unchanged on exit.
74: *
75: * INCX (input) INTEGER
76: * On entry, INCX specifies the increment for the elements of
77: * X. INCX must not be zero.
78: * Unchanged on exit.
79: *
80: * BETA (input) COMPLEX*16
81: * On entry, BETA specifies the scalar beta. When BETA is
82: * supplied as zero then Y need not be set on input.
83: * Unchanged on exit.
84: *
85: * Y (input/output) COMPLEX*16 array, dimension at least
86: * ( 1 + ( N - 1 )*abs( INCY ) ).
87: * Before entry, the incremented array Y must contain the n
88: * element vector y. On exit, Y is overwritten by the updated
89: * vector y.
90: *
91: * INCY (input) INTEGER
92: * On entry, INCY specifies the increment for the elements of
93: * Y. INCY must not be zero.
94: * Unchanged on exit.
95: *
96: * =====================================================================
97: *
98: * .. Parameters ..
99: COMPLEX*16 ONE
100: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
101: COMPLEX*16 ZERO
102: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
103: * ..
104: * .. Local Scalars ..
105: INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
106: COMPLEX*16 TEMP1, TEMP2
107: * ..
108: * .. External Functions ..
109: LOGICAL LSAME
110: EXTERNAL LSAME
111: * ..
112: * .. External Subroutines ..
113: EXTERNAL XERBLA
114: * ..
115: * .. Intrinsic Functions ..
116: INTRINSIC MAX
117: * ..
118: * .. Executable Statements ..
119: *
120: * Test the input parameters.
121: *
122: INFO = 0
123: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
124: INFO = 1
125: ELSE IF( N.LT.0 ) THEN
126: INFO = 2
127: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
128: INFO = 5
129: ELSE IF( INCX.EQ.0 ) THEN
130: INFO = 7
131: ELSE IF( INCY.EQ.0 ) THEN
132: INFO = 10
133: END IF
134: IF( INFO.NE.0 ) THEN
135: CALL XERBLA( 'ZSYMV ', INFO )
136: RETURN
137: END IF
138: *
139: * Quick return if possible.
140: *
141: IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
142: $ RETURN
143: *
144: * Set up the start points in X and Y.
145: *
146: IF( INCX.GT.0 ) THEN
147: KX = 1
148: ELSE
149: KX = 1 - ( N-1 )*INCX
150: END IF
151: IF( INCY.GT.0 ) THEN
152: KY = 1
153: ELSE
154: KY = 1 - ( N-1 )*INCY
155: END IF
156: *
157: * Start the operations. In this version the elements of A are
158: * accessed sequentially with one pass through the triangular part
159: * of A.
160: *
161: * First form y := beta*y.
162: *
163: IF( BETA.NE.ONE ) THEN
164: IF( INCY.EQ.1 ) THEN
165: IF( BETA.EQ.ZERO ) THEN
166: DO 10 I = 1, N
167: Y( I ) = ZERO
168: 10 CONTINUE
169: ELSE
170: DO 20 I = 1, N
171: Y( I ) = BETA*Y( I )
172: 20 CONTINUE
173: END IF
174: ELSE
175: IY = KY
176: IF( BETA.EQ.ZERO ) THEN
177: DO 30 I = 1, N
178: Y( IY ) = ZERO
179: IY = IY + INCY
180: 30 CONTINUE
181: ELSE
182: DO 40 I = 1, N
183: Y( IY ) = BETA*Y( IY )
184: IY = IY + INCY
185: 40 CONTINUE
186: END IF
187: END IF
188: END IF
189: IF( ALPHA.EQ.ZERO )
190: $ RETURN
191: IF( LSAME( UPLO, 'U' ) ) THEN
192: *
193: * Form y when A is stored in upper triangle.
194: *
195: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
196: DO 60 J = 1, N
197: TEMP1 = ALPHA*X( J )
198: TEMP2 = ZERO
199: DO 50 I = 1, J - 1
200: Y( I ) = Y( I ) + TEMP1*A( I, J )
201: TEMP2 = TEMP2 + A( I, J )*X( I )
202: 50 CONTINUE
203: Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
204: 60 CONTINUE
205: ELSE
206: JX = KX
207: JY = KY
208: DO 80 J = 1, N
209: TEMP1 = ALPHA*X( JX )
210: TEMP2 = ZERO
211: IX = KX
212: IY = KY
213: DO 70 I = 1, J - 1
214: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
215: TEMP2 = TEMP2 + A( I, J )*X( IX )
216: IX = IX + INCX
217: IY = IY + INCY
218: 70 CONTINUE
219: Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
220: JX = JX + INCX
221: JY = JY + INCY
222: 80 CONTINUE
223: END IF
224: ELSE
225: *
226: * Form y when A is stored in lower triangle.
227: *
228: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
229: DO 100 J = 1, N
230: TEMP1 = ALPHA*X( J )
231: TEMP2 = ZERO
232: Y( J ) = Y( J ) + TEMP1*A( J, J )
233: DO 90 I = J + 1, N
234: Y( I ) = Y( I ) + TEMP1*A( I, J )
235: TEMP2 = TEMP2 + A( I, J )*X( I )
236: 90 CONTINUE
237: Y( J ) = Y( J ) + ALPHA*TEMP2
238: 100 CONTINUE
239: ELSE
240: JX = KX
241: JY = KY
242: DO 120 J = 1, N
243: TEMP1 = ALPHA*X( JX )
244: TEMP2 = ZERO
245: Y( JY ) = Y( JY ) + TEMP1*A( J, J )
246: IX = JX
247: IY = JY
248: DO 110 I = J + 1, N
249: IX = IX + INCX
250: IY = IY + INCY
251: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
252: TEMP2 = TEMP2 + A( I, J )*X( IX )
253: 110 CONTINUE
254: Y( JY ) = Y( JY ) + ALPHA*TEMP2
255: JX = JX + INCX
256: JY = JY + INCY
257: 120 CONTINUE
258: END IF
259: END IF
260: *
261: RETURN
262: *
263: * End of ZSYMV
264: *
265: END