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1.8 bertrand 1: *> \brief \b DSYR
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 DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA
15: * INTEGER INCX,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),X(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DSYR performs the symmetric rank 1 operation
29: *>
30: *> A := alpha*x*x**T + A,
31: *>
32: *> where alpha is a real scalar, x is an n element vector and A is an
33: *> n by n symmetric matrix.
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 array A is to be referenced as
44: *> follows:
45: *>
46: *> UPLO = 'U' or 'u' Only the upper triangular part of A
47: *> is to be referenced.
48: *>
49: *> UPLO = 'L' or 'l' Only the lower triangular part of A
50: *> is to be referenced.
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,out] A
82: *> \verbatim
83: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
84: *> Before entry with UPLO = 'U' or 'u', the leading n by n
85: *> upper triangular part of the array A must contain the upper
86: *> triangular part of the symmetric matrix and the strictly
87: *> lower triangular part of A is not referenced. On exit, the
88: *> upper triangular part of the array A is overwritten by the
89: *> upper triangular part of the updated matrix.
90: *> Before entry with UPLO = 'L' or 'l', the leading n by n
91: *> lower triangular part of the array A must contain the lower
92: *> triangular part of the symmetric matrix and the strictly
93: *> upper triangular part of A is not referenced. On exit, the
94: *> lower triangular part of the array A is overwritten by the
95: *> lower triangular part of the updated matrix.
96: *> \endverbatim
97: *>
98: *> \param[in] LDA
99: *> \verbatim
100: *> LDA is INTEGER
101: *> On entry, LDA specifies the first dimension of A as declared
102: *> in the calling (sub) program. LDA must be at least
103: *> max( 1, n ).
104: *> \endverbatim
105: *
106: * Authors:
107: * ========
108: *
109: *> \author Univ. of Tennessee
110: *> \author Univ. of California Berkeley
111: *> \author Univ. of Colorado Denver
112: *> \author NAG Ltd.
113: *
114: *> \date November 2011
115: *
116: *> \ingroup double_blas_level2
117: *
118: *> \par Further Details:
119: * =====================
120: *>
121: *> \verbatim
122: *>
123: *> Level 2 Blas routine.
124: *>
125: *> -- Written on 22-October-1986.
126: *> Jack Dongarra, Argonne National Lab.
127: *> Jeremy Du Croz, Nag Central Office.
128: *> Sven Hammarling, Nag Central Office.
129: *> Richard Hanson, Sandia National Labs.
130: *> \endverbatim
131: *>
132: * =====================================================================
1.1 bertrand 133: SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
1.8 bertrand 134: *
135: * -- Reference BLAS level2 routine (version 3.4.0) --
136: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
137: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138: * November 2011
139: *
1.1 bertrand 140: * .. Scalar Arguments ..
141: DOUBLE PRECISION ALPHA
142: INTEGER INCX,LDA,N
143: CHARACTER UPLO
144: * ..
145: * .. Array Arguments ..
146: DOUBLE PRECISION A(LDA,*),X(*)
147: * ..
148: *
149: * =====================================================================
150: *
151: * .. Parameters ..
152: DOUBLE PRECISION ZERO
153: PARAMETER (ZERO=0.0D+0)
154: * ..
155: * .. Local Scalars ..
156: DOUBLE PRECISION TEMP
157: INTEGER I,INFO,IX,J,JX,KX
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: EXTERNAL LSAME
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL XERBLA
165: * ..
166: * .. Intrinsic Functions ..
167: INTRINSIC MAX
168: * ..
169: *
170: * Test the input parameters.
171: *
172: INFO = 0
173: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
174: INFO = 1
175: ELSE IF (N.LT.0) THEN
176: INFO = 2
177: ELSE IF (INCX.EQ.0) THEN
178: INFO = 5
179: ELSE IF (LDA.LT.MAX(1,N)) THEN
180: INFO = 7
181: END IF
182: IF (INFO.NE.0) THEN
183: CALL XERBLA('DSYR ',INFO)
184: RETURN
185: END IF
186: *
187: * Quick return if possible.
188: *
189: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
190: *
191: * Set the start point in X if the increment is not unity.
192: *
193: IF (INCX.LE.0) THEN
194: KX = 1 - (N-1)*INCX
195: ELSE IF (INCX.NE.1) THEN
196: KX = 1
197: END IF
198: *
199: * Start the operations. In this version the elements of A are
200: * accessed sequentially with one pass through the triangular part
201: * of A.
202: *
203: IF (LSAME(UPLO,'U')) THEN
204: *
205: * Form A when A is stored in upper triangle.
206: *
207: IF (INCX.EQ.1) THEN
208: DO 20 J = 1,N
209: IF (X(J).NE.ZERO) THEN
210: TEMP = ALPHA*X(J)
211: DO 10 I = 1,J
212: A(I,J) = A(I,J) + X(I)*TEMP
213: 10 CONTINUE
214: END IF
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 I = 1,J
223: A(I,J) = A(I,J) + X(IX)*TEMP
224: IX = IX + INCX
225: 30 CONTINUE
226: END IF
227: JX = JX + INCX
228: 40 CONTINUE
229: END IF
230: ELSE
231: *
232: * Form A when A is stored in lower triangle.
233: *
234: IF (INCX.EQ.1) THEN
235: DO 60 J = 1,N
236: IF (X(J).NE.ZERO) THEN
237: TEMP = ALPHA*X(J)
238: DO 50 I = J,N
239: A(I,J) = A(I,J) + X(I)*TEMP
240: 50 CONTINUE
241: END IF
242: 60 CONTINUE
243: ELSE
244: JX = KX
245: DO 80 J = 1,N
246: IF (X(JX).NE.ZERO) THEN
247: TEMP = ALPHA*X(JX)
248: IX = JX
249: DO 70 I = J,N
250: A(I,J) = A(I,J) + X(IX)*TEMP
251: IX = IX + INCX
252: 70 CONTINUE
253: END IF
254: JX = JX + INCX
255: 80 CONTINUE
256: END IF
257: END IF
258: *
259: RETURN
260: *
261: * End of DSYR .
262: *
263: END