Annotation of rpl/lapack/blas/dsyr2.f, revision 1.16
1.8 bertrand 1: *> \brief \b DSYR2
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
1.13 bertrand 12: *
1.8 bertrand 13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA
15: * INTEGER INCX,INCY,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
20: * ..
1.13 bertrand 21: *
1.8 bertrand 22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DSYR2 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 n
33: *> 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
1.14 bertrand 68: *> X is DOUBLE PRECISION array, dimension at least
1.8 bertrand 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
1.14 bertrand 83: *> Y is DOUBLE PRECISION array, dimension at least
1.8 bertrand 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] A
97: *> \verbatim
1.14 bertrand 98: *> A is DOUBLE PRECISION array, dimension ( LDA, N )
1.8 bertrand 99: *> Before entry with UPLO = 'U' or 'u', the leading n by n
100: *> upper triangular part of the array A must contain the upper
101: *> triangular part of the symmetric matrix and the strictly
102: *> lower triangular part of A is not referenced. On exit, the
103: *> upper triangular part of the array A is overwritten by the
104: *> upper triangular part of the updated matrix.
105: *> Before entry with UPLO = 'L' or 'l', the leading n by n
106: *> lower triangular part of the array A must contain the lower
107: *> triangular part of the symmetric matrix and the strictly
108: *> upper triangular part of A is not referenced. On exit, the
109: *> lower triangular part of the array A is overwritten by the
110: *> lower triangular part of the updated matrix.
111: *> \endverbatim
112: *>
113: *> \param[in] LDA
114: *> \verbatim
115: *> LDA is INTEGER
116: *> On entry, LDA specifies the first dimension of A as declared
117: *> in the calling (sub) program. LDA must be at least
118: *> max( 1, n ).
119: *> \endverbatim
120: *
121: * Authors:
122: * ========
123: *
1.13 bertrand 124: *> \author Univ. of Tennessee
125: *> \author Univ. of California Berkeley
126: *> \author Univ. of Colorado Denver
127: *> \author NAG Ltd.
1.8 bertrand 128: *
129: *> \ingroup double_blas_level2
130: *
131: *> \par Further Details:
132: * =====================
133: *>
134: *> \verbatim
135: *>
136: *> Level 2 Blas routine.
137: *>
138: *> -- Written on 22-October-1986.
139: *> Jack Dongarra, Argonne National Lab.
140: *> Jeremy Du Croz, Nag Central Office.
141: *> Sven Hammarling, Nag Central Office.
142: *> Richard Hanson, Sandia National Labs.
143: *> \endverbatim
144: *>
145: * =====================================================================
1.1 bertrand 146: SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
1.8 bertrand 147: *
1.16 ! bertrand 148: * -- Reference BLAS level2 routine --
1.8 bertrand 149: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: *
1.1 bertrand 152: * .. Scalar Arguments ..
153: DOUBLE PRECISION ALPHA
154: INTEGER INCX,INCY,LDA,N
155: CHARACTER UPLO
156: * ..
157: * .. Array Arguments ..
158: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
159: * ..
160: *
161: * =====================================================================
162: *
163: * .. Parameters ..
164: DOUBLE PRECISION ZERO
165: PARAMETER (ZERO=0.0D+0)
166: * ..
167: * .. Local Scalars ..
168: DOUBLE PRECISION TEMP1,TEMP2
169: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL XERBLA
177: * ..
178: * .. Intrinsic Functions ..
179: INTRINSIC MAX
180: * ..
181: *
182: * Test the input parameters.
183: *
184: INFO = 0
185: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
186: INFO = 1
187: ELSE IF (N.LT.0) THEN
188: INFO = 2
189: ELSE IF (INCX.EQ.0) THEN
190: INFO = 5
191: ELSE IF (INCY.EQ.0) THEN
192: INFO = 7
193: ELSE IF (LDA.LT.MAX(1,N)) THEN
194: INFO = 9
195: END IF
196: IF (INFO.NE.0) THEN
197: CALL XERBLA('DSYR2 ',INFO)
198: RETURN
199: END IF
200: *
201: * Quick return if possible.
202: *
203: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
204: *
205: * Set up the start points in X and Y if the increments are not both
206: * unity.
207: *
208: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
209: IF (INCX.GT.0) THEN
210: KX = 1
211: ELSE
212: KX = 1 - (N-1)*INCX
213: END IF
214: IF (INCY.GT.0) THEN
215: KY = 1
216: ELSE
217: KY = 1 - (N-1)*INCY
218: END IF
219: JX = KX
220: JY = KY
221: END IF
222: *
223: * Start the operations. In this version the elements of A are
224: * accessed sequentially with one pass through the triangular part
225: * of A.
226: *
227: IF (LSAME(UPLO,'U')) THEN
228: *
229: * Form A when A is stored in the upper triangle.
230: *
231: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
232: DO 20 J = 1,N
233: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
234: TEMP1 = ALPHA*Y(J)
235: TEMP2 = ALPHA*X(J)
236: DO 10 I = 1,J
237: A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
238: 10 CONTINUE
239: END IF
240: 20 CONTINUE
241: ELSE
242: DO 40 J = 1,N
243: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
244: TEMP1 = ALPHA*Y(JY)
245: TEMP2 = ALPHA*X(JX)
246: IX = KX
247: IY = KY
248: DO 30 I = 1,J
249: A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
250: IX = IX + INCX
251: IY = IY + INCY
252: 30 CONTINUE
253: END IF
254: JX = JX + INCX
255: JY = JY + INCY
256: 40 CONTINUE
257: END IF
258: ELSE
259: *
260: * Form A when A is stored in the lower triangle.
261: *
262: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
263: DO 60 J = 1,N
264: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
265: TEMP1 = ALPHA*Y(J)
266: TEMP2 = ALPHA*X(J)
267: DO 50 I = J,N
268: A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
269: 50 CONTINUE
270: END IF
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 I = J,N
280: A(I,J) = A(I,J) + 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: 80 CONTINUE
288: END IF
289: END IF
290: *
291: RETURN
292: *
1.16 ! bertrand 293: * End of DSYR2
1.1 bertrand 294: *
295: END
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