Annotation of rpl/lapack/blas/dspr2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DSPR2
! 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 DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * DOUBLE PRECISION ALPHA
! 15: * INTEGER INCX,INCY,N
! 16: * CHARACTER UPLO
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * DOUBLE PRECISION AP(*),X(*),Y(*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> DSPR2 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
! 33: *> n by n symmetric matrix, supplied in packed form.
! 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 matrix A is supplied in the packed
! 44: *> array AP as follows:
! 45: *>
! 46: *> UPLO = 'U' or 'u' The upper triangular part of A is
! 47: *> supplied in AP.
! 48: *>
! 49: *> UPLO = 'L' or 'l' The lower triangular part of A is
! 50: *> supplied in AP.
! 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] Y
! 82: *> \verbatim
! 83: *> Y is DOUBLE PRECISION array of dimension at least
! 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] AP
! 97: *> \verbatim
! 98: *> AP is DOUBLE PRECISION array of DIMENSION at least
! 99: *> ( ( n*( n + 1 ) )/2 ).
! 100: *> Before entry with UPLO = 'U' or 'u', the array AP must
! 101: *> contain the upper triangular part of the symmetric matrix
! 102: *> packed sequentially, column by column, so that AP( 1 )
! 103: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
! 104: *> and a( 2, 2 ) respectively, and so on. On exit, the array
! 105: *> AP is overwritten by the upper triangular part of the
! 106: *> updated matrix.
! 107: *> Before entry with UPLO = 'L' or 'l', the array AP must
! 108: *> contain the lower triangular part of the symmetric matrix
! 109: *> packed sequentially, column by column, so that AP( 1 )
! 110: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
! 111: *> and a( 3, 1 ) respectively, and so on. On exit, the array
! 112: *> AP is overwritten by the lower triangular part of the
! 113: *> updated matrix.
! 114: *> \endverbatim
! 115: *
! 116: * Authors:
! 117: * ========
! 118: *
! 119: *> \author Univ. of Tennessee
! 120: *> \author Univ. of California Berkeley
! 121: *> \author Univ. of Colorado Denver
! 122: *> \author NAG Ltd.
! 123: *
! 124: *> \date November 2011
! 125: *
! 126: *> \ingroup double_blas_level2
! 127: *
! 128: *> \par Further Details:
! 129: * =====================
! 130: *>
! 131: *> \verbatim
! 132: *>
! 133: *> Level 2 Blas routine.
! 134: *>
! 135: *> -- Written on 22-October-1986.
! 136: *> Jack Dongarra, Argonne National Lab.
! 137: *> Jeremy Du Croz, Nag Central Office.
! 138: *> Sven Hammarling, Nag Central Office.
! 139: *> Richard Hanson, Sandia National Labs.
! 140: *> \endverbatim
! 141: *>
! 142: * =====================================================================
1.1 bertrand 143: SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
1.8 ! bertrand 144: *
! 145: * -- Reference BLAS level2 routine (version 3.4.0) --
! 146: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 148: * November 2011
! 149: *
1.1 bertrand 150: * .. Scalar Arguments ..
151: DOUBLE PRECISION ALPHA
152: INTEGER INCX,INCY,N
153: CHARACTER UPLO
154: * ..
155: * .. Array Arguments ..
156: DOUBLE PRECISION AP(*),X(*),Y(*)
157: * ..
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: DOUBLE PRECISION ZERO
163: PARAMETER (ZERO=0.0D+0)
164: * ..
165: * .. Local Scalars ..
166: DOUBLE PRECISION TEMP1,TEMP2
167: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA
175: * ..
176: *
177: * Test the input parameters.
178: *
179: INFO = 0
180: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
181: INFO = 1
182: ELSE IF (N.LT.0) THEN
183: INFO = 2
184: ELSE IF (INCX.EQ.0) THEN
185: INFO = 5
186: ELSE IF (INCY.EQ.0) THEN
187: INFO = 7
188: END IF
189: IF (INFO.NE.0) THEN
190: CALL XERBLA('DSPR2 ',INFO)
191: RETURN
192: END IF
193: *
194: * Quick return if possible.
195: *
196: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
197: *
198: * Set up the start points in X and Y if the increments are not both
199: * unity.
200: *
201: IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
202: IF (INCX.GT.0) THEN
203: KX = 1
204: ELSE
205: KX = 1 - (N-1)*INCX
206: END IF
207: IF (INCY.GT.0) THEN
208: KY = 1
209: ELSE
210: KY = 1 - (N-1)*INCY
211: END IF
212: JX = KX
213: JY = KY
214: END IF
215: *
216: * Start the operations. In this version the elements of the array AP
217: * are accessed sequentially with one pass through AP.
218: *
219: KK = 1
220: IF (LSAME(UPLO,'U')) THEN
221: *
222: * Form A when upper triangle is stored in AP.
223: *
224: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
225: DO 20 J = 1,N
226: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
227: TEMP1 = ALPHA*Y(J)
228: TEMP2 = ALPHA*X(J)
229: K = KK
230: DO 10 I = 1,J
231: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
232: K = K + 1
233: 10 CONTINUE
234: END IF
235: KK = KK + J
236: 20 CONTINUE
237: ELSE
238: DO 40 J = 1,N
239: IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
240: TEMP1 = ALPHA*Y(JY)
241: TEMP2 = ALPHA*X(JX)
242: IX = KX
243: IY = KY
244: DO 30 K = KK,KK + J - 1
245: AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
246: IX = IX + INCX
247: IY = IY + INCY
248: 30 CONTINUE
249: END IF
250: JX = JX + INCX
251: JY = JY + INCY
252: KK = KK + J
253: 40 CONTINUE
254: END IF
255: ELSE
256: *
257: * Form A when lower triangle is stored in AP.
258: *
259: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
260: DO 60 J = 1,N
261: IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
262: TEMP1 = ALPHA*Y(J)
263: TEMP2 = ALPHA*X(J)
264: K = KK
265: DO 50 I = J,N
266: AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
267: K = K + 1
268: 50 CONTINUE
269: END IF
270: KK = KK + N - J + 1
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 K = KK,KK + N - J
280: AP(K) = AP(K) + 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: KK = KK + N - J + 1
288: 80 CONTINUE
289: END IF
290: END IF
291: *
292: RETURN
293: *
294: * End of DSPR2 .
295: *
296: END
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