Annotation of rpl/lapack/blas/dspr.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DSPR
! 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 DSPR(UPLO,N,ALPHA,X,INCX,AP)
! 12: *
! 13: * .. Scalar Arguments ..
! 14: * DOUBLE PRECISION ALPHA
! 15: * INTEGER INCX,N
! 16: * CHARACTER UPLO
! 17: * ..
! 18: * .. Array Arguments ..
! 19: * DOUBLE PRECISION AP(*),X(*)
! 20: * ..
! 21: *
! 22: *
! 23: *> \par Purpose:
! 24: * =============
! 25: *>
! 26: *> \verbatim
! 27: *>
! 28: *> DSPR 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, 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,out] AP
! 82: *> \verbatim
! 83: *> AP is DOUBLE PRECISION array of DIMENSION at least
! 84: *> ( ( n*( n + 1 ) )/2 ).
! 85: *> Before entry with UPLO = 'U' or 'u', the array AP must
! 86: *> contain the upper triangular part of the symmetric matrix
! 87: *> packed sequentially, column by column, so that AP( 1 )
! 88: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
! 89: *> and a( 2, 2 ) respectively, and so on. On exit, the array
! 90: *> AP is overwritten by the upper triangular part of the
! 91: *> updated matrix.
! 92: *> Before entry with UPLO = 'L' or 'l', the array AP must
! 93: *> contain the lower triangular part of the symmetric matrix
! 94: *> packed sequentially, column by column, so that AP( 1 )
! 95: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
! 96: *> and a( 3, 1 ) respectively, and so on. On exit, the array
! 97: *> AP is overwritten by the lower triangular part of the
! 98: *> updated matrix.
! 99: *> \endverbatim
! 100: *
! 101: * Authors:
! 102: * ========
! 103: *
! 104: *> \author Univ. of Tennessee
! 105: *> \author Univ. of California Berkeley
! 106: *> \author Univ. of Colorado Denver
! 107: *> \author NAG Ltd.
! 108: *
! 109: *> \date November 2011
! 110: *
! 111: *> \ingroup double_blas_level2
! 112: *
! 113: *> \par Further Details:
! 114: * =====================
! 115: *>
! 116: *> \verbatim
! 117: *>
! 118: *> Level 2 Blas routine.
! 119: *>
! 120: *> -- Written on 22-October-1986.
! 121: *> Jack Dongarra, Argonne National Lab.
! 122: *> Jeremy Du Croz, Nag Central Office.
! 123: *> Sven Hammarling, Nag Central Office.
! 124: *> Richard Hanson, Sandia National Labs.
! 125: *> \endverbatim
! 126: *>
! 127: * =====================================================================
1.1 bertrand 128: SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
1.8 ! bertrand 129: *
! 130: * -- Reference BLAS level2 routine (version 3.4.0) --
! 131: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
! 132: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 133: * November 2011
! 134: *
1.1 bertrand 135: * .. Scalar Arguments ..
136: DOUBLE PRECISION ALPHA
137: INTEGER INCX,N
138: CHARACTER UPLO
139: * ..
140: * .. Array Arguments ..
141: DOUBLE PRECISION AP(*),X(*)
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Parameters ..
147: DOUBLE PRECISION ZERO
148: PARAMETER (ZERO=0.0D+0)
149: * ..
150: * .. Local Scalars ..
151: DOUBLE PRECISION TEMP
152: INTEGER I,INFO,IX,J,JX,K,KK,KX
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL XERBLA
160: * ..
161: *
162: * Test the input parameters.
163: *
164: INFO = 0
165: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
166: INFO = 1
167: ELSE IF (N.LT.0) THEN
168: INFO = 2
169: ELSE IF (INCX.EQ.0) THEN
170: INFO = 5
171: END IF
172: IF (INFO.NE.0) THEN
173: CALL XERBLA('DSPR ',INFO)
174: RETURN
175: END IF
176: *
177: * Quick return if possible.
178: *
179: IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
180: *
181: * Set the start point in X if the increment is not unity.
182: *
183: IF (INCX.LE.0) THEN
184: KX = 1 - (N-1)*INCX
185: ELSE IF (INCX.NE.1) THEN
186: KX = 1
187: END IF
188: *
189: * Start the operations. In this version the elements of the array AP
190: * are accessed sequentially with one pass through AP.
191: *
192: KK = 1
193: IF (LSAME(UPLO,'U')) THEN
194: *
195: * Form A when upper triangle is stored in AP.
196: *
197: IF (INCX.EQ.1) THEN
198: DO 20 J = 1,N
199: IF (X(J).NE.ZERO) THEN
200: TEMP = ALPHA*X(J)
201: K = KK
202: DO 10 I = 1,J
203: AP(K) = AP(K) + X(I)*TEMP
204: K = K + 1
205: 10 CONTINUE
206: END IF
207: KK = KK + J
208: 20 CONTINUE
209: ELSE
210: JX = KX
211: DO 40 J = 1,N
212: IF (X(JX).NE.ZERO) THEN
213: TEMP = ALPHA*X(JX)
214: IX = KX
215: DO 30 K = KK,KK + J - 1
216: AP(K) = AP(K) + X(IX)*TEMP
217: IX = IX + INCX
218: 30 CONTINUE
219: END IF
220: JX = JX + INCX
221: KK = KK + J
222: 40 CONTINUE
223: END IF
224: ELSE
225: *
226: * Form A when lower triangle is stored in AP.
227: *
228: IF (INCX.EQ.1) THEN
229: DO 60 J = 1,N
230: IF (X(J).NE.ZERO) THEN
231: TEMP = ALPHA*X(J)
232: K = KK
233: DO 50 I = J,N
234: AP(K) = AP(K) + X(I)*TEMP
235: K = K + 1
236: 50 CONTINUE
237: END IF
238: KK = KK + N - J + 1
239: 60 CONTINUE
240: ELSE
241: JX = KX
242: DO 80 J = 1,N
243: IF (X(JX).NE.ZERO) THEN
244: TEMP = ALPHA*X(JX)
245: IX = JX
246: DO 70 K = KK,KK + N - J
247: AP(K) = AP(K) + X(IX)*TEMP
248: IX = IX + INCX
249: 70 CONTINUE
250: END IF
251: JX = JX + INCX
252: KK = KK + N - J + 1
253: 80 CONTINUE
254: END IF
255: END IF
256: *
257: RETURN
258: *
259: * End of DSPR .
260: *
261: END
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