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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SSPR2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 00012 * 00013 * .. Scalar Arguments .. 00014 * REAL ALPHA 00015 * INTEGER INCX,INCY,N 00016 * CHARACTER UPLO 00017 * .. 00018 * .. Array Arguments .. 00019 * REAL AP(*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> SSPR2 performs the symmetric rank 2 operation 00029 *> 00030 *> A := alpha*x*y**T + alpha*y*x**T + A, 00031 *> 00032 *> where alpha is a scalar, x and y are n element vectors and A is an 00033 *> n by n symmetric matrix, supplied in packed form. 00034 *> \endverbatim 00035 * 00036 * Arguments: 00037 * ========== 00038 * 00039 *> \param[in] UPLO 00040 *> \verbatim 00041 *> UPLO is CHARACTER*1 00042 *> On entry, UPLO specifies whether the upper or lower 00043 *> triangular part of the matrix A is supplied in the packed 00044 *> array AP as follows: 00045 *> 00046 *> UPLO = 'U' or 'u' The upper triangular part of A is 00047 *> supplied in AP. 00048 *> 00049 *> UPLO = 'L' or 'l' The lower triangular part of A is 00050 *> supplied in AP. 00051 *> \endverbatim 00052 *> 00053 *> \param[in] N 00054 *> \verbatim 00055 *> N is INTEGER 00056 *> On entry, N specifies the order of the matrix A. 00057 *> N must be at least zero. 00058 *> \endverbatim 00059 *> 00060 *> \param[in] ALPHA 00061 *> \verbatim 00062 *> ALPHA is REAL 00063 *> On entry, ALPHA specifies the scalar alpha. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] X 00067 *> \verbatim 00068 *> X is REAL array of dimension at least 00069 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00070 *> Before entry, the incremented array X must contain the n 00071 *> element vector x. 00072 *> \endverbatim 00073 *> 00074 *> \param[in] INCX 00075 *> \verbatim 00076 *> INCX is INTEGER 00077 *> On entry, INCX specifies the increment for the elements of 00078 *> X. INCX must not be zero. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] Y 00082 *> \verbatim 00083 *> Y is REAL array of dimension at least 00084 *> ( 1 + ( n - 1 )*abs( INCY ) ). 00085 *> Before entry, the incremented array Y must contain the n 00086 *> element vector y. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] INCY 00090 *> \verbatim 00091 *> INCY is INTEGER 00092 *> On entry, INCY specifies the increment for the elements of 00093 *> Y. INCY must not be zero. 00094 *> \endverbatim 00095 *> 00096 *> \param[in,out] AP 00097 *> \verbatim 00098 *> AP is REAL array of DIMENSION at least 00099 *> ( ( n*( n + 1 ) )/2 ). 00100 *> Before entry with UPLO = 'U' or 'u', the array AP must 00101 *> contain the upper triangular part of the symmetric matrix 00102 *> packed sequentially, column by column, so that AP( 1 ) 00103 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 00104 *> and a( 2, 2 ) respectively, and so on. On exit, the array 00105 *> AP is overwritten by the upper triangular part of the 00106 *> updated matrix. 00107 *> Before entry with UPLO = 'L' or 'l', the array AP must 00108 *> contain the lower triangular part of the symmetric matrix 00109 *> packed sequentially, column by column, so that AP( 1 ) 00110 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 00111 *> and a( 3, 1 ) respectively, and so on. On exit, the array 00112 *> AP is overwritten by the lower triangular part of the 00113 *> updated matrix. 00114 *> \endverbatim 00115 * 00116 * Authors: 00117 * ======== 00118 * 00119 *> \author Univ. of Tennessee 00120 *> \author Univ. of California Berkeley 00121 *> \author Univ. of Colorado Denver 00122 *> \author NAG Ltd. 00123 * 00124 *> \date November 2011 00125 * 00126 *> \ingroup single_blas_level2 00127 * 00128 *> \par Further Details: 00129 * ===================== 00130 *> 00131 *> \verbatim 00132 *> 00133 *> Level 2 Blas routine. 00134 *> 00135 *> -- Written on 22-October-1986. 00136 *> Jack Dongarra, Argonne National Lab. 00137 *> Jeremy Du Croz, Nag Central Office. 00138 *> Sven Hammarling, Nag Central Office. 00139 *> Richard Hanson, Sandia National Labs. 00140 *> \endverbatim 00141 *> 00142 * ===================================================================== 00143 SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 00144 * 00145 * -- Reference BLAS level2 routine (version 3.4.0) -- 00146 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00148 * November 2011 00149 * 00150 * .. Scalar Arguments .. 00151 REAL ALPHA 00152 INTEGER INCX,INCY,N 00153 CHARACTER UPLO 00154 * .. 00155 * .. Array Arguments .. 00156 REAL AP(*),X(*),Y(*) 00157 * .. 00158 * 00159 * ===================================================================== 00160 * 00161 * .. Parameters .. 00162 REAL ZERO 00163 PARAMETER (ZERO=0.0E+0) 00164 * .. 00165 * .. Local Scalars .. 00166 REAL TEMP1,TEMP2 00167 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 00168 * .. 00169 * .. External Functions .. 00170 LOGICAL LSAME 00171 EXTERNAL LSAME 00172 * .. 00173 * .. External Subroutines .. 00174 EXTERNAL XERBLA 00175 * .. 00176 * 00177 * Test the input parameters. 00178 * 00179 INFO = 0 00180 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00181 INFO = 1 00182 ELSE IF (N.LT.0) THEN 00183 INFO = 2 00184 ELSE IF (INCX.EQ.0) THEN 00185 INFO = 5 00186 ELSE IF (INCY.EQ.0) THEN 00187 INFO = 7 00188 END IF 00189 IF (INFO.NE.0) THEN 00190 CALL XERBLA('SSPR2 ',INFO) 00191 RETURN 00192 END IF 00193 * 00194 * Quick return if possible. 00195 * 00196 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 00197 * 00198 * Set up the start points in X and Y if the increments are not both 00199 * unity. 00200 * 00201 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 00202 IF (INCX.GT.0) THEN 00203 KX = 1 00204 ELSE 00205 KX = 1 - (N-1)*INCX 00206 END IF 00207 IF (INCY.GT.0) THEN 00208 KY = 1 00209 ELSE 00210 KY = 1 - (N-1)*INCY 00211 END IF 00212 JX = KX 00213 JY = KY 00214 END IF 00215 * 00216 * Start the operations. In this version the elements of the array AP 00217 * are accessed sequentially with one pass through AP. 00218 * 00219 KK = 1 00220 IF (LSAME(UPLO,'U')) THEN 00221 * 00222 * Form A when upper triangle is stored in AP. 00223 * 00224 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00225 DO 20 J = 1,N 00226 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00227 TEMP1 = ALPHA*Y(J) 00228 TEMP2 = ALPHA*X(J) 00229 K = KK 00230 DO 10 I = 1,J 00231 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00232 K = K + 1 00233 10 CONTINUE 00234 END IF 00235 KK = KK + J 00236 20 CONTINUE 00237 ELSE 00238 DO 40 J = 1,N 00239 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00240 TEMP1 = ALPHA*Y(JY) 00241 TEMP2 = ALPHA*X(JX) 00242 IX = KX 00243 IY = KY 00244 DO 30 K = KK,KK + J - 1 00245 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00246 IX = IX + INCX 00247 IY = IY + INCY 00248 30 CONTINUE 00249 END IF 00250 JX = JX + INCX 00251 JY = JY + INCY 00252 KK = KK + J 00253 40 CONTINUE 00254 END IF 00255 ELSE 00256 * 00257 * Form A when lower triangle is stored in AP. 00258 * 00259 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00260 DO 60 J = 1,N 00261 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00262 TEMP1 = ALPHA*Y(J) 00263 TEMP2 = ALPHA*X(J) 00264 K = KK 00265 DO 50 I = J,N 00266 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00267 K = K + 1 00268 50 CONTINUE 00269 END IF 00270 KK = KK + N - J + 1 00271 60 CONTINUE 00272 ELSE 00273 DO 80 J = 1,N 00274 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00275 TEMP1 = ALPHA*Y(JY) 00276 TEMP2 = ALPHA*X(JX) 00277 IX = JX 00278 IY = JY 00279 DO 70 K = KK,KK + N - J 00280 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00281 IX = IX + INCX 00282 IY = IY + INCY 00283 70 CONTINUE 00284 END IF 00285 JX = JX + INCX 00286 JY = JY + INCY 00287 KK = KK + N - J + 1 00288 80 CONTINUE 00289 END IF 00290 END IF 00291 * 00292 RETURN 00293 * 00294 * End of SSPR2 . 00295 * 00296 END