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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SSYR2 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 SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) 00012 * 00013 * .. Scalar Arguments .. 00014 * REAL ALPHA 00015 * INTEGER INCX,INCY,LDA,N 00016 * CHARACTER UPLO 00017 * .. 00018 * .. Array Arguments .. 00019 * REAL A(LDA,*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> SSYR2 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 n 00033 *> by n symmetric matrix. 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 array A is to be referenced as 00044 *> follows: 00045 *> 00046 *> UPLO = 'U' or 'u' Only the upper triangular part of A 00047 *> is to be referenced. 00048 *> 00049 *> UPLO = 'L' or 'l' Only the lower triangular part of A 00050 *> is to be referenced. 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] A 00097 *> \verbatim 00098 *> A is REAL array of DIMENSION ( LDA, n ). 00099 *> Before entry with UPLO = 'U' or 'u', the leading n by n 00100 *> upper triangular part of the array A must contain the upper 00101 *> triangular part of the symmetric matrix and the strictly 00102 *> lower triangular part of A is not referenced. On exit, the 00103 *> upper triangular part of the array A is overwritten by the 00104 *> upper triangular part of the updated matrix. 00105 *> Before entry with UPLO = 'L' or 'l', the leading n by n 00106 *> lower triangular part of the array A must contain the lower 00107 *> triangular part of the symmetric matrix and the strictly 00108 *> upper triangular part of A is not referenced. On exit, the 00109 *> lower triangular part of the array A is overwritten by the 00110 *> lower triangular part of the updated matrix. 00111 *> \endverbatim 00112 *> 00113 *> \param[in] LDA 00114 *> \verbatim 00115 *> LDA is INTEGER 00116 *> On entry, LDA specifies the first dimension of A as declared 00117 *> in the calling (sub) program. LDA must be at least 00118 *> max( 1, n ). 00119 *> \endverbatim 00120 * 00121 * Authors: 00122 * ======== 00123 * 00124 *> \author Univ. of Tennessee 00125 *> \author Univ. of California Berkeley 00126 *> \author Univ. of Colorado Denver 00127 *> \author NAG Ltd. 00128 * 00129 *> \date November 2011 00130 * 00131 *> \ingroup single_blas_level2 00132 * 00133 *> \par Further Details: 00134 * ===================== 00135 *> 00136 *> \verbatim 00137 *> 00138 *> Level 2 Blas routine. 00139 *> 00140 *> -- Written on 22-October-1986. 00141 *> Jack Dongarra, Argonne National Lab. 00142 *> Jeremy Du Croz, Nag Central Office. 00143 *> Sven Hammarling, Nag Central Office. 00144 *> Richard Hanson, Sandia National Labs. 00145 *> \endverbatim 00146 *> 00147 * ===================================================================== 00148 SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) 00149 * 00150 * -- Reference BLAS level2 routine (version 3.4.0) -- 00151 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00152 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00153 * November 2011 00154 * 00155 * .. Scalar Arguments .. 00156 REAL ALPHA 00157 INTEGER INCX,INCY,LDA,N 00158 CHARACTER UPLO 00159 * .. 00160 * .. Array Arguments .. 00161 REAL A(LDA,*),X(*),Y(*) 00162 * .. 00163 * 00164 * ===================================================================== 00165 * 00166 * .. Parameters .. 00167 REAL ZERO 00168 PARAMETER (ZERO=0.0E+0) 00169 * .. 00170 * .. Local Scalars .. 00171 REAL TEMP1,TEMP2 00172 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY 00173 * .. 00174 * .. External Functions .. 00175 LOGICAL LSAME 00176 EXTERNAL LSAME 00177 * .. 00178 * .. External Subroutines .. 00179 EXTERNAL XERBLA 00180 * .. 00181 * .. Intrinsic Functions .. 00182 INTRINSIC MAX 00183 * .. 00184 * 00185 * Test the input parameters. 00186 * 00187 INFO = 0 00188 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00189 INFO = 1 00190 ELSE IF (N.LT.0) THEN 00191 INFO = 2 00192 ELSE IF (INCX.EQ.0) THEN 00193 INFO = 5 00194 ELSE IF (INCY.EQ.0) THEN 00195 INFO = 7 00196 ELSE IF (LDA.LT.MAX(1,N)) THEN 00197 INFO = 9 00198 END IF 00199 IF (INFO.NE.0) THEN 00200 CALL XERBLA('SSYR2 ',INFO) 00201 RETURN 00202 END IF 00203 * 00204 * Quick return if possible. 00205 * 00206 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 00207 * 00208 * Set up the start points in X and Y if the increments are not both 00209 * unity. 00210 * 00211 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 00212 IF (INCX.GT.0) THEN 00213 KX = 1 00214 ELSE 00215 KX = 1 - (N-1)*INCX 00216 END IF 00217 IF (INCY.GT.0) THEN 00218 KY = 1 00219 ELSE 00220 KY = 1 - (N-1)*INCY 00221 END IF 00222 JX = KX 00223 JY = KY 00224 END IF 00225 * 00226 * Start the operations. In this version the elements of A are 00227 * accessed sequentially with one pass through the triangular part 00228 * of A. 00229 * 00230 IF (LSAME(UPLO,'U')) THEN 00231 * 00232 * Form A when A is stored in the upper triangle. 00233 * 00234 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00235 DO 20 J = 1,N 00236 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00237 TEMP1 = ALPHA*Y(J) 00238 TEMP2 = ALPHA*X(J) 00239 DO 10 I = 1,J 00240 A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 00241 10 CONTINUE 00242 END IF 00243 20 CONTINUE 00244 ELSE 00245 DO 40 J = 1,N 00246 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00247 TEMP1 = ALPHA*Y(JY) 00248 TEMP2 = ALPHA*X(JX) 00249 IX = KX 00250 IY = KY 00251 DO 30 I = 1,J 00252 A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 00253 IX = IX + INCX 00254 IY = IY + INCY 00255 30 CONTINUE 00256 END IF 00257 JX = JX + INCX 00258 JY = JY + INCY 00259 40 CONTINUE 00260 END IF 00261 ELSE 00262 * 00263 * Form A when A is stored in the lower triangle. 00264 * 00265 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00266 DO 60 J = 1,N 00267 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00268 TEMP1 = ALPHA*Y(J) 00269 TEMP2 = ALPHA*X(J) 00270 DO 50 I = J,N 00271 A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 00272 50 CONTINUE 00273 END IF 00274 60 CONTINUE 00275 ELSE 00276 DO 80 J = 1,N 00277 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00278 TEMP1 = ALPHA*Y(JY) 00279 TEMP2 = ALPHA*X(JX) 00280 IX = JX 00281 IY = JY 00282 DO 70 I = J,N 00283 A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 00284 IX = IX + INCX 00285 IY = IY + INCY 00286 70 CONTINUE 00287 END IF 00288 JX = JX + INCX 00289 JY = JY + INCY 00290 80 CONTINUE 00291 END IF 00292 END IF 00293 * 00294 RETURN 00295 * 00296 * End of SSYR2 . 00297 * 00298 END