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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DSYMV 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 DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00012 * 00013 * .. Scalar Arguments .. 00014 * DOUBLE PRECISION ALPHA,BETA 00015 * INTEGER INCX,INCY,LDA,N 00016 * CHARACTER UPLO 00017 * .. 00018 * .. Array Arguments .. 00019 * DOUBLE PRECISION A(LDA,*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> DSYMV performs the matrix-vector operation 00029 *> 00030 *> y := alpha*A*x + beta*y, 00031 *> 00032 *> where alpha and beta are scalars, x and y are n element vectors and 00033 *> A is an n 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 DOUBLE PRECISION. 00063 *> On entry, ALPHA specifies the scalar alpha. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] A 00067 *> \verbatim 00068 *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). 00069 *> Before entry with UPLO = 'U' or 'u', the leading n by n 00070 *> upper triangular part of the array A must contain the upper 00071 *> triangular part of the symmetric matrix and the strictly 00072 *> lower triangular part of A is not referenced. 00073 *> Before entry with UPLO = 'L' or 'l', the leading n by n 00074 *> lower triangular part of the array A must contain the lower 00075 *> triangular part of the symmetric matrix and the strictly 00076 *> upper triangular part of A is not referenced. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] LDA 00080 *> \verbatim 00081 *> LDA is INTEGER 00082 *> On entry, LDA specifies the first dimension of A as declared 00083 *> in the calling (sub) program. LDA must be at least 00084 *> max( 1, n ). 00085 *> \endverbatim 00086 *> 00087 *> \param[in] X 00088 *> \verbatim 00089 *> X is DOUBLE PRECISION array of dimension at least 00090 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00091 *> Before entry, the incremented array X must contain the n 00092 *> element vector x. 00093 *> \endverbatim 00094 *> 00095 *> \param[in] INCX 00096 *> \verbatim 00097 *> INCX is INTEGER 00098 *> On entry, INCX specifies the increment for the elements of 00099 *> X. INCX must not be zero. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] BETA 00103 *> \verbatim 00104 *> BETA is DOUBLE PRECISION. 00105 *> On entry, BETA specifies the scalar beta. When BETA is 00106 *> supplied as zero then Y need not be set on input. 00107 *> \endverbatim 00108 *> 00109 *> \param[in,out] Y 00110 *> \verbatim 00111 *> Y is DOUBLE PRECISION array of dimension at least 00112 *> ( 1 + ( n - 1 )*abs( INCY ) ). 00113 *> Before entry, the incremented array Y must contain the n 00114 *> element vector y. On exit, Y is overwritten by the updated 00115 *> vector y. 00116 *> \endverbatim 00117 *> 00118 *> \param[in] INCY 00119 *> \verbatim 00120 *> INCY is INTEGER 00121 *> On entry, INCY specifies the increment for the elements of 00122 *> Y. INCY must not be zero. 00123 *> \endverbatim 00124 * 00125 * Authors: 00126 * ======== 00127 * 00128 *> \author Univ. of Tennessee 00129 *> \author Univ. of California Berkeley 00130 *> \author Univ. of Colorado Denver 00131 *> \author NAG Ltd. 00132 * 00133 *> \date November 2011 00134 * 00135 *> \ingroup double_blas_level2 00136 * 00137 *> \par Further Details: 00138 * ===================== 00139 *> 00140 *> \verbatim 00141 *> 00142 *> Level 2 Blas routine. 00143 *> The vector and matrix arguments are not referenced when N = 0, or M = 0 00144 *> 00145 *> -- Written on 22-October-1986. 00146 *> Jack Dongarra, Argonne National Lab. 00147 *> Jeremy Du Croz, Nag Central Office. 00148 *> Sven Hammarling, Nag Central Office. 00149 *> Richard Hanson, Sandia National Labs. 00150 *> \endverbatim 00151 *> 00152 * ===================================================================== 00153 SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00154 * 00155 * -- Reference BLAS level2 routine (version 3.4.0) -- 00156 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00158 * November 2011 00159 * 00160 * .. Scalar Arguments .. 00161 DOUBLE PRECISION ALPHA,BETA 00162 INTEGER INCX,INCY,LDA,N 00163 CHARACTER UPLO 00164 * .. 00165 * .. Array Arguments .. 00166 DOUBLE PRECISION A(LDA,*),X(*),Y(*) 00167 * .. 00168 * 00169 * ===================================================================== 00170 * 00171 * .. Parameters .. 00172 DOUBLE PRECISION ONE,ZERO 00173 PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) 00174 * .. 00175 * .. Local Scalars .. 00176 DOUBLE PRECISION TEMP1,TEMP2 00177 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY 00178 * .. 00179 * .. External Functions .. 00180 LOGICAL LSAME 00181 EXTERNAL LSAME 00182 * .. 00183 * .. External Subroutines .. 00184 EXTERNAL XERBLA 00185 * .. 00186 * .. Intrinsic Functions .. 00187 INTRINSIC MAX 00188 * .. 00189 * 00190 * Test the input parameters. 00191 * 00192 INFO = 0 00193 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00194 INFO = 1 00195 ELSE IF (N.LT.0) THEN 00196 INFO = 2 00197 ELSE IF (LDA.LT.MAX(1,N)) THEN 00198 INFO = 5 00199 ELSE IF (INCX.EQ.0) THEN 00200 INFO = 7 00201 ELSE IF (INCY.EQ.0) THEN 00202 INFO = 10 00203 END IF 00204 IF (INFO.NE.0) THEN 00205 CALL XERBLA('DSYMV ',INFO) 00206 RETURN 00207 END IF 00208 * 00209 * Quick return if possible. 00210 * 00211 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00212 * 00213 * Set up the start points in X and Y. 00214 * 00215 IF (INCX.GT.0) THEN 00216 KX = 1 00217 ELSE 00218 KX = 1 - (N-1)*INCX 00219 END IF 00220 IF (INCY.GT.0) THEN 00221 KY = 1 00222 ELSE 00223 KY = 1 - (N-1)*INCY 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 * First form y := beta*y. 00231 * 00232 IF (BETA.NE.ONE) THEN 00233 IF (INCY.EQ.1) THEN 00234 IF (BETA.EQ.ZERO) THEN 00235 DO 10 I = 1,N 00236 Y(I) = ZERO 00237 10 CONTINUE 00238 ELSE 00239 DO 20 I = 1,N 00240 Y(I) = BETA*Y(I) 00241 20 CONTINUE 00242 END IF 00243 ELSE 00244 IY = KY 00245 IF (BETA.EQ.ZERO) THEN 00246 DO 30 I = 1,N 00247 Y(IY) = ZERO 00248 IY = IY + INCY 00249 30 CONTINUE 00250 ELSE 00251 DO 40 I = 1,N 00252 Y(IY) = BETA*Y(IY) 00253 IY = IY + INCY 00254 40 CONTINUE 00255 END IF 00256 END IF 00257 END IF 00258 IF (ALPHA.EQ.ZERO) RETURN 00259 IF (LSAME(UPLO,'U')) THEN 00260 * 00261 * Form y when A is stored in upper triangle. 00262 * 00263 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00264 DO 60 J = 1,N 00265 TEMP1 = ALPHA*X(J) 00266 TEMP2 = ZERO 00267 DO 50 I = 1,J - 1 00268 Y(I) = Y(I) + TEMP1*A(I,J) 00269 TEMP2 = TEMP2 + A(I,J)*X(I) 00270 50 CONTINUE 00271 Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2 00272 60 CONTINUE 00273 ELSE 00274 JX = KX 00275 JY = KY 00276 DO 80 J = 1,N 00277 TEMP1 = ALPHA*X(JX) 00278 TEMP2 = ZERO 00279 IX = KX 00280 IY = KY 00281 DO 70 I = 1,J - 1 00282 Y(IY) = Y(IY) + TEMP1*A(I,J) 00283 TEMP2 = TEMP2 + A(I,J)*X(IX) 00284 IX = IX + INCX 00285 IY = IY + INCY 00286 70 CONTINUE 00287 Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2 00288 JX = JX + INCX 00289 JY = JY + INCY 00290 80 CONTINUE 00291 END IF 00292 ELSE 00293 * 00294 * Form y when A is stored in lower triangle. 00295 * 00296 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00297 DO 100 J = 1,N 00298 TEMP1 = ALPHA*X(J) 00299 TEMP2 = ZERO 00300 Y(J) = Y(J) + TEMP1*A(J,J) 00301 DO 90 I = J + 1,N 00302 Y(I) = Y(I) + TEMP1*A(I,J) 00303 TEMP2 = TEMP2 + A(I,J)*X(I) 00304 90 CONTINUE 00305 Y(J) = Y(J) + ALPHA*TEMP2 00306 100 CONTINUE 00307 ELSE 00308 JX = KX 00309 JY = KY 00310 DO 120 J = 1,N 00311 TEMP1 = ALPHA*X(JX) 00312 TEMP2 = ZERO 00313 Y(JY) = Y(JY) + TEMP1*A(J,J) 00314 IX = JX 00315 IY = JY 00316 DO 110 I = J + 1,N 00317 IX = IX + INCX 00318 IY = IY + INCY 00319 Y(IY) = Y(IY) + TEMP1*A(I,J) 00320 TEMP2 = TEMP2 + A(I,J)*X(IX) 00321 110 CONTINUE 00322 Y(JY) = Y(JY) + ALPHA*TEMP2 00323 JX = JX + INCX 00324 JY = JY + INCY 00325 120 CONTINUE 00326 END IF 00327 END IF 00328 * 00329 RETURN 00330 * 00331 * End of DSYMV . 00332 * 00333 END