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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DSPMV 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 DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 00012 * 00013 * .. Scalar Arguments .. 00014 * DOUBLE PRECISION ALPHA,BETA 00015 * INTEGER INCX,INCY,N 00016 * CHARACTER UPLO 00017 * .. 00018 * .. Array Arguments .. 00019 * DOUBLE PRECISION AP(*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> DSPMV 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, 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 DOUBLE PRECISION. 00063 *> On entry, ALPHA specifies the scalar alpha. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] AP 00067 *> \verbatim 00068 *> AP is DOUBLE PRECISION array of DIMENSION at least 00069 *> ( ( n*( n + 1 ) )/2 ). 00070 *> Before entry with UPLO = 'U' or 'u', the array AP must 00071 *> contain the upper triangular part of the symmetric matrix 00072 *> packed sequentially, column by column, so that AP( 1 ) 00073 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) 00074 *> and a( 2, 2 ) respectively, and so on. 00075 *> Before entry with UPLO = 'L' or 'l', the array AP must 00076 *> contain the lower triangular part of the symmetric matrix 00077 *> packed sequentially, column by column, so that AP( 1 ) 00078 *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) 00079 *> and a( 3, 1 ) respectively, and so on. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] X 00083 *> \verbatim 00084 *> X is DOUBLE PRECISION array of dimension at least 00085 *> ( 1 + ( n - 1 )*abs( INCX ) ). 00086 *> Before entry, the incremented array X must contain the n 00087 *> element vector x. 00088 *> \endverbatim 00089 *> 00090 *> \param[in] INCX 00091 *> \verbatim 00092 *> INCX is INTEGER 00093 *> On entry, INCX specifies the increment for the elements of 00094 *> X. INCX must not be zero. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] BETA 00098 *> \verbatim 00099 *> BETA is DOUBLE PRECISION. 00100 *> On entry, BETA specifies the scalar beta. When BETA is 00101 *> supplied as zero then Y need not be set on input. 00102 *> \endverbatim 00103 *> 00104 *> \param[in,out] Y 00105 *> \verbatim 00106 *> Y is DOUBLE PRECISION array of dimension at least 00107 *> ( 1 + ( n - 1 )*abs( INCY ) ). 00108 *> Before entry, the incremented array Y must contain the n 00109 *> element vector y. On exit, Y is overwritten by the updated 00110 *> vector y. 00111 *> \endverbatim 00112 *> 00113 *> \param[in] INCY 00114 *> \verbatim 00115 *> INCY is INTEGER 00116 *> On entry, INCY specifies the increment for the elements of 00117 *> Y. INCY must not be zero. 00118 *> \endverbatim 00119 * 00120 * Authors: 00121 * ======== 00122 * 00123 *> \author Univ. of Tennessee 00124 *> \author Univ. of California Berkeley 00125 *> \author Univ. of Colorado Denver 00126 *> \author NAG Ltd. 00127 * 00128 *> \date November 2011 00129 * 00130 *> \ingroup double_blas_level2 00131 * 00132 *> \par Further Details: 00133 * ===================== 00134 *> 00135 *> \verbatim 00136 *> 00137 *> Level 2 Blas routine. 00138 *> The vector and matrix arguments are not referenced when N = 0, or M = 0 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 DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) 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 DOUBLE PRECISION ALPHA,BETA 00157 INTEGER INCX,INCY,N 00158 CHARACTER UPLO 00159 * .. 00160 * .. Array Arguments .. 00161 DOUBLE PRECISION AP(*),X(*),Y(*) 00162 * .. 00163 * 00164 * ===================================================================== 00165 * 00166 * .. Parameters .. 00167 DOUBLE PRECISION ONE,ZERO 00168 PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) 00169 * .. 00170 * .. Local Scalars .. 00171 DOUBLE PRECISION TEMP1,TEMP2 00172 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 00173 * .. 00174 * .. External Functions .. 00175 LOGICAL LSAME 00176 EXTERNAL LSAME 00177 * .. 00178 * .. External Subroutines .. 00179 EXTERNAL XERBLA 00180 * .. 00181 * 00182 * Test the input parameters. 00183 * 00184 INFO = 0 00185 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00186 INFO = 1 00187 ELSE IF (N.LT.0) THEN 00188 INFO = 2 00189 ELSE IF (INCX.EQ.0) THEN 00190 INFO = 6 00191 ELSE IF (INCY.EQ.0) THEN 00192 INFO = 9 00193 END IF 00194 IF (INFO.NE.0) THEN 00195 CALL XERBLA('DSPMV ',INFO) 00196 RETURN 00197 END IF 00198 * 00199 * Quick return if possible. 00200 * 00201 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00202 * 00203 * Set up the start points in X and Y. 00204 * 00205 IF (INCX.GT.0) THEN 00206 KX = 1 00207 ELSE 00208 KX = 1 - (N-1)*INCX 00209 END IF 00210 IF (INCY.GT.0) THEN 00211 KY = 1 00212 ELSE 00213 KY = 1 - (N-1)*INCY 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 * First form y := beta*y. 00220 * 00221 IF (BETA.NE.ONE) THEN 00222 IF (INCY.EQ.1) THEN 00223 IF (BETA.EQ.ZERO) THEN 00224 DO 10 I = 1,N 00225 Y(I) = ZERO 00226 10 CONTINUE 00227 ELSE 00228 DO 20 I = 1,N 00229 Y(I) = BETA*Y(I) 00230 20 CONTINUE 00231 END IF 00232 ELSE 00233 IY = KY 00234 IF (BETA.EQ.ZERO) THEN 00235 DO 30 I = 1,N 00236 Y(IY) = ZERO 00237 IY = IY + INCY 00238 30 CONTINUE 00239 ELSE 00240 DO 40 I = 1,N 00241 Y(IY) = BETA*Y(IY) 00242 IY = IY + INCY 00243 40 CONTINUE 00244 END IF 00245 END IF 00246 END IF 00247 IF (ALPHA.EQ.ZERO) RETURN 00248 KK = 1 00249 IF (LSAME(UPLO,'U')) THEN 00250 * 00251 * Form y when AP contains the upper triangle. 00252 * 00253 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00254 DO 60 J = 1,N 00255 TEMP1 = ALPHA*X(J) 00256 TEMP2 = ZERO 00257 K = KK 00258 DO 50 I = 1,J - 1 00259 Y(I) = Y(I) + TEMP1*AP(K) 00260 TEMP2 = TEMP2 + AP(K)*X(I) 00261 K = K + 1 00262 50 CONTINUE 00263 Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 00264 KK = KK + J 00265 60 CONTINUE 00266 ELSE 00267 JX = KX 00268 JY = KY 00269 DO 80 J = 1,N 00270 TEMP1 = ALPHA*X(JX) 00271 TEMP2 = ZERO 00272 IX = KX 00273 IY = KY 00274 DO 70 K = KK,KK + J - 2 00275 Y(IY) = Y(IY) + TEMP1*AP(K) 00276 TEMP2 = TEMP2 + AP(K)*X(IX) 00277 IX = IX + INCX 00278 IY = IY + INCY 00279 70 CONTINUE 00280 Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 00281 JX = JX + INCX 00282 JY = JY + INCY 00283 KK = KK + J 00284 80 CONTINUE 00285 END IF 00286 ELSE 00287 * 00288 * Form y when AP contains the lower triangle. 00289 * 00290 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00291 DO 100 J = 1,N 00292 TEMP1 = ALPHA*X(J) 00293 TEMP2 = ZERO 00294 Y(J) = Y(J) + TEMP1*AP(KK) 00295 K = KK + 1 00296 DO 90 I = J + 1,N 00297 Y(I) = Y(I) + TEMP1*AP(K) 00298 TEMP2 = TEMP2 + AP(K)*X(I) 00299 K = K + 1 00300 90 CONTINUE 00301 Y(J) = Y(J) + ALPHA*TEMP2 00302 KK = KK + (N-J+1) 00303 100 CONTINUE 00304 ELSE 00305 JX = KX 00306 JY = KY 00307 DO 120 J = 1,N 00308 TEMP1 = ALPHA*X(JX) 00309 TEMP2 = ZERO 00310 Y(JY) = Y(JY) + TEMP1*AP(KK) 00311 IX = JX 00312 IY = JY 00313 DO 110 K = KK + 1,KK + N - J 00314 IX = IX + INCX 00315 IY = IY + INCY 00316 Y(IY) = Y(IY) + TEMP1*AP(K) 00317 TEMP2 = TEMP2 + AP(K)*X(IX) 00318 110 CONTINUE 00319 Y(JY) = Y(JY) + ALPHA*TEMP2 00320 JX = JX + INCX 00321 JY = JY + INCY 00322 KK = KK + (N-J+1) 00323 120 CONTINUE 00324 END IF 00325 END IF 00326 * 00327 RETURN 00328 * 00329 * End of DSPMV . 00330 * 00331 END