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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHPR2 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 ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 00012 * 00013 * .. Scalar Arguments .. 00014 * COMPLEX*16 ALPHA 00015 * INTEGER INCX,INCY,N 00016 * CHARACTER UPLO 00017 * .. 00018 * .. Array Arguments .. 00019 * COMPLEX*16 AP(*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> ZHPR2 performs the hermitian rank 2 operation 00029 *> 00030 *> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, 00031 *> 00032 *> where alpha is a scalar, x and y are n element vectors and A is an 00033 *> n by n hermitian 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 COMPLEX*16 00063 *> On entry, ALPHA specifies the scalar alpha. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] X 00067 *> \verbatim 00068 *> X is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 hermitian 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 hermitian 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 *> Note that the imaginary parts of the diagonal elements need 00115 *> not be set, they are assumed to be zero, and on exit they 00116 *> are set to zero. 00117 *> \endverbatim 00118 * 00119 * Authors: 00120 * ======== 00121 * 00122 *> \author Univ. of Tennessee 00123 *> \author Univ. of California Berkeley 00124 *> \author Univ. of Colorado Denver 00125 *> \author NAG Ltd. 00126 * 00127 *> \date November 2011 00128 * 00129 *> \ingroup complex16_blas_level2 00130 * 00131 *> \par Further Details: 00132 * ===================== 00133 *> 00134 *> \verbatim 00135 *> 00136 *> Level 2 Blas routine. 00137 *> 00138 *> -- Written on 22-October-1986. 00139 *> Jack Dongarra, Argonne National Lab. 00140 *> Jeremy Du Croz, Nag Central Office. 00141 *> Sven Hammarling, Nag Central Office. 00142 *> Richard Hanson, Sandia National Labs. 00143 *> \endverbatim 00144 *> 00145 * ===================================================================== 00146 SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) 00147 * 00148 * -- Reference BLAS level2 routine (version 3.4.0) -- 00149 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00151 * November 2011 00152 * 00153 * .. Scalar Arguments .. 00154 COMPLEX*16 ALPHA 00155 INTEGER INCX,INCY,N 00156 CHARACTER UPLO 00157 * .. 00158 * .. Array Arguments .. 00159 COMPLEX*16 AP(*),X(*),Y(*) 00160 * .. 00161 * 00162 * ===================================================================== 00163 * 00164 * .. Parameters .. 00165 COMPLEX*16 ZERO 00166 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00167 * .. 00168 * .. Local Scalars .. 00169 COMPLEX*16 TEMP1,TEMP2 00170 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY 00171 * .. 00172 * .. External Functions .. 00173 LOGICAL LSAME 00174 EXTERNAL LSAME 00175 * .. 00176 * .. External Subroutines .. 00177 EXTERNAL XERBLA 00178 * .. 00179 * .. Intrinsic Functions .. 00180 INTRINSIC DBLE,DCONJG 00181 * .. 00182 * 00183 * Test the input parameters. 00184 * 00185 INFO = 0 00186 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 00187 INFO = 1 00188 ELSE IF (N.LT.0) THEN 00189 INFO = 2 00190 ELSE IF (INCX.EQ.0) THEN 00191 INFO = 5 00192 ELSE IF (INCY.EQ.0) THEN 00193 INFO = 7 00194 END IF 00195 IF (INFO.NE.0) THEN 00196 CALL XERBLA('ZHPR2 ',INFO) 00197 RETURN 00198 END IF 00199 * 00200 * Quick return if possible. 00201 * 00202 IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN 00203 * 00204 * Set up the start points in X and Y if the increments are not both 00205 * unity. 00206 * 00207 IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN 00208 IF (INCX.GT.0) THEN 00209 KX = 1 00210 ELSE 00211 KX = 1 - (N-1)*INCX 00212 END IF 00213 IF (INCY.GT.0) THEN 00214 KY = 1 00215 ELSE 00216 KY = 1 - (N-1)*INCY 00217 END IF 00218 JX = KX 00219 JY = KY 00220 END IF 00221 * 00222 * Start the operations. In this version the elements of the array AP 00223 * are accessed sequentially with one pass through AP. 00224 * 00225 KK = 1 00226 IF (LSAME(UPLO,'U')) THEN 00227 * 00228 * Form A when upper triangle is stored in AP. 00229 * 00230 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00231 DO 20 J = 1,N 00232 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00233 TEMP1 = ALPHA*DCONJG(Y(J)) 00234 TEMP2 = DCONJG(ALPHA*X(J)) 00235 K = KK 00236 DO 10 I = 1,J - 1 00237 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00238 K = K + 1 00239 10 CONTINUE 00240 AP(KK+J-1) = DBLE(AP(KK+J-1)) + 00241 + DBLE(X(J)*TEMP1+Y(J)*TEMP2) 00242 ELSE 00243 AP(KK+J-1) = DBLE(AP(KK+J-1)) 00244 END IF 00245 KK = KK + J 00246 20 CONTINUE 00247 ELSE 00248 DO 40 J = 1,N 00249 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00250 TEMP1 = ALPHA*DCONJG(Y(JY)) 00251 TEMP2 = DCONJG(ALPHA*X(JX)) 00252 IX = KX 00253 IY = KY 00254 DO 30 K = KK,KK + J - 2 00255 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00256 IX = IX + INCX 00257 IY = IY + INCY 00258 30 CONTINUE 00259 AP(KK+J-1) = DBLE(AP(KK+J-1)) + 00260 + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) 00261 ELSE 00262 AP(KK+J-1) = DBLE(AP(KK+J-1)) 00263 END IF 00264 JX = JX + INCX 00265 JY = JY + INCY 00266 KK = KK + J 00267 40 CONTINUE 00268 END IF 00269 ELSE 00270 * 00271 * Form A when lower triangle is stored in AP. 00272 * 00273 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 00274 DO 60 J = 1,N 00275 IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN 00276 TEMP1 = ALPHA*DCONJG(Y(J)) 00277 TEMP2 = DCONJG(ALPHA*X(J)) 00278 AP(KK) = DBLE(AP(KK)) + 00279 + DBLE(X(J)*TEMP1+Y(J)*TEMP2) 00280 K = KK + 1 00281 DO 50 I = J + 1,N 00282 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 00283 K = K + 1 00284 50 CONTINUE 00285 ELSE 00286 AP(KK) = DBLE(AP(KK)) 00287 END IF 00288 KK = KK + N - J + 1 00289 60 CONTINUE 00290 ELSE 00291 DO 80 J = 1,N 00292 IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN 00293 TEMP1 = ALPHA*DCONJG(Y(JY)) 00294 TEMP2 = DCONJG(ALPHA*X(JX)) 00295 AP(KK) = DBLE(AP(KK)) + 00296 + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) 00297 IX = JX 00298 IY = JY 00299 DO 70 K = KK + 1,KK + N - J 00300 IX = IX + INCX 00301 IY = IY + INCY 00302 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 00303 70 CONTINUE 00304 ELSE 00305 AP(KK) = DBLE(AP(KK)) 00306 END IF 00307 JX = JX + INCX 00308 JY = JY + INCY 00309 KK = KK + N - J + 1 00310 80 CONTINUE 00311 END IF 00312 END IF 00313 * 00314 RETURN 00315 * 00316 * End of ZHPR2 . 00317 * 00318 END