LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhpr.f
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00001 *> \brief \b ZHPR
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 ZHPR(UPLO,N,ALPHA,X,INCX,AP)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       DOUBLE PRECISION ALPHA
00015 *       INTEGER INCX,N
00016 *       CHARACTER UPLO
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       COMPLEX*16 AP(*),X(*)
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> ZHPR    performs the hermitian rank 1 operation
00029 *>
00030 *>    A := alpha*x*x**H + A,
00031 *>
00032 *> where alpha is a real scalar, x is an n element vector 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 DOUBLE PRECISION.
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,out] AP
00082 *> \verbatim
00083 *>          AP is COMPLEX*16 array of DIMENSION at least
00084 *>           ( ( n*( n + 1 ) )/2 ).
00085 *>           Before entry with  UPLO = 'U' or 'u', the array AP must
00086 *>           contain the upper triangular part of the hermitian matrix
00087 *>           packed sequentially, column by column, so that AP( 1 )
00088 *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00089 *>           and a( 2, 2 ) respectively, and so on. On exit, the array
00090 *>           AP is overwritten by the upper triangular part of the
00091 *>           updated matrix.
00092 *>           Before entry with UPLO = 'L' or 'l', the array AP must
00093 *>           contain the lower triangular part of the hermitian matrix
00094 *>           packed sequentially, column by column, so that AP( 1 )
00095 *>           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00096 *>           and a( 3, 1 ) respectively, and so on. On exit, the array
00097 *>           AP is overwritten by the lower triangular part of the
00098 *>           updated matrix.
00099 *>           Note that the imaginary parts of the diagonal elements need
00100 *>           not be set, they are assumed to be zero, and on exit they
00101 *>           are set to zero.
00102 *> \endverbatim
00103 *
00104 *  Authors:
00105 *  ========
00106 *
00107 *> \author Univ. of Tennessee 
00108 *> \author Univ. of California Berkeley 
00109 *> \author Univ. of Colorado Denver 
00110 *> \author NAG Ltd. 
00111 *
00112 *> \date November 2011
00113 *
00114 *> \ingroup complex16_blas_level2
00115 *
00116 *> \par Further Details:
00117 *  =====================
00118 *>
00119 *> \verbatim
00120 *>
00121 *>  Level 2 Blas routine.
00122 *>
00123 *>  -- Written on 22-October-1986.
00124 *>     Jack Dongarra, Argonne National Lab.
00125 *>     Jeremy Du Croz, Nag Central Office.
00126 *>     Sven Hammarling, Nag Central Office.
00127 *>     Richard Hanson, Sandia National Labs.
00128 *> \endverbatim
00129 *>
00130 *  =====================================================================
00131       SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
00132 *
00133 *  -- Reference BLAS level2 routine (version 3.4.0) --
00134 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00135 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00136 *     November 2011
00137 *
00138 *     .. Scalar Arguments ..
00139       DOUBLE PRECISION ALPHA
00140       INTEGER INCX,N
00141       CHARACTER UPLO
00142 *     ..
00143 *     .. Array Arguments ..
00144       COMPLEX*16 AP(*),X(*)
00145 *     ..
00146 *
00147 *  =====================================================================
00148 *
00149 *     .. Parameters ..
00150       COMPLEX*16 ZERO
00151       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00152 *     ..
00153 *     .. Local Scalars ..
00154       COMPLEX*16 TEMP
00155       INTEGER I,INFO,IX,J,JX,K,KK,KX
00156 *     ..
00157 *     .. External Functions ..
00158       LOGICAL LSAME
00159       EXTERNAL LSAME
00160 *     ..
00161 *     .. External Subroutines ..
00162       EXTERNAL XERBLA
00163 *     ..
00164 *     .. Intrinsic Functions ..
00165       INTRINSIC DBLE,DCONJG
00166 *     ..
00167 *
00168 *     Test the input parameters.
00169 *
00170       INFO = 0
00171       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00172           INFO = 1
00173       ELSE IF (N.LT.0) THEN
00174           INFO = 2
00175       ELSE IF (INCX.EQ.0) THEN
00176           INFO = 5
00177       END IF
00178       IF (INFO.NE.0) THEN
00179           CALL XERBLA('ZHPR  ',INFO)
00180           RETURN
00181       END IF
00182 *
00183 *     Quick return if possible.
00184 *
00185       IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
00186 *
00187 *     Set the start point in X if the increment is not unity.
00188 *
00189       IF (INCX.LE.0) THEN
00190           KX = 1 - (N-1)*INCX
00191       ELSE IF (INCX.NE.1) THEN
00192           KX = 1
00193       END IF
00194 *
00195 *     Start the operations. In this version the elements of the array AP
00196 *     are accessed sequentially with one pass through AP.
00197 *
00198       KK = 1
00199       IF (LSAME(UPLO,'U')) THEN
00200 *
00201 *        Form  A  when upper triangle is stored in AP.
00202 *
00203           IF (INCX.EQ.1) THEN
00204               DO 20 J = 1,N
00205                   IF (X(J).NE.ZERO) THEN
00206                       TEMP = ALPHA*DCONJG(X(J))
00207                       K = KK
00208                       DO 10 I = 1,J - 1
00209                           AP(K) = AP(K) + X(I)*TEMP
00210                           K = K + 1
00211    10                 CONTINUE
00212                       AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP)
00213                   ELSE
00214                       AP(KK+J-1) = DBLE(AP(KK+J-1))
00215                   END IF
00216                   KK = KK + J
00217    20         CONTINUE
00218           ELSE
00219               JX = KX
00220               DO 40 J = 1,N
00221                   IF (X(JX).NE.ZERO) THEN
00222                       TEMP = ALPHA*DCONJG(X(JX))
00223                       IX = KX
00224                       DO 30 K = KK,KK + J - 2
00225                           AP(K) = AP(K) + X(IX)*TEMP
00226                           IX = IX + INCX
00227    30                 CONTINUE
00228                       AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP)
00229                   ELSE
00230                       AP(KK+J-1) = DBLE(AP(KK+J-1))
00231                   END IF
00232                   JX = JX + INCX
00233                   KK = KK + J
00234    40         CONTINUE
00235           END IF
00236       ELSE
00237 *
00238 *        Form  A  when lower triangle is stored in AP.
00239 *
00240           IF (INCX.EQ.1) THEN
00241               DO 60 J = 1,N
00242                   IF (X(J).NE.ZERO) THEN
00243                       TEMP = ALPHA*DCONJG(X(J))
00244                       AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J))
00245                       K = KK + 1
00246                       DO 50 I = J + 1,N
00247                           AP(K) = AP(K) + X(I)*TEMP
00248                           K = K + 1
00249    50                 CONTINUE
00250                   ELSE
00251                       AP(KK) = DBLE(AP(KK))
00252                   END IF
00253                   KK = KK + N - J + 1
00254    60         CONTINUE
00255           ELSE
00256               JX = KX
00257               DO 80 J = 1,N
00258                   IF (X(JX).NE.ZERO) THEN
00259                       TEMP = ALPHA*DCONJG(X(JX))
00260                       AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX))
00261                       IX = JX
00262                       DO 70 K = KK + 1,KK + N - J
00263                           IX = IX + INCX
00264                           AP(K) = AP(K) + X(IX)*TEMP
00265    70                 CONTINUE
00266                   ELSE
00267                       AP(KK) = DBLE(AP(KK))
00268                   END IF
00269                   JX = JX + INCX
00270                   KK = KK + N - J + 1
00271    80         CONTINUE
00272           END IF
00273       END IF
00274 *
00275       RETURN
00276 *
00277 *     End of ZHPR  .
00278 *
00279       END
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