LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zher.f
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00001 *> \brief \b ZHER
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 ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       DOUBLE PRECISION ALPHA
00015 *       INTEGER INCX,LDA,N
00016 *       CHARACTER UPLO
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       COMPLEX*16 A(LDA,*),X(*)
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> ZHER   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.
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] 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] A
00082 *> \verbatim
00083 *>          A is COMPLEX*16 array of DIMENSION ( LDA, n ).
00084 *>           Before entry with  UPLO = 'U' or 'u', the leading n by n
00085 *>           upper triangular part of the array A must contain the upper
00086 *>           triangular part of the hermitian matrix and the strictly
00087 *>           lower triangular part of A is not referenced. On exit, the
00088 *>           upper triangular part of the array A is overwritten by the
00089 *>           upper triangular part of the updated matrix.
00090 *>           Before entry with UPLO = 'L' or 'l', the leading n by n
00091 *>           lower triangular part of the array A must contain the lower
00092 *>           triangular part of the hermitian matrix and the strictly
00093 *>           upper triangular part of A is not referenced. On exit, the
00094 *>           lower triangular part of the array A is overwritten by the
00095 *>           lower triangular part of the updated matrix.
00096 *>           Note that the imaginary parts of the diagonal elements need
00097 *>           not be set, they are assumed to be zero, and on exit they
00098 *>           are set to zero.
00099 *> \endverbatim
00100 *>
00101 *> \param[in] LDA
00102 *> \verbatim
00103 *>          LDA is INTEGER
00104 *>           On entry, LDA specifies the first dimension of A as declared
00105 *>           in the calling (sub) program. LDA must be at least
00106 *>           max( 1, n ).
00107 *> \endverbatim
00108 *
00109 *  Authors:
00110 *  ========
00111 *
00112 *> \author Univ. of Tennessee 
00113 *> \author Univ. of California Berkeley 
00114 *> \author Univ. of Colorado Denver 
00115 *> \author NAG Ltd. 
00116 *
00117 *> \date November 2011
00118 *
00119 *> \ingroup complex16_blas_level2
00120 *
00121 *> \par Further Details:
00122 *  =====================
00123 *>
00124 *> \verbatim
00125 *>
00126 *>  Level 2 Blas routine.
00127 *>
00128 *>  -- Written on 22-October-1986.
00129 *>     Jack Dongarra, Argonne National Lab.
00130 *>     Jeremy Du Croz, Nag Central Office.
00131 *>     Sven Hammarling, Nag Central Office.
00132 *>     Richard Hanson, Sandia National Labs.
00133 *> \endverbatim
00134 *>
00135 *  =====================================================================
00136       SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
00137 *
00138 *  -- Reference BLAS level2 routine (version 3.4.0) --
00139 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00140 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00141 *     November 2011
00142 *
00143 *     .. Scalar Arguments ..
00144       DOUBLE PRECISION ALPHA
00145       INTEGER INCX,LDA,N
00146       CHARACTER UPLO
00147 *     ..
00148 *     .. Array Arguments ..
00149       COMPLEX*16 A(LDA,*),X(*)
00150 *     ..
00151 *
00152 *  =====================================================================
00153 *
00154 *     .. Parameters ..
00155       COMPLEX*16 ZERO
00156       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00157 *     ..
00158 *     .. Local Scalars ..
00159       COMPLEX*16 TEMP
00160       INTEGER I,INFO,IX,J,JX,KX
00161 *     ..
00162 *     .. External Functions ..
00163       LOGICAL LSAME
00164       EXTERNAL LSAME
00165 *     ..
00166 *     .. External Subroutines ..
00167       EXTERNAL XERBLA
00168 *     ..
00169 *     .. Intrinsic Functions ..
00170       INTRINSIC DBLE,DCONJG,MAX
00171 *     ..
00172 *
00173 *     Test the input parameters.
00174 *
00175       INFO = 0
00176       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00177           INFO = 1
00178       ELSE IF (N.LT.0) THEN
00179           INFO = 2
00180       ELSE IF (INCX.EQ.0) THEN
00181           INFO = 5
00182       ELSE IF (LDA.LT.MAX(1,N)) THEN
00183           INFO = 7
00184       END IF
00185       IF (INFO.NE.0) THEN
00186           CALL XERBLA('ZHER  ',INFO)
00187           RETURN
00188       END IF
00189 *
00190 *     Quick return if possible.
00191 *
00192       IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN
00193 *
00194 *     Set the start point in X if the increment is not unity.
00195 *
00196       IF (INCX.LE.0) THEN
00197           KX = 1 - (N-1)*INCX
00198       ELSE IF (INCX.NE.1) THEN
00199           KX = 1
00200       END IF
00201 *
00202 *     Start the operations. In this version the elements of A are
00203 *     accessed sequentially with one pass through the triangular part
00204 *     of A.
00205 *
00206       IF (LSAME(UPLO,'U')) THEN
00207 *
00208 *        Form  A  when A is stored in upper triangle.
00209 *
00210           IF (INCX.EQ.1) THEN
00211               DO 20 J = 1,N
00212                   IF (X(J).NE.ZERO) THEN
00213                       TEMP = ALPHA*DCONJG(X(J))
00214                       DO 10 I = 1,J - 1
00215                           A(I,J) = A(I,J) + X(I)*TEMP
00216    10                 CONTINUE
00217                       A(J,J) = DBLE(A(J,J)) + DBLE(X(J)*TEMP)
00218                   ELSE
00219                       A(J,J) = DBLE(A(J,J))
00220                   END IF
00221    20         CONTINUE
00222           ELSE
00223               JX = KX
00224               DO 40 J = 1,N
00225                   IF (X(JX).NE.ZERO) THEN
00226                       TEMP = ALPHA*DCONJG(X(JX))
00227                       IX = KX
00228                       DO 30 I = 1,J - 1
00229                           A(I,J) = A(I,J) + X(IX)*TEMP
00230                           IX = IX + INCX
00231    30                 CONTINUE
00232                       A(J,J) = DBLE(A(J,J)) + DBLE(X(JX)*TEMP)
00233                   ELSE
00234                       A(J,J) = DBLE(A(J,J))
00235                   END IF
00236                   JX = JX + INCX
00237    40         CONTINUE
00238           END IF
00239       ELSE
00240 *
00241 *        Form  A  when A is stored in lower triangle.
00242 *
00243           IF (INCX.EQ.1) THEN
00244               DO 60 J = 1,N
00245                   IF (X(J).NE.ZERO) THEN
00246                       TEMP = ALPHA*DCONJG(X(J))
00247                       A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(J))
00248                       DO 50 I = J + 1,N
00249                           A(I,J) = A(I,J) + X(I)*TEMP
00250    50                 CONTINUE
00251                   ELSE
00252                       A(J,J) = DBLE(A(J,J))
00253                   END IF
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                       A(J,J) = DBLE(A(J,J)) + DBLE(TEMP*X(JX))
00261                       IX = JX
00262                       DO 70 I = J + 1,N
00263                           IX = IX + INCX
00264                           A(I,J) = A(I,J) + X(IX)*TEMP
00265    70                 CONTINUE
00266                   ELSE
00267                       A(J,J) = DBLE(A(J,J))
00268                   END IF
00269                   JX = JX + INCX
00270    80         CONTINUE
00271           END IF
00272       END IF
00273 *
00274       RETURN
00275 *
00276 *     End of ZHER  .
00277 *
00278       END
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