LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zhemv.f
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00001 *> \brief \b ZHEMV
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 ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       COMPLEX*16 ALPHA,BETA
00015 *       INTEGER INCX,INCY,LDA,N
00016 *       CHARACTER UPLO
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       COMPLEX*16 A(LDA,*),X(*),Y(*)
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> ZHEMV  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 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 COMPLEX*16
00063 *>           On entry, ALPHA specifies the scalar alpha.
00064 *> \endverbatim
00065 *>
00066 *> \param[in] A
00067 *> \verbatim
00068 *>          A is COMPLEX*16 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 hermitian 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 hermitian matrix and the strictly
00076 *>           upper triangular part of A is not referenced.
00077 *>           Note that the imaginary parts of the diagonal elements need
00078 *>           not be set and are assumed to be zero.
00079 *> \endverbatim
00080 *>
00081 *> \param[in] LDA
00082 *> \verbatim
00083 *>          LDA is INTEGER
00084 *>           On entry, LDA specifies the first dimension of A as declared
00085 *>           in the calling (sub) program. LDA must be at least
00086 *>           max( 1, n ).
00087 *> \endverbatim
00088 *>
00089 *> \param[in] X
00090 *> \verbatim
00091 *>          X is COMPLEX*16 array of dimension at least
00092 *>           ( 1 + ( n - 1 )*abs( INCX ) ).
00093 *>           Before entry, the incremented array X must contain the n
00094 *>           element vector x.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] INCX
00098 *> \verbatim
00099 *>          INCX is INTEGER
00100 *>           On entry, INCX specifies the increment for the elements of
00101 *>           X. INCX must not be zero.
00102 *> \endverbatim
00103 *>
00104 *> \param[in] BETA
00105 *> \verbatim
00106 *>          BETA is COMPLEX*16
00107 *>           On entry, BETA specifies the scalar beta. When BETA is
00108 *>           supplied as zero then Y need not be set on input.
00109 *> \endverbatim
00110 *>
00111 *> \param[in,out] Y
00112 *> \verbatim
00113 *>          Y is COMPLEX*16 array of dimension at least
00114 *>           ( 1 + ( n - 1 )*abs( INCY ) ).
00115 *>           Before entry, the incremented array Y must contain the n
00116 *>           element vector y. On exit, Y is overwritten by the updated
00117 *>           vector y.
00118 *> \endverbatim
00119 *>
00120 *> \param[in] INCY
00121 *> \verbatim
00122 *>          INCY is INTEGER
00123 *>           On entry, INCY specifies the increment for the elements of
00124 *>           Y. INCY must not be zero.
00125 *> \endverbatim
00126 *
00127 *  Authors:
00128 *  ========
00129 *
00130 *> \author Univ. of Tennessee 
00131 *> \author Univ. of California Berkeley 
00132 *> \author Univ. of Colorado Denver 
00133 *> \author NAG Ltd. 
00134 *
00135 *> \date November 2011
00136 *
00137 *> \ingroup complex16_blas_level2
00138 *
00139 *> \par Further Details:
00140 *  =====================
00141 *>
00142 *> \verbatim
00143 *>
00144 *>  Level 2 Blas routine.
00145 *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
00146 *>
00147 *>  -- Written on 22-October-1986.
00148 *>     Jack Dongarra, Argonne National Lab.
00149 *>     Jeremy Du Croz, Nag Central Office.
00150 *>     Sven Hammarling, Nag Central Office.
00151 *>     Richard Hanson, Sandia National Labs.
00152 *> \endverbatim
00153 *>
00154 *  =====================================================================
00155       SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
00156 *
00157 *  -- Reference BLAS level2 routine (version 3.4.0) --
00158 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00159 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00160 *     November 2011
00161 *
00162 *     .. Scalar Arguments ..
00163       COMPLEX*16 ALPHA,BETA
00164       INTEGER INCX,INCY,LDA,N
00165       CHARACTER UPLO
00166 *     ..
00167 *     .. Array Arguments ..
00168       COMPLEX*16 A(LDA,*),X(*),Y(*)
00169 *     ..
00170 *
00171 *  =====================================================================
00172 *
00173 *     .. Parameters ..
00174       COMPLEX*16 ONE
00175       PARAMETER (ONE= (1.0D+0,0.0D+0))
00176       COMPLEX*16 ZERO
00177       PARAMETER (ZERO= (0.0D+0,0.0D+0))
00178 *     ..
00179 *     .. Local Scalars ..
00180       COMPLEX*16 TEMP1,TEMP2
00181       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
00182 *     ..
00183 *     .. External Functions ..
00184       LOGICAL LSAME
00185       EXTERNAL LSAME
00186 *     ..
00187 *     .. External Subroutines ..
00188       EXTERNAL XERBLA
00189 *     ..
00190 *     .. Intrinsic Functions ..
00191       INTRINSIC DBLE,DCONJG,MAX
00192 *     ..
00193 *
00194 *     Test the input parameters.
00195 *
00196       INFO = 0
00197       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00198           INFO = 1
00199       ELSE IF (N.LT.0) THEN
00200           INFO = 2
00201       ELSE IF (LDA.LT.MAX(1,N)) THEN
00202           INFO = 5
00203       ELSE IF (INCX.EQ.0) THEN
00204           INFO = 7
00205       ELSE IF (INCY.EQ.0) THEN
00206           INFO = 10
00207       END IF
00208       IF (INFO.NE.0) THEN
00209           CALL XERBLA('ZHEMV ',INFO)
00210           RETURN
00211       END IF
00212 *
00213 *     Quick return if possible.
00214 *
00215       IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
00216 *
00217 *     Set up the start points in  X  and  Y.
00218 *
00219       IF (INCX.GT.0) THEN
00220           KX = 1
00221       ELSE
00222           KX = 1 - (N-1)*INCX
00223       END IF
00224       IF (INCY.GT.0) THEN
00225           KY = 1
00226       ELSE
00227           KY = 1 - (N-1)*INCY
00228       END IF
00229 *
00230 *     Start the operations. In this version the elements of A are
00231 *     accessed sequentially with one pass through the triangular part
00232 *     of A.
00233 *
00234 *     First form  y := beta*y.
00235 *
00236       IF (BETA.NE.ONE) THEN
00237           IF (INCY.EQ.1) THEN
00238               IF (BETA.EQ.ZERO) THEN
00239                   DO 10 I = 1,N
00240                       Y(I) = ZERO
00241    10             CONTINUE
00242               ELSE
00243                   DO 20 I = 1,N
00244                       Y(I) = BETA*Y(I)
00245    20             CONTINUE
00246               END IF
00247           ELSE
00248               IY = KY
00249               IF (BETA.EQ.ZERO) THEN
00250                   DO 30 I = 1,N
00251                       Y(IY) = ZERO
00252                       IY = IY + INCY
00253    30             CONTINUE
00254               ELSE
00255                   DO 40 I = 1,N
00256                       Y(IY) = BETA*Y(IY)
00257                       IY = IY + INCY
00258    40             CONTINUE
00259               END IF
00260           END IF
00261       END IF
00262       IF (ALPHA.EQ.ZERO) RETURN
00263       IF (LSAME(UPLO,'U')) THEN
00264 *
00265 *        Form  y  when A is stored in upper triangle.
00266 *
00267           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
00268               DO 60 J = 1,N
00269                   TEMP1 = ALPHA*X(J)
00270                   TEMP2 = ZERO
00271                   DO 50 I = 1,J - 1
00272                       Y(I) = Y(I) + TEMP1*A(I,J)
00273                       TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
00274    50             CONTINUE
00275                   Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
00276    60         CONTINUE
00277           ELSE
00278               JX = KX
00279               JY = KY
00280               DO 80 J = 1,N
00281                   TEMP1 = ALPHA*X(JX)
00282                   TEMP2 = ZERO
00283                   IX = KX
00284                   IY = KY
00285                   DO 70 I = 1,J - 1
00286                       Y(IY) = Y(IY) + TEMP1*A(I,J)
00287                       TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
00288                       IX = IX + INCX
00289                       IY = IY + INCY
00290    70             CONTINUE
00291                   Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
00292                   JX = JX + INCX
00293                   JY = JY + INCY
00294    80         CONTINUE
00295           END IF
00296       ELSE
00297 *
00298 *        Form  y  when A is stored in lower triangle.
00299 *
00300           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
00301               DO 100 J = 1,N
00302                   TEMP1 = ALPHA*X(J)
00303                   TEMP2 = ZERO
00304                   Y(J) = Y(J) + TEMP1*DBLE(A(J,J))
00305                   DO 90 I = J + 1,N
00306                       Y(I) = Y(I) + TEMP1*A(I,J)
00307                       TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
00308    90             CONTINUE
00309                   Y(J) = Y(J) + ALPHA*TEMP2
00310   100         CONTINUE
00311           ELSE
00312               JX = KX
00313               JY = KY
00314               DO 120 J = 1,N
00315                   TEMP1 = ALPHA*X(JX)
00316                   TEMP2 = ZERO
00317                   Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J))
00318                   IX = JX
00319                   IY = JY
00320                   DO 110 I = J + 1,N
00321                       IX = IX + INCX
00322                       IY = IY + INCY
00323                       Y(IY) = Y(IY) + TEMP1*A(I,J)
00324                       TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
00325   110             CONTINUE
00326                   Y(JY) = Y(JY) + ALPHA*TEMP2
00327                   JX = JX + INCX
00328                   JY = JY + INCY
00329   120         CONTINUE
00330           END IF
00331       END IF
00332 *
00333       RETURN
00334 *
00335 *     End of ZHEMV .
00336 *
00337       END
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