LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zherk.f
Go to the documentation of this file.
00001 *> \brief \b ZHERK
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 ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       DOUBLE PRECISION ALPHA,BETA
00015 *       INTEGER K,LDA,LDC,N
00016 *       CHARACTER TRANS,UPLO
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       COMPLEX*16 A(LDA,*),C(LDC,*)
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> ZHERK  performs one of the hermitian rank k operations
00029 *>
00030 *>    C := alpha*A*A**H + beta*C,
00031 *>
00032 *> or
00033 *>
00034 *>    C := alpha*A**H*A + beta*C,
00035 *>
00036 *> where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
00037 *> matrix and  A  is an  n by k  matrix in the  first case and a  k by n
00038 *> matrix in the second case.
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] UPLO
00045 *> \verbatim
00046 *>          UPLO is CHARACTER*1
00047 *>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
00048 *>           triangular  part  of the  array  C  is to be  referenced  as
00049 *>           follows:
00050 *>
00051 *>              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
00052 *>                                  is to be referenced.
00053 *>
00054 *>              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
00055 *>                                  is to be referenced.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] TRANS
00059 *> \verbatim
00060 *>          TRANS is CHARACTER*1
00061 *>           On entry,  TRANS  specifies the operation to be performed as
00062 *>           follows:
00063 *>
00064 *>              TRANS = 'N' or 'n'   C := alpha*A*A**H + beta*C.
00065 *>
00066 *>              TRANS = 'C' or 'c'   C := alpha*A**H*A + beta*C.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] N
00070 *> \verbatim
00071 *>          N is INTEGER
00072 *>           On entry,  N specifies the order of the matrix C.  N must be
00073 *>           at least zero.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] K
00077 *> \verbatim
00078 *>          K is INTEGER
00079 *>           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
00080 *>           of  columns   of  the   matrix   A,   and  on   entry   with
00081 *>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
00082 *>           matrix A.  K must be at least zero.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] ALPHA
00086 *> \verbatim
00087 *>          ALPHA is DOUBLE PRECISION .
00088 *>           On entry, ALPHA specifies the scalar alpha.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] A
00092 *> \verbatim
00093 *>          A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
00094 *>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
00095 *>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
00096 *>           part of the array  A  must contain the matrix  A,  otherwise
00097 *>           the leading  k by n  part of the array  A  must contain  the
00098 *>           matrix A.
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.   When  TRANS = 'N' or 'n'
00106 *>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
00107 *>           be at least  max( 1, k ).
00108 *> \endverbatim
00109 *>
00110 *> \param[in] BETA
00111 *> \verbatim
00112 *>          BETA is DOUBLE PRECISION.
00113 *>           On entry, BETA specifies the scalar beta.
00114 *> \endverbatim
00115 *>
00116 *> \param[in,out] C
00117 *> \verbatim
00118 *>          C is COMPLEX*16 array of DIMENSION ( LDC, n ).
00119 *>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
00120 *>           upper triangular part of the array C must contain the upper
00121 *>           triangular part  of the  hermitian matrix  and the strictly
00122 *>           lower triangular part of C is not referenced.  On exit, the
00123 *>           upper triangular part of the array  C is overwritten by the
00124 *>           upper triangular part of the updated matrix.
00125 *>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
00126 *>           lower triangular part of the array C must contain the lower
00127 *>           triangular part  of the  hermitian matrix  and the strictly
00128 *>           upper triangular part of C is not referenced.  On exit, the
00129 *>           lower triangular part of the array  C is overwritten by the
00130 *>           lower triangular part of the updated matrix.
00131 *>           Note that the imaginary parts of the diagonal elements need
00132 *>           not be set,  they are assumed to be zero,  and on exit they
00133 *>           are set to zero.
00134 *> \endverbatim
00135 *>
00136 *> \param[in] LDC
00137 *> \verbatim
00138 *>          LDC is INTEGER
00139 *>           On entry, LDC specifies the first dimension of C as declared
00140 *>           in  the  calling  (sub)  program.   LDC  must  be  at  least
00141 *>           max( 1, n ).
00142 *> \endverbatim
00143 *
00144 *  Authors:
00145 *  ========
00146 *
00147 *> \author Univ. of Tennessee 
00148 *> \author Univ. of California Berkeley 
00149 *> \author Univ. of Colorado Denver 
00150 *> \author NAG Ltd. 
00151 *
00152 *> \date November 2011
00153 *
00154 *> \ingroup complex16_blas_level3
00155 *
00156 *> \par Further Details:
00157 *  =====================
00158 *>
00159 *> \verbatim
00160 *>
00161 *>  Level 3 Blas routine.
00162 *>
00163 *>  -- Written on 8-February-1989.
00164 *>     Jack Dongarra, Argonne National Laboratory.
00165 *>     Iain Duff, AERE Harwell.
00166 *>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
00167 *>     Sven Hammarling, Numerical Algorithms Group Ltd.
00168 *>
00169 *>  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
00170 *>     Ed Anderson, Cray Research Inc.
00171 *> \endverbatim
00172 *>
00173 *  =====================================================================
00174       SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
00175 *
00176 *  -- Reference BLAS level3 routine (version 3.4.0) --
00177 *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
00178 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00179 *     November 2011
00180 *
00181 *     .. Scalar Arguments ..
00182       DOUBLE PRECISION ALPHA,BETA
00183       INTEGER K,LDA,LDC,N
00184       CHARACTER TRANS,UPLO
00185 *     ..
00186 *     .. Array Arguments ..
00187       COMPLEX*16 A(LDA,*),C(LDC,*)
00188 *     ..
00189 *
00190 *  =====================================================================
00191 *
00192 *     .. External Functions ..
00193       LOGICAL LSAME
00194       EXTERNAL LSAME
00195 *     ..
00196 *     .. External Subroutines ..
00197       EXTERNAL XERBLA
00198 *     ..
00199 *     .. Intrinsic Functions ..
00200       INTRINSIC DBLE,DCMPLX,DCONJG,MAX
00201 *     ..
00202 *     .. Local Scalars ..
00203       COMPLEX*16 TEMP
00204       DOUBLE PRECISION RTEMP
00205       INTEGER I,INFO,J,L,NROWA
00206       LOGICAL UPPER
00207 *     ..
00208 *     .. Parameters ..
00209       DOUBLE PRECISION ONE,ZERO
00210       PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
00211 *     ..
00212 *
00213 *     Test the input parameters.
00214 *
00215       IF (LSAME(TRANS,'N')) THEN
00216           NROWA = N
00217       ELSE
00218           NROWA = K
00219       END IF
00220       UPPER = LSAME(UPLO,'U')
00221 *
00222       INFO = 0
00223       IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
00224           INFO = 1
00225       ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND.
00226      +         (.NOT.LSAME(TRANS,'C'))) THEN
00227           INFO = 2
00228       ELSE IF (N.LT.0) THEN
00229           INFO = 3
00230       ELSE IF (K.LT.0) THEN
00231           INFO = 4
00232       ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
00233           INFO = 7
00234       ELSE IF (LDC.LT.MAX(1,N)) THEN
00235           INFO = 10
00236       END IF
00237       IF (INFO.NE.0) THEN
00238           CALL XERBLA('ZHERK ',INFO)
00239           RETURN
00240       END IF
00241 *
00242 *     Quick return if possible.
00243 *
00244       IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR.
00245      +    (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
00246 *
00247 *     And when  alpha.eq.zero.
00248 *
00249       IF (ALPHA.EQ.ZERO) THEN
00250           IF (UPPER) THEN
00251               IF (BETA.EQ.ZERO) THEN
00252                   DO 20 J = 1,N
00253                       DO 10 I = 1,J
00254                           C(I,J) = ZERO
00255    10                 CONTINUE
00256    20             CONTINUE
00257               ELSE
00258                   DO 40 J = 1,N
00259                       DO 30 I = 1,J - 1
00260                           C(I,J) = BETA*C(I,J)
00261    30                 CONTINUE
00262                       C(J,J) = BETA*DBLE(C(J,J))
00263    40             CONTINUE
00264               END IF
00265           ELSE
00266               IF (BETA.EQ.ZERO) THEN
00267                   DO 60 J = 1,N
00268                       DO 50 I = J,N
00269                           C(I,J) = ZERO
00270    50                 CONTINUE
00271    60             CONTINUE
00272               ELSE
00273                   DO 80 J = 1,N
00274                       C(J,J) = BETA*DBLE(C(J,J))
00275                       DO 70 I = J + 1,N
00276                           C(I,J) = BETA*C(I,J)
00277    70                 CONTINUE
00278    80             CONTINUE
00279               END IF
00280           END IF
00281           RETURN
00282       END IF
00283 *
00284 *     Start the operations.
00285 *
00286       IF (LSAME(TRANS,'N')) THEN
00287 *
00288 *        Form  C := alpha*A*A**H + beta*C.
00289 *
00290           IF (UPPER) THEN
00291               DO 130 J = 1,N
00292                   IF (BETA.EQ.ZERO) THEN
00293                       DO 90 I = 1,J
00294                           C(I,J) = ZERO
00295    90                 CONTINUE
00296                   ELSE IF (BETA.NE.ONE) THEN
00297                       DO 100 I = 1,J - 1
00298                           C(I,J) = BETA*C(I,J)
00299   100                 CONTINUE
00300                       C(J,J) = BETA*DBLE(C(J,J))
00301                   ELSE
00302                       C(J,J) = DBLE(C(J,J))
00303                   END IF
00304                   DO 120 L = 1,K
00305                       IF (A(J,L).NE.DCMPLX(ZERO)) THEN
00306                           TEMP = ALPHA*DCONJG(A(J,L))
00307                           DO 110 I = 1,J - 1
00308                               C(I,J) = C(I,J) + TEMP*A(I,L)
00309   110                     CONTINUE
00310                           C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(I,L))
00311                       END IF
00312   120             CONTINUE
00313   130         CONTINUE
00314           ELSE
00315               DO 180 J = 1,N
00316                   IF (BETA.EQ.ZERO) THEN
00317                       DO 140 I = J,N
00318                           C(I,J) = ZERO
00319   140                 CONTINUE
00320                   ELSE IF (BETA.NE.ONE) THEN
00321                       C(J,J) = BETA*DBLE(C(J,J))
00322                       DO 150 I = J + 1,N
00323                           C(I,J) = BETA*C(I,J)
00324   150                 CONTINUE
00325                   ELSE
00326                       C(J,J) = DBLE(C(J,J))
00327                   END IF
00328                   DO 170 L = 1,K
00329                       IF (A(J,L).NE.DCMPLX(ZERO)) THEN
00330                           TEMP = ALPHA*DCONJG(A(J,L))
00331                           C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(J,L))
00332                           DO 160 I = J + 1,N
00333                               C(I,J) = C(I,J) + TEMP*A(I,L)
00334   160                     CONTINUE
00335                       END IF
00336   170             CONTINUE
00337   180         CONTINUE
00338           END IF
00339       ELSE
00340 *
00341 *        Form  C := alpha*A**H*A + beta*C.
00342 *
00343           IF (UPPER) THEN
00344               DO 220 J = 1,N
00345                   DO 200 I = 1,J - 1
00346                       TEMP = ZERO
00347                       DO 190 L = 1,K
00348                           TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
00349   190                 CONTINUE
00350                       IF (BETA.EQ.ZERO) THEN
00351                           C(I,J) = ALPHA*TEMP
00352                       ELSE
00353                           C(I,J) = ALPHA*TEMP + BETA*C(I,J)
00354                       END IF
00355   200             CONTINUE
00356                   RTEMP = ZERO
00357                   DO 210 L = 1,K
00358                       RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
00359   210             CONTINUE
00360                   IF (BETA.EQ.ZERO) THEN
00361                       C(J,J) = ALPHA*RTEMP
00362                   ELSE
00363                       C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
00364                   END IF
00365   220         CONTINUE
00366           ELSE
00367               DO 260 J = 1,N
00368                   RTEMP = ZERO
00369                   DO 230 L = 1,K
00370                       RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J)
00371   230             CONTINUE
00372                   IF (BETA.EQ.ZERO) THEN
00373                       C(J,J) = ALPHA*RTEMP
00374                   ELSE
00375                       C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J))
00376                   END IF
00377                   DO 250 I = J + 1,N
00378                       TEMP = ZERO
00379                       DO 240 L = 1,K
00380                           TEMP = TEMP + DCONJG(A(L,I))*A(L,J)
00381   240                 CONTINUE
00382                       IF (BETA.EQ.ZERO) THEN
00383                           C(I,J) = ALPHA*TEMP
00384                       ELSE
00385                           C(I,J) = ALPHA*TEMP + BETA*C(I,J)
00386                       END IF
00387   250             CONTINUE
00388   260         CONTINUE
00389           END IF
00390       END IF
00391 *
00392       RETURN
00393 *
00394 *     End of ZHERK .
00395 *
00396       END
 All Files Functions