zherk.f

Go to the documentation of this file.

*> \brief \b ZHERK
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
* 
*       .. Scalar Arguments ..
*       DOUBLE PRECISION ALPHA,BETA
*       INTEGER K,LDA,LDC,N
*       CHARACTER TRANS,UPLO
*       ..
*       .. Array Arguments ..
*       COMPLEX*16 A(LDA,*),C(LDC,*)
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZHERK  performs one of the hermitian rank k operations
*>
*>    C := alpha*A*A**H + beta*C,
*>
*> or
*>
*>    C := alpha*A**H*A + beta*C,
*>
*> where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
*> matrix and  A  is an  n by k  matrix in the  first case and a  k by n
*> matrix in the second case.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
*>           triangular  part  of the  array  C  is to be  referenced  as
*>           follows:
*>
*>              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
*>                                  is to be referenced.
*>
*>              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
*>                                  is to be referenced.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>           On entry,  TRANS  specifies the operation to be performed as
*>           follows:
*>
*>              TRANS = 'N' or 'n'   C := alpha*A*A**H + beta*C.
*>
*>              TRANS = 'C' or 'c'   C := alpha*A**H*A + beta*C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>           On entry,  N specifies the order of the matrix C.  N must be
*>           at least zero.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
*>           of  columns   of  the   matrix   A,   and  on   entry   with
*>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
*>           matrix A.  K must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*>          ALPHA is DOUBLE PRECISION .
*>           On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
*>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
*>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
*>           part of the array  A  must contain the matrix  A,  otherwise
*>           the leading  k by n  part of the array  A  must contain  the
*>           matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>           On entry, LDA specifies the first dimension of A as declared
*>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
*>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
*>           be at least  max( 1, k ).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*>          BETA is DOUBLE PRECISION.
*>           On entry, BETA specifies the scalar beta.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is COMPLEX*16 array of DIMENSION ( LDC, n ).
*>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
*>           upper triangular part of the array C must contain the upper
*>           triangular part  of the  hermitian matrix  and the strictly
*>           lower triangular part of C is not referenced.  On exit, the
*>           upper triangular part of the array  C is overwritten by the
*>           upper triangular part of the updated matrix.
*>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
*>           lower triangular part of the array C must contain the lower
*>           triangular part  of the  hermitian matrix  and the strictly
*>           upper triangular part of C is not referenced.  On exit, the
*>           lower triangular part of the array  C is overwritten by the
*>           lower triangular part of the updated matrix.
*>           Note that the imaginary parts of the diagonal elements need
*>           not be set,  they are assumed to be zero,  and on exit they
*>           are set to zero.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>           On entry, LDC specifies the first dimension of C as declared
*>           in  the  calling  (sub)  program.   LDC  must  be  at  least
*>           max( 1, n ).
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complex16_blas_level3
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*>
*>  Level 3 Blas routine.
*>
*>  -- Written on 8-February-1989.
*>     Jack Dongarra, Argonne National Laboratory.
*>     Iain Duff, AERE Harwell.
*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
*>     Sven Hammarling, Numerical Algorithms Group Ltd.
*>
*>  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
*>     Ed Anderson, Cray Research Inc.
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE zherk(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
*
*  -- Reference BLAS level3 routine (version 3.4.0) --
*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER K,LDA,LDC,N
      CHARACTER TRANS,UPLO
*     ..
*     .. Array Arguments ..
      COMPLEX*16 A(lda,*),C(ldc,*)
*     ..
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC dble,dcmplx,dconjg,max
*     ..
*     .. Local Scalars ..
      COMPLEX*16 TEMP
      DOUBLE PRECISION RTEMP
      INTEGER I,INFO,J,L,NROWA
      LOGICAL UPPER
*     ..
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      parameter(one=1.0d+0,zero=0.0d+0)
*     ..
*
*     Test the input parameters.
*
      IF (lsame(trans,'N')) THEN
          nrowa = n
      ELSE
          nrowa = k
      END IF
      upper = lsame(uplo,'U')
*
      info = 0
      IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
          info = 1
      ELSE IF ((.NOT.lsame(trans,'N')) .AND.
     +         (.NOT.lsame(trans,'C'))) THEN
          info = 2
      ELSE IF (n.LT.0) THEN
          info = 3
      ELSE IF (k.LT.0) THEN
          info = 4
      ELSE IF (lda.LT.max(1,nrowa)) THEN
          info = 7
      ELSE IF (ldc.LT.max(1,n)) THEN
          info = 10
      END IF
      IF (info.NE.0) THEN
          CALL xerbla('ZHERK ',info)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
     +    (k.EQ.0)).AND. (beta.EQ.one))) RETURN
*
*     And when  alpha.eq.zero.
*
      IF (alpha.EQ.zero) THEN
          IF (upper) THEN
              IF (beta.EQ.zero) THEN
                  DO 20 j = 1,n
                      DO 10 i = 1,j
                          c(i,j) = zero
   10                 CONTINUE
   20             CONTINUE
              ELSE
                  DO 40 j = 1,n
                      DO 30 i = 1,j - 1
                          c(i,j) = beta*c(i,j)
   30                 CONTINUE
                      c(j,j) = beta*dble(c(j,j))
   40             CONTINUE
              END IF
          ELSE
              IF (beta.EQ.zero) THEN
                  DO 60 j = 1,n
                      DO 50 i = j,n
                          c(i,j) = zero
   50                 CONTINUE
   60             CONTINUE
              ELSE
                  DO 80 j = 1,n
                      c(j,j) = beta*dble(c(j,j))
                      DO 70 i = j + 1,n
                          c(i,j) = beta*c(i,j)
   70                 CONTINUE
   80             CONTINUE
              END IF
          END IF
          RETURN
      END IF
*
*     Start the operations.
*
      IF (lsame(trans,'N')) THEN
*
*        Form  C := alpha*A*A**H + beta*C.
*
          IF (upper) THEN
              DO 130 j = 1,n
                  IF (beta.EQ.zero) THEN
                      DO 90 i = 1,j
                          c(i,j) = zero
   90                 CONTINUE
                  ELSE IF (beta.NE.one) THEN
                      DO 100 i = 1,j - 1
                          c(i,j) = beta*c(i,j)
  100                 CONTINUE
                      c(j,j) = beta*dble(c(j,j))
                  ELSE
                      c(j,j) = dble(c(j,j))
                  END IF
                  DO 120 l = 1,k
                      IF (a(j,l).NE.dcmplx(zero)) THEN
                          temp = alpha*dconjg(a(j,l))
                          DO 110 i = 1,j - 1
                              c(i,j) = c(i,j) + temp*a(i,l)
  110                     CONTINUE
                          c(j,j) = dble(c(j,j)) + dble(temp*a(i,l))
                      END IF
  120             CONTINUE
  130         CONTINUE
          ELSE
              DO 180 j = 1,n
                  IF (beta.EQ.zero) THEN
                      DO 140 i = j,n
                          c(i,j) = zero
  140                 CONTINUE
                  ELSE IF (beta.NE.one) THEN
                      c(j,j) = beta*dble(c(j,j))
                      DO 150 i = j + 1,n
                          c(i,j) = beta*c(i,j)
  150                 CONTINUE
                  ELSE
                      c(j,j) = dble(c(j,j))
                  END IF
                  DO 170 l = 1,k
                      IF (a(j,l).NE.dcmplx(zero)) THEN
                          temp = alpha*dconjg(a(j,l))
                          c(j,j) = dble(c(j,j)) + dble(temp*a(j,l))
                          DO 160 i = j + 1,n
                              c(i,j) = c(i,j) + temp*a(i,l)
  160                     CONTINUE
                      END IF
  170             CONTINUE
  180         CONTINUE
          END IF
      ELSE
*
*        Form  C := alpha*A**H*A + beta*C.
*
          IF (upper) THEN
              DO 220 j = 1,n
                  DO 200 i = 1,j - 1
                      temp = zero
                      DO 190 l = 1,k
                          temp = temp + dconjg(a(l,i))*a(l,j)
  190                 CONTINUE
                      IF (beta.EQ.zero) THEN
                          c(i,j) = alpha*temp
                      ELSE
                          c(i,j) = alpha*temp + beta*c(i,j)
                      END IF
  200             CONTINUE
                  rtemp = zero
                  DO 210 l = 1,k
                      rtemp = rtemp + dconjg(a(l,j))*a(l,j)
  210             CONTINUE
                  IF (beta.EQ.zero) THEN
                      c(j,j) = alpha*rtemp
                  ELSE
                      c(j,j) = alpha*rtemp + beta*dble(c(j,j))
                  END IF
  220         CONTINUE
          ELSE
              DO 260 j = 1,n
                  rtemp = zero
                  DO 230 l = 1,k
                      rtemp = rtemp + dconjg(a(l,j))*a(l,j)
  230             CONTINUE
                  IF (beta.EQ.zero) THEN
                      c(j,j) = alpha*rtemp
                  ELSE
                      c(j,j) = alpha*rtemp + beta*dble(c(j,j))
                  END IF
                  DO 250 i = j + 1,n
                      temp = zero
                      DO 240 l = 1,k
                          temp = temp + dconjg(a(l,i))*a(l,j)
  240                 CONTINUE
                      IF (beta.EQ.zero) THEN
                          c(i,j) = alpha*temp
                      ELSE
                          c(i,j) = alpha*temp + beta*c(i,j)
                      END IF
  250             CONTINUE
  260         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of ZHERK .
*
      END