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CSYR2K(1)			 BLAS routine			     CSYR2K(1)

NAME
       CSYR2K  -  performs  one	 of  the  symmetric  rank 2k operations	  C :=
       alpha*A*B' + alpha*B*A' + beta*C,

SYNOPSIS
       SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

	   COMPLEX						      ALPHA,BETA

	   INTEGER						      K,LDA,LDB,LDC,N

	   CHARACTER						      TRANS,UPLO

	   COMPLEX						      A(LDA,*),B(LDB,*),C(LDC,*)

PURPOSE
       CSYR2K  performs one of the symmetric rank 2k operations

       or

	  C := alpha*A'*B + alpha*B'*A + beta*C,

       where  alpha and beta  are scalars,  C is an  n by n  symmetric	matrix
       and   A	and B  are  n by k  matrices  in the  first  case  and	k by n
       matrices in the second case.

ARGUMENTS
       UPLO   - 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.

	      Unchanged on exit.

       TRANS  - CHARACTER*1.
	      On entry,	 TRANS	specifies the operation	 to  be	 performed  as
	      follows:

	      TRANS = 'N' or 'n'    C := alpha*A*B' + alpha*B*A' + beta*C.

	      TRANS = 'T' or 't'    C := alpha*A'*B + alpha*B'*A + beta*C.

	      Unchanged on exit.

       N      - INTEGER.
	      On  entry,  N specifies the order of the matrix C.  N must be at
	      least zero.  Unchanged on exit.

       K      - INTEGER.
	      On entry with  TRANS = 'N' or 'n',  K  specifies	the number  of
	      columns  of the  matrices	 A and B,  and on  entry  with TRANS =
	      'T' or 't',  K  specifies	 the number of rows of the matrices  A
	      and B.  K must be at least zero.	Unchanged on exit.

       ALPHA  - COMPLEX		.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX		 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.
	      Unchanged on exit.

       LDA    - 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 ).  Unchanged on exit.

       B      - COMPLEX		 array of DIMENSION ( LDB, kb ), where kb 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	 B  must contain the matrix  B,	 otherwise the leading
	      k	 by  n	 part  of  the	array	B  must contain	 the matrix B.
	      Unchanged on exit.

       LDB    - INTEGER.
	      On entry, LDB specifies the first dimension of B as declared  in
	      the   calling   (sub)   program.	 When  TRANS = 'N' or 'n' then
	      LDB must be at least  max( 1, n ), otherwise   LDB  must	be  at
	      least  max( 1, k ).  Unchanged on exit.

       BETA   - COMPLEX		.
	      On entry, BETA specifies the scalar beta.	 Unchanged on exit.

       C      - COMPLEX		 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 tri‐
	      angular  part   of the  symmetric matrix	and the strictly lower
	      triangular part of C is not referenced.  On exit, the upper tri‐
	      angular  part of the array  C is overwritten by the upper trian‐
	      gular 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   symmet‐
	      ric  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.

       LDC    - 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 ).  Unchanged on exit.

FURTHER DETAILS
       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.

BLAS routine			 November 2008			     CSYR2K(1)
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