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RedHat 9 (Linux i386) - man page for zsyr2k (redhat section l)

ZSYR2K(l)				   BLAS routine 				ZSYR2K(l)

NAME
       ZSYR2K  - perform one of the symmetric rank 2k operations   C := alpha*A*B' + alpha*B*A' +
       beta*C,

SYNOPSIS
       SUBROUTINE ZSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

	   CHARACTER*1	  UPLO, TRANS

	   INTEGER	  N, K, LDA, LDB, LDC

	   COMPLEX*16	  ALPHA, BETA

	   COMPLEX*16	  A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE
       ZSYR2K  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.

PARAMETERS
       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 num-
	      ber of rows of the matrices  A and B.  K must be at least zero.  Unchanged on exit.

       ALPHA  - COMPLEX*16	.
	      On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - 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.
	      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*16	 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*16	.
	      On entry, BETA specifies the scalar beta.  Unchanged on exit.

       C      - 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	symmetric  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  sym-
	      metric  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  trian-
	      gular 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.

	      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 Hammar-
	      ling, Numerical Algorithms Group Ltd.

BLAS routine				 16 October 1992				ZSYR2K(l)


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