BLAS/SRC/zsyr2k.f(3)       Library Functions Manual       BLAS/SRC/zsyr2k.f(3)

NAME
       BLAS/SRC/zsyr2k.f

SYNOPSIS
   Functions/Subroutines
       subroutine zsyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c,
           ldc)
           ZSYR2K

Function/Subroutine Documentation
   subroutine zsyr2k (character uplo, character trans, integer n, integer k,
       complex*16 alpha, complex*16, dimension(lda,*) a, integer lda,
       complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta,
       complex*16, dimension(ldc,*) c, integer ldc)
       ZSYR2K

       Purpose:


            ZSYR2K  performs one of the symmetric rank 2k operations

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

            or

               C := alpha*A**T*B + alpha*B**T*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

                     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.

           TRANS

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

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

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

           N

                     N is INTEGER
                      On entry,  N specifies the order of the matrix C.  N must be
                      at least zero.

           K

                     K is 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.

           ALPHA

                     ALPHA is COMPLEX*16
                      On entry, ALPHA specifies the scalar alpha.

           A

                     A is COMPLEX*16 array, 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.

           LDA

                     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 ).

           B

                     B is COMPLEX*16 array, 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.

           LDB

                     LDB is 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 ).

           BETA

                     BETA is COMPLEX*16
                      On entry, BETA specifies the scalar beta.

           C

                     C is COMPLEX*16 array, 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  symmetric 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

                     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 ).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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.

       Definition at line 187 of file zsyr2k.f.

Author
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LAPACK                          Version 3.12.0            BLAS/SRC/zsyr2k.f(3)