CSYR2K  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.

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


           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX 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 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


           On entry, BETA specifies the scalar beta.

C

          C is COMPLEX 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 ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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.