dsyr2k.f(3)

NAME
dsyr2k.f -

SYNOPSIS

  Functions/Subroutines
subroutine dsyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYR2K

Function/Subroutine Documentation

  subroutine dsyr2k (characterUPLO, characterTRANS, integerN, integerK, double precisionALPHA, double precision, dimension(lda,*)A, integerLDA, double precision, dimension(ldb,*)B, integerLDB, double precisionBETA, double precision, dimension(ldc,*)C, integerLDC)

DSYR2K Purpose:

     DSYR2K  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.
                  TRANS = 'C' or 'c'   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' or 'C' or 'c',  K  specifies  the  number
               of rows of the matrices  A and B.  K must be at least  zero.

    ALPHA

              ALPHA is DOUBLE PRECISION.
               On entry, ALPHA specifies the scalar alpha.

    A

              A is DOUBLE PRECISION 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.

    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 DOUBLE PRECISION 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.

    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 DOUBLE PRECISION.
               On entry, BETA specifies the scalar beta.

    C

              C is DOUBLE PRECISION 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  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.

Date:
    November 2011

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 193 of file dsyr2k.f.

Author

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