ssyr2k, dsyr2k, csyr2k, zsyr2k 

Rank-2k update of a symmetric matrix

FORMAT

  {S,D,C,Z}SYR2K

  ( uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc )

Arguments

  uplo                character*1
                      On entry, specifies whether the upper- or lower-
                      triangular part of the symmetric matrix C is to be
                      referenced:

                      If uplo = 'U' or 'u', the upper-triangular part of C is
                      to be referenced.

                      If uplo = 'L' or 'l', the lower-triangular part of C is
                      to be referenced.
                      On exit, uplo is unchanged.

  trans               character*1
                      On entry, specifies the operation to be performed:

                      If trans = 'N' or 'n', C  =  alpha * A*transp(B) +
                      alpha * B*transp(A) + beta*C

                      If trans = 'T' or 't', C  =  alpha * transp(A)*B +
                      alpha * transp(B)A + beta*C
                      On exit, trans is unchanged.

  n                   integer*4
                      On entry, the order n of the matrix C; n >= 0
                      On exit, n is unchanged.

  k                   integer*4
                      On entry,  the number of columns of the matrices A and
                      B when trans = 'N' or the number of rows of the matrix
                      A and B when trans = 'T' or k >= 0.
                      On exit, k is unchanged.

  alpha               real*4 | real*8 | complex*8 | complex*16
                      On entry, specifies the scalar alpha.
                      On exit, alpha is unchanged.

  a                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array A with dimensions lda
                      by ka.
                      For trans = 'N' or ka >= k and the leading n by k
                      portion of the array A contains the matrix A.
                      For trans = 'T' or ka >= n and the leading k by n part
                      of the array A contains the matrix A.
                      On exit, a is unchanged.

  lda                 integer*4
                      On entry, the first dimension of array A.
                      For trans = 'N' or 'n' lda >= MAX(1,n).
                      For trans = 'T' or lda >= MAX(1,k).
                      On exit, lda is unchanged.

  b                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array B with dimensions ldb
                      by kb.
                      For trans = 'N' or kb >= k and the leading n by k
                      portion of the array B contains the matrix B.
                      For trans = 'T' or kb >= n and the leading k by n part
                      of the array B contains the matrix B.
                      On exit, b is unchanged.

  ldb                 integer*4
                      On entry, the first dimension of array B.
                      For trans = 'N' or ldb >= MAX(1,n).
                      For trans = 'T' or ldb >= MAX(1,k).
                      On exit, ldb is unchanged.

  beta                real*4 | real*8 | complex*8 | complex*16
                      On entry, specifies the scalar beta.
                      On exit, beta is unchanged.

  c                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array C of dimensions ldc
                      by at least n.

  If uplo specifies the upper part, the leading n by n upper-triangular part
  of the array C must contain the upper-triangular part of the symmetric
  matrix C, and the strictly lower-triangular part of C is not referenced.

  If uplo specifies the lower part, the leading n by n lower-triangular part
  of the array C must contain the lower-triangular part of the symmetric
  matrix C, and the strictly upper-triangular part of C is not referenced.
  On exit, c is overwritten; the triangular part of the array C is
  overwritten by the triangular part of the updated matrix.

  ldc                 integer*4
                      On entry, the first dimension  of array C; ldc >=
                      MAX(1,n)
                      On exit, ldc is unchanged.

Description

  The _SYR2K routines perform the rank-2k update of a symmetric matrix: C  =
  alpha * A*transp(B) + alpha * B*transp(A)
   + beta*C C  = alpha * transp(A)*B + alpha * transp(B)A
   + beta*C
  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.

Example

  REAL*4 A(40,10), B(40,10), C(20,20), alpha, beta
  LDA = 40
  LDB = 30
  LDC = 20
  N = 18
  K = 10
  alpha = 1.0
  beta = 2.0
  CALL SSYR2K ('U','N',N,K,alpha,A,LDA,B,LDB,beta,C,LDC)

  This FORTRAN code computes the rank-2k update of the real symmetric matrix
  C: C  =  alpha * A*transp(B) + alpha * B*transp(A) + beta*C.  Only the
  upper-triangular part of C is referenced.  The leading 18 by 10 part of
  array A contains the matrix A.  The leading 18 by 10 part of array B
  contains the matrix B.  The leading 18 by 18 upper-triangular part of array
  C contains the upper-triangular matrix C.