ssyr, dsyr, cher, zher 

Rank-one update of a symmetric or hermitian matrix

FORMAT

  {S,D}SYR (uplo, n, alpha, x, incx, a, lda) {C,Z}HER (uplo, n, alpha, x,
  incx, a, lda)

Arguments

  uplo                character*1
                      On entry, specifies whether the upper- or lower-
                      triangular part of the array A is referenced:

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

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

  n                   integer*4
                      On entry, the order of the matrix A and the number of
                      elements in vector x; n >= 0.
                      On exit, n is unchanged.

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

  x                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a one-dimensional array X of length at least
                      (1+(n-1)*|incx|).  Array X contains the vector x.
                      On exit, x is unchanged.

  incx                integer*4
                      On entry, the increment for the elements of X; incx
                      must not equal zero.
                      On exit, incx is unchanged.

  a                   real*4 | real*8 | complex*8 | complex*16
                      On entry, a two-dimensional array with dimensions lda
                      by n.

  When uplo specifies the upper portion of the matrix, the leading n by n
  part of the array contains the upper-triangular part of the matrix, and the
  lower-triangular part of array A is not referenced.

  When uplo specifies the lower  portion of the matrix,  the leading n by n
  part of the array contains the lower-triangular part of the matrix, and the
  upper-triangular part of array A is not referenced.

  For CHER and ZHER routines, the imaginary parts of the diagonal elements
  are not accessed, need not be set, and are assumed to be zero.

  On exit, a is overwritten; the specified part of the array A is overwritten
  by the part of the updated matrix.

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

Description

  SSYR and DSYR perform the rank-one update of a real symmetric matrix: A  =
  alpha*x*transp(x) + A

  CHER and ZHER perform the rank-one update of a complex Hermitian matrix: A
  =  alpha*x*conjug_transp(x) + A

  alpha is a scalar, x is vector with n elements, and A is an n by n matrix
  in packed form. In the case of SSYR and DSYR, matrix A is a symmetric
  matrix and in the case of CHER and ZHER, matrix A is a Hermitian matrix.

EXAMPLES

  REAL*4 A(50,20), X(20), alpha
  INCX = 1
  LDA = 50
  N = 20
  alpha = 2.0
  CALL SSYR('L',N,alpha,X,INCX,A,LDA)

  This FORTRAN code computes the rank-1 update of the matrix A, given by A  =
  alpha*x*transp(x)
   + A.  A is a real symmetric matrix with its lower-triangular part stored.

  COMPLEX*16 A(50,20), X(20), alpha
  INCX = 1
  LDA = 50
  N = 20
  alpha = (2.0D0, 1.0D0)
  CALL ZHER('L',N,alpha,X,INCX,A,LDA)

  This FORTRAN code computes the rank-1 update of the matrix A, given by A  =
  alpha*x*conjug_transp(x) + A.  A is a complex Hermitian matrix with its
  lower-triangular part stored.