Name

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

uplocharacter∗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. 

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

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

xreal∗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. 

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

areal∗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. 

ldainteger∗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.