Name

ssyrk, dsyrk, csyrk, zsyrk − Rank-k update of a symmetric matrix

FORMAT

{S,D,C,Z}SYRK ( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )

Arguments

uplocharacter∗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. 

transcharacter∗1
On entry, specifies the operation to be performed:

If trans = ’N’ or ’n’, C  =  alpha ∗ A∗transp(A) + beta∗C

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

ninteger∗4
On entry, specifies the order of the matrix C; n >= 0
On exit, n is unchanged. 

kinteger∗4
On entry,  the number of columns of the matrix A when trans = ’N’ or the number of rows of the matrix A when trans = ’T’ or
On exit, k is unchanged. 

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

areal∗4 | real∗8 | complex∗8 | complex∗16
On entry, a two-dimensional array A with dimensions lda by ka.
For trans = ’N’ or 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. 

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

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

creal∗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. 

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

Description

The _SYRK routines perform the rank-k update of a symmetric matrix: C  = alpha ∗ A∗transp(A) + beta∗C C  = alpha ∗ transp(A)A + beta∗C
alpha and beta are scalars,  C is an n by n symmetric matrix. In the first case, A is an n by k matrix, and in the second case, A is a k by n matrix.

Example

REAL∗4 A(40,20), C(20,20), alpha, beta
LDA = 40
LDC = 20
N = 10
K = 15
alpha = 1.0
beta = 2.0
CALL SSYRK (’U’,’N’,N,K,alpha,A,LDA,beta,C,LDC)

This FORTRAN code computes the rank-k update of the real symmetric matrix C: C  =  alpha ∗ A∗transp(A) + beta∗C. C is a 10 by 10 matrix, and A is a 10 by 15 matrix. Only the upper-triangular part of C is referenced. The leading 10 by 15 part of array A contains the matrix A. The leading 10 by 10 upper-triangular part of array C contains the upper-triangular matrix C.