{S,D,C,Z}SYR2K ( uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc )
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.
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.
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.