C Library Functions - csyrk (3)

NAME

csyrk(3f) - [BLAS:COMPLEX_BLAS_LEVEL3] C:=alpha*A*TRANSPOSE(A)+beta*C, C symmetric.

Synopsis
Definition
Options
C
Authors
Further Details
See Also

SYNOPSIS

subroutine csyrk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)

      .. Scalar Arguments ..
      complex,intent(in)    :: alpha,beta
      integer,intent(in)    :: k,lda,ldc,n
      character,intent(in)  :: trans,uplo
      ..
      .. Array Arguments ..
      complex,intent(in)    :: a(lda,*)
      complex,intent(inout) :: c(ldc,*)
      ..

DEFINITION

CSYRK performs one of the symmetric rank k operations
    C := alpha*A*A**T + beta*C,
or
    C := alpha*A**T*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

OPTIONS

UPLO

UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

UPLO = ’U’ or ’u’ Only the upper triangular part of C is to be referenced.

UPLO = ’L’ or ’l’ Only the lower triangular part of C is to be referenced.

TRANS

TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows:

              TRANS = ’N’ or ’n’   C := alpha*A*A**T + beta*C.

              TRANS = ’T’ or ’t’   C := alpha*A**T*A + beta*C.

N

N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero.

K

K is INTEGER On entry with TRANS = ’N’ or ’n’, K specifies the number of columns of the matrix A, and on entry with TRANS = ’T’ or ’t’, K specifies the number of rows of the matrix A. K must be at least zero.

ALPHA

ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.

A

A is COMPLEX array, dimension ( LDA, ka ), where ka is k when TRANS = ’N’ or ’n’, and is n otherwise. Before entry with TRANS = ’N’ or ’n’, the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.

LDA

LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = ’N’ or ’n’ then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).

BETA

BETA is COMPLEX On entry, BETA specifies the scalar beta.

C

C is COMPLEX array, dimension ( LDC, N ) Before entry with UPLO = ’U’ or ’u’, the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = ’L’ or ’l’, the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix.

LDC

LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ).

AUTHORS

o Univ. of Tennessee

o Univ. of California Berkeley

o Univ. of Colorado Denver

o NAG Ltd.
 date:December 2016

FURTHER DETAILS

Level 3 Blas routine.
-- Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.