C Library Functions - dsyr2k (3)

NAME

dsyr2k(3f) - [BLAS:DOUBLE_BLAS_LEVEL3]

Synopsis
Definition
Options
C
Authors
Further Details
See Also

SYNOPSIS

subroutine dsyr2k(uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc)

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

DEFINITION

DSYR2K performs one of the symmetric rank 2k operations
    C := alpha*A*B**T + alpha*B*A**T + beta*C,
or
    C := alpha*A**T*B + alpha*B**T*A + beta*C,
where 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.

OPTIONS

UPLO

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

On entry, TRANS specifies the operation to be performed as follows:

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

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

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

N

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 matrices A and B, and on entry with TRANS = ’T’ or ’t’ or ’C’ or ’c’, K specifies the number of rows of the matrices A and B. K must be at least zero.

ALPHA

ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.

A

A is DOUBLE PRECISION 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 ).

B

B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb 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 B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B.

LDB

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

BETA

BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta.

C

C is DOUBLE PRECISION 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.