subroutine csyr2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CSYR2K
CSYR2K
Purpose:
CSYR2K 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.
Parameters:
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*B**T + alpha*B*A**T +
beta*C.
TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**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 matrices A and B, and on entry with
TRANS = 'T' or 't', K specifies the number of rows of the
matrices A and B. 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 ).
B
B is COMPLEX 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 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 ).
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
Definition at line 190 of file csyr2k.f.
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