_SYRK(3F) _SYRK(3F)
dsyrk, ssyrk, zsyrk, csyrk - BLAS level three Symmetric Rank K Update.
FORTRAN 77 SYNOPSIS
subroutine dsyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
character*1 uplo, trans
integer n, k, lda, ldc
double precision alpha, beta
double precision a( lda,*), c(ldc,*)
subroutine ssyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
character*1 uplo, trans
integer n, k, lda, ldc
real alpha, beta
real a( lda,*), c(ldc,*)
subroutine zsyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
character*1 uplo, trans
integer n, k, lda, ldc
double complex alpha, beta
double complex a( lda,*), c(ldc,*)
subroutine csyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
character*1 uplo, trans
integer n, k, lda, ldc
complex alpha, beta
complex a( lda,*), c(ldc,*)
void dsyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldc;
double alpha, beta;
double (*a)[lda*k], (*c)[lda*n];
void ssyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldc;
float alpha, beta;
float (*a)[lda*k], (*c)[lda*n];
void zsyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldc;
Zomplex alpha, beta;
Zomplex (*a)[lda*k], (*c)[lda*n];
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_SYRK(3F) _SYRK(3F)
void csyrk( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldc;
Complex alpha, beta;
Complex (*a)[lda*k], (*c)[lda*n];
dsyrk , ssyrk , zsyrk and csyrk perform one of the matrix-matrix
operations
C := alpha*A*A' + beta*C,
or
C := alpha*A'*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.
uplo On entry, uplo specifies whether the matrix is an upper or lower
triangular matrix as follows:
FORTRAN
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.
C
uplo = UpperTriangle Only the upper triangular part of C
is to be referenced.
uplo = LowerTriangle Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
trans On entry, trans specifies the operation to be performed as
follows:
FORTRAN
trans = 'N' or 'n' C := alpha*A*A' + beta*C.
trans = 'T' or 't' C := alpha*A'*A + beta*C.
C
trans = NoTranspose C := alpha*A*A' + beta*C.
trans = Transpose C := alpha*A'*A + beta*C.
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_SYRK(3F) _SYRK(3F)
Unchanged on exit.
n On entry, n specifies the order of the matrix C. n must be at
least zero.
Unchanged on exit.
k On entry with, trans = 'N' or 'n' or NoTranspose k specifies the
number of columns of the matrix A, and on entry with trans = 'T'
or 't' or Transpose, k specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
alpha specifies the scalar alpha.
Unchanged on exit.
a An array containing the matrix A.
FORTRAN
Array of dimension (lda, ka).
C
A pointer to an array of size lda*ka.
See note below about array storage convention for C.
ka is k when transa = 'N' or 'n' or NoTranspose and is n
otherwise. Before entry with trans = 'N' or 'n' or NoTranspose,
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.
Unchanged on exit.
lda On entry, lda specifies the first dimension of a as declared in
the calling (sub) program. When transa = 'N' or 'n' or
NoTranspose, then lda must be at least max( 1, n ), otherwise lda
must be at least max( 1, k ).
Unchanged on exit.
beta On entry, beta specifies the scalar beta.
Unchanged on exit.
c An array containing the matrix C.
FORTRAN
An array of dimension ( ldc, n ).
C
A pointer to an array of size ldc*n.
See note below about array storage convention for C.
Before entry with uplo = 'U' or 'u' or UpperTraingle, the
leading n by n triangular part of the symmetric matrix and
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_SYRK(3F) _SYRK(3F)
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 On entry, ldc specifies the first dimension of c as declared in
the calling (sub) program. ldc must be at least max( 1, n ).
Unchanged on exit.
C ARRAY STORAGE CONVENTION
The matrices are assumed to be stored in a one dimensional C array
in an analogous fashion as a Fortran array (column major). Therefore,
the element A(i+1,j) of matrix A is stored immediately after the
element A(i,j), while A(i,j+1) is lda elements apart from A(i,j).
The element A(i,j) of the matrix can be accessed directly by reference
to a[ (j-1)*lda + (i-1) ].
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.
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