_HER2K(3F)_HER2K(3F)NAME
zher2k, cher2k - BLAS level three Hermitian Rank 2K Update
FORTRAN 77 SYNOPSIS
subroutine zher2k( uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
character*1 uplo, trans
integer n, k, lda, ldb, ldc
double complex alpha, beta
double complex a( lda,*), b( ldb,*), c(ldc,*)
subroutine cher2k( uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
character*1 uplo, trans
integer n, k, lda, ldb, ldc
complex alpha, beta
complex a( lda,*), b( ldb,*), c(ldc,*)
C SYNOPSIS
subroutine zher2k( uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldb, ldc;
Zomplex alpha, beta;
Zomplex (*a)[lda*k], (*b)[lda*k], (*c)[lda*n];
void zher2k( uplo,trans,n,k,alpha,a,lda,b,ldb,beta,c,ldc )
MatrixTriangle uplo;
MatrixTranspose trans;
Integer n, k, lda, ldb, ldc;
Complex alpha, beta;
Complex (*a)[lda*k], (*b)[lda*k], (*c)[lda*n];
DESCRIPTION
zher2k and cher2k perform one of the hermitian rank 2k operations
C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C,
or
C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,
where alpha and beta are scalars with beta real, C is an n by n hermitian
matrix and A and B are n by k matrices in the first case and k by n
matrices in the second case.
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_HER2K(3F)_HER2K(3F)PARAMETERS
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*conjg( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.
trans = 'C' or 'c' C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*A +
beta*C.
C
trans = NoTranspose C := alpha*A*conjg( B' ) +
conjg( alpha )*B*conjg( A' ) +
beta*C.
trans = ConjugateTranspose C := alpha*conjg( A' )*B +
conjg( alpha )*conjg( B' )*A +
beta*C.
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 matrices A and B, and on entry with
trans = 'T' or 't' or Transpose, k specifies the number of rows
of the matries A and B. K must be at least zero.
Unchanged on exit.
alpha specifies the scalar alpha.
Unchanged on exit.
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_HER2K(3F)_HER2K(3F)
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.
b An array containing the matrix B.
FORTRAN
Array of dimension (lda, kb).
C
A pointer to an array of size lda*kb.
See note below about array storage convention for C.
kb 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 b must contain the matrix B,
otherwise the leading k by n part of the array b must contain
the matrix B.
Unchanged on exit.
ldb On entry, ldb specifies the first dimension of b as declared in
the calling (sub) program. When trans = 'N' or 'n' or
NoTranspose, then ldb must be at least max( 1, n ), otherwise lda
must be at least max( 1, k ).
Unchanged on exit.
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) ].
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_HER2K(3F)_HER2K(3F)AUTHORS
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
TUNING
Optimized and parallelized for SGI R3000, R4x00 and R8000 platforms.
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