_HEMM(3F) _HEMM(3F)
zhemm, chemm  BLAS level three Hermitian Matrix Product
FORTRAN 77 SYNOPSIS
subroutine zhemm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
character*1 side,uplo
integer m, n, lda, ldb, ldc
double complex alpha, beta
double complex a( lda,*), b(ldb,*), c(ldc,*)
subroutine chemm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
character*1 side,uplo
integer m, n, lda, ldb, ldc
complex alpha, beta
complex a( lda,*), b(ldb,*), c(ldc,*)
void zhemm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
OperationSide side;
MatrixTriangle uplo;
Integer m, n, lda, ldb, ldc;
Zomplex (*a)[lda*ka], (*b)[lda*n], (*c)[lda*kb];
void chemm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc )
OperationSide side;
MatrixTriangle uplo;
Integer m, n, lda, ldb, ldc;
Complex (*a)[lda*ka], (*b)[lda*n], (*c)[lda*kb];
zhemm and chemm perform one of the matrixmatrix operations
C := alpha*A*B + beta*C, or
C := alpha*B*A + beta*C,
where alpha and beta are scalars, A is an hermitian matrix and B and C
are m by n matrices.
side specifies whether the hermitian matrix A appears on the left or
right in the operation as follows:
FORTRAN
side = 'L' or 'l' C := alpha*A*B + beta*C
side = 'R' or 'r' C := alpha*B*A + beta*C
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C
side = LeftSide C := alpha*A*B + beta*C
side = RightSide C := alpha*B*A + beta*C
Unchanged on exit.
uplo On entry, uplo specifies whether the upper or lower triangular
part of the hermitian matrix A is to be referenced as follows:
FORTRAN
uplo = 'U' or 'u' Only the upper triangular part of the
hermitian matrix is to be referenced.
uplo = 'L' or 'l' Only the lower triangular part of the
hermitian matrix is to be referenced.
C
uplo = UpperTriangle Only the upper triangular part of
the matrix is to be referenced.
uplo = LowerTriangle Only the lower triangular part of
the matrix is to be referenced.
Unchanged on exit.
m On entry, m specifies the number of rows of the matrix C. m must
be at least zero.
Unchanged on exit.
n On entry, n specifies the number of columns of the matrix C. n
must be at least zero.
Unchanged on exit.
alpha On entry, alpha specifies the scalar alpha.
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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 m when side = 'L' or 'l' or LeftSide and is n when side =
'R' or 'r' or RightSide.
Before entry with uplo = 'L' or 'l' or LowerTriangle , the
elements of the array a corresponding to the m by m matrix A must
contain the hermitian matrix, such that when uplo = 'U' or 'u' or
UpperTriangle , the elements of the array a corresponding to the
leading m by m upper triangular part of the matrix A must contain
the upper triangular part of the hermitian matrix and the
elements corresponding to the strictly lower triangular part of A
are not referenced. When uplo = 'L' or 'l' or LowerTriangle , the
elements of the array a corresponding to the leading m by m lower
triangular part of the matrix A must contain the lower triangular
part of the hermitian matrix and the elements corresponding to
the strictly upper triangular part of A are not referenced.
Before entry with side = 'R' or 'r' or RightSide , the elements
of the array a corresponding to the n by n matrix A must contain
the hermitian matrix, such that when uplo = 'U' or 'u' or
UpperTriangle , the elements of the array a corresponding to the
leading n by n upper triangular part of the matrix A must contain
the upper triangular part of the hermitian matrix and the
elements corresponding to the strictly lower triangular part of A
are not referenced. When uplo = 'L' or 'l' or LowerTriangle , the
elements of the array a corresponding to the leading n by n lower
triangular part of the matrix A must contain the lower triangular
part of the hermitian matrix and the elements corresponding to
the strictly upper triangular part of A are not referenced.
Note that the imaginary parts corresponding to the diagonal
elements need not be set, they are assumed to be zero.
Unchanged on exit.
lda On entry, lda specifies the first dimension of A as declared in
the calling (sub) program. When side = 'L' or 'l' or LeftSide,
then lda must be at least max( 1, m ). When side = 'R' or 'r' or
RightSide, then lda must be at least max( 1, n ).
Unchanged on exit.
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B An array containing the matrix B.
FORTRAN
An array of dimension ( ldb, n ).
C
A pointer to an array of size ldb*n.
See note below about array storage convention for C.
Before entry, the elements of b that correspond to the leading m
by n part of the matrix B should contain the elements
corresponding to the m by n matrix B.
Unchanged on exit.
ldb On entry, ldb specifies the first dimension of B as declared in
the calling (sub)program. ldb
must be at least max( 1, m ).
Unchanged on exit.
beta On entry, beta specifies the scalar beta. When beta is supplied
as zero then c need not be set on input.
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, the leading m by n part of the array c must contain
the matrix C, except when beta is zero, in which case c need not
be set on entry.
On exit, the array c is overwritten by the m by n 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, m ).
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[ (j1)*lda + (i1) ].
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_HEMM(3F) _HEMM(3F)
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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