hemm(3F)
zhemm, chemm - BLAS level three Hermitian Matrix Product
As shipped in IRIX 6.5. First release of IRIX 6.5.
NAME 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,*) C SYNOPSIS 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]; DESCRIPTION zhemm and chemm perform one of the matrix-matrix 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. PARAMETERS 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 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. 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. 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[ (j-1)*lda + (i-1) ]. 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.