symm(3F)
dsymm, ssymm, zsymm, csymm - BLAS level three Symmetric Matrix Product
As shipped in IRIX 6.5. First release of IRIX 6.5.
NAME dsymm, ssymm, zsymm, csymm - BLAS level three Symmetric Matrix Product FORTRAN 77 SYNOPSIS subroutine dsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) character*1 side,uplo integer m, n, lda, ldb, ldc double precision alpha, beta double precision a( lda,*), b(ldb,*), c(ldc,*) subroutine ssymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) character*1 side,uplo integer m, n, lda, ldb, ldc real alpha, beta real a( lda,*), b(ldb,*), c(ldc,*) subroutine zsymm( 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 csymm( 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 dsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) OperationSide side; MatrixTriangle uplo; Integer m, n, lda, ldb, ldc; double alpha, beta; double (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n]; void ssymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) OperationSide side; MatrixTriangle uplo; Integer m, n, lda, ldb, ldc; float alpha, beta; float (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n]; void zsymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) OperationSide side; MatrixTriangle uplo; Integer m, n, lda, ldb, ldc; Zomplex alpha, beta; Zomplex (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n]; void csymm( side,uplo,m,n,alpha,a,lda,b,ldb,beta,c,ldc ) OperationSide side; MatrixTriangle uplo; Integer m, n, lda, ldb, ldc; Complex alpha, beta; Complex (*a)[lda*ka], (*b)[lda*n], (*c)[lda*n]; DESCRIPTION dsymm, ssymm, zsymm and csymm 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 a symmetric matrix and B and C are m by n matrices. PARAMETERS side On entry, side specifies whether op( A ) multiplies B from the left or right as follows: FORTRAN side = 'L' or 'l' B := alpha*op( A )*B. side = 'R' or 'r' B := alpha*B*op( A ). C side = LeftSide B := alpha*op( A )*B. side = RightSide B := alpha*B*op( A ). Unchanged on exit. uplo On entry, uplo specifies whether the matrix A is an upper or lower triangular matrix as follows: FORTRAN uplo = 'U' or 'u' A is an upper triangular matrix. uplo = 'L' or 'l' A is a lower triangular matrix. C uplo = UpperTriangle A is an upper triangular matrix. uplo = LowerTriangle A is a lower triangular matrix. 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. When alpha is zero then a is not referenced and b need not be set before entry. 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 otherwise. Before entry with side = 'L' or 'l' or LeftSide, the array elements corresponding to the m by m part of the matrix A must contain the symmetric matrix, such that when: uplo = 'U' or 'u' or UpperTriangle, the array elements that correspond to the leading m by m upper triangular part of the matrix A must contain the upper triangular part of the symmetric matrix and the corresponding strictly lower triangular part of A is not referenced, and when uplo = 'L' or 'l' or LowerTriangle, the array elements that correspond to the leading m by m lower triangular part of the matrix A must contain the lower triangular part of the symmetric matrix and the corresponding strictly upper triangular part of A is not referenced. Before entry with side = 'R' or 'r' or RightSide, the array elements corresponding to the n by n part of the matrix A must contain the symmetric matrix, such that when: uplo = 'U' or 'u' or UpperTriangle, the array elements that correspond to the leading n by n upper triangular part of the matrix A must contain the upper triangular part of the symmetric matrix and the corresponding strictly lower triangular part of A is not referenced, and when uplo = 'L' or 'l' or LowerTriangle, the array elements that correspond to the leading n by n lower triangular part of the matrix A must contain the lower triangular part of the symmetric matrix and the corresponding strictly upper triangular part of A is not referenced. 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 ), otherwise 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 array elements corresponding to the leading m by n part of the matrix 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. 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 elements corresponding to the leading m by n part of the matrix 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.